Handbook of Particle Detection and Imaging [2nd ed. 2021] 3319937847, 9783319937847

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Ivor Fleck Maxim Titov Claus Grupen Irène Buvat Editors

Handbook of Particle Detection and Imaging Second Edition

Handbook of Particle Detection and Imaging

Ivor Fleck • Maxim Titov • Claus Grupen Irène Buvat Editors

Handbook of Particle Detection and Imaging Second Edition With 666 Figures and 78 Tables

Editors Ivor Fleck Center for Particle Physics University of Siegen Siegen, Germany Claus Grupen Department of Physics University of Siegen Siegen, Germany

Maxim Titov IRFU CEA Saclay Gif-sur-Yvette, France Irène Buvat Unité Imagerie Moléculaire In Vivo Orsay, France

ISBN 978-3-319-93784-7 ISBN 978-3-319-93785-4 (eBook) ISBN 978-3-319-93786-1 (print and electronic bundle) https://doi.org/10.1007/978-3-319-93785-4 1st edition: © Springer-Verlag Berlin Heidelberg 2012 2nd edition: © Springer Nature Switzerland AG 2021 All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Foreword

Science is about generating knowledge for the benefit of humanity. From the invention of the wheel to the discovery of gravitational waves, science has always enriched our minds and improved our lives. In other words, science has led us to a better world than that inhabited by our ancestors. An important role in this development has been and always will be the interplay between theory and experiment. Sometimes it can take decades between theoretical prediction and experimental verification, but that interplay is always present. Examples from recent years include the prediction of the so-called Higgs-Boson and its experimental discovery 48 years later, and gravitational waves, which were discovered 100 years after theory predicted them. Why does it take so long? Because there is a third and equally important player in the game: instrumentation. Without technological progress and innovation in instrumentation, the tools of discovery would not be available, and those tools take time to develop and mature. It’s a perfect example of the virtuous circle whereby basic research delivers knowledge that leads to innovation, which in turn brings new technology enabling more sophisticated experiments, more new knowledge and increasingly sophisticated tools. The prize, which is well worth the wait, is landmark discoveries like gravitational waves and the Higgs Boson, accompanied by countless innovations that benefit not only science but society as a whole. There are many examples to demonstrate how the virtuous circle reaches beyond the realms of blue sky research, leading directly to applications for society. Take the journey from the discovery of antimatter to its application in hospitals. It took some 40 years from the discovery of the positron to its use in PET scanners. A decade later, physics experiments demanded better particle detection, so physicists teamed up with industry to develop crystal detectors with unprecedented sensitivity. This turned out to be just what the PET industry needed, so those crystals found their way into the latest scanners. Fast-forward ten more years, and particle physics needed to use crystal detectors inside a strong magnetic field, providing a way forward to combined PET/MRI scanners. This is but one example among many. Particle accelerators and detectors - the basic tools of the trade – are now widely employed in industry and healthcare. There is an inseparable link between progress in fundamental science and technological evolution, providing spin-offs that help society develop and improve the quality of life. The lesson is clear: cutting-edge science relies on cutting-edge instrumentation. v

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Foreword

It is therefore important always to have the most relevant, and the timeliest information about instrumentation and imaging to hand. And that is where this Handbook comes in. In this second edition, well known experts in their respective fields describe the state-of-the-art today. Each chapter has been updated to include the latest developments in this fast-moving field. The Handbook covers aspects ranging from the fundamental concepts of detectors and the physics processes involved, to their deployment in experiments and in the area of medical applications. Along the way, the various detector types and concepts are covered in depth. Particular attention is given to recently developed detector types in the medical arena. This new edition will be a great companion not only to scientists, but also to anyone dealing with modern instrumentation in the design and application of innovative technologies. It completes the indispensable trio of theory, experiment and instrumentation, which together add up to progress. CERN Director-General (2008–2015)

Prof. Dr. Rolf-Dieter Heuer

Preface to the Second Edition

Research for the fundamental constituents of matter has always been a driving force for the development of more and more sophisticated detectors. The fundamental understanding of the reactions of particles with matter allowed to use this knowledge to construct devices that make these reactions visible and create images that are used in a variety of applications. For many millennia images were created by humans in order to capture one given moment in time, either from reality or imagination. With the emerge of photography, for the first time reactions of particles, the optical photons, with matter, the film emulsion, were recorded directly and permanently. These images stand in the tradition of the paintings. The same technology was used to image the shadow of bones in an x-ray beam or to visualize the path of elementary particles. Further methods to visualize the path taken by elementary particles include the bubble and cloud chambers where elementary reactions in the right environment create a visualization that can be recorded by means of a photograph. With the emerge of the computer these analog images were replaced by digital ones. There is no more the need to create an image directly. Signals from many different types of detectors can be combined to create one three-dimensional image. These images range from air showers of cosmic rays, collisions in a particle accelerator to images for medical purposes. Improved detection technologies combined with mathematical algorithms and the power of modern computers allowed to go from a single x-ray image to a three-dimensional reconstruction of bones in a human body (CT). Using the fundamental quantum mechanical property of spin allowed to manipulate the spins of the nuclei in the human body to make further three-dimensional images that can better differentiate between different kinds of tissues (MRI). Another imaging technique, the positron emission tomography (PET), makes use of anti-particles. In combination with modern detection and readout technologies with timing resolution in the order of picoseconds a new area of precision imaging has emerged, allowing for finding tumors of ever smaller dimensions. These few examples show the application of fundamental principles of physics and detection technologies that have been developed from and for fundamental research.

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Preface to the Second Edition

In this book proven experts in their field show how fundamental particles interact with matter, how these interactions are used to detect these particles and how detectors are used in a wide area of applications from particle physics, security to medicine. All chapters show the current state of the art and give references for further reading. Ivor Fleck, Maxim Titov Editors

Preface to the First Edition

Sophisticated instrumentations and imaging devices have become powerful tools in the modern world of technology. Advances in electronics, fast data processing, image reconstruction, and pattern recognition, just to name a few, have enabled the development of very elaborate investigation techniques that are now used in many different fields of science and many domains of applications. A large number of technological advances were originally developed in particle physics, but then spread to astrophysics, medicine, biology, materials science, art, archaeology, and many other application domains. The field of imaging has known incredible advances in the recent decades. With atomic force microscopes or scanning force microscopes, very-high-resolution images can now be obtained. Resolutions on the order of fractions of a nanometer, more than 1000 times better than the optical diffraction limit have been reached. With the scanning tunneling microscope, atoms can even be dragged along and positioned to build atomic-scale artificial structures. Increasingly higher resolutions require more and more storage space. A Triumph calculator from the fifties in the last century using ferrite cores had a storage capacity of 32 bits! The Large Hadron Collider (LHC) at CERN will produce roughly 15 petabytes (15 million gigabytes) of data annually. The discovery of a giant magnetoresistance by the 2007 Nobel laureates Peter Grünberg and Albert Fert enabled a breakthrough in gigabyte hard disk drives, and so this technique allows massive number crunching and can cope with huge data files. Also the image quality and image reconstruction accuracy have substantially increased. For a decent photo one needs more than 100 million photons in the optical range. In observational astronomy the sensitivity of instruments has improved over a period of 380 years – from Galileo’s telescope to the Hubble Space Telescope – by a factor of 100 millions. For the discovery of an X-ray source in our galaxy, approximately 100 photons are sufficient. Using the imaging atmospheric Cherenkov technique, the discovery of a gamma-ray source can be claimed if more than about 10 photons – with little background – come from the same point in the sky. These advances also come about because high-resolution pixel detectors are available. In the 1960s the best charge-sensitive amplifiers used for the readout of semiconductor counters had a noise level equivalent to that of 1000 electrons. Nowadays one can unambiguously count single electrons, because the noise level has decreased by a factor of 1000. ix

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Preface to the First Edition

Imaging also plays a major role in medical diagnosis. The old X-ray technique has been improved and has been made more sensitive by using image intensifiers. Antiparticles, discovered in cosmic rays in the thirties of the last century are now routinely used in positron emission tomography (PET) for cancer diagnosis and therapy monitoring. Also γ rays are used in gamma cameras, scintigraphy, single photon emission computed tomography (SPECT), and PET, with all sorts of diagnostic indications, including suspicion of heart or brain disease. The operation of Compton telescopes, known from astroparticle physics experiments, has now found its way into medical diagnosis as Compton cameras, although image reconstruction from Compton cameras remains a major challenge. Beyond diagnostic imaging, nuclear techniques have also entered the domain of medical therapy. The strong ionization of charged particles at the end of their range (Bragg peak) has initiated new methods in cancer treatment (particle therapy) with substantial advantages over therapy with cobalt-60 γ rays. Apart from γ rays and charged particles, also neutrons have important applications in therapy. On the detector side, a lot of progress has also been achieved. Early detectors, like the Wilson cloud chamber, provided lots of details about charged particles and their interactions. One drawback was a poor time resolution or repetition time. If you can only record one event per minute, such a detector is not suited for accelerator experiments. In the LHC, protons collide every 25 nanoseconds, resulting in a possible event rate of 40 million per second. Modern detectors cannot only measure the spatial coordinates, the energy and momentum of a particle, but they can also determine the identity of the particle. Particle identification is essential for the unambiguous characterization of interactions or new particle production. These techniques are also important in many other fields measuring electromagnetic radiation as γ rays, X rays, terahertz radiation, ultraviolett (UV), or infrared (IR) photons up to microwave photons. This handbook centers on detection techniques in the field of particle physics, medical imaging, and related subjects. It is structured into four parts. The first two parts deal with basic ideas about particle detectors, like interactions of radiation and particles with matter and specific types of detectors. In the third part applications of these devices in high energy physics and related fields are presented. Finally, the last part concerns the ever-growing field of medical imaging using similar detection techniques. The different chapters of the book are written by wellknown experts in their field. Clear instructions on the detection techniques and principles in terms of relevant operation parameters for scientists and graduate students are given. Detailed tables, diagrams, and figures will make this a very useful handbook for the application of these techniques in many different fields like physics, medicine, biology, other areas of natural science, and applications in metrology and technology. Also, it is our hope that such a broad presentation of particle detectors and radiation-based imaging can be a source of cross-fertilization between different fields of applications. June 2011

Irene Buvat and Claus Grupen Orsay and Siegen

Contents

Volume 1 Part I Basic Principles of Detectors and Accelerators . . . . . . . . . . . . . .

1

1

Interactions of Particles and Radiation with Matter . . . . . . . . . . . . . Simon I. Eidelman and Boris A. Shwartz

3

2

Electronics Part I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Helmuth Spieler

29

3

Electronics Part II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Helmuth Spieler

59

4

Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Günther Dissertori

91

5

Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Glen Cowan

117

6

Particle Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jürgen Engelfried

145

7

Accelerators for Particle Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Helmut Burkhardt

161

8

Accelerator-Based Photon Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . Shaukat Khan and Klaus Wille

185

9

Calibration of Radioactive Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dirk Arnold, Karsten Kossert, and Ole Jens Nähle

221

10

Radiation Protection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Claus Grupen

239

Part II 11

Specific Types of Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

273

Gaseous Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Maxim Titov

275 xi

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Contents

12

Tracking Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Manfred Krammer and Winfried Mitaroff

317

13

Photon Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Samo Korpar and Peter Križan

353

14

Neutrino Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M. Wurm, F. von Feilitzsch, and Jean-Come Lanfranchi

371

15

Scintillators and Scintillation Detectors . . . . . . . . . . . . . . . . . . . . . . . . Zane W. Bell

413

16

Semiconductor Radiation Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . Douglas S. McGregor

451

17

Silicon Photomultipliers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Erika Garutti

495

18

Gamma-Ray Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . William L. Dunn, Douglas S. McGregor, and J. Kenneth Shultis

515

19

Cherenkov Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Blair Ratcliff and Jochen Schwiening

583

20

Muon Spectrometers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Thomas Hebbeker and Kerstin Hoepfner

609

21

Calorimeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Felix Sefkow and Frank Simon

635

22

New Solid State Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Christoph J. Ilgner

669

23

Radiation Damage Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ren-Yuan Zhu

687

24

Complementary Metal-Oxide-Semiconductor (CMOS) Pixel Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Marc Winter and Michael Deveaux

713

Volume 2 Part III

Applications of Detectors in Particle and Astroparticle Physics, Security, Environment, and Art . . . . . . . . . . . . . . . . . . . . . . . . . . 759

25

Astrophysics and Space Instrumentation . . . . . . . . . . . . . . . . . . . . . . . John W. Mitchell and Thomas Hams

761

26

Indirect Detection of Cosmic Rays . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ralph Engel and David Schmidt

801

Contents

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27

Gravitational Wave Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Barry C. Barish

851

28

Technology for Border Security . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dudley Creagh

873

29

Radiation Detection Technology for Homeland Security . . . . . . . . . Richard Kouzes

897

30

Accelerator Mass Spectrometry and Its Applications in Archaeology, Geology, and Environmental Research . . . . . . . . . . . . Wolfgang Kretschmer

31

32

Geoscientific Applications of Particle Detection and Imaging Techniques with Special Focus on Monitoring Clay Mineral Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Laurence N. Warr and Georg H. Grathoff Particle Detectors Used in Isotope Ratio Mass Spectrometry, with Applications in Geology, Environmental Science, and Nuclear Forensics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nicholas S. Lloyd, Johannes B. Schwieters, Matthew S. A. Horstwood, and Randall R. Parrish

929

945

963

33

Particle Detectors in Materials Science . . . . . . . . . . . . . . . . . . . . . . . . Xin Jiang and Thorsten Staedler

34

Spallation: Neutrons Beyond Nuclear Fission . . . . . . . . . . . . . . . . . . . 1001 Harald Conrad

35

Neutron Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1041 Alfred Klett

36

Instrumentation for Nuclear Fusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 1075 Rudolf Neu

37

Use of Neutron Technology in Archaeological and Cultural Heritage Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1097 Dudley Creagh

38

Radiation Detectors and Art . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1119 Andrea Denker

Part IV

983

Applications of Particle Detectors in Medicine . . . . . . . . . . . . 1143

39

Radiation-Based Medical Imaging Techniques: An Overview . . . . . 1145 John O. Prior and Paul Lecoq

40

CT Imaging: Basics and New Trends . . . . . . . . . . . . . . . . . . . . . . . . . . 1173 F. Peyrin and K. Engelke

xiv

Contents

41

SPECT Imaging: Basics and New Trends . . . . . . . . . . . . . . . . . . . . . . 1217 Brian F. Hutton

42

PET Imaging: Basic and New Trends . . . . . . . . . . . . . . . . . . . . . . . . . . 1237 Magnus Dahlbom

43

Image Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1279 Claude Comtat

44

Multi Imaging Devices: PET/MRI . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1317 Han Gyu Kang and Taiga Yamaya

45

Motion Compensation in Emission Tomography . . . . . . . . . . . . . . . . 1359 J. van den Hoff, J. Maus, and G. Schramm

46

Quantitative Image Analysis in Tomography . . . . . . . . . . . . . . . . . . . 1407 Irène Buvat

47

Compartmental Modeling in Emission Tomography . . . . . . . . . . . . . 1431 Adriaan A. Lammertsma

48

Evaluation and Image Quality in Radiation-Based Medical Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1451 Matthew A. Kupinski

49

Simulation of Medical Imaging Systems: Emission and Transmission Tomography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1465 Robert L. Harrison

50

High-Resolution and Animal Imaging Instrumentation and Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1497 Nicola Belcari, Alberto Del Guerra, and Daniele Panetta

51

Imaging Instrumentation and Techniques for Precision Radiotherapy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1537 Katia Parodi and Christian Thieke

52

Tumor Therapy with Ion Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1573 Gerhard Kraft and Uli Weber

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1603

About the Editors

Ivor Fleck was born in Hannover, Germany. He has studied physics at the Universities of Hannover and Munich and did his PhD at the University of Hamburg with the first data from the ZEUS experiment at DESY. He worked as a postdoc at the Universities of Glasgow and Tokyo and was a fellow at CERN before he went to Freiburg University, where he did his Habilitation. In 2005 he became Professor of Physics at the University of Siegen, Germany. He spent sabbaticals at the University of Cambridge and the University of Tokyo. Since 2015 he is Dean for Research of the School of Science and Technology at the University of Siegen and is Founding Chairman of the Center for Particle Physics Siegen. He has worked at many of the large facilities for particle physics, namely DESY, CERN, KEK and Fermilab. His research fields are experimental particle physics and detector development. His analysis topics range from structure functions at ZEUS to search for Supersymmetry at OPAL and top quark properties at D0 and ATLAS. He also works on developing detector components for the ILD detector at the International Linear Collider (ILC) and the International Axion Observatory (IAXO).

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About the Editors

Maxim Titov was born in Kyiv, Ukraine on May 6, 1973. He received his Master Degree from the Moscow Institute of Physics and Technology and defended his PhD in 2001 in the Institute of Experimental and Theoretical Physics, Moscow, Russia. He completed his Habilitation as a Director of Research (HDR) in 2013 from University Pierre and Marie Curie (Paris VI), France. Currently, he is a Senior Scientist at CEA Saclay, Irfu, France. A nuclear and particle physics researcher for his entire carrier, Prof Titov has been involved in the development of novel detector technologies and analysis of physics data at collider experiments, inevitably within large international collaborations: HERA-B Experiment at DESY, Hamburg; D0 Experiment at FERMILAB, Chicago; ATLAS and CMS Experiments and RD51 Collaboration at CERN, Geneva; and International Linear Collider (ILC) He was Founding Member and served as the Spokesperson of the RD51 Collaboration at CERN (2007-2015). Nowadays, he is Member of CMS, RD51 and Particle Data Group (PDG) Collaborations and involved into science-policy preparation of the ILC project in Japan. Claus Grupen Universität Siegen, Siegen, Germany Irène Buvat Unité Imagerie Moléculaire In Vivo, Orsay, France

Contributors

Dirk Arnold Physikalisch-Technische Bundesanstalt (PTB), Germany

Braunschweig,

Barry C. Barish California Institute of Technology and University of California, Riverside, Riverside, CA, USA Nicola Belcari Department of Physics “E. Fermi”, University of Pisa, Pisa, Italy Zane W. Bell Isotopes and Fuel Cycle Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN, USA Helmut Burkhardt Accelerator Department BE, CERN, Geneva, Switzerland Irène Buvat Imaging and Modeling in Neurobiology and Cancerology (IMNC) Lab, Orsay Cedex, France Claude Comtat Paris-Saclay Multimodal Biomedical Imaging Lab (BioMaps), French Alternative Energies and Atomic Energy Commission (CEA), Orsay, France Harald Conrad Jülich Center for Neutron Science, Forschungszentrum Jülich GmbH, Jülich, Germany Glen Cowan Department of Physics, Royal Holloway, University of London, Egham, Surrey, UK Dudley Creagh Emeritus Professor, Faculty of Science and Technology, University of Canberra, Canberra, ACT, Australia Magnus Dahlbom Division of Nuclear Medicine and Ahmanson Translational Imaging Division, Department of Molecular and Medical Pharmacology, David Geffen School of Medicine at UCLA, University of California, Los Angeles, CA, USA Alberto Del Guerra Department of Physics “E. Fermi”, University of Pisa, Pisa, Italy Andrea Denker Protonentherapie, Helmholtz-Zentrum Berlin für Materialien und Energie, Berlin, Germany

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Contributors

Michael Deveaux Helmholtzzentrum für Schwerionenforschung GmbH (GSI), Darmstadt, Germany Günther Dissertori ETH Zurich, Institute for Particle Physics and Astrophysics, Zurich, Switzerland William L. Dunn Mechanical and Nuclear Engineering, Kansas State University, Manhattan, KS, USA Simon I. Eidelman Budker Institute of Nuclear Physics, Novosibirsk, Russia Ralph Engel Karlsruhe Institute of Technology (KIT), Institute for Astroparticle Physics, Karlsruhe, Germany Jürgen Engelfried Instituto de Física, Universidad Autónoma de San Luis Potosí, San Luis Potosí, Mexico K. Engelke Institute of Medical Physics, University of Erlangen, Germany

Erlangen,

Department of Medicine, FAU University Erlangen-Nürnberg and Universitätsklinikum Erlangen, Erlangen, Germany Erika Garutti Institute of Experimental Physics, Hamburg University, Hamburg, Germany Georg H. Grathoff Economic Geology and Mineralogy Section, Institute of Geography and Geology, University of Greifswald, Greifswald, Germany Claus Grupen Department of Physics, University of Siegen, Siegen, Germany Thomas Hams Astrophysics Science Division, NASA/GSFC, Greenbelt, MD, USA Robert L. Harrison Department of Radiology, University of Washington, Seattle, WA, USA Thomas Hebbeker Department of Physics, RWTH Aachen University, Aachen, Germany Kerstin Hoepfner Department of Physics, RWTH Aachen University, Aachen, Germany Matthew S. A. Horstwood NERC Isotope Geosciences Laboratory, British Geological Survey, Keyworth, Nottingham, UK Brian F. Hutton Institute of Nuclear Medicine, University College London & UCLH NHS Trust, London, UK Christoph J. Ilgner WUBS, Magdeburg-Stendal University of Applied Sciences, Magdeburg, Germany Xin Jiang Institute of Materials Engineering, University of Siegen, Siegen, Germany

Contributors

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Han Gyu Kang Department of Nuclear Medicine Science, National Institute of Radiological Sciences (NIRS), National Institutes for Quantum and Radiological Science and Technology (QST), Chiba, Japan Shaukat Khan Zentrum für Synchrotronstrahlung (DELTA), Technische Universität Dortmund, Dortmund, Germany Alfred Klett Berthold Technologies GmbH & Co KG, Bad Wildbad, Germany Samo Korpar Faculty of Chemistry and Chemical Engineering, University of Maribor, Maribor, Slovenia J. Stefan Institute, Ljubljana, Slovenia Karsten Kossert Physikalisch-Technische Bundesanstalt (PTB), Braunschweig, Germany Richard Kouzes US Department of Energy, Pacific Northwest National Laboratory, Richland, WA, USA Gerhard Kraft Biophysik, GSI Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt, Germany Manfred Krammer Experimental Physics Department, CERN, Geneva, Switzerland Wolfgang Kretschmer Leitung Forschungsbereich AMS, Physikalisches Institut, Universität Erlangen-Nürnberg, Erlangen, Germany Peter Križan J. Stefan Institute, Ljubljana, Slovenia Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana, Slovenia Matthew A. Kupinski James C. Wyant College of Optical Sciences, University of Arizona, Tucson, AZ, USA Adriaan A. Lammertsma Department of Nuclear Medicine & PET Research, VU University Medical Center, Amsterdam, The Netherlands Jean-Come Lanfranchi Physik-Department, Technische Univeristät München, Garching, Germany Paul Lecoq CERN, Geneva, Switzerland Nicholas S. Lloyd Thermo Fisher Scientific (Bremen) GmbH, Bremen, Germany J. Maus PET Center, Institute of Radiopharmaceutical Cancer Research, Helmholtz-Zentrum Dresden-Rossendorf (HZDR), Dresden, Germany Douglas S. McGregor Semiconductor Materials and Radiological Technologies Laboratory, Mechanical and Nuclear Engineering, Kansas State University, Manhattan, KS, USA

xx

Contributors

Winfried Mitaroff Institute of High Energy Physics, Austrian Academy of Sciences, Vienna, Austria John W. Mitchell Astrophysics Science Division, NASA/GSFC, Greenbelt, MD, USA Ole Jens Nähle Physikalisch-Technische Bundesanstalt (PTB), Braunschweig, Germany Rudolf Neu Max-Planck-Institut für Plasmaphysik, Garching, Germany Daniele Panetta CNR Institute of Clinical Physiology, Pisa, Italy Katia Parodi Department of Medical Physics, Ludwig-Maximilians-Universität München (LMU Munich), Garching, Germany Randall R. Parrish University of Portsmouth, Portsmouth, UK F. Peyrin Univ. Lyon, INSA-Lyon, Université Claude Bernard Lyon 1, CNRS, Inserm, CREATIS, UMR 5220, U1206, Lyon, France John O. Prior Department of Nuclear Medicine and Molecular Imaging, Lausanne University Hospital and University of Lausanne, Lausanne, Switzerland Blair Ratcliff SLAC National Accelerator Laboratory, Stanford, CA, USA David Schmidt Karlsruhe Institute of Technology (KIT), Institute of Experimental Particle Physics, Karlsruhe, Germany G. Schramm Department of Imaging and Pathology, Division of Nuclear Medicine, KU/UZ Leuven, Leuven, Belgium Jochen Schwiening GSI Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt, Germany Johannes B. Schwieters Thermo Fisher Scientific (Bremen) GmbH, Bremen, Germany Felix Sefkow Deutsches Elektronensynchrotron DESY, Hamburg, Germany J. Kenneth Shultis Mechanical and Nuclear Engineering, Kansas State University, Manhattan, KS, USA Boris A. Shwartz Budker Institute of Nuclear Physics, Novosibirsk, Russia Frank Simon Max-Planck-Institut für Physik, München, Germany Helmuth Spieler LBNL Physics Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA Thorsten Staedler Institute of Materials Engineering, University of Siegen, Siegen, Germany Christian Thieke Department of Radiation Oncology, University Hospital, Ludwig-Maximilians-Universität München (LMU Munich), München, Germany

Contributors

xxi

Maxim Titov IRFU, CEA, Université Paris-Saclay, Gif-sur-Yvette, France J. van den Hoff PET Center, Institute of Radiopharmaceutical Cancer Research, Helmholtz-Zentrum Dresden-Rossendorf (HZDR), Dresden, Germany F. von Feilitzsch Physik-Department, Technische Univeristät München, Garching, Germany Laurence N. Warr Economic Geology and Mineralogy Section, Institute of Geography and Geology, University of Greifswald, Greifswald, Germany Uli Weber Partikel Therapie, Universitätsklinikum Gießen/Marburg, Darmstadt, Germany Klaus Wille Zentrum für Synchrotronstrahlung (DELTA), Technische Universität Dortmund, Dortmund, Germany Marc Winter Department of Subatomic Physics, Institut Pluridisciplinaire Hubert Curien (IPHC), Strasbourg Cedex 2, France M. Wurm Institute of Physics, Johannes Gutenberg-Universität Mainz, Mainz, Germany Taiga Yamaya Department of Nuclear Medicine Science, National Institute of Radiological Sciences (NIRS), National Institutes for Quantum and Radiological Science and Technology (QST), Chiba, Japan Ren-Yuan Zhu High Energy Physics Group, Physics, Mathematics and Astronomy Division, California Institute of Technology, Pasadena, CA, USA

Part I Basic Principles of Detectors and Accelerators

1

Interactions of Particles and Radiation with Matter Simon I. Eidelman and Boris A. Shwartz

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Penetration of Charged Particles Through Matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Energy and Angular Spectra of Delta-Electrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Energy Loss by Ionization and Excitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fluctuations of Ionization Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Multiple Scattering of Charged Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Channeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Radiation Losses, Radiation Length, and Critical Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . Charged Particle Range Due to Ionization Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cherenkov and Transition Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Penetration of High Energy Photons in Matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Photoelectric Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Compton Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Production of Electron-Positron Pairs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Photon Flux Attenuation by Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Electron-Photon Cascades . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nuclear Interactions of Hadrons with Matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Neutrino Interactions with Matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusion and Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4 4 4 6 7 9 10 12 14 15 16 17 17 18 18 19 22 24 26 27

Abstract The main types of interactions of charged particles and photons are briefly described. For charged particles, we present basic formulae for energy losses

S. I. Eidelman () · B. A. Shwartz Budker Institute of Nuclear Physics, Novosibirsk, Russia e-mail: [email protected]; [email protected]; [email protected]; [email protected] © Springer Nature Switzerland AG 2021 I. Fleck et al. (eds.), Handbook of Particle Detection and Imaging, https://doi.org/10.1007/978-3-319-93785-4_1

3

4

S. I. Eidelman and B. A. Shwartz

by ionization and excitation, fluctuations of ionization losses, δ electrons, channeling, multiple scattering, and bremsstrahlung. We consider photoelectric effect, Compton effect, and electron-positron pair production for photons. Also discussed are nuclear interactions of hadrons with matter as well as neutrino interactions.

Introduction Knowledge of phenomena, which occur when particles and radiation interact with matter, is necessary for the development and usage of particle detectors, radiation protection, material studies with the help of ionizing radiation, etc. In this chapter the main types of interactions of charged particles, photons, and neutrino are briefly described. There is an extensive literature devoted to interactions of particles and radiation with matter. A brief review and further references are given in Bichsel et al. (2018), while the detailed consideration of the main relevant issues can be found in the classical book of Rossi (1952).

Penetration of Charged Particles Through Matter The common phenomenon for all charged particles, which causes a change of their energy and direction in matter, is the electromagnetic interactions with electrons and nuclei. Electromagnetic interactions are responsible for particle scattering, ionization and excitation of atoms, bremsstrahlung, and Cherenkov and transition radiation. It should be noted that Cherenkov and transition radiation result in a negligible energy loss and do not change a direction of particle motion. The main contribution to the energy loss caused by the electromagnetic interactions comes from ionization and bremsstrahlung, while the change of the particle trajectory is mostly due to collisions with nuclei.

Energy and Angular Spectra of Delta-Electrons When an incident charged particle collides with an electron at rest, the maximum energy transfer is: εmax = 2me

P2 , M 2 + m2e + 2Eme /c2

(1)

where M, P , and E are the mass, momentum, and total energy of the incident particle, while me is the electron mass. The following approximations are useful in particular cases:

1 Interactions of Particles and Radiation with Matter

γ ∼1

5

εmax [MeV] ≈ 2(γ − 1)

1  γ  M/(2me )

εmax [MeV] ≈ γ 2

γ  M/(2me )

(2)

εmax ≈ E,

where γ = E/Mc2 . Recoil electrons are usually referred to as δ electrons. The recoil angle, ϑδ , is related to the δ electron kinetic energy (i.e., is equivalent to the energy loss of the incident particle): cos ϑδ =

E + me c 2 P



ε . ε + 2me c2

(3)

The collision of the heavy incident particle with a free electron can be approximately described by the well-known Rutherford formula: dσ z2 re2 = dΩ 4



me c βc pc

2

1 4

sin θc /2

(4)

,

where βc , pc , and θc are the electron velocity, momentum, and scattering angle in the center-of-mass system, z is the charge of the incident particle in units of the electron charge, and re is the classical electron radius. The quantities pc and θc can be easily related to the δ electron kinetic energy ε: ε=

pc2 (1 − cos θc ) ; me

dε = −

pc2 d cos θc ; me

pc2 =

me εmax . 2

(5)

Taking into account these relations, we obtain the differential cross section dσ/dε: dσ =

2π z2 re2 me c2 dε. β 2 ε2

(6)

When the incident particle is much heavier than the electron, we can take the electron velocity βc equal to the velocity of the incident particle β in the laboratory frame. Then the energy distribution of δ electrons is: Z 1 d 2n Z dσ = NA = 0.15354 , dεdx A dε A β 2 ε2

(7)

where Z and A are the atomic number and atomic mass, respectively. The thickness x of the material is measured in units of [g/cm2 ] and ε is expressed in [MeV]. To take into account the electron spin, we have to use the formula for the Mott cross section (Mott 1929) instead of Eq. (4):

6

S. I. Eidelman and B. A. Shwartz

z2 re2 dσ = dΩ 4



me c βc pc

2

1 4

sin θc /2

(1 − βc2 sin2 θc /2).

(8)

This modifies the energy distribution to: d 2n Z 1 = 0.15354 dεdx A β 2 ε2

  ε 1 − β2 . εmax

(9)

The formulae for the δ electron energy distributions in the case of the incident electron, positron, and heavy spin 1/2 particle are given in Rossi (1952):   ε 2  d 2n ε E2 1 − =C + dεdx E E (E − ε)2 ε2   ε 2  d 2n ε 1 =C 2 1− + dεdx E E ε d 2n 1 =C 2 2 dεdx β ε

 1−β

2

ε εmax

1 ε2 + 2 E2

(electron),

(positron),

(10)

(11)

 (heavy spin 1/2 particle),

(12)

where E is the total energy of the incident particle and C = 0.15354 × Z/A [MeV/(g/cm2 )].

Energy Loss by Ionization and Excitation The total energy transferred by the initial particle to δ electrons with the kinetic energy ε, exceeding certain εmin , can be found by integrating Eq. (9). However, εmin cannot approach 0 since electrons are assumed to be free in this expression. The accurate calculations in the Born approximation result in the Bethe-Bloch equation (Bethe 1930, 1932, 1933) for the specific energy loss by a heavy spinless particle:  −

dE dx

 = Kz2 ion

Z 1 A β2



 1 2me c2 β 2 γ 2 εmax δ 2 ln , − β − 2 2 I2

(13)

where K = 4π NA re2 me c2 = 0.307075 MeV/(g·cm2 ), I is a mean excitation energy (average ionization potential), and δ is the density effect correction. The ionization energy-loss rate in various materials is shown in Fig. 1 (Bichsel et al. 2018). Common features of the shown dependencies are fast growth, as 1/β 2 , at low energy, a wide minimum in the range 3 ≤ βγ ≤ 4, and slow increase at high energy. A particle having dE/dx near the minimum is often referred to as a minimum ionizing particle or mip. The mip’s ionization losses for all materials

1 Interactions of Particles and Radiation with Matter Fig. 1 The ionization energy-loss rate in various materials (Bichsel et al. 2018)

7

10

− dE/dx (MeV g−1cm2)

8 6 5

H2 liquid

4 He gas

3 2

1 0.1

Sn Pb

1.0 0.1

0.1

0.1

1.0

10 100 βγ = p/Mc

Fe

Al

C

1000

10 000

1.0 10 100 Muon momentum (GeV/c)

1000

1.0 10 100 Pion momentum (GeV/c) 10 100 1000 Proton momentum (GeV/c)

1000

10 000

except hydrogen are in the range between 1 and 2 MeV/(g/cm2 ) slightly decreasing from low to large Z. The I values are obtained from experimental data. A compilation given in Bichsel et al. (2018) is presented in Fig. 2. A useful approximation for I is: ⎧ for H2 ⎨ 18.7 I (eV) = Z(12 + 7/Z) for Z ≤ 13 ⎩ Z(9.76 + 58.8 · Z −1.19 ) for Z > 13

(14)

The density effect limits the increase of ionization losses in liquids and solids. This is a result of the medium polarization that effectively truncates distant collisions. The density effect correction can be calculated according to Sternheimer (1952); Sternheimer and Peierls (1971).

Fluctuations of Ionization Losses When a charged particle passes the layer of material, the energy distribution of the δ electrons (see Eq. (9)) and fluctuations of their total number (nδ ) cause fluctuations of the energy losses, ΔE. One of the typical cases is passage through a relatively thin layer of material by a relativistic particle, when the average energy loss ΔE  εmax while nδ  1.

8

S. I. Eidelman and B. A. Shwartz

Fig. 2 Mean excitation energies, I , normalized to nucleus charge, Z (Bichsel et al. 2018)

22 20

Iadj/Z (eV)

18

ICRU 37 (1984) (interpolated values are not marked with points)

16 14

Barkas & Berger 1964

12

Bichsel 1992

10 8

0

10

20

30

40

50 Z

60

70

80

90

100

The probability density function (PDF) for ΔE is strongly asymmetric with the maximum at ΔEp and a long tail at high losses. The most probable energy loss is (Rossi 1952; Bichsel 1988):   2me c2 β 2 γ 2 ξ 2 ΔE = ξ ln + j − β − δ , I2

(15)

where ξ = (K/2)(Z/A)(x/β 2 ) and j = 0.20. The energy dependence of ΔEp /x is shown in Fig. 3 in comparison with dE/dx. As can be seen, the value of dE/dx is slowly growing due to increasing εmax , while ΔEp /x reaches the Fermi plateau at high energy. A similar behavior can be seen for so-called restricted energy loss, i.e., average energy loss after rejection of the events with a loss exceeding certain threshold, Tcut . The PDF for ultrarelativistic particles, when the parameter G=ξ · (2me c2 /εmax )  0.05, was given by Landau (1944) and Vavilov (1957). This distribution is often referred to as the Landau distribution. The position of the peak of this distribution is determined by Eq. (15), and the full width at half maximum is F W H M ≈ 4ξ . The ionization loss distributions at 0.05 < G < 10 are discussed in detail in Rossi (1952). It should be noted that ionization losses in very thin layers, when nδ  1÷10, are not described by the Landau distribution. The most probable loss is still given by Eq. (15), but the distribution is much wider than the Landau function. This case is typical for the gaseous and thin silicon detectors (Onuchin and Telnov 1974; Bichsel 1988, 2006). Figure 4 shows the energy-loss distributions for 500 MeV pions passing through a silicon layer of varying thickness (Bichsel et al. 2018).

1 Interactions of Particles and Radiation with Matter

9

MeV g−1 cm2 (Electonic loses only)

3.0

Silicon 2.5 Bethe-Bloch 2.0

Restricted energy loss for: Tcut = 10 dE/dx|min Tcut = 2 dE/dx|min

1.5

Landau/Vavilov/Bichsel Δp /x for: x/ρ = 1600 μm 320 μm 80 μm

1.0

0.5 0.1

1.0

10.0

100.0

1000.0

Muon kinetic energy (GeV) Fig. 3 The energy dependence of ΔEp /x in comparison to the average energy loss defined by the Bethe-Bloch formula and the restricted energy loss when the δ electron kinetic energy is limited by a certain value (Bichsel et al. 2018). Here Δp /x = ΔEp /x and dE/dx|min is the dE/dx for a minimum ionizing particle

Multiple Scattering of Charged Particles A particle passing through material undergoes multiple small-angle scattering, mostly due to large impact parameter interactions with nuclei. Then an initially parallel particle beam gets the angular spread after traveling through the layer of material. The angular distribution due to the multiple Coulomb scattering is described by Moliére theory (Bethe 1953). For small scattering angles, it is normally distributed around the average value θ = 0. Larger scattering angles caused by rare collisions of charged particles with nuclei are, however, more probable than expected from a Gaussian distribution. The root mean square of the projected scattering angle distribution is expressed as (Lynch and Dahl 1991): proj θrms

=



 x 13.6 MeV z [1 + 0.038 ln(x/X0 )], θ  = βcp X0

(16)

where p (in MeV/c) is the momentum, βc – the velocity, and z – the charge of the scattered particle. The quantity x/X0 is the thickness of the scattering medium measured in units of the radiation length (X0 ). The meaning of the latter

10

S. I. Eidelman and B. A. Shwartz

Δ/x (MeV g−1 cm2) 0.50

1.00

1.50

1.0

2.50

500 MeV pion in silicon 640 μm (149 mg/cm2) 320 μm (74.7 mg/cm2) 160 μm (37.4 mg/cm2) 80 μm (18.7 mg/cm2)

0.8

f (Δ/x)

2.00

0.6

w 0.4

Δp/x

Mean energy loss rate

0.2

0.0 100

200

300

400

500

600

Δ/x (eV/μm) Fig. 4 Energy-loss distribution for 500 MeV pions passing through a silicon layer (Bichsel et al. 2018)

and formulae for its calculation are given in section “Radiation Losses, Radiation Length, and Critical Energy.”

Channeling The energy loss of charged particles as described by the Bethe-Bloch formula should be modified for crystals where the collision partners are arranged on a regular lattice. When one looks at a crystal, it becomes immediately clear that the energy loss along certain crystal directions will be quite different from that along a nonaligned direction or in an amorphous substance. Motion along such channeling directions is governed mainly by coherent scattering off strings and planes of atoms rather than by the individual scattering off single atoms. This leads to anomalous energy losses of charged particles in crystalline materials (Moller 1994). It is obvious from the crystal structure that charged particles can only be channeled along a crystal direction if they are moving more or less parallel to crystal axes. The critical angle necessary for that is small (approximately 0.3◦ for β ≈ 0.1) and decreases with energy. For the axial direction (111, body diagonal), it can be estimated from:

1 Interactions of Particles and Radiation with Matter

11

ψ [degrees] = 0.307 · [z · Z/(E · d)]0.5 ,

(17)

where z and Z are the charges of the incident particle and the crystal atom, E is the particle energy in MeV, and d is the interatomic spacing in Å. The quantity ψ is measured in degrees (Gemmel 1974). For protons (z = 1) passing through a silicon crystal (Z = 14; d = 2.35 Å), the critical angle for channeling along the direction-of-body diagonals becomes: ψ = 13 μrad/ E [TeV].

(18)

For planar channeling along the face diagonals (110 axis) in silicon, one gets (Moller 1994): ψ = 5 μrad/ E [TeV].

(19)

Of course, the channeling process also depends on the charge of the incident particle. For a field inside a crystal of silicon atoms along the 110 crystal direction, one obtains 1.3 · 1010 V/cm. This field extends over macroscopic distances and can be used for the deflection of high-energy charged particles using bent crystals (Gemmel 1974). Channeled positive particles are kept away from a string of atoms and consequently suffer from a relatively small energy loss. Figure 5 shows the energy-loss spectra for 15 GeV/c protons passing through a 740-μm-thick germanium crystal (Gemmel 1974). The energy loss of channeled protons is lower by about a factor of two compared to random directions in the crystal.

Fig. 5 The energy-loss spectra for 15 GeV/c protons passing through a 740-μm-thick germanium crystal (Gemmel 1974)

15 GeV/c p −> 740µm Ge

40000

Random 400

30000

Aligned [110] 20000

200 10000

0 0

200

400 600 800 energy loss [keV]

0 1000

counts random

counts aligned

600

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S. I. Eidelman and B. A. Shwartz

Radiation Losses, Radiation Length, and Critical Energy Fast charged particles may lose energy not only due to the ionization, but also by bremsstrahlung when these particles are decelerated in the Coulomb field of the nucleus. For electrons, the radiation losses become dominant from the energy of a few tens of MeV. Radiation losses are characterized by the radiation length, X0 . After passing a layer of material with a thickness X0 , the average electron energy decreases to 1/e from the initial energy. Then the radiation energy loss can be expressed as: 

dE − dx

 = rad

E . X0

(20)

The values of X0 for various materials were calculated and tabulated by Tsai (1974): 1 NA 2 {Z [Lrad − f (Z)] + ZL rad } = = 4αre2 X0 A 1 A · 716.408 g/cm2

(21)

{Z 2 [Lrad − f (Z)] + ZL rad }.

The function f (Z) can be approximated (Davies et al. 1954): f (Z) = a 2 [(1 + a 2 )−1 + 0.20206 − 0.0369a 2 + 0.0083a 4 − 0.002a 6 ],

(22)

where a = αZ. For Z > 4, Lrad = ln(184.15 Z −1/3 ) and L rad = ln(1194 Z −2/3 ). For the lightest elements, the values of Lrad , L rad deviate from those given by the quoted formulae by ∼10–15% and can be found in Tsai (1974). The radiation length of a mixture of elements or a compound can be approximated by: X0 =

1 ρi /X0i

(23)

,

where ρi are the mass fractions of the components with the radiation length X0i . Contributions of various processes of the energy loss for electrons and positrons are presented in Fig. 6 (Bichsel et al. 2018). The energy at which specific radiation losses, (dE/dx)rad , reach the ionization losses, (dE/dx)ion , is called the critical energy, Ec . The critical energy for electrons can be approximated by the formulae: Ec =

610 MeV (for solids and liquids), Z + 1.24

Ec =

710 MeV (for gases). Z + 0.92

(24)

In a wide energy range from about 100 MeV up to 1 TeV, the differential probability of the emission of a photon with energy εph can be approximated by

1 Interactions of Particles and Radiation with Matter

0.20

Positrons

Lead (Z = 82)

Electrons

1.0

0.15 Bremsstrahlung

0.10

Ionization Møller (e −)

0.5

Bhabha (e +)

0

(cm2g−1)

− 1 dE (X0−1) E dx

13

0.05

Positron annihilation

1

10

100

1000

E (MeV) Fig. 6 Contributions of the different processes to the energy loss for electrons and positrons (Bichsel et al. 2018)

(Rossi 1952): 1 dn = dεph dx X0 · εph



 4 4 − y + y2 , 3 3

(25)

where y = εph /Ee is a portion of the initial electron energy, Ee , transferred to the photon. The path in a material and X0 are measured in g/cm2 . This formula is valid in the so-called complete-screening approximation, which is determined by the condition: 50 MeV y Z −1/3  1. Ee 1 − y

(26)

Obviously, this is not fulfilled at y ≈ 1; however, Eq. (25) is not accurate at y ≈ 0, especially at very high energies (Ee > 100 GeV) due to bulk-medium effects (see Bichsel et al. 2018 for discussion and further references). The angular distribution for emitted photons is quite narrow at high electron energy. The root mean square of the emission angle is (Rossi 1952):

θ  ∼

me c 2 Ee ln . Ee me c 2

(27)

S. I. Eidelman and B. A. Shwartz

μ+ on Cu μ−

100

10

LindhardScharff

Stopping power [MeV cm2/g]

14

Bethe-Bloch

Radiative

AndersonZiegler

Eμc Radiative losses

Radiative Minimum effects ionization reach 1%

Nuclear losses

Without δ

1 0.001

0.01

0.1

1

10

100

1000

10 4

10

1 00

1

10 5

10 6

10

100

βγ 0.1

1

10

100

[MeV/c]

1

[GeV/c] Muon momentum

[TeV/c]

Fig. 7 The total energy losses (−dE/dx) for muons in copper (solid line) (Bichsel et al. 2018). Vertical bands indicate different approximations

At very high energies, the radiation processes become important for all charged particles. Figure 7 shows the specific energy loss by muons in copper including excitation, ionization, and radiation processes (Bichsel et al. 2018).

Charged Particle Range Due to Ionization Losses The range of charged particles can be calculated from their energy losses:  R= 0

E0

dE . (dE/dx)

(28)

In practice, a range for heavy particles is well defined only when the main mechanism of the energy loss is medium ionization. In this case dE/dx should be taken from Eq. (13). The range of heavy particles for several substances as a function of particle momentum is presented in Fig. 8 (Bichsel et al. 2018). The range for electrons is not well defined because of large energy fluctuations in the bremsstrahlung losses and large path-length variations due to multiple scattering.

1 Interactions of Particles and Radiation with Matter

15

50000 20000

C Fe

10000

Pb

R/M (g cm−2 GeV−1)

5000 2000

H2 liquid He gas

1000 500 200 100 50 20 10 5 2 1 0.1

2

0.02

1.0

5

0.05

2

0.2

0.1

5

βγ = p/Mc 0.5

10.0

1.0

2

5

2.0

5.0

100.0

10.0

Muon momentum (GeV/c) 0.02

0.05

0.1

0.2

0.5

1.0

2.0

5.0

10.0

Pion momentum (GeV/c) 0.1

0.2

0.5

1.0

2.0

5.0

10.0 20.0

50.0

Proton momentum (GeV/c) Fig. 8 Range of heavy charged particles in various substances (Bichsel et al. 2018)

Cherenkov and Transition Radiation When a charged particle moves in a transparent medium with a velocity v exceeding the velocity of light c/n in that medium (n is refractive index), it emits a specific electromagnetic radiation, called Cherenkov radiation (Cherenkov 1937; Jelley 1958). This radiation is emitted under the angle θc to the particle track described by the simple expression: cos θc =

1 , nβ

(29)

16

S. I. Eidelman and B. A. Shwartz

where β = v/c. The number of Cherenkov photons emitted per unit path length in the optical wavelengths range, 400–700 nm, can be estimated as: dN = 490 sin2 θc [cm−1 ], dx

(30)

In comparison to ionization and excitation processes, the contribution of Cherenkov radiation to the energy loss is small even for gaseous media. For gases with Z ≥ 7, the energy loss by Cherenkov radiation amounts to less than 1% of the ionization loss of minimum-ionizing particles, while for light gases (H e, H ), this fraction increases to about 5%. Cherenkov radiation is widely used for charged particles identification since radiation threshold as well as angle θc depends on the particle velocity. Another type of electromagnetic radiation appears when a charged particle crosses the boundary between media with different dielectric properties (Ginzburg and Tsytovich 1990), for example, when particle transits from solid material to a gas gap. This radiation is referred to as transition radiation. The energy radiated from a single boundary (transition from vacuum to a medium with dielectric constant ε) is proportional to the Lorentz factor of the incident charged particle: S=

1 2 αz hω ¯ pγ 3

,

hω ¯ p=



4π Ne re3 me c2 /α,

(31)

where z is the charge of the incident particle, Ne is the electron density in the material, re is classical electron radius, and hω ¯ p is the plasma energy. For commonly used plastic radiators (styrene or similar materials), one has: hω ¯ p ≈ 20 eV.

(32)

The energy loss by transition radiation is negligibly small in comparison to the total energy loss of charged particles. However, this radiation becomes an effective mean for particle identification at high energies since its intensity as well as the number of emitted photons increases with the Lorentz factor γ .

Penetration of High Energy Photons in Matter In contrast to the charged particles, photons in each interaction with electrons or nuclei disappear or change dramatically their energy and direction. Thus, the photon beam subsides according to an exponential law: I = I0 exp(−μx),

(33)

where I is a photon flux and μ – mass attenuation coefficient. The processes of photon interactions inside material are discussed in the next subsections.

1 Interactions of Particles and Radiation with Matter

17

Photoelectric Effect The photoelectric effect implies an absorption of a photon by an electron bound in an atom and transfer of the photon energy to this electron. The photoeffect cross section for the photon of energy Eγ > EK , where EK is the K-shell energy, is particularly large for the K-shell electrons. The total cross section is:  K σph

=

32 4 5 α Z σT h [cm2 /atom], ζ7

(34)

where ζ = Eγ /me c2 and σT h = 83 π re2 = 665 mb is the cross section of Thompson scattering. The total photoelectric cross section for carbon and lead is shown in Fig. 10. The photoelectric cross section has sharp discontinuities when Eγ is equal to the binding energy of the atomic shells. After a photoelectric effect in the K-shell, the atomic electrons are rearranged and characteristic X-rays (like Kα ) or Auger electrons are emitted.

Compton Effect The Compton effect is inelastic scattering of photons by quasi-free atomic electrons. After this scattering the photon energy, Eγ , and the scattering angle, θγ , are related by the formula: Eγ

Eγ

=

1 , 1 + ζ (1 − cos θγ )

(35)

where ζ = Eγ /me c2 . The total cross section of Compton scattering derived by the integration of the Klein-Nishina formula (Klein and Nishina 1929; Tamm 1930) is:

σC =

π re2 ζ

   1 4 2 2 1 . 1 − − 2 ln(1 + 2ζ ) + + − ζ 2 ζ ζ 2(1 + 2ζ )2

(36)

This formula provides the cross section per one electron. In the ultrarelativistic case, when ζ  1, the formula for the Compton cross section reduces to:

σC =

π re2 ζ

  1 ln 2ζ + . 2

(37)

18

S. I. Eidelman and B. A. Shwartz

Production of Electron-Positron Pairs The production of an electron-positron pair by the photon becomes possible when the photon energy, Eγ , exceeds the threshold: Eγ ≥ 2me c2 +

2m2e c2 ≈ 2me c2 . Mnucleus

(38)

As for the bremsstrahlung, the screening parameter is defined from: γ = 100

me c 2 1 Z −1/3 ; Eγ ν(1 − ν)

ν=

Ee + m e c 2 , Eγ

(39)

where Ee is an electron (or positron) kinetic energy. In the case of complete screening (γ  1), the pair-production cross section is given by:  σpair = 4αre2 Z 2

7 183 1 ln 1/3 − 9 Z 54

 [cm2 /atom].

(40)

Then the probability dw of photon conversion at the small path length dx is approximately equal to: dw =

7 dx . 9 X0

(41)

The energy distribution of the produced electrons and positrons is given by the differential probability: dw αr 2 NA 2 = e Z f (Z, Eγ , ν) dE+ dx Eγ A

(42)

where E+ is the energy of the positron and f (Z, Eγ , ν) is a dimensionless function shown in Fig. 9 (Rossi 1952). As can be seen from the figure, the distributions are close to being flat except areas near the edges of the spectra.

Photon Flux Attenuation by Material An overview of the processes contributing to the attenuation of the photon flux is presented in Fig. 10 (Bichsel et al. 2018) for carbon and lead. The flux of the photons penetrated in matter is described by Eq. (33), where μ is called the total mass attenuation coefficient (measured in cm2 /g) which is related to the sum of cross sections of all contributing processes:

1 Interactions of Particles and Radiation with Matter Fig. 9 Energy-partition function f (Z, Eγ , x) with ε = Eγ /me c2 as a parameter (Rossi 1952)

19

ε=

8

15

ε = 2000 10 f( ε ,Z)

ε = 200 ε = 80 ε = 40

5

ε = 20 ε = 10 ε =6

0

0

0.1

μ=

0.2

0.3

NA  σi , A

0.4

0.5 0.6 0.7 E+ − mec 2 x= hν − 2mec 2

0.8

0.9

1

(43)

i

where σi is the atomic cross section for the process i. The value 1/μ, called the photon attenuation length, is shown in Fig. 11 for several elements as a function of the photon energy (Bichsel et al. 2018). For a chemical compound, the effective value of μeff = 1/λeff can be found as 1/λeff = wZ /λZ , where wZ and λZ are the weight content and attenuation length, respectively, for the element with a nucleus charge Z.

Electron-Photon Cascades At high energies (higher than 100 MeV), electrons lose their energy almost exclusively by bremsstrahlung, while the main interaction process for photons is electronpositron pair production. Thus, these processes lead to development of an electromagnetic cascade in matter when the number of particles, electrons, positrons, and photons increases until the energy of the particles decreases to the critical energy, Ec (see section “Radiation Losses, Radiation Length, and Critical Energy,” Eq. (24)). Since both processes, bremsstrahlung and pair production, are characterized by the radiation length, X0 , this unit is a natural measure for the electron-photon shower development. Shower development is characterized by the number of charged particles and photons as well as the energy deposition rate at the depth t = x/X0 in an absorber. The longitudinal distribution of the energy deposition in electromagnetic cascades can be approximated by the following expression evaluated from the Monte Carlo simulation (Longo and Sestili 1975):

20

S. I. Eidelman and B. A. Shwartz

(a) Carbon ( Z = 6) - experimental σtot

Cross section (barns/atom)

1 Mb

σp.e. 1 kb

σRayleigh

1b

κ nuc σCompton

κe

10 mb

(b) Lead ( Z = 82)

Cross section (barns/atom)

1 Mb

- experimental σtot

σp.e.

σRayleigh 1 kb

κ nuc σg.d.r. 1b

10 mb 10 eV

κe

σCompton

1 keV

1 MeV

1 GeV

100 GeV

Photon Energy Fig. 10 Photon total and partial cross sections in carbon and lead (Bichsel et al. 2018). Here σp.e. is for photoelectric effect; σRayleigh – Rayleigh (coherent) scattering; σCompton – Compton (incoherent) scattering by atomic electrons; κnuc – pair production at nuclei; κe – pair production at electrons; σg.d.r. – photonuclear interactions, most notably the giant dipole resonance

1 Interactions of Particles and Radiation with Matter

21

100

Absorption length λ (g/cm 2 )

10

Sn

1

Si

Fe

Pb

0.1

H

C

0.01 0.001 10 10 10

–4

–5 –6

10 eV

100 eV

1 keV

10 keV

100 keV

1 MeV

10 MeV

100 MeV

1 GeV

10 GeV

100 GeV

Photon energy

Fig. 11 The photon absorption length (Bichsel et al. 2018)

dE (bt)a−1 exp−bt = E0 b , dt Γ (a)

(44)

where Γ (g) is Euler’s Γ function, defined by:  Γ (g) =

∞

exp−x x g−1 dx.

(45)

0

The gamma function has the property: Γ (g + 1) = gΓ (g).

(46)

Here a and b are model parameters and E0 is the energy of the incident particle. In this approximation, the maximum of shower development is reached at: tmax

  E0 a−1 + Cγ e , = ln = b Ec

(47)

where Cγ e = 0.5 for a gamma-induced shower and Cγ e = −0.5 for an incident electron. The parameter b as obtained from simulation results is b ≈ 0.5 for heavy absorbers from iron to lead. Then the energy-dependent parameter a can be derived from Eq. (47). The experimentally measured distributions (Baumgart 1987; Akchurin 2001) are well described by Monte Carlo simulation using the code EGS4 (Bichsel et al. 2018; Nelson et al. 1985). Formula (44) provides a reasonable approximation for electrons and photons with energies larger than 1 GeV and a shower depth of more than 2 X0 , while for other conditions it gives a rough estimate only. The longitudinal

22

S. I. Eidelman and B. A. Shwartz

0.125 30 GeV electron incident on iron

(1/E0) dE/dt

0.100

80

0.075

60 Energy

0.050

40 Photons × 1/6.8

0.025

20

Electrons 0.000

0

5 10 15 t = depth in radiation lengths

20

Number crossing plane

100

0

Fig. 12 Longitudinal shower development of a 30 GeV electron-induced cascade obtained by the EGS4 simulation in iron (Bichsel et al. 2018; Nelson et al. 1985). The solid histogram shows the energy deposition; black circles and open squares represent the number of electrons and photons, respectively, with the energy larger than 1.5 MeV; the solid line is the approximation given by (44)

development of the electromagnetic shower initiated by an electron in matter is shown in Fig. 12. The angular distribution of the particles produced by bremsstrahlung and pair production is very narrow, and the characteristic angles are of the order of me c2 /Eγ . That is why the lateral width of an electromagnetic cascade is mainly determined by multiple scattering and can be described in units of the Molière radius: RM =

21 Με῞ X0 [g/cm2 ]. Ec

(48)

The largest fraction of energy is deposited in a relatively narrow shower core. About 95% of the shower energy is contained in a cylinder around the shower axis whose radius is R(95%) = 2RM almost independently of the energy of the incident particle.

Nuclear Interactions of Hadrons with Matter As an example of the hadronic cross section, the pion-deuteron and pion-proton total and inelastic cross sections are presented in Fig. 13. The total pion-nucleus cross section has similar momentum dependence scaled as A2/3 ; however, the peaks in the range of the isobar production are less pronounced. Similar cross section dependence is typical for other hadrons as well. As can be seen, the momentum

1 Interactions of Particles and Radiation with Matter

23

Cross section, mb

1000

100

π± d, total π− p, total 10

π− p, elastic Plab, GeV/c

1 0.1

1

10

100

1000

Fig. 13 Pion-proton and pion-deuteron cross sections (Bichsel et al. 2018)

dependence in the range higher than 1 GeV is rather flat. For momenta exceeding a few hundred MeV, the interaction is mostly inelastic which implies a production of secondaries and knock-out nucleons from the nuclei. These processes induce a development of the hadron cascades when the energy of the incident hadron is high enough (10 GeV). The longitudinal development of the hadron shower is determined by the average nuclear interaction length, λI , which can be roughly estimated as: λI ≈ 35 g/cm2 · A1/3.

(49)

In most detector materials, this quantity is much larger than the radiation length X0 , which describes the behavior of electron-photon cascades. In the inelastic hadronic processes mainly charged and neutral pions, but with lower multiplicities, also kaons, nucleons, and other hadrons are produced. The average particle multiplicity per interaction varies only weakly with energy (∝ ln E). The average transverse momentum of secondary particles can be characterized by: pT  ≈ 0.35 GeV/c.

(50)

The average inelasticity, that is, the fraction of energy, which is transferred to secondary particles in the interaction, is around 50%.

24

S. I. Eidelman and B. A. Shwartz

A large component of the secondary particles in hadron cascades is neutral pions, which represent approximately one third of the pions produced in each inelastic collision. Since the main π 0 decay channel is π 0 → γ γ , a considerable fraction of the energy of the hadron shower, fem , is deposited in the form of an electromagnetic shower which can be approximated by (Gabriel 1994):  fem = 1 −

E E0

k−1 ,

(51)

where E is the energy of the incident hadron, E0 is a parameter varying from 0.7 GeV (for iron) to 1.3 GeV (for lead), and k is between 0.8 and 0.85. Details can be found in Wigmans (2000). In contrast to electrons and photons, whose electromagnetic energy is almost completely recorded in the detector, a substantial fraction of the energy in hadron cascades remains “invisible” (finv ). This is related to the fact that some part of the hadron energy is used to break up nuclear bonds. This nuclear binding energy is provided by the primary and secondary hadrons and does not contribute to the energy deposition within a hadronic shower. In addition, long-lived or stable neutral particles like neutrons, KL0 , or neutrinos can escape from the calorimeter, thereby reducing the visible energy. The total invisible energy fraction of a hadronic cascade can be estimated as finv ≈ 30–40% (Wigmans 2000). Figure 14 shows the measured longitudinal shower development of 100 GeV pions in iron (Amaral 2000) in comparison to Monte Carlo calculations and empirical approximations. Apart from the longer longitudinal development of hadron cascades, their lateral width is also sizably increased compared to electron cascades. While the lateral structure of electron showers is mainly determined by multiple scattering, in hadron cascades it is caused by large transverse momentum transfers in nuclear interactions.

Neutrino Interactions with Matter Neutrinos interact with matter due to the charged-current and neutral-current weak interactions. The typical charged-current interactions are: νl + n → X + l − ,

(52)

+

(53)

νl + p → X + l ,

where l stands for an electron, muon, or τ -lepton. X means just p (52) or n (53) for the low energy neutrino and multiparticle final state for high energy neutrino. The total neutrino-nucleon cross sections measured in fixed-target experiments are shown in Fig. 15. These cross sections at high neutrino energies can be approximated as: σνN [cm2 ] = (0.677 ± 0.014) · 10−38 E [GeV],

(54)

ΔE/Δx (GeV/λπFe)

1 Interactions of Particles and Radiation with Matter

25

10

1

0

2

4

6

8

10

X (λπFe) Fig. 14 The longitudinal energy distribution in a hadronic shower in iron induced by 100 GeV pions. The depth X is measured in units of the interaction length λI . Open circles and triangles are experimental data; diamonds are predictions of simulation. The dash-dotted line is a simple fit by formula (44) with optimal a and b; the other lines are more sophisticated approximations. Crosses and squares are contributions of electromagnetic showers and the non-electromagnetic part, respectively (Amaral 2000)

σνN [cm2 ] = (0.334 ± 0.008) · 10−38 E [GeV]. The charged-current interaction also contributes to the elastic νe scattering. The neutral-current interactions induce the processes of the elastic and quasielastic scattering: νl + N → νl + X , νl + N → νl + X , νl + e → νl + e ,

(55)

σCC / Eν (10-38 cm2 / GeV)

26

S. I. Eidelman and B. A. Shwartz MINERvA, PRD 95, 072009 (2017) T2K, PRD 93, 072002 (2016) T2K (Fe) PRD 90, 052010 (2014) T2K (CH) PRD 90, 052010 (2014) T2K (C), PRD 87, 092003 (2013) ArgoNeuT PRD 89, 112003 (2014) ArgoNeuT, PRL 108, 161802 (2012) ANL, PRD 19, 2521 (1979) BEBC, ZP C2, 187 (1979) BNL, PRD 25, 617 (1982)

1.6 1.4 1.2

CCFR (1997 Seligman Thesis) CDHS, ZP C35, 443 (1987) GGM-SPS, PL 104B, 235 (1981) GGM-PS, PL 84B (1979) IHEP-ITEP, SJNP 30, 527 (1979) IHEP-JINR, ZP C70, 39 (1996) MINOS, PRD 81, 072002 (2010) NOMAD, PLB 660, 19 (2008) NuTeV, PRD 74, 012008 (2006) SciBooNE, PRD 83, 012005 (2011) SKAT, PL 81B, 255 (1979)

1

νμ N → μ - X

0.8 0.6 0.4

νμ N → μ + X

0.2 0

1

10

100

150

200

250

300

350

Eν (GeV)

Fig. 15 Total cross sections for muon neutrino interactions with nucleons at high energies (Bichsel et al. 2018). The straight lines are the isoscalar-corrected values averaged over 30– 200 GeV

ν l + e → ν l + e.

(56)

Cross sections of these processes are much smaller than those induced by the charged currents. In general, all neutrino cross sections are too small to provide a noticeable attenuation of the neutrino flux for any material thickness available on the Earth.

Conclusion and Further Reading It is obviously impossible to give a detailed review of the variety of phenomena related to interactions of particles and radiation with matter in a brief chapter. Moreover, since many different physical processes contribute to these interactions, the subject itself becomes so multidisciplinary that its complete description is hardly possible in one, even large review. For more details and further references, we can recommend the following books. B. Rossi, High Energy Particle, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1952. K. Kleinknecht, Detectors for particle radiation, Cambridge University Press, Cambridge, 1986. G.F. Knoll, Radiation detection and measurement, 3rd ed., New York, Wiley, 2000.

1 Interactions of Particles and Radiation with Matter

27

C. Grupen and B. Shwartz, Particle Detectors, Cambridge University Press, Cambridge, UK, 2008. R. Wigmans, Calorimetry: Energy Measurement in Particle Physics, Clarendon Press, Oxford 2000.

References Akchurin N et al (2001) Nucl Instr Methods A 471:303 Amaral P et al (2000) Nucl Instr Methods A 443:51 Baumgart R et al (1987) Nucl Instr Methods A 256:254 Bethe HA (1930) Ann d Phys 5:325 Bethe HA (1932) Zs f Phys 76:293 Bloch F (1933) Zs f Phys 81:369 Bethe HA (1953) Phys Rev 89:1256 Bichsel H (1988) Rev Mod Phys 60:663 Bichsel H (2006) Nucl Instr Methods A 562:154 Bichsel H, Groom DE, Klein SR, Tanabashi M et al (Particle Data Group) (2018) Phys Rev D 98:030001 Cherenkov PA (1937) Phys Rev 52:378 Davies H, Bethe HA, Maximon LC (1954) Phys Rev 93:788 Gabriel TA et al (1994) Nucl Instr Methods A 338:336 Gemmel DS (1974) Rev Mod Phys 46:129 Ginzburg VL, Tsytovich VN (1990) Transition radiation and transition scattering. Institute of Physics Publishing, Bristol Jelley JV (1958) Cherenkov radiation and its applications, Pergamon Press, London/New York Klein O, Nishina Y (1929) Z Phys 52:853 Landau LD (1944) J Exp Phys (USSR) 8:201 Longo E, Sestili I (1975) Nucl Instr Methods 128:283 Lynch GR, Dahl OI (1991) Nucl Instr Methods B 58:6 Moller SP (1994) CERN-94-05 Mott NF (1929) Proc R Soc (Lond) A 124:425 Nelson WR et al (1985) The EGS4 Code System, SLAC-R-265 Onuchin AP, Telnov VI (1974) Nucl Instr Methods 120:365 Rossi B (1952) High energy particles. Prentice-Hall, Inc., Englewood Cliffs Sternheimer RM (1952) Phys Rev 88:851 Sternheimer RM, Peierls RF (1971) Phys Rev B 3:3681 Tamm IE (1930) Z Phys 62:545 Tsai YS (1974) Rev Mod Phys 46:815 Vavilov PV (1957) Sov Phys JETP 5:749 Wigmans R (2000) Calorimetry: energy measurement in particle physics. Clarendon Press, Oxford

2

Electronics Part I Helmuth Spieler

Contents Why Understand Electronics? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Detector Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Signal Fluctuations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Signal Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Electronic Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Electronic Noise Levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Noise in Amplifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Noise Versus Dynamic Range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Signal Charge Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Charge-Sensitive Amplifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Noise in a Charge-Sensitive Amplifier System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Realistic Charge-Sensitive Amplifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Detector Equivalent Circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Thermistor Detecting IR Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Piezoelectric Transducer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ionization Chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Position-Sensitive Detector with Resistive Charge Division . . . . . . . . . . . . . . . . . . . . . . . . . Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

30 31 31 35 41 43 45 48 49 50 51 52 54 55 55 55 56 58 58

Abstract Detectors come in many different forms and apply a wide range of technologies, but their principles can be understood by applying basic physics. In analyzing the signal acquisition, relatively simple models provide sufficient information to assess the effect of different readout schemes. This chapter discusses signal

H. Spieler () LBNL Physics Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA e-mail: [email protected] © Springer Nature Switzerland AG 2021 I. Fleck et al. (eds.), Handbook of Particle Detection and Imaging, https://doi.org/10.1007/978-3-319-93785-4_2

29

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H. Spieler

formation in various types of detectors and fluctuations in signal magnitude. It then moves on to baseline fluctuations, i.e., electronic noise, and the properties of amplifiers used for signal acquisition.

Why Understand Electronics? Detector electronics is a highly developed field, and most users simply take it for granted. Many standard items are readily available, or if custom systems are required, they can often be developed by applying standard recipes. However, real scientists understand their tools, and if they are capable of applying basic physics to practical uses, understanding the electronic functions is quite practical without detailed knowledge of electronics engineering. It does require a real understanding of basic classical physics and the ability to recognize which aspects of physics apply in practical situations. For scientists and engineers to work together efficiently, it is necessary that scientists understand basic principles, so they do not request things that cannot work. Conversely, engineers should also understand the relevant aspects of the applications, so scientists have to be capable of explaining the important requirements. In detector systems that push the envelope, practical solutions are a balance between functions allowed by physics and the constraints of technology. However, revolutionary detector techniques often are not based on new inventions but on combining existing technologies in novel ways. Understanding electronics can also help in recognizing subtle malfunctions that can fake physics results. Radiation detectors are used for three basic functions: detecting the presence of radiation, measuring the energy spectrum, and recording the relative timing between events. These functions also provide position sensing. Energy resolution is one of the most useful properties, as shown in Fig. 1. Energy resolution is determined by processes within the detector, where fluctuations in signal magnitude are inherent, and the readout system, where baseline fluctuations are superimposed on the signal. Figure 2 shows the effect of noise added to a signal taken at four different times. The resulting peak amplitude can be both higher and lower. The effect of noise on timing measurements can also be seen. If the timing signal is derived from a threshold discriminator, where the output fires when the signal crosses a fixed threshold, amplitude fluctuations in the leading edge translate into time shifts. If one derives the time of arrival from a centroid analysis, the timing signal also shifts (compare the top and bottom right figures). Random fluctuations in the detector and in the baseline add in quadrature. Figure 3 shows how either detector or readout baseline fluctuations can dominate to yield the same overall resolution. The baseline fluctuations can have many origins, external interference, artifacts due to imperfect electronics, etc., but the fundamental limit is electronic noise. Whether one or the other fluctuation dominates depends on the type of detector.

2 Electronics Part I

31

106

2000

2000

104

2000

10

Counts

Counts

Nal(TI)Scintillator 105

3

Ge Detector

1.75 keV FWHM

5.6 keV

10.8 keV

10

2

10

1000 0

500

1,000 Energy (keV)

1,500

2,000

240

300 360 420 Energy (keV)

Fig. 1 The comparison of gamma-ray spectra taken with a scintillator and a semiconductor detector (left) clearly shows how improved resolution reveals detailed structure. (Adapted from Philippot 1970). Higher resolution also improves the signal-to-noise ratio (right). (Adapted from Armantrout et al. 1972. Figures ©IEEE, reprinted with permission)

Detector Types Detectors can transform absorbed energy directly or indirectly into signals. Figure 4 shows the principle of an ionization chamber where absorbed radiation is converted directly into a charge signal. Here the statistical fluctuations in the number of signal charges place a fundamental limit on the energy resolution. A scintillation detector as shown in Fig. 5 is an example of an indirect detector. In this case, another function comes into play that affects the energy resolution.

Signal Fluctuations In a photomultiplier, the photocathode converts only a fraction of the impinging scintillation photons into photoelectrons. This quantum efficiency is commonly in the 10–30% range. Furthermore not all of the scintillation light ends up at the photocathode. Assume a 511 keV gamma ray absorbed in a NaI(Tl) scintillator:

32

H. Spieler

Fig. 2 Signal plus noise at four different times, shown for a signal-to-noise ratio of about 20. The noiseless signal is superimposed for comparison

Fig. 3 Signal and baseline fluctuations add in quadrature. For large signal variance (top), as in scintillation detectors or proportional chambers, the baseline noise is usually negligible, whereas for small signal variance as in semiconductor detectors or liquid-Ar ionization chambers, baseline noise is critical

2 Electronics Part I

33

Fig. 4 In an ionization chamber, the absorbed energy is converted directly into signal charges

Fig. 5 In a scintillation detector, charged particle or photon energy absorbed in the scintillator is converted into visible or near-visible light. When the scintillation photons impinge on the photocathode, they produce photoelectrons, which can be detected directly or sent through a gain mechanism as in a photomultiplier

• • • •

25,000 photons are created in the scintillator. 15,000 photons impinge on the photocathode. 3000 photoelectrons arrive at the first dynode. 3 · 109 electrons appear at the anode.

Defects and incomplete translation of absorbed energy into signal quanta can degrade detector resolution, but the inherent resolution of the detector cannot be better than the statistical variance in the number of signal quanta N produced by the absorbed energy E, √ N 1 N E = = =√ . (1) E N N N The smallest quantity in the above sequence is the number of photoelectrons impinging on the first dynode, so in this example (see also Eq. 5)

34

H. Spieler

1 E = 2%rms ≈ 5%FWHM. =√ E 3000

(2)

The gain in a photomultiplier does not add much additional variance, so the relative resolution is the same at the anode, although the number of electrons is 106 times larger. Other nonstatistical mechanisms can also contribute to fluctuations. In many scintillators the ratio of scintillation photons to absorbed energy changes slightly with energy. In events where the absorbed energy is distributed over several separate interactions that deposit different energies, e.g., Compton scattering, these differences in the individual interactions lead to variations in the total scintillation light. Equation 1 illustrates a basic mechanism. In general, however, additional considerations come into play when assessing statistical fluctuations. σN =

√

 FN =

F

E , ESQ

(3)

where ESQ is the energy required to form a signal quantum, e.g., electron-ion pair, and F is the Fano factor (Fano 1947), which in some detectors is Vd

E Emax

Emax

Emin W

d

x

d

x

Fig. 11 Electric field in a reverse-biased semiconductor diode in partial depletion (left) and with overbias (right) 0.6

0.4

Vd = 60 V,Vb = 90 V Signal current (μA)

Signal current (μA)

Vd = 60 V,Vb = 60 V 0.3 0.2 e 0.1

0.4

e

0.2

h

h 0

0 0

10

20

30

Time (ns)

40

50

0

10

20

30

40

50

Time (ns)

Fig. 12 Current signals for tracks traversing a semiconductor detector with parallel-plate electrodes and applied bias voltages of 60 and 90 V. The left-hand plot is at the depletion voltage, where the field at the ohmic contact is zero and the right-hand plot shows the effect of overbias

equations to analyze the signals in multigrid vacuum tubes. Another example is the photomultiplier tube (PMT). Figure 14 shows the PMT configuration together with a typical resistive voltage divider that applies the dynode voltages. Electrons moving from the last dynode to the anode form the anode signal, as illustrated in Fig. 15. Note that the current path is closed through the bypass capacitor of the last dynode, so the practical implementation should be configured to keep it short, especially if fast pulse response is required. The circuit in Fig. 14 is drawn accordingly. The gain of a photomultiplier tube is very sensitive to the operating voltage. Given an individual dynode gain of G in the regime where the gain is proportional to the voltage difference between dynodes, the gain of a tube with N dynodes is GN . Then the overall gain will be proportional to VN , so fluctuations in the supply

40

H. Spieler 0.6

0.4

Signal current (μA)

Signal current (μA)

0.5 e n -Strip signal

0.3 0.2 0.1

p -Strip signal

0.4

0.2

h

h

e 0

0 0

10

30

20

0

10

Time (ns)

20

30

Time (ns)

Fig. 13 Strip detector signals for an n-bulk device with 60 V depletion voltage operated at a bias voltage of 90 V. The electron (e) and hole (h) components are shown together with the total signal (bold). Despite marked differences in shape, the total charge is the same on both sides Photocathode 3R

D1

D2 R

D3 R

D4 R

D5 R

D6 R

D7 R

D8 R

D9 R

D10 Anode R

Anode out

R

Hight voltage

Fig. 14 Voltage divider circuit for a photomultiplier tube. The voltage ratios between the various electrodes are set by the resistance value R. D1 through D10 are the dynode connections. The resistor connected to the anode is included to avoid the anode charging up to a high voltage when the output is disconnected. When made much larger than the output load resistance, the signal fed to the readout will not be significantly reduced

voltage V can degrade the energy resolution. Another contribution to changes in gain is the event rate. The charge required for the additional electrons emitted from each dynode is supplied by the voltage divider. At the final dynodes, this charge can be sufficient to cause a significant voltage drop. Just to estimate the current drawn by the dynode, assume a triangular output pulse with 1 V peak amplitude and a base width of 10 ns. Into a 50  load the peak current Ipk = 20 mA. Also assume that the PMT is operating with a supply voltage of 1 kV and a divider current of 1 mA. Then the peak signal current of 20 mA is much larger than the current that can be provided by the voltage divider, so the gain will drop. This effect is reduced by the capacitors connected between the final dynodes. For a dynode voltage Vd = Vn − Vn − 1 (e.g., the voltage difference between dynodes 10 and 9), the stored charge Q = C · Vd . If this charge is much larger than the signal charge, then the voltage drop will be small. In this example, the signal charge at the last dynode is about 100 fC. If Vd = 100 V and C = 1 nF, the stored charge Q = 100 nC, so the relative voltage drop will be 10−3 , small with respect to a typical scintillator resolution. However, the capacitor

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41

V+

N×R

Last dynode

Equivalent circuit

Anode R

is(t) Input resistance of amplifier or ADC

Output current loop

Fig. 15 The anode signal in a photomultiplier tube is formed by electrons moving from the last dynode to the anode. The equivalent circuit is shown at the right

has to charge up before the next pulse if the gain is to be maintained. The voltage will recover in time as V(t) = Vd (1 − et/τ ), where τ = RC, i.e., about 100 μs(10−4 s), so the time between pulses should be at least 10−3 − 10−2 s. A more accurate calculation takes into account that since the total supply voltage remains constant, a reduced voltage at one dynode will change the voltage distribution and increase the voltages at the preceding dynodes, but the simple estimate performed above indicates where attention is required to maintain energy resolution. In principle the rate capability can be increased by raising the divider current, but power dissipation is a major constraint (1 W in the above example). The voltages at the last dynodes are most susceptible. They can be stabilized by incorporating transistor drivers at the critical stages. Another scheme splits the voltage divider and feeds the final dynodes from a separate supply with a higher divider current. However, the simplest solution is to reduce the gain of the PMT and make up for it by feeding a low-noise amplifier. This has been a practical solution for decades, but not widely applied, since the combination of amplifier speed and electronic noise must be considered, and many PMT users believe that they don’t have to understand low-noise electronics.

Electronic Noise Although the mechanisms are different from signal formation in detectors, electronic noise is also caused by statistical fluctuations. Consider a current flowing through a sample bounded by two electrodes, i.e., n electrons with a total charge ne, moving with velocity v. The induced current depends on the spacing s between the electrodes (see “Ramo’s theorem” discussed above), so

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H. Spieler

i=

nev . s

(8)

The fluctuation of this current is given by the total differential di2 =

2  ev 2 dv + dn , s s

 ne

(9)

where the two terms add in quadrature, as they are statistically uncorrelated. From this, one sees that two mechanisms contribute to the total noise: velocity and number fluctuations. Velocity fluctuations originate from thermal motion. Superimposed on the average drift velocity are random velocity fluctuations due to thermal excitation. The induced charge fluctuations can be translated from the Maxwellian velocity distributions and by applying the Wiener–Khinchine theorem in the Fourier transform to the frequency domain. However, a simpler procedure is to derive the maximum power that can be extracted from a thermal component in equilibrium by applying Planck’s theory of blackbody radiation. The energy per mode at an absolute temperature T as a function of frequency f is E=

hf , ehf/kT − 1

(10)

where k is the Boltzmann constant. Thus, since E = P dt, the spectral density of the emitted power dP hf = hf/kT . df e −1

(11)

This is the power that can be extracted in equilibrium. At low frequencies hf  kT , the spectral power density dP hf  = kT , ≈ hf df 1 + kT −1

(12)

so the spectral density is independent of frequency (“white noise”), and for a total bandwidth f, the noise power that can be transferred to an external device is Pn = kT · f. The important result in this context is that the noise increases with bandwidth, so fast electronics where short rise times contain high-frequency Fourier components will have higher noise. Number fluctuations occur in many circumstances. One source is carrier flow that is limited by emission over a potential barrier. Examples are thermionic emission or current flow in a semiconductor diode. The probability of a carrier crossing the barrier is independent of any other carrier being emitted, so the individual emissions are random and not correlated. Another mechanism applies in a reverse-biased

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43

diode, where the current is created by statistically independent generation and recombination processes. These number fluctuations are called “shot noise,” which also has a “white” spectrum. Another source of number fluctuations is carrier trapping. Impurities or imperfections in a crystal lattice can trap charge carriers and release them after a characteristic lifetime. Typically, multiple defects with a range of lifetimes are present. This leads to a frequency-dependent power spectrum dPn /df = 1/f α , where α is typically in the range of 0.5–2. Given a random distribution of trapping levels with a wide range of lifetimes, the noise power spectrum has a 1/f distribution (see Spieler 2005, pp. 113–114).

Electronic Noise Levels As noted above, both thermal and shot noise have “white” power spectra, i.e., if the noise power is measured with a fixed bandwidth, the magnitude is independent of frequency. A typical source of thermal noise is a resistor. For a resistance R, the spectral noise power density dPn = 4 kT , df

(13)

where k is the Boltzmann constant and T the absolute temperature. Since the power in a resistance R is P =

v2 = i 2 R, R

(14)

the spectral voltage noise density dvn2 ≡ en2 = 4 kT R df

(15)

and the spectral current noise density din2 4 kT ≡ in2 = . df R

(16)

The spectral noise density of shot noise in2 = 2 eI,

(17)

where I is the average current and e the electronic charge. Note that the criterion for shot noise is that carriers are injected independently of one another, as in thermionic or semiconductor diodes. Current flow determined by an ohmic conductor (I = V/R)

44

H. Spieler

does not carry shot noise. Any local fluctuation in electron density relative to the stationary positive charge of the host atoms will set up an electric field that can easily draw in additional carriers to equalize the disturbance. The above expressions for voltage and current noise can be derived in various ways (see Spieler 2005, pp. 109–115). Other aspects that have to be considered when assessing the effect of current noise on the noise charge will be explained in  Chap. 3, “Electronics Part II” on signal processing. The spectral distribution of noise is a power density dPn /df, or in other words, the power in a narrow slice of frequency space. However, in analyzing electronic noise, we need √ to describe√the noise in terms of voltage and current spectral densities dvn / df and din / df . In circuit design literature √ √ and data sheets, these are commonly abbreviated as dvn / df ≡ en and din / df ≡ in , so we’ll follow that convention. This does lead to inconsistencies; is might represent a signal current √ with the unit A, whereas in represents a spectral density A/ Hz. In the following, just bear in mind that en and in have this special connotation. The total noise is obtained by integrating the noise power over the relevant frequency range of the system, the bandwidth. Since power is proportional to either the voltage or current squared, the output noise of an amplifier with a frequencydependent gain A(f) is

∞ 2 vno

=

∞ en2 A2 (f )df

0

or

2 ino

=

in2 A2 (f )df.

(18)

0

The total noise vno or ino increases with the square root of bandwidth. Since large bandwidths correspond to fast rise times, increasing the speed of a pulse measurement system will increase the noise. In practice, amplifier stages limit the bandwidth with both low- and highfrequency cutoff frequencies, beyond which the gain drops off. The distribution of bandwidths must also be considered. If a low-noise amplifier with a small bandwidth is feeding a wide-bandwidth stage prior to measurement, e.g., a wide-bandwidth digitizer, the noise of the second stage can dominate. The frequency and time response of an amplifier are related as shown in Fig. 16. Beginning at low frequencies, basic amplifiers have a constant gain, which begins to drop off at a cutoff frequency fu , beyond which the gain drops linearly with frequency. In the time domain, a fast-rise-time input pulse is slowed down to a rise time constant τ = 1/(2π fu ). At higher frequencies, additional cutoff frequencies may come into play, but well-designed amplifiers have a frequency response that is characterized by a single cutoff frequency (“pole”) until the gain has dropped off significantly. The basic electronic noise sources are expressed in terms of voltage and current, but the overall detector signal is a charge. The noise level can be expressed accordingly by measuring the noise level at the output of the amplifier and the amplitude of the signal for a known input charge. From this measured signal-to-noise ratio, the

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45

Fig. 16 The time constants of an amplifier affect both the frequency and the time response. Both are fully equivalent representations

signal charge yielding a signal-to-noise ratio of one can be determined. This is the equivalent noise charge (ENC).

Noise in Amplifiers The noise of an amplifier can be fully characterized in terms of a voltage and current √ noise source at√the input as shown in Fig. 17. Typical magnitudes are nV/ Hz and fA to pA/ Hz. Rather than specifying the total noise over the full bandwidth, the magnitude of each noise source is characterized by its spectral density. This is convenient because the effects of frequency-dependent impedances in the input circuit and of the amplifier bandwidth can be assessed separately. The noise sources do not have to be physically present at the input. Noise also originates within the amplifier. Assume that at the output the combined contribution of all internal noise sources has the spectral density eno . If the amplifier has a voltage gain Av , this is equivalent to a voltage noise source at the input en = eno /Av . First, let’s assess the effect of external noise sources. Assume a signal fed to the amplifier input through a series resistance RS , e.g., the resistance of a detector strip electrode or the series resistor used as part of an overvoltage protection circuit. Furthermore, a source of noise current is shunting the amplifier input. The equivalent circuit is shown in Fig. 18. The signal at the input of the amplifier vSi = vS

Ri . RS + Ri

(19)

The noise current flows through both the series resistance RS and the amplifier input resistance Ri . Since the two are effectively in parallel, the resulting voltage at the input is the noise current flowing through the resistance of RS and Ri in parallel.

46

H. Spieler

Fig. 17 An amplifier’s noise can be fully characterized by assessing the effects of equivalent voltage and current sources at the input

Fig. 18 The amplifier’s noise equivalent circuit including a resistance in the signal path

Since the contributions from independent, i.e., uncorrelated, noise sources add in quadrature, the noise voltage at the input of the amplifier  2 eni = (4 kT R S )

Ri Ri + RS

2

 + in2

Ri RS Ri + RS

2 ,

(20)

where the bracket in the in2 term is the parallel combination of Ri and RS . The signalto-noise ratio at the output of the amplifier  S 2 N

=

2 A2v vSi 2 2 Av eni

=

 S 2 N

2 Ri Ri +RS 2  Ri R R +in2 R i+RS kT RS ) R +R i S i S vS2 (4 kT RS )+in2 RS2 vS2 

(4

=



2 ,

(21)

,

is the same as for an infinite input resistance, since the effect of the amplifier input resistance on the external noise arriving at the amplifier input is the same as for the signal. This result also holds for a complex input impedance, i.e., a combination of resistive and capacitive or inductive components. Since S/N is independent of amplifier input impedance, we can perform valid noise analyses using “idealized” voltage amplifiers with infinite input impedance. When taking the amplifier noise into account, the origins of the noise shown in Fig. 17 must be considered. In amplifiers the major contributions to the noise at the output originate inside the amplifier. The equivalent input noise is then the output noise divided by the amplifier gain. The contribution of this noise is independent

2 Electronics Part I

47

of the input or source resistances. If an amplifier noise source is directly present at the input, e.g., the base current of a bipolar transistor, the noise current will flow through the source resistance and generate an input voltage, but not through the amplifier input resistance, as this is an integral part of the noise source. In general, the amplifier noise sources shown in Fig. 17 only feed the impedances external to the amplifier. When analyzing a voltage-sensitive amplifier with a very high input impedance, the amplifier equivalent input noise voltage appears in series with the input signal and adds in quadrature with any other noise voltages in the input loop. The noise current originating at the input will flow through the source impedances resulting in a voltage that adds in quadrature. With a current-sensitive amplifier, the output noise divided by the amplifier gain results in an equivalent input noise current, whose contribution in this case is independent of the source impedances. Any noise voltage sources in series with the input, e.g., resistors, will result in a noise current flowing through the input loop. This current will depend on the total source impedance. Consider a chain of two amplifiers (or amplifying devices), with gains A1 and A2 , and input noise levels N1 and N2 , as shown in Fig. 19. When a signal S is applied to the first amplifier, the input signal-to-noise ratio is S/N1 . At the output of the first amplifier, the signal is A1 S and the noise A1 N. Both the signal and the noise are amplified by the second amplifier, but in addition the second amplifier contributes its noise, which adds in quadrature to the noise from the first stage. Then the signal-to-noise ratio at the output of the second amplifier  S 2 N

=

(SA1 A2 )2 (N1 A1 A2 )2 +(N2 A2 )2

 S 2 N

=



S N1

2

=

S2

 2 N N12 + A2 1

1  2 . N2 1+ A N

, (22)

1 1

The second stage adds to the overall noise, but if the gain of the first stage is sufficiently high, it can be negligible. In a well-designed system the noise is dominated by the first gain stage.

Fig. 19 In cascaded amplifiers the equivalent input noise of the first amplifier amplified by the first stage’s gain can override the noise of the second stage

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H. Spieler

Noise Versus Dynamic Range Photomultiplier tubes often provide sufficient gain that they can directly feed an analog-to-digital converter (ADC) without an additional amplifier. However, ADCs also have internal noise sources, i.e., their input stage is an amplifier. Often the equivalent input noise is quite high, e.g., an order of magnitude higher than a good amplifier, and the ADC’s resolution is worse than implied by the number of bits. The dynamic range is determined by the maximum signal level of the digitizer divided by the equivalent input noise. As noted above, the rate capability of a PMT can be increased by operating the PMT at a reduced gain and using a low-noise amplifier to bring the signal to the level required by the ADC. Adding an amplifier can reduce the overall noise, but the required gain can reduce the overall dynamic range. Given the preamplifier’s input noise of vn1 and gain G together with ADC’s equivalent input noise vn2 , the resulting noise referred to the preamplifier input  vn =

2 (vn1 G)2 + vn2 = G

 2 + vn1

 v 2 n2

G

(23)

,

so the ratio of the combined noise to the ADC noise

vn = vn2

 

vn1 vn2

2

 +

1 G

2 (24)

.

For example, for a gain of 10 and vn1 = vn2 /10, the resulting noise is reduced by √ a factor 2/10, so the minimum signal level is about seven times lower. However the maximum signal level is reduced by the preamplifier gain G, so the dynamic range V max /G Vi0max V max Vimax 1 , (25) = i0   = = i0 ·  2 vn vn2 2 2 2 + vn2 2 vn1 G) + v (v vn1 n1 n2 G +1 G vn2

where the second factor is the reduction in dynamic range. For the above √ example with a gain of 10 and vn1 = vn2 /10, the overall dynamic range is 1/ 2 smaller. Figure 20 shows the dynamic range and noise versus gain for various noise ratios vn1 /vn2 . For vn1 /vn2 = 0.05 and a gain of 5, the dynamic range is reduced by only 3%, and the noise is reduced to 20.6% of the ADC noise. Doubling the preamp noise to vn1 /vn2 = 0.1 reduces the dynamic range by 11%, and the noise is reduced to 22.4%.

49

1 1 0.8 0.6 0.1 0.2 0.3 0.4

0.4 0.2

Noise change factor

Dynamic range reduction factor

2 Electronics Part I

un1/un2 = 0.05

0.5

0

un1/un2 0.5 0.4 0.3 0.2 0.1 0.05

0.5

0 0

20

40

60

80

100

0

5

10

15

20

25

Gain

Gain

Fig. 20 Changes in dynamic range (left) and noise (right) versus gain for various noise ratios of the preamplifier to the ADC’s equivalent input noise vn1 /vn2

Signal Charge Measurements As shown in Fig. 8, the change in induced charge produces the signal in an ionization chamber. The form of the measured signal depends on the input time constant formed by the detector capacitance and the input resistance of the amplifier: τ = Ri Cd . If the time constant is much smaller than the detector charge collection time, the detector capacitance will discharge quickly, and the current flowing into the amplifier’s input resistance will match the induced detector current. On the other hand, if the input time constant is much larger than the collection time, the signal charge QS will be stored on the capacitance Cd and produce a peak voltage VS = QS /Cd . This illustrates that a given amplifier can be either current- or voltagesensitive, depending on the detector capacitance, not its label. If the amplifier is operating in the voltage mode with an equivalent input noise voltage vn , then the signal-to-noise ratio VS S QS 1 = = · , N vn Cd vn

(26)

which is inversely proportional to the capacitance. This is a general result for many systems, but not for the same reason, as illustrated in section “Noise in a Charge-Sensitive Amplifier System.” In an ideal current-sensitive amplifier, the noise can be independent of capacitance, but in reality the effect of parasitic noise sources can depend on detector capacitance, so it should always be considered. A drawback of using a voltage amplifier to measure the signal charge is that the calibration depends on the capacitance. With a partially depleted detector, the capacitance depends on the applied bias voltage, so the same energy deposition can yield different signal levels depending on the detector bias. Tracking detectors using semiconductor detectors often use varying strip lengths, so within a given system,

50

H. Spieler

the calibration will vary. A solution to this problem is to use an amplifier whose output depends only on the signal charge, but not on the detector capacitance.

Charge-Sensitive Amplifiers Figure 21 shows the principle of a charge-sensitive amplifier. The basic building block is an inverting voltage amplifier with a high input resistance. For simplicity assume an infinite input resistance, so that no signal current can flow into the amplifier. Since the amplifier inverts, the voltage gain dvo /dvi = − A, so vo = − Avi . A feedback capacitor Cf is connected from the output to the input. If an input signal produces a voltage vi at the amplifier input, the voltage at the amplifier output is −Avi . Thus, the voltage difference across the feedback capacitor vf = (A + 1) vi and the charge deposited on Cf is Qf = Cf vf = Cf (A + 1) vi . Since no current can flow into the amplifier’s infinite input resistance, all of the signal current must charge up the feedback capacitance, so Qf = Qi . The amplifier input appears as a “dynamic” input capacitance Ci =

Qi = Cf (A + 1) . vi

(27)

The enhanced input capacitance corresponds to a reduction in input impedance 1/(ωCi ), as expected for a shunt-feedback amplifier. The voltage output per unit input charge AQ =

1 vo Avi A A 1 · = = = ≈ (A 1) , Qi Ci vi Ci A + 1 Cf Cf

(28)

so the charge gain is determined by a well-controlled component, the feedback capacitor. The signal charge QS will be distributed between the sensor capacitance Cd and the dynamic input capacitance Ci . The ratio of measured charge to signal charge

Fig. 21 Principle of a charge-sensitive amplifier

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51

Fig. 22 Adding a test input to a charge-sensitive amplifier provides a simple means of absolute charge calibration

Test input

ΔV

CT

Q-AMP Cd

Ci

Dynamic input capacitance

Qi Qi 1 Ci = = , = Qs Qd + Qs,amp C d + Ci 1 + CCdi

(29)

so the dynamic input capacitance must be large compared to the sensor capacitance. Another very useful feature of the integrating amplifier is the ease of charge calibration. By adding a test capacitor as shown in Fig. 22, a voltage step injects a well-defined charge into the input node. If the dynamic input capacitance Ci is much larger than the test capacitance CT , the voltage step V at the test input will be applied nearly completely across the test capacitance CT , thus injecting a charge CT V into the input. More precisely, the injected charge QT =

CT 1+

CT Ci +Cd

 · V ≈ CT 1 −

CT C i + Cd

V ,

(30)

so for the best accuracy, the system should be calibrated with the detector connected.

Noise in a Charge-Sensitive Amplifier System Unlike an ideal voltage-sensitive amplifier, where the noise is independent of the detector capacitance, but the signal voltage is inversely proportional, VS = QS /C, in a charge-sensitive amplifier, the dependence of the signal output voltage on the detector capacitance is small. However, in this case the noise increases with detector capacitance since the detector is part of the feedback loop as shown in Fig. 23. When no detector is connected to the input, all of the output noise is fed back to the input, resulting in an additional correlated noise of opposite sign at the output, which reduces the output noise. With a detector connected, the feedback capacitor

52

H. Spieler Cf

Detector en Cd

enf

eni

Av

–A eno

en

eno

Fig. 23 Circuit for the noise analysis of a charge-sensitive amplifier. The convention for setting the phase of en is shown at the right

and the detector capacitance form a voltage divider, so only a fraction of the output noise is fed to the input, and less negative feedback results in a noise increase. In circuits of this type, where the signal source is part of the feedback loop, the noise gain differs from the signal gain. For a more detailed description of the calculation, see Spieler (2005, pp. 123– 125). Given a sufficiently high open-loop amplifier gain A to make the charge gain AQ = 1/Cf , the signal-to-noise ratio Qs 1 Qs 1 1 Qs  ≈ = Qni FS en f Cd + Cf FS Cd en

  Cd Cf ,

(31)

√ where the factor FS = AV S fn combines the noise bandwidth and gain that characterize the system. This is the same result as for a voltage-sensitive amplifier, but here the signal is constant, and the noise grows with increasing Cd . However, note that the additional feedback capacitor adds to the detector capacitance in determining the noise.

Realistic Charge-Sensitive Amplifiers The preceding discussion assumed that the amplifiers are infinitely fast, so they respond instantaneously to the applied signal. In reality this is not the case; chargesensitive amplifiers often respond much more slowly than the time duration of the current pulse from the sensor. However, as shown in Fig. 24, this does not obviate the basic principle. Initially, signal charge is integrated on the sensor capacitance, as indicated by the left-hand current loop. Subsequently, as the amplifier responds, the signal charge is transferred to the amplifier. Thus, the signal charge is preserved, and the full signal appears at the amplifier output, even if the amplifier is much slower than the collection time. ◦ At low frequencies, where the amplifier’s open-loop phase shift is 180 , the input impedance of a charge-sensitive amplifier utilizing capacitive shunt feedback is capacitive. However, the open-loop corner frequency where the gain begins to

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53

Fig. 24 Charge integration in a realistic charge-sensitive amplifier. First, charge is integrated on the sensor capacitance and subsequently transferred to the charge-sensitive loop, as it becomes active

◦

roll off and introduces a 90 phase shift is typically well below the passband set by the shaper, approximately centered at the inverse peaking time. There the input impedance is resistive. The relevant frequency range is determined by the pulse shaper. Some common examples are shown in  Chap. 3, “Electronics Part II”. Figure 25 shows the input impedance versus frequency for an amplifier with an open-loop corner frequency of 100 kHz. At low frequencies, where the amplifier ◦ phase shift is 180 , the input impedance is capacitive and decreases with frequency. Beyond the amplifier cutoff frequency where its phase shift is 90◦ , the input ◦ impedance levels off and is resistive (phase shift 0 ). Its value Zi =

1 ω0 Cf

(32)

depends on the amplifier’s unity gain frequency, extrapolated from the frequency regime where the gain falls off linearly with frequency, as shown in the left panel of Fig. 25. Note that the amplifier also has a second pole (cutoff frequency) at 100 MHz, which reduces the gain more rapidly at higher frequencies. The lowfrequency gain of the amplifier is 1000, which improves the baseline stability, but at a peaking time of 20 ns, corresponding to a mid-band frequency of about 10 MHz, the resistive input impedance is about 1.6 k. This is also the impedance presented by a capacitance of 10 pF, so in a 6 cm-long silicon strip detector, about half of the signal current will go to the neighbors. The mid-band frequency scales inversely with the peaking time. It depends on the type of shaper, and, as noted above, examples are shown in  Chap. 3, “Electronics Part II”. The frequency response shown in Fig. 25 was chosen in a circuit simulation to demonstrate the effect of the open-loop phase shift. Today low-power amplifiers with a much higher unity gain frequency ω0 are quite feasible, so sufficiently low input impedances can be achieved. However, this should not be taken for granted. Besides optimizing charge transfer to the front-end amplifier, the input impedance is also important in strip and pixel detectors because it determines cross-talk between adjacent electrodes. As shown in Fig. 26, if the amplifier had an infinite input impedance, the signal current from a given electrode would simply flow to the neighbors, and the charge deposited on the neighbor electrodes would depend on the inter-electrode capacitance Css and the backplane capacitance Cb . To capture the bulk of the signal charge on the target electrode, the amplifier’s input impedance must be small compared to the impedance presented by the

54

H. Spieler Input impedance (Cf = 1 pF)

Open loop gain and phase 1000

200 160 ω0

Phase

120

1 80 0.1 40

0.01

0

0.001 104

105

106

107

Phase

108

109

Frequency (Hz)

−20

5

10

−40 104 −60

Impedance

Phase (deg)

10

0

10

Input impedance (Ω)

Gain

Phase (deg)

Open loop gain |Av 0|

100

103

6

3

10

−80 −100

102 103

104

105

106

107

108

109

Frequency (Hz)

Fig. 25 At low frequencies where the amplifier’s open-loop phase shift is 180◦ , the input impedance is capacitive (phase shift 90◦ ). Beyond the amplifier cutoff frequency where an additional phase shift of −90◦ is introduced, the input impedance levels off and is resistive (phase shift 0◦ ) Fig. 26 The amplifier input impedance determines cross-coupling between channels. It must be small compared to the impedance presented by the inter-electrode capacitance Css

inter-electrode capacitance Css . This impedance 1/(ωCss ) depends on the range of frequencies at which the signal amplitude is measured, i.e., the shaping time. The above example illustrates the relevant parameters. The effect of the input impedance is illustrated for a 20 ns peaking time, but in this example, the resistive impedance will be effective at shaping times up to 1 μs. Whether the effective input impedance meets the specific application’s requirements depends on the preamplifier and the signal shaper, so the complete system must be analyzed both in the time and frequency domain .

Detector Equivalent Circuits In calculating the signal-to-noise ratio, the magnitude of the signal applied to the amplifier input must also be assessed. As indicated in Fig. 18 and discussed in the preceding section, the equivalent circuit of the detector affects both the signal and

2 Electronics Part I

55

the noise. Figure 15 illustrates how the signal from a PMT can be described by an equivalent circuit, where the anode is a current source with a shunt capacitance formed by the capacitance of the last dynode to the anode plus any additional stray capacitance. The same equivalent circuit can be applied to a microchannel plate. Simple circuits can often represent rather complex detectors.

Thermistor Detecting IR Radiation A thermistor is a resistor whose value depends on temperature. When biased with a constant current, the voltage across the thermistor is proportional to the thermistor resistance. Constant current bias can be simply implemented by feeding the thermistor from a voltage source through a resistor whose value is much larger than the thermistor resistance RT , so a change in RT will not significantly affect the bias current. Figure 27 shows the actual circuit and the model.

Piezoelectric Transducer In a piezoelectric transducer, the molecular dipole moments of the sensitive material create a change in voltage across the sensitive volume when the material is stressed. Figure 27 shows the equivalent circuit.

Ionization Chamber Gas-filled ionization or proportional chambers directly convert absorber radiation into charge, whose motion through the detector volume induces a signal current. The same principle applies to semiconductor detectors, ranging from simple twoelectrode configurations to strips or pixels. Figure 28 shows the basic detector configuration and the equivalent circuit.

Thermistor

Piezoelectric transduced Vbias

Vbias R >> RT ΔT

ΔV

RT

R

RT ΔV

Actual circuit

Δx

ΔV Model

ΔV

C

Actual circuit

C ΔV

ΔV Model

Fig. 27 Left panel: equivalent circuit of a thermistor biased at a constant current. Right panel: equivalent circuit of a piezoelectric transducer. The bias voltage is applied through a high-value resistor

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H. Spieler Detector Configuration Incident radiation

Detector

Model Amplifier

is

+ –

is (t )

C

C

is

Fig. 28 In an ionization chamber, the charge formed by the absorbed radiation moves under the influence of the applied electric field, and the induced current appears at the detector electrodes. The equivalent current source is shunted by the capacitance formed by the detector electrodes

Position-Sensitive Detector with Resistive Charge Division The input impedance is also important in other applications, for example, using charge division to measure the z coordinate in long-strip detectors. This technique is less susceptible to “ghosting” than crossed-strip configurations, as in crossed strips the probability of “ghosting” is proportional to the area subtended by the crossed strips, whereas here multiple-hit probability depends only on the area covered by the strip and its neighbors. It also reduces the material and mechanical complexity of crossed-strip configurations. However, several interlinked contributions must be considered in optimizing the design, and it is easy to obtain inferior results and discredit the technique. This technique is not necessarily an adequate replacement for crossed strips and can easily require a higher signal-to-noise ratio, so it must be evaluated in detail. The principle is illustrated in Fig. 29. The position sensitivity is given by   Rin 2 x L + Rstrip dx = −L , R d (i1 /i2 ) 1 + 2 R in

(33)

strip

so the input impedance must be small with respect to the strip resistance. Figure 30 shows the simplest equivalent circuit together with a more complex version that takes the distributed resistance and capacitance into account in applications where a fast preamplifier is used. For a given input impedance, one could choose a higher strip resistance. However, noise is also an issue. With increasing strip resistance, the thermal noise of the strip resistance increases. The noise from the strip is anticorrelated in the two readout channels, so for a given signal-to-noise ratio, this puts an upper limit on the strip resistance. On the other hand, in a shunt-feedback amplifier, the load, whether

2 Electronics Part I

57 Track i1 x

i2

L R2

R1 R in

R strip

R in

Fig. 29 The track coordinate can be determined by measuring the ratio of currents at both ends of the strip. Maximum position sensitivity requires a low amplifier input impedance

Fig. 30 A simple equivalent circuit is shown at the left. When using a fast readout, it may be necessary to include the distributed resistance and capacitance as shown to the right

capacitive or resistive, that is presented to the input determines the noise gain, so the strip resistance in series with the input impedance of the amplifier at the other end forms a load to the preamplifier, in addition to the strip capacitance. This increases the amplifier noise and constrains the minimum strip resistance. This effect can be reduced by lowering the noise of the preamplifier. If this is done by increasing the current in the input transistor, i.e., its transconductance, the gain-bandwidth product will also increase, which will lower the input impedance. Reducing the amplifier noise is also useful for another reason, as the strip resistance cross-couples noise from√the two amplifiers, as shown in Fig. 31. This will typically increase noise by about 2, somewhat reduced by the strip-to-backplane capacitance. Cross-coupling of noise from neighboring strips through the strip-tostrip capacitance is another contribution. For a more detailed discussion of noise cross-coupling, see Spieler (2005, pp. 129–132). As noted above, charge division can offer advantages in certain applications. However, details depend on the application requirements, and a more sophisticated analysis than in standard strip detectors is needed to achieve optimum results.

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H. Spieler Amplifier 1 in1

Detector strip

Amplifier 2 in1

Cf

Cf

in1

uno1

Zi 1

Rstrip

Zi2

uno2

Fig. 31 Noise from one amplifier is cross-coupled to the other. A noise voltage at the output of one amplifier will inject a current through the feedback capacitor and strip resistance into the other amplifier. Note that for a signal originating from its output, the left-hand amplifier presents a high impedance at its input, so the current i n1 flows to the right-hand amplifier, which presents a low impedance to an external signal (see Spieler 2005)

Summary Optimizing a detector system requires an understanding of both the detector physics and the characteristics of the readout electronics. In the preceding discussions, the basic sources of fluctuations were discussed. However, when electronic noise is a significant contribution, signal processing is a key element. This is discussed in  Chap. 3, “Electronics Part II”.

References Armantrout GA (1972) IEEE Trans Nucl Sci NS-19(3), 289 Fano U (1947) Ionization yield of radiations. II. The fluctuations of the number of ions. Phys Rev 72:26–29 Grupen C, Shwartz BA (2008) Particle detectors, 2nd edn. Cambridge University Press, Cambridge Philippot JCl (1970) IEEE Trans Nucl Sci NS-17(3), 446 Ramo S (1939) Currents induced by electron motion. Proc IRE 27:584–585 Spieler H (2005) Semiconductor detector systems. Oxford University Press, Oxford

3

Electronics Part II Helmuth Spieler

Contents Basic Principles of Signal Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Signal Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Noise Analysis of a Detector–Preamplifier–Shaper System . . . . . . . . . . . . . . . . . . . . . . . . . . . . Timing Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Digital Electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Logic Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Propagation Delays and Power Dissipation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Logic Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Analog-to-Digital Conversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Time-to-Digital Converters (TDCs) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Digital Signal Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

59 62 66 71 73 73 76 77 78 82 84 88 89

Abstract Signal processing is needed to optimize energy and time resolution. This chapter discusses the basic principles of signal processing and the resulting electronic noise, beginning with analog systems and then moving on to digital electronics and digital signal processing.

Basic Principles of Signal Processing Radiation impinges on a sensor and creates an electrical signal, either directly or indirectly, as discussed in  Chap. 2, “Electronics Part I.” Especially in highresolution systems, the signal level is often low and must be amplified to allow H. Spieler () LBNL Physics Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA e-mail: [email protected] © Springer Nature Switzerland AG 2021 I. Fleck et al. (eds.), Handbook of Particle Detection and Imaging, https://doi.org/10.1007/978-3-319-93785-4_3

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H. Spieler

digitization and storage. Both the sensor and the electronics introduce signal fluctuations, i.e., fluctuations in the signal magnitude introduced by the sensor and noise from the electronics that is superimposed on the signal. The detection limit and measurement precision are determined by the signal-to-noise ratio. Electronic noise affects all types of measurements. To merely detect the presence of a hit, the noise level determines the minimum threshold. If the threshold is set too low, the output will be dominated by noise hits. In energy measurements the noise “smears” the signal amplitude, and in time measurements noise alters the time dependence of the signal pulse, as shown in  Chap. 2, “Electronics Part I.” To increase the signal-to-noise ratio, one can increase the signal, reduce the noise, or both. Problems are often best solved by viewing components from different perspectives. Since pulses are viewed in the time domain, whereas noise is characterized in the frequency domain, optimizing the signal-to-noise ratio is best addressed in both the time and frequency domain. Figure 1 shows

Fig. 1 Signal distribution in both the time and frequency domains, a unipolar pulse in the upper row and a bipolar pulse below. The bipolar pulse has a zero net area, so the amplitude in the frequency domain goes to zero at zero frequency. The bipolar pulse slope is greater at the zero crossing, so the frequency spectrum extends to higher frequencies

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Fig. 2 A typical noise spectrum in the frequency domain. Distinguishing the individual components in the time domain is more difficult

a unipolar and bipolar pulse in the time and frequency domains. The upper extent of the frequency distribution depends on the maximum slope of the signal pulse, as a fast change in time requires Fourier components at high frequencies. The unipolar pulse has a net charge, so the frequency spectrum extends all the way down to zero. The bipolar pulse has zero net area, so in the frequency domain, the distribution goes down to zero at zero frequency. The increased slope at the zero crossing extends the spectrum to higher frequencies. Figure 2 shows a typical noise spectrum in the frequency domain. A constant noise level extends over the midrange, but noise increases at low frequencies due to “1/f ” noise and also increases at high frequencies because the amplifier gain is decreasing. As noted in  Chap. 2, “Electronics Part I,” operating with excessive bandwidth will increase the noise level without improving the signal level. Since the signal and noise spectra differ, minimizing noise will also reduce the signal amplitude, so the choice of the optimum frequency response requires balancing between reduction in noise and loss of signal. This optimum depends on the measurement goal. For example, a short detector pulse would imply a fast, i.e., high bandwidth, electronics response. This would be appropriate when signal timing is important. However, if only the magnitude of the signal charge is to be measured, the fast pulse can be integrated to form a long-duration pulse whose amplitude is proportional to the signal charge, as obtained from a charge-sensitive amplifier. This allows a subsequent amplifier chain with a smaller bandwidth, which will yield a lower noise level. However, most radiation measurements are not restricted to single pulses but to a random sequence in time. This imposes an additional constraint on signal processing as the duration of a signal pulse determines the probability of pulse pileup, as illustrated in Fig. 3.

H. Spieler

Amplitude

Amplitude

62

Time

Time

Fig. 3 Longer pulses will increase the probability of pileup, which will affect the peak amplitude of the second pulse. A smaller pulse width reduces pileup

Signal Processing The upper half of Fig. 4 shows the basic components of a detector readout. A preamplifier integrates the detector current to derive the signal charge and also transforms a short detector pulse into a long step output, which allows the following stages to have a small bandwidth to reduce the noise. The pulse shaper forms the signal into a pseudo-Gaussian shape whose peak amplitude is proportional to the signal charge. This peak amplitude is recorded by an analog-to-digital converter, and the digitized signal is stored and used for further data analysis. The bottom section of Fig. 4 digitizes the detector signal and then sends the digitized signal to a digital signal processor, which performs pulse shaping, but can also perform other functions, such as correcting the signal amplitude when pileup occurs. Digital signal processing is discussed in section “Digital Signal Processing.” Other components of signal processing systems handle the data readout. In single-channel detector systems, the digitized output is sent directly to the memory. This becomes more complicated in large-scale detector systems where the data from thousands or millions of detector channels must be recorded. Monolithic integrated circuits (ICs) commonly include 128 readout channels, and a detector module includes multiple ICs. Figure 5 shows the barrel strip-detector module in the ATLAS SemiConductor Tracker (SCT) (ATLAS Collaboration 2008). The ICs are read out sequentially as shown in Fig. 6. For more details on large-scale semiconductor detector systems, see Spieler (2005). To explain the basic functions of a signal processor, the simplest form is shown in Fig. 7. The first shaper function sets the pulse duration by sending the step input through a C–R “differentiator,” which in the frequency domain acts as a high-pass filter. This reduces the pulse width, which increases the signal rate capability, but has just little effect on the noise bandwidth. To reduce the noise bandwidth, the signal is sent through an R–C “integrator,” which is also a low-pass filter. This results in a pulse with a rounded peak, whose amplitude can be accurately measured by the subsequent digitizer. Pulse shapers can also produce outputs with a sharp peak, but

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63

Incident radiation

Sensor

Incident radiation

Sensor

Integrating preamplifier

Preamplifier +prefilter

Pulse shaping

Analog-todigital conversion

Analog-todigital conversion

Digital data bus

Pulse shaping

Digital data bus

Digital signal processor

Fig. 4 A typical signal processing system consists of a preamplifier, here shown as a chargesensitive amplifier, a pulse shaper, and a digitizer that converts the signal for subsequent signal storage. Pulse processing can be performed both with analog and digital circuitry. In the bottom system, the sensor signal is prefiltered in the preamplifier and then digitized. Pulse processing to optimize the signal-to-noise ratio and perform other functions is then performed in a digital signal processor

BeO facings Hybrid assembly Slotted washer

Baseboard TPG Silicon sensors

Datum washer

Connector

BeO facings Fig. 5 ATLAS SCT barrel detector module. Two single-sided sensors are glued back-to-back with an intermediate thermal pyrolytic graphite (TPG) heat spreader. The “ear” extending from the module attaches to the support/cooling stave of the SCT barrel structure (Unno et al. 2003). (Figure courtesy of T. Kondo)

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Fig. 6 Multiple ICs are ganged to read out a strip detector. The rightmost chip IC1 is the master. A command on the control bus initiates the readout. When IC1 has written all of its data, it passes the token to IC2. When IC2 has finished, it passes the token to IC3, which in turn returns the token to the master IC1

Fig. 7 A simple pulse shaper using a CR “differentiator” as a high-pass and an RC “integrator” as a low-pass filter. For a given decay time constant τ d , optimum noise results when τ i = τ d

since digitizers also have a limited bandwidth and need sufficient time to reach the peak amplitude, the accuracy of recording the peak amplitude can be uncertain. The simple CR–RC shaper shows the basic functions of a pulse shaper, limiting the noise bandwidth and constraining the pulse duration. Although this simple shaper is 37% worse than the optimum shaper, it is quite useful, especially in circuits where size and power dissipation are important. However, by adding additional integrator stages, the output pulses can be made more symmetrical, as shown in Fig. 8, so for a given peaking time, the pulse will return to the baseline more quickly and allow higher pulse rates. Typically several gain stages are needed to bring the signal level up to the requirements of the digitizer, so by tailoring the bandwidths of the amplifiers, the equivalent of a two- to four-stage integrator can be achieved without additional circuit complexity. For higher integration levels, more complex circuits are commonly used. Figure 9 shows the frequency response of a CR–RC and CR–4 RC shaper, both with a peaking time of 100 ns. The frequency spectrum simply scales inversely with peaking time. For the 100 ns peaking time shown in the figure, the peaking

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Fig. 8 Pulse shape versus number of integrators in a CR–nRC shaper. The integration and differentiation time constants are scaled with the number of integrators (τ = τ n = 1 /n) to maintain the peaking time

Fig. 9 The frequency response of CR–RC and CR–4 RC pulse shapers, both with a peaking time of 100 ns. The peaking frequencies are 1.6 MHz for the CR–RC shaper and 3.2 MHz for the CR–4 RC

frequency of the CR–RC shaper is 1.6 MHz, and for a 10 ns peaking time, it is 16 MHz. The bandwidth scales accordingly. For the CR–RC shaper, the peaking frequency is easily derived from the peaking time, which is equal to the integration and differentiation time constants τ . Then the peaking frequency is ωP = 1/τ or fP = (2π τ )−1 . However for the CR–4 RC shaper with 100 ns peaking time, the peaking frequency is 3.2 MHz, i.e., about twice as high as for the CR–RC shaper. The bandwidth, i.e., the difference between the upper and lower half-power frequencies is 3.2 MHz for the CR–RC shaper and 4.3 MHz for the CR–4 RC shaper. For a given input signal, the signal level at the shaper output depends on the shaper type, assuming that the total gain of the amplifiers in the signal chain is the same. The shaper type also affects the noise bandwidth, so both the signal attenuation and the noise bandwidth must be assessed to optimize the signal-tonoise ratio.

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Noise Analysis of a Detector–Preamplifier–Shaper System To determine how the pulse shaper affects the signal-to-noise ratio, consider the detector front-end in Fig. 10. The detector is represented by the capacitance Cd , a relevant model for many radiation sensors. Sensor bias voltage is applied through the resistor Rb . The bypass capacitor Cb shunts any external interference coming through the bias supply line to ground. For high-frequency signals, this capacitor appears as a low impedance, so for sensor signals, the “far end” of the bias resistor is connected to ground. The coupling capacitor Cc blocks the sensor bias voltage from the amplifier input, which is why a capacitor serving this role is also called a “blocking capacitor.” The series resistor Rs represents any resistance present in the connection from the sensor to the amplifier input. This includes the resistance of the sensor electrodes, the resistance of the connecting wires or traces, any resistance used to protect the amplifier against large voltage transients (“input protection”), and parasitic resistances in the input transistor. The following implicitly includes a constraint on the bias resistance, whose role is often misunderstood. It is often thought that the signal current generated in the sensor flows through Rb , and the resulting voltage drop is measured. If the time constant Rb Cd is small compared to the peaking time of the shaper TP , the sensor will have discharged through Rb , and much of the signal will be lost. Thus, we have the condition Rb Cd  TP , or Rb  TP /Cd . The bias resistor must be sufficiently large to block the flow of signal charge, so that all of the signal is available for the amplifier. To analyze this circuit, a voltage amplifier will be assumed, so all noise contributions will be calculated as a noise voltage appearing at the amplifier input. Steps in the analysis are as follows: (1) Determine the frequency distributions of all noise voltages presented to the amplifier input from all individual noise sources. (2) Integrate over the frequency response of the shaper (for simplicity a CR–RC shaper), and determine the total noise voltage at the shaper output. (3) Determine the peak amplitude of the output pulse for a known input signal charge. The equivalent noise charge (ENC) is the signal charge for which (S/N = 1). The equivalent circuit for the noise analysis (second panel of Fig. 10) includes both current and voltage noise sources. The “shot noise” ind of the sensor leakage current is represented by a current noise generator in parallel with the sensor

Fig. 10 A detector front-end circuit and its equivalent circuit for noise calculations

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capacitance. As noted in  Chap. 2, “Electronics Part I,” resistors can be modeled either as a voltage or current generator. Generally, resistors shunting the input act as noise current sources, and resistors in series with the input act as noise voltage sources (which is why some in the detector community refer to current and voltage noise as “parallel” and “series” noise). Since the bias resistor effectively shunts the input, as the capacitor Cb passes current fluctuations to ground, it acts as a current generator inb , and its noise current has the same effect as the shot-noise current from the detector. The shunt resistor can also be modeled as a noise voltage source, yielding the result that it acts as a current source. Choosing the appropriate model merely simplifies the calculation. Any other shunt resistances can be incorporated in the same way. Conversely, the series resistor Rs acts as a voltage generator. The electronic noise of the amplifier is described fully by a combination of voltage and current sources at its input, shown as ena and ina . Thus, the noise sources are Sensor bias current Shunt resistance Series resistance Amplifier

2 = 2eI , : ind d 2 = 4kT , : inb Rb 2 = 4kT R , : ens s : ena , ina ,

where e is the electronic charge, Id the sensor bias current, k the Boltzmann constant, and √ T the temperature. √ Typical amplifier √ noise parameters ena and ina are of order nV/ Hz and fA/ Hz (FETs) to pA/ Hz (bipolar transistors). Amplifiers tend to exhibit a “white” noise spectrum at high frequencies (greater than order kHz), but at low frequencies show excess noise components with the spectral density 2 = enf

Af , f

(1)

where the noise coefficient Af is device specific and of order 10−10 − 10−12 V2 . The noise voltage generators are in series and simply add in quadrature. White noise distributions remain white. However, a portion of the noise currents flows through the detector capacitance, resulting in a frequency-dependent noise voltage in /(ωCd ), so the originally white spectrum of the sensor shot noise and the bias resistor now acquire a 1/f dependence, and their contribution increases as the shaper is shifted to lower frequencies, i.e., longer shaping times. The frequency distribution of all noise sources is further altered by the combined frequency response of the amplifier–shaper chain A(f ). Integrating over the cumulative noise spectrum at the amplifier–shaper output and comparing to the output voltage for a known input signal yield the signal-to-noise ratio. In this example, the shaper is a simple CR– RC shaper, where for a given differentiation time constant the signal-to-noise ratio is maximized when the integration time constant equals the differentiation time constant, τ i = τ d ≡ τ . Then the output pulse assumes its maximum amplitude at the time TP = τ .

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Although the basic noise sources are currents or voltages, since radiation detectors are typically used to measure charge, the system’s noise level is conveniently expressed as an equivalent noise charge Qn . As noted previously, this is equal to the detector signal that yields a signal-to-noise ratio of one. The equivalent noise charge is commonly expressed in coulombs, the corresponding number of electrons, or the equivalent deposited energy (eV). For the above circuit, the equivalent noise charge is  Q2n

=

e2 8

 

    C2 4kT d 2 2 2 2eI d + + 4Af Cd . + ina · τ + 4kT R s + ena · Rb τ (2)

The prefactor e2 /8 = exp (2)/8 = 0.924 normalizes the noise to the signal gain. The first term combines all noise current sources and increases with shaping time. The second term combines all noise voltage sources and decreases with shaping time, but increases with sensor capacitance. The third term is the contribution of amplifier 1/f noise and, as a voltage source, also increases with sensor capacitance. The 1/f term is independent of shaping time, since for a 1/f spectrum the total noise depends on the ratio of upper to lower cutoff frequency, which depends only on shaper topology, but not on the shaping time. The equivalent noise charge can be expressed in a more general form that applies to all types of pulse shapers: Q2n = in2 Fi TS + en2 Fv

C2 + Fv Af C 2 , TS

(3)

where Fi , Fv , and Fv f depend on the shape of the pulse determined by the shaper and TS is a characteristic time, e.g., the peaking time of a CR–nRC-shaped pulse or the prefilter time constant in a correlated double sampler. C is the total parallel capacitance at the input, including the amplifier input capacitance. The shape factors Fi , Fv are easily calculated: Fi =

1 2TS



∞ −∞

[W (t)]2 dt and Fv =

TS 2



∞ −∞



dW (t) dt

2 dt.

(4)

For time-invariant pulse shaping, W(t) is simply the system’s impulse response (the output signal seen on an oscilloscope) with the peak output signal normalized to unity. For a time-variant shaper, the same equations apply, but W(t) is determined differently. See references Goulding (1972), Goulding and Landis (1982), and Radeka (1972, 1974) for more details. A CR–RC shaper with equal time constants τ i = τ d has Fi = Fv = 0.9 and Fvf = 4, independent of the shaping time constant, so for the circuit in Fig. 10, Eq. 3 becomes

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Equivalent noise charge (e)

104

Total

103 Total

1/f Noise Current noise

Voltage noise

102 0.01

0.1

1

10

100

Shaping time (μs) Fig. 11 Equivalent noise charge versus shaping time. At small shaping times (large bandwidth), the equivalent noise charge is dominated by voltage noise, whereas at long shaping times (large integration times), the current noise contributions dominate. The total noise assumes a minimum where the current and voltage contributions are equal. The “1/f ” noise contribution is independent of shaping time and flattens the noise minimum. Increasing the voltage or current noise contribution shifts the noise minimum. Increased voltage noise is shown as an example

Q2n

   C2  4KT 2 2 Fv = 2qe Id + + ina Fi TS + 4kT R + ena + Fv f Af C 2 . (5) Rb TS

Pulse shapers can be designed to reduce the effect of current noise, to mitigate radiation damage, for example. Increasing pulse symmetry tends to decrease Fi and increase Fv , e.g., to Fi = 0.45 and Fv = 1.0, for a shaper with one CR differentiator and four cascaded RC integrators. Figure 11 shows how equivalent noise charge is affected by shaping time. At short shaping times, the voltage noise dominates, whereas at long shaping times, the current noise takes over. Minimum noise is obtained where the current and voltage contributions are equal. The noise minimum is flattened by the presence of 1/f noise. Also shown is that increasing the detector capacitance will increase the voltage noise contribution and shift the noise minimum to longer shaping times, albeit with an increase in minimum noise. For quick estimates, one can use the following equation, which assumes a field effect transistor (FET) amplifier (negligible ina ) and a simple CR–RC shaper with peaking time τ . The noise is expressed in units of the electronic charge e, and C is the total parallel capacitance at the input, including Cd , all stray capacitances, and the amplifier’s input capacitance,

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 Q2n = 12

2

 2 e2 ns τ e2 5 e k 4 2C e Id τ + 6 · 10 . + 3.6 · 10 n nA ns ns Rb τ (pF)2 (nV)2 /Hz (6)

The noise charge is improved by reducing the detector capacitance and leakage current, judiciously selecting all resistances in the input circuit, and choosing the optimum shaping time constant. The noise parameters of a well-designed amplifier depend primarily on the input device. Fast, high-gain transistors are generally best. In field effect transistors, both junction field effect transistors (JFETs) and metal oxide semiconductor field effect transistors (MOSFETs), the noise current contribution is very small, so reducing the detector leakage current and increasing the bias resistance will allow long shaping times with correspondingly lower noise. The equivalent input noise voltage is en2 ≈ 4kT /gm , where gm is the transconductance, which increases with operating current. For a given current, the transconductance increases when the channel length is reduced, so reductions in feature size with new process technologies are beneficial. At a given channel length, minimum noise is obtained when a device is operated at maximum transconductance. If lower noise is required, the width of the device can be increased (equivalent to connecting multiple devices in parallel). This increases the transconductance (and required current) with a corresponding decrease in noise voltage but also increases the input capacitance. At some point the reduction in noise voltage is outweighed by the increase in total input capacitance. The optimum is obtained when the FET’s input capacitance equals the external capacitance (sensor + stray capacitance). Note that this capacitive matching criterion only applies when the input current noise contribution of the amplifying device is negligible. Capacitive matching comes at the expense of power dissipation. Since the minimum is shallow, one can operate at significantly lower currents and reduced input capacitance with just a minor increase in noise. In large detector arrays, power dissipation is critical, so FETs are hardly ever operated at their minimum noise. Instead, one seeks an acceptable compromise between noise and power dissipation (see Spieler 2005 for a detailed discussion). Similarly, the choice of input devices is frequently driven by available fabrication processes. High-density integrated circuits tend to include only MOSFETs, so this determines the input device, even where a bipolar transistor would provide better performance. In bipolar transistors the shot noise associated with the base current IB is 2 = 2eI . Since I = I /β significant, inB B B C DC , where IC is the collector current and β DC the direct current gain, this contribution increases with device current. On the other hand, the equivalent input noise voltage en2 =

2(kT )2 eIC

(7)

decreases with collector current, so the noise assumes a minimum at a specific collector current,

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71

Fv 1 C  kT  = 4kT √ Fi Fv at IC = . C βDC e F i TS βDC

(8)

For a CR–RC shaper and β DC = 100,



√ C e μA ns · · C at IC = 260 . Q2n,min ≈ 250 √ pF TS pF

(9)

The minimum obtainable noise is independent of shaping time (unlike FETs), but only at the optimum collector current IC , which does depend on shaping time. In bipolar transistors, the input capacitance √ is usually much smaller than the sensor capacitance (of order 1 pF for en ≈ 1 nV/ Hz and substantially smaller than in FETs with comparable noise. Since the transistor input capacitance enters into the total input capacitance, this is an advantage. Note that capacitive matching does not apply to bipolar transistors because their noise current contribution is significant. Due to the base current noise, bipolar transistors are best at short shaping times, where they also require lower power than FETs for a given noise level. When the input noise current is negligible, the noise increases linearly with the total capacitance at the input. If the detector capacitance dominates, the noise slope dQn ≈ 2en · dCd

Fv TS

(10)

depends both on the preamplifier (en ) and the shaper (Fv , TS ). The zero intercept can be used to determine the amplifier input capacitance plus any additional capacitance at the input node. Note that the noise slope also depends on the pulse shaping, so this should be included in the specification (and often isn’t). Practical noise levels range from 12 channels, whereas in the 11-bit range, the digital resolution matches the analog resolution. Although this ADC can provide 13 bits of digital resolution, its analog resolution is only 10–11 bits, so the 12th and 13th bits are superfluous. Conceptually, the simplest technique is flash conversion, illustrated in Fig. 21. The signal is fed in parallel to a bank of threshold comparators. The individual threshold levels are set by a resistive divider. The comparator outputs are encoded such that the output of the highest-level comparator that fires yields the correct bit pattern. The threshold levels can be set to provide a linear conversion characteristic where each bit corresponds to the same analog increment, or a nonlinear characteristic to provide increments proportional to the absolute level, which provides constant relative resolution over the range, for example. The big advantage of this scheme is speed; conversion proceeds in one step, and conversion times 500 MS/s (megasamples per second) at 8-bit resolution and a power dissipation of about 5 W. The most commonly used technique is the successive-approximation ADC, shown in Fig. 22. The input pulse is sent to a pulse stretcher, which follows the signal until it reaches its cusp and then holds the peak value. The stretcher output feeds a comparator, whose reference is provided by a digital-to-analog converter (DAC). The DAC is cycled beginning with the most significant bits. The corresponding bit is set when the comparator fires, i.e., the DAC output becomes less than the pulse height. Then the DAC cycles through the less significant bits, always setting the corresponding bit when the comparator fires. Thus, n-bit resolution requires n steps and yields 2n bins. This technique makes efficient use of circuitry and is fairly fast. High-resolution devices (16–20 bits) with conversion times of order μs are readily available. Currently a 16-bit ADC with a conversion time of 1 μs (1 MS/s) requires about 100 mW. A common limitation is differential nonlinearity (DNL) since the resistors that set the DAC levels must be extremely accurate. For DNL

hits

④ in magnetic field:

(x1,y1,z1, t1)

reconstruct track momentum

(x2,y2,z2, t2) ...

Event 1 Event 2

Analog signals

Track 1 Track 2

⑤ Store the info for every event and

px p = py pz

every track 1)

n/ (n − 2) (n > 2)

k/λ

k/λ2

α α+β

αβ (α+β)2 (α+β+1)

E[u(x)v(y)] = E[u(x)]E[v(y)], and also one finds V[x + y] = V[x] + V[y]. If x and y are not independent, V[x + y] = V[x] + V[y] + 2 cov [x, y], and E[uv] does not necessarily factorize. Consider a set of n continuous random variables x = (x1 , . . . , xn ) with joint p.d.f. f (x), and a set of n new variables y = (y1 , . . . , yn ) related to x by means of a function y(x) that is one-to-one, i.e., the inverse x(y) exists. The joint p.d.f. for y is given by g (y) = f (x (y)) | J |,

(18)

where J is the absolute value of the determinant of the square matrix Jij = ∂xi /∂yj (the Jacobian determinant). If the transformation from x to y is not one-to-one, the x space must be broken into regions where the function y(x) can be inverted and the contributions to g(y) from each region summed. Several probability functions and p.d.f.s along with their properties are given in Table 1.

Parameter Estimation Here, we review point estimation of parameters, first with an overview of the frequentist approach and its two most important methods, maximum likelihood and least squares, treated in sections “The Method of Maximum Likelihood” and

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“The Method of Least Squares.” The Bayesian approach is outlined in section “The Bayesian Approach.” An estimator  θ (written with a hat) is a function of the data whose value, the estimate, is intended as a meaningful guess for the value of the parameter θ . There is no fundamental rule dictating how an estimator must be constructed. One tries, therefore, to choose that estimator which has the best properties. The most important of these are (a) consistency, (b) bias, (c) efficiency, and (d) robustness. a. An estimator is said to be consistent if the estimate  θ converges to the true value θ as the amount of data increases. This property is so important that it is possessed by all commonlyused  estimators. b. The bias, b = E  θ − θ , is the difference between the expectation value of the estimator and the true value of the parameter. The expectation value is taken over a hypothetical set of similar experiments in which  θ is constructed in the same way. When b = 0, the estimator is said to be unbiased. The bias depends on the 2 chosen metric, i.e., if  θ is an unbiased estimator of θ , then θ is not in general 2 an unbiased estimator for θ .   c. Efficiency is the inverse of the ratio of the variance V  θ to the minimum possible variance for any estimator of θ . Under rather general conditions, the minimum variance for a single parameter θ is given by the Rao–Cramér–Frechet bound,     2 ∂b 2 ∂ ln L (θ ) 2 σmin , (19) =− 1+ /E ∂θ ∂θ 2 where is L(θ ) is the likelihood function (see below). The mean-squared error,  2   MSE = E  θ −θ =V  θ + b2 , (20) is a measure of an estimator’s quality which combines the uncertainties due to bias and variance. d. Robustness is the property of being insensitive to departures from assumptions in the p.d.f., for example, owing to uncertainties in the distribution’s tails. Simultaneously optimizing for all the measures of estimator quality described above can lead to conflicting requirements. For example, there is in general a trade-off between bias and variance. For some common estimators, the properties above are known exactly. More generally, it is possible to evaluate them by Monte Carlo simulation. Note that they will often depend on the unknown θ .

Estimators for Mean, Variance, and Median Suppose we have a set of N independent measurements, xi , assumed to be unbiased measurements of the same unknown quantity μ with a common, but unknown, variance σ 2 . Then

124

G. Cowan N 1  xi , N

 μ =

(21)

i=1

2 = σ

1 N −1

N 

μ)2 (xi − 

(22)

i=1

are unbiased estimators of μ and σ 2 . The variance of  μ is σ 2 /N and the variance of  2 σ is    1 N −3 4  2 (23) m4 − σ , V σ = N N −1 where m4 is the fourth central moment of x. For Gaussian-distributed xi , this becomes 2σ 4 /(N − 1) for any N ≥√2, and for large N, the standard deviation of  σ (the “error of the error”) is σ/ 2N . Again, if the xi are Gaussian,  μ is an 2 are uncorrelated. Otherwise efficient estimator for μ, and the estimators  μ and σ the arithmetic mean (Eq. 21) is not necessarily the most efficient estimator; this is discussed further in Sect. 8.7 of James (Höcker et al. 2007).

The Method of Maximum Likelihood Suppose we have a set of N measured quantities x = (x1 , . . . , xN ) described by a joint p.d.f. f (x; θ ), where θ = (θ 1 , . . . , θ n ) is set of n parameters whose values are unknown. The likelihood function is given by the p.d.f. evaluated with the data x, but viewed as a function of the parameters, i.e., L(θ ) = f (x; θ ). If the measurements xi are statistically independent and each follow the p.d.f. f (x; θ ), then the joint p.d.f. for x factorizes and the likelihood function is L (θ ) =

N 

f (xi ; θ )

(24)

i=1

The method of maximum likelihood takes the estimators  θ to be those values of θ that maximize L(θ ). Note that the likelihood function is not a p.d.f. for the parameters θ ; in frequentist statistics this is not defined. In Bayesian statistics, one can obtain from the likelihood the posterior p.d.f. for θ, but this requires multiplying by a prior p.d.f. (see section “Bayesian Intervals”). It is usually easier to work with lnL, and since both are maximized for the same parameter values θ , the maximum likelihood (ML) estimators can be found by solving the likelihood equations ∂ ln L = 0, ∂θi

i = 1, . . . , n.

(25)

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Often the solution must be found numerically. Maximum-likelihood estimators are important because they are approximately unbiased and efficient for large data samples under quite general conditions, and the method has a wide range of applicability. In evaluating the likelihood function, it is important that any normalization factors in the p.d.f. that involve θ be included. However, we will only be interested in the maximum of L and in ratios of L at different values of the parameters; hence, any multiplicative factors that do not involve the parameters that we want to estimate may be dropped, including factors that depend on the data but not on θ . Under a one-to-one change of parameters from θ to η, the ML estimators  θ    transform to η θ . That is, the ML solution is invariant under change of parameters. However, other properties of ML estimators, in particular the bias, are not invariant under change of parameters. Under requirements usually satisfied in practical analyses and for a sufficiently  large data sample, the inverse V−1 of the covariance matrix Vij = cov  θi ,  θj for a set of ML estimators can be estimated by using 

 ∂ 2 ln L  −1  =− . V ij ∂θi ∂θj θ

(26)

In the large-sample limit (or in a linear model with Gaussian errors), L has a Gaussian form and lnL is (hyper)parabolic. In this case, it can be seen that a numerically equivalent way of determining s-standard-deviation errors is from the  contour given by the θ such that   ln L θ  = ln Lmax − s 2 /2,

(27)

where lnLmax is the value of lnL at the solution point (compare with Eq. 65). The extreme limits of this contour on the θ i axis give an approximate s-standarddeviation confidence interval for θ i (see section “Frequentist Confidence Intervals”). In the case where the size n of the data sample x1 , . . . , xn is small, the unbinned maximum-likelihood method, i.e., use of Eq. 24, is preferred since binning can only result in a loss of information, and hence larger statistical errors for the parameter estimates. The sample size n can be regarded as fixed, or the user can choose to treat it as a Poisson-distributed variable; this latter option is sometimes called “extended maximum likelihood” (see, e.g., Barlow 1990; Cowan 1998; Lyons 1986). If the sample is large, it can be convenient to bin the values in a histogram, so that one obtains a vector of data n = (n1 , . . . , nN ) with expectation values ν = E[n] and probabilities f (n; ν). Then one may maximize the likelihood function based on the contents of the bins (so i labels bins). This is equivalent to maximizing the likelihood ratio λ(θ) = f (n; ν(θ))/f (n; n) or to minimizing the equivalent quantity −2 ln λ(θ). For independent Poisson-distributed ni this is Baker (1984)

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 N   ni νi (θ) − ni + ni ln , −2 ln λ (θ ) = 2 νi (θ )

(28)

i=1

where for bins with ni = 0, the last term in Eq. 28 is zero. The expression Eq. 28 without the terms vi − ni also gives −2 ln λ(θ) for multinomially distributed ni , i.e., when the total number of entries is regarded as fixed. In the limit of zero bin width, maximizing Eq. 28 is equivalent to maximizing the unbinned likelihood function (Eq. 24). A benefit of binning is that it allows for a goodness-of-fit test (see section “Significance Tests”). According to Wilks’ theorem, for sufficiently large vi and providing certain regularity conditions are met, the minimum of −2 ln λ as defined by Eq. 28 follows a chi-square distribution (see, e.g., Stuart et al. 1999). If there are N bins and m fitted parameters, then the number of degrees of freedom for the chi-square distribution is N − m if the data are treated as Poisson-distributed, and N − m − 1 if the ni are multinomially distributed.  Suppose the ni are Poisson-distributed and the overall normalization ν tot = i ν i is taken as an adjustable parameter, so that ν i = ν tot pi (θ ), where the probability to be in the ith bin, pi (θ), does not depend on vtot . Then by minimizing Eq. 28, one obtains that the area under the fitted function is equal to the sum of the histogram contents, i.e., i vi = i ni . This is not the case for parameter estimation methods based on a least-squares procedure with traditional weights (see, e.g., Cowan 1998).

The Method of Least Squares The method of least squares (LS) coincides with the method of maximum likelihood in the following special case. Consider a set of N independent measurements yi at known points xi . The measurement yi is assumed to be Gaussian distributed with mean μ(xi ; θ ) and known variance σi2 . The goal is to construct estimators for the unknown parameters θ . The likelihood function contains the sum of squares

χ 2 (θ ) = −2 ln L (θ) + constant =

N  (yi − μ (xi ; θ ))2 . σi2 i=1

(29)

The set of parameters θ which maximize L is the same as those which minimize χ 2 . The minimum of Eq. 29 defines the least-squares estimators  θ for the more general case where the yi are not Gaussian distributed as long as they are independent. If they are not independent but rather have a covariance matrix Vij = cov [yi , yj ], then the LS estimators are determined by the minimum of χ 2 (θ) = (y − μ (θ))T V −1 (y − μ (θ )) ,

(30)

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where y = (y1 , . . . , yN ) is the vector of measurements, μ(θ ) is the corresponding vector of predicted values (understood as a column vector in Eq. 30), and the superscript T denotes transposed (i.e., row) vector. In many practical cases, one further restricts the problem to the situation where μ(xi ; θ ) is a linear function of the parameters, i.e., μ (xi ; θ ) =

m 

θj hj (xi ) .

(31)

j =1

Here, the hj (x) are m linearly independent functions, for example, 1, x, x2 , . . . , or Legendre polynomials. We require m < N, and at least m of the xi must be distinct. Minimizing χ 2 in this case with m parameters reduces to solving a system of m linear equations. Defining Hij = hj (xi ) and minimizing χ 2 by setting its derivatives with respect to the θ i equal to zero gives the LS estimators xm − 1 ,

−1

 H T V −1 ψ ≡ Dψ. θ = H T V −1 H

(32)

  The covariance matrix for the estimators Uij = cov  θi ,  θj is given by

−1 U = DV D T = H T V −1 H ,

(33)

or equivalently, its inverse U−1 can be found from

U

−1

 ij

 N

  1 ∂ 2 χ 2  −1 V = = h hj (xl ) . (x ) i k kl 2 ∂θi ∂θj θ =θ

(34)

k,l=1

The LS estimators can also be found from the expression  θ = U γ,

(35)

where the vector g is defined by gi =

N 



yj hi (xk ) V −1 . jk

j,k=1

(36)

For the case of uncorrelated yi , for example, one can use Eq. 35 with N  −1   U = ij

k=1

hi (xk )hj (xk ) , σk2

(37)

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gi =

N  k=1

yk hi (xk ) . σk2

(38)

θ , one finds that the contour in parameter space Expanding χ 2 (θ ) about  defined by   2 +1 θ + 1 = χmin χ 2 (θ ) = χ 2 

(39)

has tangent planes located at approximately plus-or-minus-one standard deviation σθ from the LS estimates  θ. In constructing the quantity χ 2 (θ), one requires the variances or, in the case of correlated measurements, the covariance matrix. Often, these quantities are not known a priori and must be estimated from the data; an important example is where the measured value yi represents a counted number of events in the bin of a histogram. If, for example, yi represents a Poisson variable, for which the variance is equal to the mean, then one can either estimate the variance from the predicted value, μ(xi ; θ), or from the observed number itself, yi . In the first option, the variances become functions of the fitted parameters, which may lead to calculational difficulties. The second option can be undefined if yi is zero, and in both cases for small yi , the variance will be poorly estimated. In either case, one should constrain the normalization of the fitted curve to the correct value, i.e., one should determine the area under the fitted curve directly from the number of entries in the histogram (see Cowan 1998, Sect. 7.4). A further alternative is to use the method of maximum likelihood; for binned data this can be done by minimizing Eq. 28. As the minimum value of the χ 2 represents the level of agreement between the measurements and the fitted function, it can be used for assessing the goodness-offit; this is discussed further in section “Significance Tests.”

The Bayesian Approach In the frequentist methods discussed above, probability is associated only with data, not with the value of a parameter. This is no longer the case in Bayesian statistics, however, which we introduce in this section. Bayesian methods are considered further in section “Bayesian Intervals” for interval estimation and in section “Bayesian Model Selection” for model selection. For general introductions to Bayesian statistics see, for example, Bernardo and Smith 2000; Gregory 2005; O’Hagan and Forster 2004; Sivia and Skilling 2006. Suppose the outcome of an experiment is characterized by a vector of data x, whose probability distribution depends on an unknown parameter (or parameters) θ that we wish to determine. In Bayesian statistics, all knowledge about θ is summarized by the posterior p.d.f. p(θ | x), which gives the degree of belief for θ to take on values in a certain region given the data x. It is obtained by using Bayes’ theorem,

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p (θ|x) =

L (x|θ) π (θ )     , L x|θ  π θ  dθ 

(40)

where L(x| θ ) is the likelihood function, i.e., the joint p.d.f. for the data viewed as a function of θ , evaluated with the data actually obtained in the experiment, and π (θ) is the prior p.d.f. for θ . Note that the denominator in Eq. 40 serves to normalize the posterior p.d.f. to unity. As it can be difficult to report the full posterior p.d.f. p(θ | x), one would usually summarize it with statistics such as the mean (or median) and the covariance matrix. In addition, one may construct intervals with a given probability content, as is discussed in section “Bayesian Intervals” on Bayesian interval estimation. Bayesian statistics supplies no unique rule for determining the prior π (θ ); in a subjective Bayesian analysis this reflects the experimenter’s degree of belief (or state of knowledge) about θ before the measurement was carried out. For the result to be of value to the broader community, whose members may not share these beliefs, it is important to carry out a sensitivity analysis, i.e., to show how the result changes under a reasonable variation of the prior probabilities. One might like to construct π (θ) to represent complete ignorance about the parameters by setting it equal to a constant. A problem here is that if the prior p.d.f. is flat in θ , then it is not flat for a nonlinear function of θ, and so a different parametrization of the problem would lead in general to a non-equivalent posterior p.d.f. For the special case of a constant prior, one can see from Bayes’ theorem (Eq. 40) that the posterior is proportional to the likelihood, and therefore the mode (peak position) of the posterior is equal to the ML estimator. The posterior mode, however, will change in general upon a transformation of parameter. A summary statistic other than the mode may be used as the Bayesian estimator, such as the median, which is invariant under parameter transformation. But this will not in general coincide with the ML estimator. The difficult and subjective nature of encoding personal knowledge into priors has led to what is called objective Bayesian statistics, where prior probabilities are based not on an actual degree of belief but rather derived from formal rules. These give, for example, priors which are invariant under a transformation of parameters or which result in a maximum gain in information for a given set of measurements. For an extensive review see, for example, Kass and Wasserman 1996. An important procedure for deriving objective priors is due to Jeffreys. According to Jeffreys’ rule, one takes the prior as π (θ ) ∝



det (I (θ )),

(41)

where   2 ∂ ln L (x|θ) ∂ 2 ln L (x|θ) =− Iij (θ ) = −E L (x|θ) dx ∂θi ∂θj ∂θi ∂θj 

(42)

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is the Fisher information matrix. One can show that the Jeffreys prior leads to inference that is invariant under a transformation of parameters. √ Neither the constant nor 1/ μ priors can be normalized to unit area and are said to be improper. This can be allowed because the prior always appears multiplied by the likelihood function, and if the likelihood falls off sufficiently quickly, then one may have a normalizable posterior density. Bayesian statistics provides a framework for incorporating systematic uncertainties into a result. Suppose, for example, that a model depends not only on parameters of interest θ, but on nuisance parameters ν, whose values are known with some limited accuracy. For a single nuisance parameter v, for example, one might have a p.d.f. centered about its nominal value with a certain standard deviation σ v . Often a Gaussian p.d.f. provides a reasonable model for one’s degree of belief about a nuisance parameter; in other cases, more complicated shapes may be appropriate. If, for example, the parameter represents a nonnegative quantity, then a log-normal or gamma p.d.f. can be a more natural choice than a Gaussian truncated at zero. The likelihood function, prior, and posterior p.d.f.s then all depend on both θ and ν, and are related by Bayes’ theorem, as usual. One can obtain the posterior p.d.f. for θ alone by integrating over the nuisance parameters, i.e.,  p (θ |x) =

p (θ , ν|x) dν.

(43)

Such integrals can often not be carried out in closed form, and if the number of nuisance parameters is large, then they can be difficult to compute with standard Monte Carlo methods. Markov Chain Monte Carlo (MCMC) is often used for computing integrals of this type.

Statistical Tests In addition to estimating parameters, one often wants to assess the validity of certain statements concerning the data’s underlying distribution. Frequentist Hypothesis tests, described in section “Hypothesis Tests,” provide a rule for accepting or rejecting hypotheses depending on the outcome of a measurement. In significance tests, covered in section “Significance Tests,” one gives the probability to obtain a level of incompatibility with a certain hypothesis that is greater than or equal to the level observed with the actual data. In the Bayesian approach, the corresponding procedure is referred to as model selection, which is based fundamentally on the probabilities of competing hypotheses. In section “Bayesian Model Selection,” we describe a related construct called the Bayes factor, which can be used to quantify the degree to which the data prefer one or another hypothesis.

Hypothesis Tests Consider an experiment whose outcome is characterized by a vector of data x. A hypothesis is a statement about the distribution of x. It could, for example, define

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completely the p.d.f. for the data (a simple hypothesis), or it could specify only the functional form of the p.d.f., with the values of one or more parameters left open (a composite hypothesis). A statistical test is a rule that states for which values of x a given hypothesis (often called the null hypothesis, H0 ) should be rejected in favour of its alternative H1 . This is done by defining a region of x space called the critical region; if the outcome of the experiment lands in this region, H0 is rejected, otherwise it is accepted. Rejecting H0 , if it is true, is called an error of the first kind. The probability for this to occur is called the size or significance level of the test, α, which is chosen to be equal to some prespecified value. It can also happen that H0 is false and the true hypothesis is the alternative, H1 . If H0 is accepted in such a case, this is called an error of the second kind, which will have some probability β. The quantity 1 − β is called the power of the test relative to H1 . In high-energy physics, the components of x might represent the measured properties of candidate events, and the acceptance region is defined by the cuts that one imposes in order to select events of a certain desired type. Here, H0 could represent the background hypothesis and the alternative H1 could represent the sought after signal. Often, rather than using the full set of quantities x, it is convenient to define a test statistic, t, which can be a single number, or in any case a vector with fewer components than x. Each hypothesis for the distribution of x will determine a distribution for t, and the acceptance region in x space will correspond to a specific range of values of t. Often one tries to construct a test to maximize power for a given significance level, i.e., to maximize the signal efficiency for a given significance level. The Neyman–Pearson lemma states that this is done by defining the critical region for the test of the background hypothesis H0 (i.e., the acceptance region for signal, H1 ) such that, for x in that region, the ratio of p.d.f.s for the hypotheses H1 and H0 , λ (x) =

f (x|H1 ) , f (x|H0 )

(44)

is greater than a given constant, the value of which is chosen to give the desired signal efficiency. Here, H0 and H1 must be simple hypotheses, i.e., they should not contain undetermined parameters. The lemma is equivalent to the statement that Eq. 44 represents the test statistic with which one may obtain the highest signal efficiency for a given purity for the selected sample. It can be difficult in practice, however, to determine λ(x), since this requires knowledge of the joint p.d.f.s f (x| H0 ) and f (x| H1 ). In the usual case where the likelihood ratio (Eq. 44) cannot be used explicitly, there exist a variety of other multivariate classifiers that effectively separate different types of events. Methods often used in HEP include neural networks or Fisher discriminants. Recently, further classification methods from machine-learning have been applied in HEP analyses; these include probability density estimation (PDE) techniques, kernel-based PDE (KDE or Parzen window), support vector machines,

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and decision trees. Techniques such as “boosting” and “bagging” can be applied to combine a number of classifiers into a stronger one with greater stability with respect to fluctuations in the training data. Descriptions of these methods can be found in Hastie et al. (2009), Webb (2002), Kuncheva (2004), and Proceedings of the PHYSTAT conference series Links (2002). Software for HEP includes the TMVA Höcker et al. (2007) and StatPatternRecognition Narsky (2005) packages.

Significance Tests Often, one wants to quantify the level of agreement between the data and a hypothesis without explicit reference to alternative hypotheses. This can be done by defining a statistic t, which is a function of the data whose value reflects in some way the level of agreement between the data and the hypothesis. The user must decide what values of the statistic correspond to better or worse levels of agreement with the hypothesis in question; for many goodness-of-fit statistics, there is an obvious choice. The hypothesis in question, say, H0 , will determine the p.d.f. g(t| H0 ) for the statistic. The significance of a discrepancy between the data and what one expects under the assumption of H0 is quantified by giving the p-value, defined as the probability to find t in the region of equal or lesser compatibility with H0 than the level of compatibility observed with the actual data. For example, if t is defined such that large values correspond to poor agreement with the hypothesis, then the p-value would be  p=

∞

g (t|H0 ) dt,

(45)

tobs

where tobs is the value of the statistic obtained in the actual experiment. The p-value should not be confused with the size (significance level) of a test or the confidence level of a confidence interval (section “Intervals and Limits”), both of which are prespecified constants. The p-value is a function of the data, and is therefore itself a random variable. If the hypothesis used to compute the p-value is true, then for continuous data, p will be uniformly distributed between zero and one. Note that the p-value is not the probability for the hypothesis; in frequentist statistics, this is not defined. Rather, the p-value is the probability, under the assumption of a hypothesis H0 , of obtaining data at least as incompatible with H0 as the data actually observed. When searching for a new phenomenon, one tries to reject the hypothesis H0 that the data are consistent with known, for example, Standard Model processes. If the p-value of H0 is sufficiently low, then one is willing to accept that some alternative hypothesis is true. Often, one converts the p-value into an equivalent significance Z, defined so that a Z standard deviation upward fluctuation of a Gaussian random variable would have an upper tail area equal to p, i.e.,

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Z = −1 (1 − p) .

(46)

Here, Φ is the cumulative distribution of the Standard Gaussian, and Φ −1 is its inverse (quantile) function. Often in HEP, the level of significance where an effect is said to qualify as a discovery is Z = 5, i.e., a 5σ effect, corresponding to a p-value of 2.87 × 10−7 . One’s actual degree of belief that a new process is present, however, will depend in general on other factors as well, such as the plausibility of the new signal hypothesis and the degree to which it can describe the data, one’s confidence in the model that led to the observed p-value, and possible corrections for multiple observations out of which one focuses on the smallest p-value obtained (the “lookelsewhere effect”). For a review of how to incorporate systematic uncertainties into p-values see, for example, Demortier 2007. When estimating parameters using the method of least squares, one obtains the minimum value of the quantity χ 2 f rom Eq. 29. This statistic can be used to test the goodness-of-fit, i.e., the test provides a measure of the significance of a discrepancy between the data and the hypothesized functional form used in the fit. It may also happen that no parameters are estimated from the data, but that one simply wants to compare a histogram, for example, a vector of Poisson-distributed numbers n = (n1 , . . . , nN ), with a hypothesis for their expectation values vi = E[ni ]. As the distribution is Poisson with variances σi2 = νi , the quantity χ 2 of Eq. 29 becomes Pearson’s chi-square statistic, χ2 =

N  (ni − νi )2 . νi

(47)

i=1

If the hypothesis ν = (ν 1 , . . . , ν N ) is correct, and if the expected values vi in Eq. 47 are sufficiently large (in practice, this will be a good approximation if all vi > 5), then the χ 2 statistic will follow the chi-square p.d.f. with the number of degrees of freedom equal to the number of measurements N minus the number of fitted parameters. The minimized χ 2 from Eq. 29 also has this property if the measurements yi are Gaussian. Alternatively, one may fit parameters and evaluate goodness-of-fit by minimizing −2 ln λ from Eq. 28. One finds that the distribution of this statistic approaches the asymptotic limit faster than does Pearson’s χ 2 , and thus computing the p-value with the chi-square p.d.f. will in general be better justified (see Cousins and Baker 1984 and references therein). Assuming the goodness-of-fit statistic follows a chi-square p.d.f., the p-value for the hypothesis is then  p=

∞ χ2

f (z; nd ) dz,

(48)

where f (z; nd ) is the chi-square p.d.f. and nd is the appropriate number of degrees of freedom. If the conditions for using the chi-square p.d.f. do not hold, the statistic

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can still be defined as before, but its p.d.f. must be determined by other means in order to obtain the p-value, for example, using a Monte Carlo calculation. Since the mean of the chi-square distribution is equal to nd , one expects in a “reasonable” experiment to obtain χ 2 ≈ nd . Hence, the quantity χ 2 /nd is sometimes reported. Since the p.d.f. of χ 2 /nd depends on nd , however, one must report nd as well if one wishes to determine the p-value.

Bayesian Model Selection In Bayesian statistics, all of one’s knowledge about a model is contained in its posterior probability, which one obtains using Bayes’ theorem (Eq. 40). Thus, one could reject a hypothesis H if its posterior probability P(H| x) is sufficiently small. The difficulty here is that P(H| x) is proportional to the prior probability P(H), and there will not be a consensus about the prior probabilities for the existence of new phenomena. Nevertheless, one can construct a quantity called the Bayes factor (described below), which can be used to quantify the degree to which the data prefer one hypothesis over another and is independent of their prior probabilities. Consider two models (hypotheses), Hi and Hj , described by vectors of parameters θ i and θ j , respectively. Some of the components will be common to both models, and others may be distinct. The full prior probability for each model can be written in the form π (Hi , θ i ) = P (Hi ) π (θ i |Hi ) .

(49)

Here, P(Hi ) is the overall prior probability for Hi , and π (θ i | Hi ) is the normalized p.d.f. of its parameters. For each model, the posterior probability is found using Bayes’ theorem, P (Hi |x) =

L (x|θ i , Hi ) P (Hi ) π (θ i |Hi ) dθ i , P (x)

(50)

where the integration is carried out over the internal parameters θ i of the model. The ratio of posterior probabilities for the models is therefore L (x|θ i , Hi ) π (θ i |Hi ) dθ i P (Hi ) P (Hi |x)     =   . P Hj |x L x|θ j , Hj π θ j |Hj dθ j P Hj

(51)

The Bayes factor is defined as L (x|θ i , Hi ) π (θ i |Hi ) dθ i    . Bij =  L x|θ j , Hj π θ j |Hj dθ j

(52)

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This gives what the ratio of posterior probabilities for models i and j would be if the overall prior probabilities for the two models were equal. If the models have no nuisance parameters, i.e., no internal parameters described by priors, then the Bayes factor is simply the likelihood ratio. The Bayes factor, therefore, shows by how much the probability ratio of model i to model j changes in the light of the data, and thus can be viewed as a numerical measure of evidence supplied by the data in favour of one hypothesis over the other. Although the Bayes factor is by construction independent of the overall prior probabilities P(Hi ) and P(Hj ), it does require priors for all internal parameters of a model, i.e., one needs the functions π (θ i | Hi ) and π (θ j | Hj ). In a Bayesian analysis, where one is only interested in the posterior p.d.f. of a parameter, it may be acceptable to take an unnormalizable function for the prior (an improper prior) as long as the product of likelihood and prior can be normalized. But improper priors are only defined up to an arbitrary multiplicative constant, which does not cancel in the ratio of Eq. 52. Furthermore, although the range of a constant normalized prior is unimportant for parameter determination (provided it is wider than the likelihood), this is not so for the Bayes factor when such a prior is used for only one of the hypotheses. So to compute a Bayes factor, all internal parameters must be described by normalized priors that represent meaningful probabilities over the entire range where they are defined. An exception to this rule may be considered when the identical parameter appears in the models for both numerator and denominator of the Bayes factor. In this case, one can argue that the arbitrary constants would cancel. One must exercise some caution, however, as parameters with the same name and physical meaning may still play different roles in the two models. Both integrals in Eq. 52 are of the form  m=

L (x|θ) π (θ ) dθ ,

(53)

which is called the marginal likelihood (or in some fields called the evidence). A review of Bayes factors including a discussion of computational issues is Kass and Raftery (1995).

Intervals and Limits When the goal of an experiment is to determine a parameter θ , the result is usually expressed by quoting, in addition to the point estimate, some sort of interval which reflects the statistical precision of the measurement. In the simplest case, this can be given by the parameter’s estimated value  θ plus or minus an estimate of the standard deviation of  θ , σ . If, however, the p.d.f. of the estimator is not Gaussian or if there θ are physical boundaries on the possible values of the parameter, then one usually quotes instead an interval according to one of the procedures described below.

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The choice of method may be influenced by practical considerations such as ease of producing an interval from the results of several measurements. Of course, the experimenter is not restricted to quoting a single interval or limit; one may choose, for example, first to communicate the result with a confidence interval having certain frequentist properties, and then in addition to draw conclusions about a parameter using Bayesian statistics. It is recommended, however, that there be a clear separation between these two aspects of reporting a result. In the remainder of this section, we assess the extent to which various types of intervals achieve the goals stated here.

Bayesian Intervals As described in section “The Bayesian Approach,” a Bayesian posterior probability may be used to determine regions that will have a given probability of containing the true value of a parameter. In the single-parameter case, for example, an interval (called a Bayesian or credible interval) [θ lo , θ up ] can be determined which contains a given fraction 1 − α of the posterior probability, i.e.,  1−α =

θup

p (θ |x) dθ.

(54)

θlo

Sometimes an upper or lower limit is desired, i.e., θ lo can be set to zero or θ up to infinity. In other cases, one might choose θ lo and θ up such that p(θ | x) is higher everywhere inside the interval than outside; these are called highest posterior density (HPD) intervals. Note that HPD intervals are not invariant under a nonlinear transformation of the parameter. If a parameter is constrained to be nonnegative, then the prior p.d.f. can simply be set to zero for negative values. An important example is the case of a Poisson variable n, which counts signal events with unknown mean s, as well as background with mean b, assumed known. For the signal mean s, one often uses the prior  π(s) =

0 1

s c/n: Cherenkov radiation 2. v/cph = v · n/c changes a. |v| changes: Bremsstrahlung b. direction of v changes: Synchrotron radiation c. n changes: Transition radiation 3. Ionization and/or excitation of matter: Specific energy loss dE/dx Here v is the velocity of the particle, c the speed of light in vacuum, cph the phase velocity in a medium, and n the refractive index of the medium. Any one of these conditions can occur separately or in any combination. Any one of these effects has a different dependency on the velocity, the charge and the mass of the particle, and on the properties of the material the particle is passing and interacting with. In the following we will show how some of them can be used for the task of particle identification.

Particle Identification in Calorimeters Calorimeters are discussed in detail within this book. They are used to determine the total energy of the particle or a jet. Depending on the material(s) used and how they are arranged (homogeneous, sampling), calorimeters are usually subdivided in “electromagnetic” and “hadronic,” the idea being that particles interacting mostly electromagnetically (electrons and photons) are absorbed in the “electromagnetic” part and particles interacting strongly (like π ± , p, n, K ± , KL0 , . . . ) in the “hadronic” part. It has also to be taken into account that charged hadrons lose part of their energy (but not all) in the electromagnetic section. In hadronic calorimeters with sufficient segmentation, individual particles (as opposed to whole jets) can be detected, and their individual total energy can be measured. The distinction between a charged and neutral hadron is performed if the track of a charged particle, measured previously with some tracking system, can be associated with the shower in the calorimeter or not. Further identification, for example, the separation of p, π + or K + , is not possible within a hadronic calorimeter, and other techniques (see later) have to be used to achieve this.

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Electrons and photons are distinguished also with the track-pointing method in an electromagnetic calorimeter. In this device, in addition one can compare for a track the deposited (measured) energy over the previously measured momentum of a particle (called “E/p”). If E/p ∼ 1 a (relativistic) electron originated the signal, for hadrons E/p < 1 (deposition of only a part of the total energy), muons produce an energy deposit compatible with minimum ionization only. Calorimeters used for particle identification need to have in addition to an excellent energy resolution a fine segmentation so individual particles can be measured and tracks can be associated with the calorimeter signals.

Time of Flight (ToF) This is the most straightforward method for measuring the velocity and thus the identification of charged particles: The time difference Δt for two particles with the same momentum between the signals of two (usually scintillation or gas) counters at a known distance L is measured ⎡ Δt =

L L L − = ⎣ 1+ β1 c β2 c c

m21 c2 p2

⎤

 −

1+

m22 c2 ⎦ p2

Here p is the momentum of the particles determined by a magnetic spectrometer βi , are the velocities in units of c, and mi the masses of two particles, respectively. In the relativistic limit, (p2  m2 c2 ) this reduces to Δt ≈ (m21 − m22 )Lc/(2p2 ). Time resolutions in running systems of about 100 ps have been achieved (Klempt 1999). With the maximum distance possible between the two detectors (≈10 m for measuring decay products, ≈100 m in a beam line), kaons and pions can be separated up to a few GeV/c. At higher rate and/or more than one particles hitting the same detector elements, the time difference measurement is ambiguous, and the method will not work anymore. A current example for the use of this technique is ALICE TOF detector (ALICE 1995; Cortese et al. 2002), based on multigap resistive plate chambers (MRPC); it should reach timing resolution of about 65 ps. A new development based on DIRC-like (see  Chap. 19, “Cherenkov Radiation”) devices with fast photon detectors was constructed for the BELLE II detector. Here time resolutions as low as 5 ps have been reported in prototype devices (Korpar et al. 2007; Inami et al. 2006; Va’vra et al. 2008; Vavra 2011) and are also reported in first results (Tamponi 2019).

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Specific Energy Loss dE/dx An excellent derivation of the specific energy loss in material is given in Grupen and Shwartz (2008). A more exact treatment, summarized in great detail in Tanabashi et al. (2018), gives as the final result for the mean rate of energy loss dE in a small distance dx (the “Bethe-Bloch formula”) −
= 2π ln z − β − dx A 2 2 β2 I2

(1)

This equation describes the energy loss for 0.1 ≤ βγ ≤ 1000 with an accuracy of a few %. The density correction at high energies can be described by hω δ 1 ¯ p = ln + ln βγ − 2 I 2

hω ¯ p=

4π Ne re2

me c 2 α

(2)

where Ne is the electron density and ωp the plasma frequency of the absorbing material and α the Sommerfeld fine-structure constant. Tmax , the maximum kinetic energy which can be imparted to a free electron in a single collision, is given by Tmax =

2me c2 β 2 γ 2 1 + 2γ me /M + (me /M)2

(3)

with a low-energy (2γ me /M  1) approximation of Tmax = 2me c2 β 2 γ 2 . In Fig. 1 (taken from Tanabashi et al. 2018) we show examples for energy loss in different materials. The minimum energy loss of all particles in nearly all materials occurs at 3 ≤ βγ ≤ 4 and is in the range of MeV/(g/cm2 ) (e.g., helium, − < dE/dx >= 1.94 MeV/(g/cm2 ), uranium, 1.08 MeV/(g/cm2 )) with the exception of hydrogen, in which particles experience a larger energy loss (Z/A = 1). Due to the ln γ term, the energy loss increases for relativistic particles and reaches the so-called Fermi plateau, limited by the density effect. In gases the plateau is typically ≈60 % higher as the minimum. Due to the increased energy loss at smaller βγ , particles will deposit most of their energy at the end of their track, just before they will be completely stopped. This “Bragg peak” is used for the treatment of deep-seated tumors, selecting the particle type and initial energy to optimize the energy loss close to the tumor location, avoiding too much damage to tissue above the tumor. This is described in more detail in other chapters of this book. The energy loss is distributed asymmetrically around the mean energy loss described by the Bethe-Bloch formula (Eq. 1); the distribution can be approximated by the Landau distribution Ω(λ)

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Fig. 1 Mean energy loss for different materials. (Reproduced with permission from Tanabashi et al. 2018) 1 1 −λ Ω(λ) = √ e− 2 (λ+e ) 2π

(4)

dE m.p. m.p. /(0.123 keV), with ( dE being the most probable where λ = ( dE dx ) − ( dx ) dx ) energy loss. In gases and thin absorbers, the Landau fluctuations have to be considered; for example, a particle with βγ = 4 in Argon experiences a most m.p. probable energy loss of ( dE = 1.2 keV/cm and a mean energy loss of  dE dx ) dx = 2.69 keV/cm. The Landau fluctuation presents a problem when using the energy loss for particle identification. To obtain the mean (or most probable) value of the energy loss, one has to sample often (typically 100’s of times or more) and use adequate algorithms (e.g., “truncated mean”) to determine the correct averages. Only in the so-called relativistic rise, after the minimum and well before the Fermi plateau, are the curves for different particles sufficiently separated to be useful

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for particle identification. This limits the range to particle momenta up to a few GeV/c. A detailed description can be found in Blum et al. (2008). More historic examples for successful application of this particle identification method can be found in the literature (Nygren and J.N. Marx 1978; Heintze 1982; Fischer et al. 1986; Breuker et al. 1987; Heuer and Wagner 1988). The ALICE TPC (Dellacasa et al. 2000; Alme et al. 2010) is a recent example for the use of this technique.

Transition Radiation Detectors (TRD) Transition radiation is emitted due to the reformation of the particle field when it crosses a boundary between two media with different dielectric properties. The total energy S of radiation emitted at a single interface is given by S=

α hZ ¯ 2 (ω1 − ω2 )2 γ 3 ω1 + ω2

(5)

where α = 1/137 (the fine structure constant), ω1 and ω2 the plasma frequencies, Z the atomic number of the foil material, and γ = E/mc2 (the relativistic γ ). Typical values for the plasma frequencies are: air ω1 = 0.7 eV, polypropylene ω2 = 20 eV. The spectral (ω) and angular (ϑ) dependence of the Transition Radiation is given by 2e2 d2 = dϑdω πc



ϑ γ −2 + ϑ 2 + ω12 /ω2

−

ϑ γ −2 + ϑ 2 + ω22 /ω2

2 (6)

Most of the radiation is emitted in a cone with half angle 1/γ in the forward direction of the particle. A detailed description of the spectrum of transition radiation can be found in Paul (1991). A minimum foil thickness is needed for the particle field to reach a new equilibrium inside the medium. Since there are two transitions (into and out of the foil) which are equal (ω1 → ω2 and ω2 → ω1 ), interference effects are seen as maxima and minima in the spectrum. Spacing the foils in the stack in equal distances, one can expect in addition interference between the amplitudes of different foils. As the number of foils increases, reabsorption of the radiation (∝ Z 5 ) is observed, so usually low Z materials like Mylar, CH2 , carbon fibers, or lithium are used as foils, with a thickness of 30 μm and foil distances of 300 μm. Typical photon energies are in the few keV range. The number of X-ray photons emitted is proportional to γ (Eq. 5), but only for γ  1000 photons are emitted. This limits this technique to the identification of electrons as decay products (see the introduction to this chapter) and to the separation of heavy and light particles in high momentum (several hundred GeV/c) secondary high-energy beamlines for fixed target experiments. As mentioned before, the X-ray photons from transition radiation are emitted forward under a small angle to the particle track, so whatever detector is used

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to detect the X-rays, it will be traversed by the particle itself as well, leaving an additional dE/dx energy loss in the detector. A typical dE/dx in gas detectors is some keV/cm and is Landau distributed; signals from dE/dx and the X-rays are very similar. A detector consists typically (Bruckner et al. 1996; Terentyev et al. 1995; Errede et al. 1991, 1989; Paul 1991) of a “thin” (to minimize the dE/dx signal) MWPC, with xenon or krypton as counting gas additions and several (10–30) radiator/chamber units to be able to determine effects due to the Landau distribution. To separate the signals and to discriminate between the (Landau-distributed) dE/dx and the absorbed X-ray signal, two different analysis methods, which also translate to specifications on the readout electronics, are used: charge integration and cluster counting. The charge integration method measures the total charge of the ionization in every unit and counts how many units detected a total charge above some given threshold. The cluster counting method employs the different spatial ionization distributions of the two sources (point for X-ray, distributed for dE/dx) to separate them. In Fig. 2 we show an example of a TRD detector which identifies the beam particles in the SELEX (Russ et al. 1987; Russ 1995) experiment. It consists of ten units, each of them with three wire planes, and is operated in the charge integration mode. The electronics used is seen on the bottom. The obtained signals (either clusters or charge) are compared with a likelihood method to different particle hypotheses, with known momentum. The most probable hypothesis is selected for the identification.

Fig. 2 The SELEX (Russ et al. 1987; Russ 1995) beam transition radiation detector (Terentyev et al. 1995) separates Σ − from π − in a 600 GeV/c fixed target beam line. The exit of the magnetic channel can be seen on the left. The detector consists of 10 radiator/chamber units. The readout electronics is mounted below the detector

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The most sophisticated use of this technology is within the ATLAS (Aad et al. 2008) detector at LHC. The transition radiation tracker (TRT) (Abat et al. 2008a, b) is based on the use of straw detectors, which can operate at high rates due to their small diameter (4 mm) and the isolation of the sense wires within individual gas volumes. Electron identification capability is added by employing xenon gas to detect transition radiation photons created in a radiator between the straws. In total (barrel and endcap) 370,000 straws are used. The detector, as says it’s name, doubles as a tracking device, measuring the drift time for every signal. First performance results are available in Olivito (2010).

Cherenkov Radiation Even though the basic idea of determining the velocity of charged particles via measuring the Cherenkov angle was proposed in the 1960 (Roberts 1960) and in 1977 a first prototype was successfully operated (Seguinot and Ypsilantis 1977), it was only during the last three decades that ring imaging Cherenkov (RICH) detectors were successfully used in experiments. A very useful collection of review articles and detailed descriptions can be found in the proceedings of ten international workshops on this type of detectors, which were held in 1993 (Bari, Italy) (Nappi and Ypsilantis 1994), 1995 (Uppsala, Sweden), 1998 (Ein Gedi, Israel) (Breskin et al. 1999), 2002 (Pylos, Greece) (Ypsilantis et al. 2003), 2004 (Playa del Carmen, Mexico) (Engelfried and Paic 2005), 2007 (Trieste, Italy) (Bressan et al. 2008), 2010 (Cassis, France) (Forty et al. 2011), 2013 (Shonan, Kanagawa, Japan) (Sumiyoshi et al. 2014), 2016 (Bled, Slovenia) (Krizan et al. 2017), and 2018 (Moscow, Russia) (Nappi and Pakhlov 2020), respectively Charged particles with a velocity |v| larger than the speed of light in a medium with refractive index n will emit Cherenkov radiation under an angle θc , given by (Cerenkov 1937) cos θc =

1 βn

(7)

with β = v/c, c being the speed of light in vacuum. The threshold velocity vthres is given by βthres =

1 vthres n ≥ , or γthres = √ c n n2 − 1

(8)

with a maximum angle of θcmax = arccos 1/n. For water θcmax = 42◦ , for neon at 1 atm θcmax = 11 mrad The number of photons N emitted per energy interval dE and path length dl is given by Frank and Tamm (1937)

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1 α α d 2N 1− sin2 θ = = 2 hc hc dEdl (βn) ¯ ¯

(9)

or expressed for a wavelength interval dλ, d 2N 2π α = 2 sin2 θ dλdl λ

(10)

Mostly gas radiators are used in Cherenkov counters; but also solid (quartz) and liquid radiators can be found. Water Cherenkov counters were originally developed to set limits on the lifetime of protons but got converted for (solar) neutrino detection. On example is (Super-)Kamiokande. Cherenkov effect in water is also used in the tanks of the Auger experiment to detect muons produced in cosmic ray air showers.

Threshold Cherenkov Detectors A first (obvious) application are threshold Cherenkov counters. For a fixed momentum, and only two particle types to separate, one chooses a medium with appropriate index of refraction, with a threshold between the velocities of the two particles. If only one detects any light, the lighter particle passed. For more than two particle types and/or a wider momentum range to cover, several counters with different thresholds have to be employed. Since these counters have radiator lengths of several meters each, in practice no more than three counters are used.

Ring Imaging By measuring the Cherenkov angle θc , one can in principle determine the velocity of the particle, which will, together with the momentum p obtained via a magnetic spectrometer, lead to the determination of the mass and therefore to the identification of the particle. Neglecting multiple scattering and energy loss in the medium, all the Cherenkov light (in one plane) is parallel and can therefore be focused (for small θc ) with a spherical mirror (radius R) onto a point. Since the emission is symmetrical in the azimuthal angle around the particle trajectory, this leads to a ring of radius r in the focus, which is itself a sphere with radius R/2. The radius r is given by    R R 2 m2 c 2  r = tan θc ≈ 2− 1+ 2 2 n p2

(11)

The angular separation between two particles of masses m1 and m2 (in the small angle, relativistic, and small (n − 1) approximation) is given by

Radius [cm]

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155

SELEX RICH 97937306 negative tracks e

12

10 –

p

8

-

K

-

π

-

Σ

-

6

Ξ

μ-

-

Ω

4

2

0

0

50

100

150

200

250

Momentum [GeV/c]

Fig. 3 Radius of rings versus momentum measured by the SELEX RICH (Engelfried et al. 1999a, b, 1998, 2003). Nearly 98 million tracks from negatively charged particles were used. We can clearly identify eight different particle types. The lines are absolute predicted ring radii for μ− , π − , K − , p, ¯ Σ − , Ξ − , and Ω −

Θc ΔΘc =

m21 − m22 2p2

(12)

All these features can obviously been measured, as is shown in Fig. 3, where nearly 98 million tracks, with their momentum and ring radius measured, were used (Engelfried et al. 1999a, b, 1998, 2003). A similar plot was obtained for tracks from positively charged particles. 16 particles and antiparticles can be identified. A recent review of some historical developments on RICH detectors is given in Engelfried (2011). The first RICH detectors were used in the 1980s, with mixed results. Today there is a wide range of detectors, with gas, liquid, and solid radiators in use and in development for new experiments. The refractive index of the radiator material defines the momentum range in which particle identification can be performed. Most (but not all) photon detectors operate in the ultraviolet or even VUV region, since due to the higher photon energy it is generally easier to effectively detect the photon. Since the RICHes are usually placed downstream of a magnetic field and lower momentum particles are deflected and do not reach the RICH detector, a typical selection for the pion threshold (and thus n) is the minimum momentum of the particles reaching the detector. After the refractive index (or the gas) is selected, one has to check if the resolution at high momentum (see Eq. 12) is good enough for the experiment. If not, there are several possible solutions, all of them adding additional complexity to the detector: better spatial resolution in the photon detector, more than one radiator. Depending on the

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refractive index, π/K separation can be performed from a few GeV/c to well above 150 GeV/c. Early RICH detectors used photon-sensitive vapors like TEA or TMAE for the conversion of the Cherenkov photon to one electron and a MWPC, a TPC, or TEC to detect the electron. A window separating the radiator from the photon detector is necessary and has to be transparent to the photons which have enough energy to ionize the vapor. Also the counting gas in the chamber has to be transparent for the relevant photons. In the classical geometry, the charged particle itself could pass through the chamber, leaving a huge dE/dx signal (typically a few hundred electrons) in the chamber and disturbing the measurement of the single photoelectron. Also the classical photon detector, the photomultiplier, is used in sizes up to 40 cm diameter in Water Cherenkov detectors and as small as 13mm in RICH detectors. PMTs are used when the number of pixels required is not too large; the largest PMT system (BaBar) had about 10000 channels. Other photon detectors used or planned to be used are: Multi-anode PMTs, Microchannel plates, Hybrids (photocathode with silicon strip/pixel detector), CsI photocathode with a “GEM” to detect the electron, and solid state (silicon) devices. Recent experiments using RICH detectors include LHCb and ALICE at the LHC, COMPASS at CERN, PHENIX, NA62, and BELLE II. There are several experiments developing new detectors, like CBM, PANDA, WASA-at-COSY, and CLAS.

Muon Identification In a typical setup – in case of a fixed target experiment linear, in case of a collider experiment cylindrical – all particles except muons and neutrinos are absorbed in the calorimeters. To identify muons, one additional system of tracking detectors is used after/outside the calorimeters. If there are any signals, this indicates the presence of a muon. More details of these systems can be found in  Chap. 20, “Muon Spectrometers” of this book.

Neutrinos Neutrinos only interact weakly; in experiments where neutrinos appear in the final state (e.g., in semileptonic decays), it is impossible to measure the neutrinos directly. The only possibility to deduce that there are neutrinos is by measuring the entire final state, at least in some projection (like in transverse momentum), and conclude from the momentum imbalance that some undetectable particle escaped. This requires a very hermetic detector. Direct detection of neutrinos is discussed in  Chap. 14, “Neutrino Detectors”.

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Conclusions We summarize here the different techniques used to identify particles. p, K ± and π ± are identified in the few GeV/c momentum region by dE/dx, time of flight, or Cherenkov detectors with solid (usually quartz) radiator, at higher momenta up to several hundred GeV/c by ring imaging Cherenkov counters (RICH). Photons are measured in electromagnetic calorimeters, where electrons as well deposit all their energy, while hadrons on contrary only deposit part of it. Hadrons (the already mentioned p, π ± K ± , but also n, KL0 ) are measured in hadron calorimeters. Neutral particles are identified by the missing track impact. Highly relativistic particles (electrons from reactions or beam particles) are identified with the help of transition radiation. Finally muons are identified as the only particles passing all materials.

Cross-References  Calorimeters  Cherenkov Radiation  Gaseous Detectors  Interactions of Particles and Radiation with Matter  Muon Spectrometers  Neutrino Detectors  Photon Detectors  Scintillators and Scintillation Detectors  Tracking Detectors  Semiconductor Radiation Detectors

References (2019) Proceedings, 10th International Workshop on Ring Imaging Cherenkov Detectors (RICH 2018) Nucl Instrum Meth A Aad G et al (2008) The ATLAS experiment at the CERN large hadron collider. JINST 3:S08003. https://doi.org/10.1088/1748-0221/3/08/S08003 Abat E et al (2008a) The ATLAS TRT barrel detector. JINST 3:P02014. https://doi.org/10.1088/ 1748-0221/3/02/P02014 Abat E et al (2008b) The ATLAS TRT end-cap detectors. JINST 3:P10003. https://doi.org/10.1088/ 1748-0221/3/10/P10003 ALICE C (1995) ALICE: technical proposal for a large ion collider experiment at the CERN LHC Alme J et al (2010) The ALICE TPC, a large 3-dimensional tracking device with fast readout for ultra-high multiplicity events. Nucl Instrum Meth A 622:316–367. https://doi.org/10.1016/ j.nima.2010.04.042, 1001.1950 Blum W, Riegler W, Rolandi L (2008) Particle detection with drift chambers; 2nd edn. Springer, Berlin. https://doi.org/10.1007/978-3-540-76684-1, https://cds.cern.ch/record/1105920

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Breskin A, Chechik R, Ypsilantis T (eds) (1999) Proceedings, 3rd international workshop on ring imaging cherenkov detectors: advances in cherenkov light imaging techniques and applications (RICH 1998), no. 1-2 in Nucl Instrum Meth A 433 Bressan A, Dalla Torre S, Gobbo B, Tessarotto F (eds) (2008) Proceedings, 6th international workshop on ring imaging cherenkov detectors (RICH 2007), no. 1 in Nucl Instrum Meth A 595 Breuker H et al (1987) Particle identification with the opal jet chamber in the region of the relativistic rise. Nucl Instrum Meth A 260:329. https://doi.org/10.1016/0168-9002(87)90097-0 Bruckner W, Kallakowsky T, Lauber HM, Michaels R, Paul S, Povh B, Rohrich K, Trombini A (1996) The transition radiation detector in the hyperon beam experiment WA89 at CERN. Nucl Instrum Meth A 378:451–457. https://doi.org/10.1016/0168-9002(96)00221-5 Cerenkov PA (1937) Visible radiation produced by electrons moving in a medium with velocities exceeding that of light. Phys Rev 52:378–379. https://doi.org/10.1103/PhysRev.52.378 Cortese P et al (2002) ALICE: addendum to the technical design report of the time of flight system (TOF) Dellacasa G et al (2000) ALICE: technical design report of the time projection chamber Nappi E., Pakhlov P (eds) (2020) 10th International Workshop on Ring Imaging Cherenkov Detectors (RICH 2018), in Nucl Instrum Meth A 952 Engelfried J (2011) Cherenkov light imaging: fundamentals and recent developments. Nucl Instrum Meth A 639:1–6. https://doi.org/10.1016/j.nima.2010.10.023, 1009.0052 Engelfried J, Paic G (eds) (2005) Proceedings, 5th international workshop on ring imaging cherenkov detectors (RICH 2004), no 1–2 in Nucl Instrum Meth A 553 Engelfried J, Kilmer J, Ramberg E, Stutte L, Kozhevnikov A, Kubarovsky V, Molchanov V, Filimonov I, Nemitkin A, Rud V (1998) The E781 (SELEX) RICH detector. Nucl Instrum Meth A 409:439–442. https://doi.org/10.1016/S0168-9002(98)00121-1 Engelfried J, Filimonov I, Kilmer J, Kozhevnikov A, Kubarovsky V, Molchanov V, Nemitkin A, Ramberg E, Rud V, Stutte L (1999a) The RICH detector of the SELEX experiment. Nucl Instrum Meth A 433:149–152. https://doi.org/10.1016/S0168-9002(99)00308-3 Engelfried J, Filimonov I, Kilmer J, Kozhevnikov A, Kubarovsky V, Molchanov V, Nemitkin A, Ramberg E, Rud V, Stutte L (1999b) The SELEX phototube RICH detector. Nucl Instrum Meth A 431:53–69. https://doi.org/10.1016/S0168-9002(99)00043-1, hep-ex/9811001 Engelfried J, Filimonov IS, Kilmer J, Kozhevnikov AP, Kubarovsky VP, Molchanov VV, Nemitkin AV, Ramberg E, Rud VI, Stutte L (2003) SELEX RICH performance and physics results. Nucl Instrum Meth A 502:285–288. https://doi.org/10.1016/S0168-9002(03)00289-4, hepex/0208046 Errede D, Sheaff M, Fenker HC, Lueking L, Mantsch PM (1989) Design and performance characteristics of the E769 beamline transition radiation detector. IEEE Trans Nucl Sci 36:106– 111. https://doi.org/10.1109/23.34414 Errede D, Sheaff M, Fenker HC, Lueking L, Mantsch PM, Jedicke R (1991) Use of a transition radiation detector in a beam of high-energy hadrons. Nucl Instrum Meth A 309:386–400. https:// doi.org/10.1016/0168-9002(91)90242-I Fischer HM et al (1986) The opal jet chamber full scale prototype. Nucl Instrum Meth A 252:331– 342. https://doi.org/10.1016/0168-9002(86)91202-7 Forty R, Hallewell G, Hofmann W, Nappi E, Ratcliff B (eds) (2011) Proceedings, 7th international workshop on ring imaging cherenkov detectors (RICH 2010). Nucl Instrum Meth A 639 Frank IM, Tamm IE (1937) Coherent visible radiation of fast electrons passing through matter. Compt Rend Acad Sci URSS 14(3):109–114. https://doi.org/10.1007/978-3-642-74626-0_2, https://doi.org/10.3367/UFNr.0093.196710o.0388, [Usp. Fiz. Nauk93,no.2,388(1967)] Grupen C, Shwartz B (2008) Particle detectors, 2nd edn. Cambridge monographs on particle physics, nuclear physics and cosmology. Cambridge University Press. https://doi.org/10.1017/ CBO9780511534966 Heintze J (1982) The jet chamber of the JADE experiment. Nucl Instrum Meth 196:293–297. https://doi.org/10.1016/0029-554X(82)90658-9

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Schneider O, Scholberg K, Schwartz AJ, Scott D, Sharma V, Sharpe SR, Shutt T, Silari M, Sjöstrand T, Skands P, Skwarnicki T, Smith JG, Smoot GF, Spanier S, Spieler H, Spiering C, Stahl A, Stone SL, Sumiyoshi T, Syphers MJ, Terashi K, Terning J, Thoma U, Thorne RS, Tiator L, Titov M, Tkachenko NP, Törnqvist NA, Tovey DR, Valencia G, Van de Water R, Varelas N, Venanzoni G, Verde L, Vincter MG, Vogel P, Vogt A, Wakely SP, Walkowiak W, Walter CW, Wands D, Ward DR, Wascko MO, Weiglein G, Weinberg DH, Weinberg EJ, White M, Wiencke LR, Willocq S, Wohl CG, Womersley J, Woody CL, Workman RL, Yao WM, Zeller GP, Zenin OV, Zhu RY, Zhu SL, Zimmermann F, Zyla PA, Anderson J, Fuller L, Lugovsky VS, Schaffner P (2018) Review of particle physics. Phys Rev D 98:030001. https://doi.org/10.1103/PhysRevD. 98.030001 Terentyev N et al (1995) E781 beam transition radition detector SELEX Internal Note H-746 Vavra J (2011) PID techniques: alternatives to RICH methods. Nucl Instrum Meth A 639:193–201. https://doi.org/10.1016/j.nima.2010.09.062 Va’vra J, Ertley C, Leith DWGS, Ratcliff B, Schwiening J (2008) A high-resolution TOF detector: a possible way to compete with a RICH detector. Nucl Instrum Meth A 595:270–273. https:// doi.org/10.1016/j.nima.2008.07.021 Ypsilantis TA, Ekelof T, Resvanis LK, Seguinot J (eds) (2003) Proceedings, 4th international workshop on ring imaging cherenkov detectors (RICH 2002) – experimental techniques of cherenkov light imaging, no. 1 in Nucl Instrum Meth A 502

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Accelerators for Particle Physics Helmut Burkhardt

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Basic Concepts and Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Magnet Lattice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dispersion and Chromaticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sources and Pre-injectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . RF Acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ring Accelerators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Phase Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Applications of Accelerators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fixed-Target Accelerators and Colliders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Energy and Luminosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Vacuum and Beam Lifetime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Synchrotron Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Highest Energies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract Beams of high-energy particles with well-defined properties are very important both for fundamental research and applied sciences. Particle accelerators are the devices that allow to produce these high-energy particle beams. High-energy particle accelerators have a length of many kilometers and are the largest scientific tools used today. We give a short overview over the main types

H. Burkhardt () Accelerator Department BE, CERN, Geneva, Switzerland e-mail: [email protected] © Springer Nature Switzerland AG 2021 I. Fleck et al. (eds.), Handbook of Particle Detection and Imaging, https://doi.org/10.1007/978-3-319-93785-4_7

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of accelerators, in particular synchrotrons, storage rings, and linear accelerators, and their main properties and fields of application. The concepts and basic formulas are illustrated and discussed using the main parameters of the largest existing or planned high-energy accelerators.

Introduction Particle accelerators are the devices used to provide high-energy charged particles with well-defined properties for research and medical and industrial applications. This chapter starts with a description of the basic concepts. Electric fields are used to accelerate the charged particles, i.e., electrons, protons, or ions. Magnets are employed to guide the particles along the design path through the accelerators. This is followed by sections on how particles are obtained from sources and on the advantages of using radio frequency rather than static electric fields for the acceleration. The remainder of the text focuses mostly on high-energy accelerators for particles physics. In this context, the accelerator is often called the machine, meaning the device that provides the particles and the particles’ collisions. The collisions are observed and studied by the experiments, which refer to the large detectors and collaboration of physicists who detect, study, and analyze the particle collisions.

Basic Concepts and Units We will briefly recall basic laws and expressions that are important for accelerator physics and refer to standard textbooks like Jackson (1998) for a more detailed discussion. The force F acting on a particle with charge q in an electromagnetic field is F = q (E + v × B)

(1)

and generally referred to as Lorentz force. The term q E is the electric force and the term q v × B the magnetic force. By convention, the electric field E points from positive to negative charges and is measured in units of volt per meter (V/m). B is the magnetic field measured in tesla (T); q is the electric charge, measured in coulomb (C). When we are dealing with elementary particles, it will be more practical to specify the charge in multiples of the elementary charge e, where e = 1.6021765 × 10−19 C. The equations of motion in an electromagnetic field can be obtained by combining Eq. 1 with Newton’s second law for the relativistic momentum, F = p˙ =

d (mγ v) . dt

(2)

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Particles in accelerators reach velocities v approaching the speed of light c, and relativistic effects are of primary importance. Unless stated otherwise, we will always use the exact relativistic expressions. Two standard dimensionless quantities of relativistic dynamics are the velocity in units of the speed of light β = v/c and the Lorentz factor 1 1 γ = = . 2 2 1 − v /c 1 − β2

(3)

The relativistic momentum of a particle with rest mass m is p = m γ v, and the total (relativistic) energy Etot and kinetic energy Ekin are  Etot = γ mc2 =

2  p2 c2 + mc2 ,

Ekin = (γ − 1) mc2 .

(4)

Depending on the value of γ, we distinguish three different domains 1. γ ≈ 1, nonrelativistic, v  c 2. γ > 1 relativistic 3. γ  1 Ultrarelativistic, β ≈ 1 In the nonrelativistic case, we can expand Eqs. 3 and 4 in powers of β and get as low-energy limit the familiar classical kinetic energy Ekin ≈ 12 mc2 β 2 = 12 mv 2 . In the ultrarelativistic case, the mass becomes negligible, and we get Etot ≈ Ekin ≈ pc. We first consider the case of direct (DC) acceleration in a static electric field, which is parallel to the direction of motion as sketched in Fig. 1. A charged particle, in this case an electron of charge q = −e, is accelerated in the direction from the negatively charged cathode toward the positive anode. This type of acceleration is called direct high voltage or DC HV acceleration. The energy gain U in an electric field of potential (voltage) V is U = qV .

Fig. 1 Principle of acceleration by an electric field

(5)

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Fig. 2 Coordinates and motion in a magnetic field

y

z x

v

B

s F

In accelerator and particle physics, it is convenient to use as energy unit the electron volt eV, where 1 eV = 1.60217653 × 10−19 joule, and to express the mass unit in terms of the energy unit. For the electron, we have m e c2 = 0.5109989 MeV and for the proton m p c2 = 938.272 MeV. As simple numerical example, we consider the accelerator sketched in Fig. 1, in which a single-charged particle gains 100 keV = 0.1 MeV. If we start with an electron at rest, we would get to Etot = 0.611 MeV, with γ = 1.1957 and β = 0.548. Static or quasi-static magnetic fields are used in accelerators to guide the particle’s motion along the design path. To illustrate this, we will look at a particle moving with velocity v along a path s, perpendicular to a homogeneous magnetic field B as shown in Fig. 2. The magnetic force is perpendicular to the direction of motion. It changes only the direction of the particle. The absolute value of the momentum and the energy is conserved. As a result, the particle moves on a circular path, with radius ρ, where ρ=

p . qB

(6)

For B = 1 T, q = e, and p = 1 GeV/c, we get as radius ρ = 3.336 m.

Magnet Lattice We will now shortly describe the main principles of beam dynamics in accelerators. The aim here is to present a short, simple illustration of the basic formulas and effects. More thorough descriptions can be found in the literature. The basic principles were developed around the middle of the last century and summarized in the historic paper of Courant and Snyder (1958) and are well described in textbooks on accelerators (Lee 2004; Conte and MacKay 2008).

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F

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O D O

Fig. 3 Schematic view of a ring section with a FODO lattice

Quadrupole magnets provide fields that increase with distance from the center of the magnet. They are used to focus particles transversely to the beam direction. The combination of the dipoles used as bending magnets, quadrupoles, and higherorder multipole magnets (sextupoles, octupoles, etc.) is called the magnetic lattice and determines the optical (guiding) properties for the particle beam. A standard configuration is the FODO lattice, sketched in Fig. 3. It consists of a sequence of F (horizontally focusing) quadrupoles, bending magnets (“O”), and D (horizontally de-focusing) quadrupole magnets. Figure 3 also shows as dashed line a trajectory of a particle with a transverse offset. A quadrupole that focuses horizontally will be defocusing vertically and vice versa. The FODO lattice is an example of an alternating gradient lattice. The alternation between focusing and de-focusing elements has an overall focusing effect. This can be qualitatively understood as follows. Particles are on average further off axis in F quadrupoles such that the focusing effect dominates. In one transverse (horizontal or vertical) plane, quadrupoles act like optical lenses. Two lenses with focal length f1 , f2 at a distance D act together like a lens with focal length f, where 1/f = 1/f1 + 1/f2 – D/(f1 f2 ). In the alternating lattice, we have f2 = −f1 , which together is focusing with 1/f = +D/f12 . The formulas given in this section are written in terms of the horizontal displacement x. The equivalent expressions also hold for the vertical displacement given by the y coordinate. The basic equation of motion of particles in an accelerator lattice is of the form x  (s) + k(s)x(s) = 0,

(7)

which is a second-order differential equation known as Mathieu–Hill equation from mathematical studies for mechanical applications in the nineteenth century (Mathieu 1868; Hill 1886). It can be regarded as generalized oscillator equation in which the restoring force k is a function of the independent variable s, the distance along the equilibrium orbit measured from some fixed reference point. k(s) is the “restoring force” in the motion, given here by the focusing properties of the quadrupoles in the lattice. In a ring that is built up of regular cells with length L, k will be periodic, k(L + s) = k(s). The total circumference C is the sum of the lengths of all cells.

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The solution of Eq. 7 can be written as x(s) =

 β(s) cos(μ(s) + φ),

(8)

where ε and φ (initial phase) are integration constants determined by initial conditions. β(s) is known as β function and describes the focusing properties of the magnetic lattice and  μ(s) =

s

0

ds β(s)

(9)

is the phase advance. The phase advance, divided by 2π, is also called the betatron μ wave number or tune Q = 2π . √ From Eq. 8 we can see that the amplitude of the oscillations is given by β(s). This can be generalized to average quantities for a multiparticle beam. The r.m.s. beam size at the position s in the machine is σ (s) =

 β(s),

(10)

where ε is now an average beam quantity called emittance, which represents the beam size in phase space. Collider optics are designed with minima of the β function in the collision regions. This decreases the beam sizes at the collisions points and increases the probability for collisions. In an ideal machine, the transverse motion in the horizontal and vertical planes is independent. Such a machine is called fully decoupled. This allows for very different β functions and emittances in the horizontal and vertical plane. This is in particular important for electron rings to decrease the vertical emittance even in the presence of a large horizontal emittance from synchrotron radiation in the (horizontal) bending plane.

Dispersion and Chromaticity We now discuss shortly how the optics changes with energy. More precisely, we consider the motion of particles with a relative momentum deviation p/p from the average (design) momentum. In a bending magnet, particles with a positive momentum deviation travel on a larger circle. For horizontal bending, we get a horizontal offset

x = Dx

p . p

(11)

The proportionality factor Dx is called the horizontal dispersion. It will be positive for dipoles and can be to some extent adjusted and reduced using quadrupoles.

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Nonzero dispersion also results in a coupling of the transverse and longitudinal motion in a ring: a particle at higher energy traveling on a larger radius will take a longer time to complete a full circle and appear shifted in time and longitudinal position compared to a particle with the average momentum. Particles with a positive momentum deviation will also be less focused by quadrupoles, resulting in a decrease in tune,

Q = Q

p . p

(12)

The proportionality factor is called chromaticity. The natural (quadrupolegenerated) chromaticity is negative, Q < 0, and roughly equal to the tune contribution from the regular arcs, Q ≈ −Q. Higher-order magnets can be used to correct for aberrations by their feed-down effect, which is proportional to the transverse offset x from the magnet axis: An offset x in quadrupole results in a dipole (bending) magnet component proportional to the offset x. An offset x in a sextupole results in a focusing (quadrupole) magnet component proportional to the offset x. Example: a sextupole magnet installed in the machine in a place with dispersion can provide extra focusing proportional to the offset x and compensate the negative natural chromaticity of the quadrupoles. For machines with many FODO cells, the quadrupole strengths are often chosen such that the phase advance of each cell is close to a simple fraction of 2π, like μcell = π/2 = 90◦ or μcell = π/3 = 60◦ . This results in rather periodic structures, which are easier to correct for aberrations.

Sources and Pre-injectors A basic type of electron source is the thermionic electron gun. The principle is that of a cathode-ray tube. A cathode is placed in a vacuum tube, and the electrons are extracted from the heated cathode and accelerated using DC HV acceleration. Other types of electron guns employ photocathodes. Positrons can be produced by passing electrons of 50 MeV or more through a converter plate. In the plate, typically a metal-like tungsten of 0.5–3 radiation length (Tsai 1974) thickness, the electrons will radiate hard photons by the process of bremsstrahlung. Many of these photons will generate electron–positron pairs by the process of pair creation. The efficiency to produce positrons depends only weakly on the initial electron energy and converter thickness (Nunan 1965). The converter is typically followed by solenoids and accelerator sections to focus and accelerate the positrons. The principle is sketched in Fig. 4.

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Fig. 4 Principle of a positron source

Table 1 Frequencies and gradients reached

Machine LEP ILC CLIC

fRF (GHz) 0.35 1.3 12

Gradient (MV/m) 8 31.5 100

For a proton source, as currently in use at CERN, the primary material is hydrogen gas, as commercially available for purposes like welding. A single bottle is sufficient to supply all the protons accelerated at CERN in 1 year. Hydrogen gas is injected in a metallic vessel, which is heated to ionize the hydrogen gas and placed on +90 kV tension to accelerate the protons toward the cathode at ground potential. A hole in the cathode allows to extract the protons that can then be further accelerated. Further information on sources can be found in Scrivens (2003, 2013).

RF Acceleration High-voltage breakdown limits static electric fields to roughly 1 MV/m. One or two orders higher acceleration gradients can be reached with oscillating fields using frequencies in the radio-frequency (RF) range of MHz to GHz. RF acceleration is restricted to the acceleration of bunches (packets) of particles in which the bunch length is shorter than the RF wavelength. As an example: the ILC design bunch length is 0.3 mm, which is much smaller than the RF wavelength of 230 mm at the design RF frequency of 1.3 GHz. Higher frequencies allow higher gradients. This can be understood qualitatively as follows: at a high frequency like 1 GHz, the peak voltage is only maintained for a fraction of 1 ns (nanosecond), which is too short to develop corona discharge and high-voltage breakdown. Table 1 shows actual numbers for the RF frequencies with the gradients used in LEP and proposed and tested in prototypes of accelerator structures for future linear colliders – International Linear Collider (ILC) and Compact Linear Collider (CLIC).

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Fig. 5 RF acceleration in a ring

Future machines at the high-energy front will work in the tera scale (with collision energies of TeV). With a gradient of 100 MV/m, a TeV could be reached with a 10-km-long acceleration section. Another advantage of RF over DC acceleration is that it becomes possible to sum up the energy gain over successive turns in ring accelerators as sketched in Fig. 5.

Ring Accelerators In a cyclotron, the RF acceleration is performed at constant frequency and constant magnetic field. As the particle gains energy, the radius of curvature increases. This requires magnets as large as the whole ring, which is only practical for smaller machines. In a synchrotron, the magnetic field is ramped up together with the energy of the particles, or more precisely, proportional to the increase in particle momentum, such that the radius of curvature is kept constant. All larger ring accelerators are of this type. We take as an example the Super Proton Synchrotron (SPS) at CERN. It can accelerate protons from p = 14 GeV/c to p = 450 GeV/c in a few seconds. The SPS has a circumference of 6, 911.56 m and uses normal-conducting magnets. The RF system used to accelerate the protons is operated at a frequency of about 200 MHz at 10 MV RF voltage. The circumference is kept constant by increasing the RF frequency with the velocity. A change of 2 × 10−3 is sufficient, as the protons are already rather relativistic. See Table 2 for numerical values

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Table 2 Proton parameters for the CERN SPS at the beginning and end of the acceleration used in fixed-target mode

p(GeV/c) E(GeV) β γ fRF (MHz) B(T)

14 14.0314 0.9977617 14.9545 200.265 0.063

450 450.001 0.9999978 479.606 200.395 2.025

Phase Stability The particles in a bunch have a spread in energy and velocity. To accelerate all particles and keep them bunched, it is important to provide more voltage than required on average for the energy gain. Slower, less energetic particles lagging behind see a higher voltage and receive more acceleration as sketched in Fig. 6, which brings them closer to the bunch center. Particle A in Fig. 6 corresponds to a particle at the center of a bunch. The principle is known as phase stability and was independently discovered by Veksler and McMillan (McMillan 1945; Veksler 1945). At very high energies, all particles will travel practically at the same speed v = c; we can get in a situation, referred to as “above transition” in which the lower-energy particles travel on a shorter circumference and arrive before particle A at the RF. Phase stability is then achieved on the falling side of the sine wave. To be more quantitative, we look how the traveling time changes with velocity, path length, and momentum. The time T needed to travel a fixed length L depends on the velocity v, where T = L/v. An increase in velocity by v decreases the traveling time T, so that

T

v =− . T v

(13)

The relativistic change of velocity v with momentum p is dv 1 v = 2 . dp γ p

(14)

We also have to consider in a ring that particles with an energy offset will travel on a different path. The relative change in path length L with momentum in a ring is called the momentum-compaction factor αc , defined as αc =

L p / . L p

(15)

The momentum compaction depends on the focusing properties of the magnetic lattice. For a simple (FODO) lattice αc ≈ 1/Q2 , where Q is the tune or number of

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Fig. 6 Phase stability

betatron oscillations over the length considered. For the SPS ring, we have Q ≈ 26.2 and αc = 1.92 × 10−3 . We can now calculate the relative change in time required for one revolution in a ring by considering both the changes in path length and velocity. We get  

T

L v 1 p = − = αc − 2 . T L v p γ



(16)

η

The expression in the bracket is known as phase-slip factor η = αc − γ−2 . During acceleration, both effects exactly cancel when γ−2 = αc . This is called transition √ and the corresponding γ called γtr = 1/ αc . In the CERN SPS, the momentumcompaction factor is αc = 1.92 × 10−3 , which corresponds to γtr = 22.8. Looking at Table 2, we can see that this factor lies between the minimum and maximum γ, so that the transition is crossed during the acceleration. At transition, the phase stability is lost, and particles will start to slowly de-bunch. The blowup can be minimized by fast transition crossing and by programming a phase jump in the RF at transition.

Applications of Accelerators The concepts discussed so far were rather general and also apply to accelerators used in applications other than particle physics. Worldwide, there are more than 20,000 accelerators in use. Compared to the high-energy particle accelerators, most of these are very small machines used for industrial applications and medicine (Amaldi 2000). More information on accelerators for applications can be found in Chao and Chou (2010), Greene and Williams (1997), and TIARA (2013). The remainder of this text is on the concepts that are more specifically of interest for applications in particle physics and in particular relevant for reaching high energies and rates in particle collisions.

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Target

Beam 1

Beam 2

mT

E CM »

2EbmT c 2

E CM = 2Eb

Fig. 7 Fixed-target and collider rings

Fixed-Target Accelerators and Colliders We now distinguish between two types of accelerators depending on the use of the accelerated particles for high-energy physics. The first type is the fixed-target accelerator, in which a beam of particles is extracted at the end of the acceleration to hit a target. The second type is the collider, in which two beams of high-energy particles are brought into collisions. Both types are illustrated in Fig. 7 for ring accelerators. The same distinction also applies to linear accelerators. The energy available in√particle collisions to produce new particles is the centerof-mass energy ECM = s, where s is the total four-momentum squared. It can conveniently be calculated using the 4-vector notation of high-energy physics (with units of c = 1). The energy/momentum 4-vector of beam 1 is p1 = (Eb , p). In case of a symmetric collider, the second beam has p2 = (Eb , −p). In the fixed-target case instead, the second (target) particle is at rest, p2 = (mT , 0). The four-momentum relations for the two cases are     Collider : p1 = Eb , pb , p2 = Eb , −pb , s = (p1 + p2 )2 = (2Eb )2   Fixed target : p1 = Eb , pb , p2 = (mT , 0) , s = m2b + m2T = 2mT Eb In the case of a symmetric collider, the sum of the two beam energies, 2Eb , is available for new particle production. In the fixed-target case instead, the centerof-mass energy only increases with the square root of the beam energy (ECM =  2Eb mT c2 , for “E  m”), while the rest is “lost” in kinetic energy of the secondary particles. Figure 8 shows a comparison of the two cases√for proton machines. At the same beam energy, colliders allow for 2Eb /mT higher collision energies. For the LHC with protons at Eb = 7 TeV, the gain is a factor of 122. The difference is even more marked for collisions with the light electrons. All recent lepton particle accelerators were in fact built as colliders.

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Center-of-mass energy E CM

GeV 2,000

Tevatron

r

1,500

ide

ll Co

1,000

–S Spp

500 ISR

SPS 200

400

Fixed target

Tevatron

600 800 1,000 GeV Beam energy Eb

Fig. 8 Comparison of the center-of-mass energies available for collisions, as a function of the proton beam energy

Fixed-target accelerators cannot compete with colliders at the energy front. They have instead other advantages which make them complementary to colliders at lower and medium energies. One important area of application for fixed-target proton accelerators is the production of secondary beams. In the CERN SPS, for example, the accelerated proton beams can be extracted and send on to targets. Low-Z 100– 200-m-long aluminum targets are typically used to generate secondary beams with a high content of hadrons (protons, pions, kaons); shorter high Z targets like 3-mmlong tungsten can be used to generate secondary beams with many electrons and positrons. Secondary beams are used to test and calibrate detectors, as well as for dedicated fixed target physics experiments (Montbarbon et al. 2019). In symmetric e+ e− or pp particle/antiparticle colliders, it is possible to keep both beams oppositely circulating in a single ring. Examples are the e+ e− collider LEP that was operated at CERN from 1989 to 2000 with up to Eb = 104 GeV and the SppS (operated at CERN from 1981 to 1991, mostly at Eb = 270 GeV) and the TEVATRON proton–antiproton collider (operated at Fermilab from 1992 to 2011 with up to Eb = 980 GeV). To reach the center-of-mass energy of the LHC proton–proton collisions of 2 Eb = 14 TeV in fixed-target mode would require a beam energy of 1017 eV, far beyond the reach of present accelerator technology and dimensions in the kilometer range. Energies up to 1020 eV have actually been observed in cosmic rays reaching the earth. This can be used to demonstrate that the collision energies that are reached with the LHC are perfectly safe (Ellis et al. 2008). Examples of symmetric colliders for identical particles using two neighboring rings with crossings in several interaction regions are the ISR operated from 1971 to 1984 and the LHC. Both were built at CERN, primarily as pp colliders. In the LHC, it is also possible to accelerate and collide heavy ions and different particle species like lead ions and protons.

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It can be possible to use the same machine in both fixed-target and collider mode and to use several types of particles in the acceleration. An example is the CERN SPS. The SPS started operation in 1976 as fixed-target proton accelerator and was a few years later upgraded with an injection line for antiprotons and collision regions, to become the first proton–antiproton collider in the world. A few years later, it was upgraded with extra 352-MHz RF cavities to allow to accelerate electrons and positrons as injector for LEP. An upgrade of the 200-MHz RF system allowed to accept a larger range of revolution frequencies to also accelerate heavy ions in the SPS. Once the required hardware is installed, the switching from one mode to the other is mainly a question of controlling and adjusting the RF and magnetic parameters. This can in principle be automated. Switching the SPS from proton to ion operation is done manually, typically within a couple of days. Switching from protons to e+ , e− acceleration was automated and possible within seconds.

Energy and Luminosity Energy and luminosity are the most important performance parameters of an accelerator for particle physics. Higher energy is required to allow to produce new, heavier particles. High luminosity is needed to observe rare processes and for precision measurements. The demand for higher energies and luminosities has triggered technological developments, both for lepton and for proton colliders; new technologies have found their way into accelerators, such as superconductivity both for high-current magnets and radio-frequency accelerating systems. This and a steady advance in the understanding of beam dynamics, computing techniques, beam diagnostics, and beam control have made this possible. Figure 9 shows the increase in energy over the years. This graph shows both lepton and hadron machines and also the electron–proton collider HERA. To make proton and electron machines more comparable in their discovery potential, the energy per proton (consisting of three quarks and several gluons) was divided by 3. The dashed lines show the impressive progress in maximum energy over the years: an exponential growth with a factor of 4 every 10 years over four decades! Proton and lepton accelerators complement each other. At comparable size and cost, protons allow for higher energies. They can be considered as “discovery machines.” Lepton colliders are the precision instruments to study the details of the interactions between particles. Accelerating few particles to very high energy is not all what is required. What is about equally important is a high luminosity, i.e., to allow for a high flux of particles resulting in a sufficiently high number of collisions. The collision rate n˙ for a process of cross section σ is the product of the luminosity L and the cross section

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s

Constituent center-of-mass energy (GeV)

103

on

dr Ha Tevatron – Spp S

102

10

1

ISR

er lid l o

CLIC

LHC

c

ILC

HERA

LEP2 s er LEP,SLC lid l o Tristan – c +e PETRA e PEP

CESR Spear2 Doris Spear Adone

VEP-2 ACO

VEP-1 10–1 1960

1970

1980

1990

2000

2010

2020

2030

Year of first physics

Fig. 9 Growth in collider energies with time Fig. 10 Luminosity from particles flux and geometry

n˙ = Lσ.

(17)

The luminosity of a collider is determined by the particle flux and geometry (Herr and Muratori 2003). For head-on collisions as illustrated in Fig. 10, we have that L=

N1 N2 kb f . A

(18)

N1 , N2 are the numbers of particles per bunch, kb is the number of bunches (per train in case of a linear collider), f the revolution frequency in case of a ring and the bunch-train crossing frequency in case of a linear collider, and A the effective beam

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overlap cross section at the interaction point. For beams with Gaussian shape of horizontal and vertical √ r.m.s. beams sizes σx , σy colliding head on, we have A = 4π σx σy , where σ = β in both x, y, according to Eq. 10. Strong quadrupole magnets are used around the interaction regions to focus beams down to small values of the β functions at the interaction point (called β∗ ) to get small beam sizes and high luminosity. Cross sections are usually given in units of barn (symbol b), where 1b = 10−24 cm2 = 10−28 m2 . Typical luminosities of LEP, the highest-energy lepton collider built, were 1031 cm−2 s−1 . The cross section for e+ e− → Z is σ Z ≈ 30 nb. Over four million Z events were produced for each of the four experiments installed at LEP. collisions is σ pp ≈ 50 mb (at √ The cross section of protons in proton–proton √ s = 10 GeVand about 2 × higher at s = 10 TeV). Cross sections for the “most interesting processes” like new particle production in e+ e− or quark–antiquark annihilation can be very small and generally decrease with the center-of-mass energy squared. For Higgs particle production at the LHC, the relevant order of magnitude for cross sections is femtobarn (1fb = 10−39 cm2 ). The LHC has been designed for a peak luminosity of L = 1034 cm−12 s−1 , so that the production rate for rare processes with σ = 1 fb would still be n˙ = 10−5 s−1 or one in 28 h. A number of second- and third-generation high-luminosity e+ e− colliders have been built over the last two decades in the medium-energy range (1–10 GeV in the center of mass) (Biagini 2009). They were typically built to operate at a fixed energy that corresponds to the mass of one of the φ, ψ, or ϒresonances to allow to produce mesons with s, c, or b quarks in large quantities. Such machines are also called e+ e− factories. Two-third generation b-factories, PEP2 at SLAC in the USA and KEKB at KEK in Japan, both reached peak luminosities exceeding L = 1034 cm−2 s−1 . This was achieved by focusing the beams to micrometer beam sizes at the interaction points and by colliding many (k b > 1, 000) bunches. A new machine, called SuperKEKB, started commissioning in Japan with collisions in 2018 and aims for another major increase in luminosity toward L = 8×1035 cm−2 s−1 . An overview of e+ e− factories can be found in the ICFA Beam Dynamics Newsletter 67 (2015).

Vacuum and Beam Lifetime The particles in accelerators travel in evacuated beam pipes. Beam pipes are typically made of stainless steel or aluminum and have an elliptical cross section of some cm2 . Collisions of the beam with the rest gas are sketched in Fig. 11 and result in unwanted effects like blowup of the beam size, generation of a beam halo, and loss of particles from the beam pipe causing radiation and backgrounds to the experiments. Good vacuum conditions in the beam pipes of accelerators are important to minimize these unwanted effects. Typical numbers are a good vacuum is in the range of nanoTorr (p = 1 nTorr = 1.33 × 10−7 Pa), which at room temperature corresponds to a rest-gas density of

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Fig. 11 Beam collisions with the nuclei (N) of the rest gas

ρm =

p = 3.26 × 1013 molecules/m3 . kT

(19)

A typical cross section in beam–gas scattering for electron beams is σ = 6 barn and corresponds to a cross section for bremsstrahlung with an energy loss of >1% in a rest gas of CO or N2 molecules. The collision probability is Pcoll = σ ρ m = 1.96 × 10−14 /m. We can multiply this with the particle velocity v ≈ c (for high-energy accelerators) to obtain the loss rate with time. The inverse of this is the electron-beam lifetime from beam–gas scattering at a rest-gas pressure of 1 nTorr, τ=

1 Pcoll c

= 1.7 × 105 s = 47 h.

(20)

A long beam lifetime is particularly important for colliders. Only a very small fraction of the beam particles will actually collide at each beam crossing and leave the beam pipe. The beams can often be kept circulating for several hours before the intensity and luminosity has reduced by a significant amount. Ring accelerators with a long beam lifetime are also called storage rings.

Synchrotron Radiation Generally, radiation is emitted by any accelerated charge. For highly relativistic particles in accelerators, this is referred to as synchrotron radiation . As shown below, the synchrotron radiation remains negligible in linear acceleration but becomes very significant when high-energy electron beams are deflected by magnetic fields. For accelerators for particle physics, synchrotron radiation can be considered mostly as an unwanted effect. The energy loss has to be compensated by the acceleration system, and the radiation results in heating of accelerator components and backgrounds to the particle detectors. The combination of the energy loss by synchrotron radiation and the acceleration by the RF system, however, also has a positive effect, which is that it results in a damping of the transverse motion that limits the transverse beam size. This can be qualitatively understood as follows: the

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synchrotron radiation is emitted in the direction of the motion, which reduces the particle momentum in all three x, y, z components. The acceleration by the electrical field in z direction only compensates the energy loss of the particle in z direction. If the energy loss would be continuous, the transverse beam sizes would shrink to zero. The quantum fluctuations of the synchrotron radiation emitted in discrete steps results in a small, finite transverse beam emittance. The high achievable power and the rather unique properties of synchrotron radiation, which allow for very short energetic pulses and the possibility to cover a broad range in the ultraviolet and X-ray spectrum, make synchrotron radiation very attractive for applied research. Many electron machines have been built as dedicated synchrotron light sources. The properties of synchrotron radiation are well understood and described in textbooks (Sokolov and Ternov 1986; Jackson 1998; Hofmann 2004). As discussed by Schwinger (1949) in his classical paper, the power radiated by an accelerated particle of charge e is described by the relativistic version of Lamor’s formula, P =

 e2 γ 2 2 2 2 ˙ p , − β p ˙ 6π 0 m2 c3

(21)

where p˙ and p˙ are the time derivatives of the particle’s momentum vector and absolute value, m the mass of the particle, and β = v/c and γ = (1 − β2 )−1/2 the usual Lorentz quantities. We will now consider the two opposite cases of: Acceleration in the direction of motion as relevant for linear accelerators Acceleration perpendicular to the motion as relevant in rings   In the first case of linear acceleration with vv˙ , we have no change in direction,

2 2 dp only in magnitude, dt = ddpt , so that 

dp dt



2 − β2

dp dt

2

 p˙ 2 e2 = p˙ 2 1 − β 2 = 2 and P = p˙ 2 . γ 6π 0 m2 c3

(22)

The two terms nearly cancel, resulting in a suppression by a factor of γ2 . As numerical example, we take the highest acceleration gradient of 100 MV/m from Table 1 and find that the power loss is only 11 keV/s or 0.4 eV loss for a 1 TeV, 10-km-long CLIC-like machine. Synchrotron radiation in linear acceleration is negligible. Now the second case is motion on a circular path in a ring. At constant energy, the motion on a circular path in a ring implies that we have an acceleration perpendicular to the velocity, v ⊥ v˙ . The second term is zero (at constant energy the magnitude of

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the momentum is also constant). There is no cancellation, and we get a significant effect 

dp dt



2 − β2

 dp 2 e2 = p˙ 2 and P = γ 2 p˙ 2 . dt 6π 0 m2 c3 

(23)

0

For the circular motion in the uniform magnetic field, we have from the Lorentz force and Newton’s law that F =| p˙ |= eϑB =

mγ ϑ 2 vp = . ρ ρ

(24)

We find that the power radiated by circular motion in a uniform magnetic field increases with the fourth power of γ, P =

e2 ϑ 4 γ 4. 6π0 c3 ρ 2

(25)

We multiply this with the time it takes to complete one turn, T = 2πρ/v, and find that the energy loss of a particle by synchrotron radiation over one turn is U0 =

1 E4 e2 β 3 γ 4 ∝ , 30 ρ ρ m4

where

e2 = 6.032 × 10−9 eV m. 30

(26)

A practical limit was reached with electrons at LEP at beam energies around 100 GeV, corresponding to a Lorentz factor γ ≈ 2 × 105 when 3% of the particle energy was lost on a single turn. More details and further references can be found in review articles on LEP (Assmann et al. 2002; Bailey et al. 2002; Hübner 2004; and Burkhardt and Jowett 2009). Accelerator physics aspects are summarized in Brandt et al. (2000) and the RF system in Butterworth et al. (2008). Colliders for the TeV range require either the use of heavier particles like protons in a ring or the use of linear colliders.

The Highest Energies The world’s largest- and highest-energy particle accelerator today is the LHC at CERN. It is installed in the 26.7-km-long tunnel used previously by LEP. The LHC is built with two beam pipes that cross at four interaction regions. This allows to accelerate and collide particles of the same charge, pp (proton on proton) and heavy ions. The mass of these particles is much higher (1,836 times in case of protons) than that of electrons. Synchrotron radiation from protons at LHC energies becomes noticeable but is not yet a limitation. The maximum beam energy in the

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4

5

LHC

6 Extraction

3 450 GeV 2

7

T18 8

SPS

T12 Protons

26 GeV

LINACS Ions

1

Booster CPS 1.4 GeV

LEIR

Fig. 12 Schematic view of the LHC with its injectors

LHC, or more precisely the beam momentum p, is given by the maximum bending field strength B according to Eq. 6 and the bending radius ρ = 2, 804 m, which is constrained by the tunnel geometry. The LHC utilizes superconducting NbTi magnets operated at superfluid-helium temperature of 1.9 K, which allows for fields up to B = 8.33 T and p = 7 TeV/c. Filling the LHC with protons or ions requires a chain of pre-accelerators. The first stage is a linear accelerator. It is followed by several synchrotrons, the Booster, PS, and SPS rings; see Fig. 12. The LHC was designed as a high-luminosity hadron collider which requires collisions of many bunches, stored in each of the two rings (by design 2,808 bunches). A major challenge for the LHC is that the total energy stored in the beams and the magnets is very high. An uncontrolled loss of the beam or the superconductivity (“quench”) could result in damage of parts of the accelerator. A current of 12 kA is required to reach the design field of 8.33 T in the LHC dipoles. The inductance of an LHC dipole is L = 100 mH. The energy stored in a single dipole at full current is I2 L/ 2 = 7.2 MJ, which adds up to 9 GJ for the 1,232 dipole magnets in the LHC. This is comparable to the kinetic energy of a large passenger plane at full speed. The total energy in the beam reaches 360 MJ. This is several orders of magnitude higher than in other machines and well above the damage level for uncontrolled beam loss. The LHC is equipped with a fast beam protection system. Beam losses are monitored by several thousand monitors all around the ring. In case of magnet trips or abnormal beam losses, the LHC beams will be dumped within a few turns. The LHC was commissioned in steps. First beams were injected in the LHC in 2008. First collisions at the injection energy of 2 × 450 GeV were obtained in

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2009. Operation at a physics energy of 2 × 3.5 TeV started in spring 2010. Further information on the designs and first years of operation of the LHC can be found in Evans (2009), Evans and Bryant (2008), and Brüning (2012). In 2018, the LHC operated at an energy of 2 × 6.5 TeV with peak luminosities reaching L = 2×1034 cm−2 s−1 or two times the design luminosity. A further upgrade in luminosity is planned to assure the leading role of the LHC for the next two decades (Apollinari 2017). Plans for future linear e+ e− colliders are being studied in detail along two main paths, the International Linear Collider (ILC) and Compact Linear Collider (CLIC). The ILC aims for a beam collision energy of 0.5 TeV, upgradeable to 1 TeV in the center of mass, whereas CLIC extends the linear-collider energy reach into the multi-TeV range, nominally 3 TeV, which leads to different technologies. ILC is based on superconducting RF acceleration technology with high RF-to-beam efficiency; CLIC takes advantage of a novel scheme of two-beam acceleration with normal-conducting copper cavities at high-frequency and high-accelerating field. More information about the ILC can be found on the ILC web page (http:// www.linearcollider.org/cms/) and the ILC Reference Design Report (ILC 2007). Information about CLIC and CLIC design and parameters can be found on the CLIC web pages (http://clic-study.web.cern.ch/CLIC-Study/ and http://clic-study. web.cern.ch/CLIC-Study/Design.htm). The success of the LHC at CERN and the interest in a further major increase in collision energies have stimulated studies for Future Circular Colliders. An overview can be found in the ICFA Beam Dynamics Newsletter 72 (2017). One common feature of both linear and circular collider studies is that they stimulate innovation and lead to new improved technology with potentially wideranging applications. Examples are developments of more energy efficient radio-frequency power sources and developments of higher-field superconducting magnets; see Gerigk (2018) and Apollinari (2015).

Conclusion The availability of particle beams with well-defined properties from particle accelerators is crucial for most of the methods and techniques described in this handbook. Even detectors built to observe particles from natural sources for astrophysics and space instrumentation often rely on accelerators for testing and calibration of their detectors. The basic concepts and types of particle accelerators are described in this chapter. The development of particle accelerators has been to a large extent driven by requirements of particle physics research for higher energies and intensities. Smaller, lower-energy particle accelerators are used in many scientific, industrial, and medical applications.

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Cross-References  Accelerator Mass Spectrometry and Its Applications in Archaeology, Geology,

and Environmental Research  Calorimeters  Data Analysis  Gaseous Detectors  Neutron Detection  Particle Detectors in Materials Science  Particle Identification  Radiation Detectors and Art  Spallation: Neutrons Beyond Nuclear Fission

References Amaldi U (2000) The importance of particle accelerators. Europhys News 31(6):5–9 Apollinari G (2015) Progress with high-field superconducting magnets for high-energy colliders. https://doi.org/10.1146/annurev-nucl-102014-022128 Apollinari G (ed) (2017) High-Luminosity Large Hadron Collider (HL-LHC). http://cds.cern.ch/ record/2284929 Assmann R, Lamont M, Myers S (2002) A brief history of the LEP collider. Nucl Phys Proc Suppl 109B:17–31. CERN-SL-2002-009 Bailey R et al (2002) The LEP collider. C R Acad Sci (Paris) 9:1107–1120 Biagini M (ed) (2009) e+ e− colliders: past and present experiences and future frontiers. ICFA Beam Dyn Newsl 48:23–278. http://icfa-usa.jlab.org/archive/newsletter/icfa_bd_nl_48.pdf Brandt D, Burkhardt H, Lamont M, Myers S, Wenninger J (2000) Accelerator physics at LEP. Rep Prog Phys 63:939 Brüning O, Burkhardt H, Myers S (2012) Prog Part Nucl Phys 67:705. https://doi.org/10.1016/j. ppnp.2012.03.001 Burkhardt H, Jowett JM (2009) A retrospective on LEP. ICFA Beam Dyn Newsl 48:143–152. http://icfa-usa.jlab.org/archive/newsletter/icfa_bd_nl_48.pdf Butterworth A et al (2008) The LEP2 superconducting RF system. Nucl Instrum Method A587:151–177 Chao AW, Chou W (2010) Reviews of accelerator science and technology: medical applications of accelerators, vol 2. World Scientific, Singapore Conte M, MacKay WW (2008) An introduction of particle accelerators. World Scientific, Singapore Courant E, Snyder H (1958) Theory of the alternating-gradient synchrotron. Ann Phys 3:1 Ellis JR, Giudice G, Mangano ML, Tkachev I, Wiedemann U (2008) Review of the safety of LHC collisions. J Phys G35:115004 Evans L (2009) The large hadron collider: a marvel of technology. EPFL Press, Lausanne Evans L, Bryant P (eds) (2008) LHC machine. J Instrum 3:S08001 Gerigk F (2018) Status and future strategy for advanced high power microwave sources for accelerators. Proc IPAC. http://ipac2018.vrws.de/papers/moygb1.pdf Greene D, Williams PC (1997) Linear accelerators for radiation therapy (medical science). Taylor & Francis, New York Herr W, Muratori B (2003, September 15–26) Concept of luminosity, CAS – CERN accelerator school: intermediate course on accelerator Physics. Zeuthen, pp 361–378. http://cdsweb.cern. ch/record/941318

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Hill GW (1886) On the part of the motion of lunar perigee which is a function of the mean motions of the Sun and Moon. Acta Math 8:1–36 Hofmann A (2004) The physics of synchrotron radiation. Cambridge University Press, Cambridge, UK Hübner K (2004) Designing and building LEP. Phys Rep 403–404:177–188 ICFA Beam Dynamics Newsletter 67 (2015) Future e+ e− colliders. http://icfa-usa.jlab.org/archive/ newsletter/icfa_bd_nl_67.pdf ICFA Beam Dynamics Newsletter 72 (2017) Future energy-frontier circular colliders. http://icfabd.kek.jp/Newsletter72.pdf ILC (2007) ILC reference design report. http://www.linearcollider.org/cms/?pid=1000437 Jackson JD (1998) Classical electrodynamics, 3rd edn. Wiley, New York Lee SY (2004) Accelerator physics. World Scientific, Singapore Mathieu E (1868) Mémoire sur le mouvement vibratoire d’une membrane de forme elliptique. J Math Pure Appl 13:137–203 McMillan EM (1945) The synchrotron – a proposed high energy particle accelerator. Phys Rev 68(5–6):143–144 Montbarbon E et al (2019) The new CERN east area primary and secondary beams. Proc IPAC. http://accelconf.web.cern.ch/AccelConf/ipac2019/papers/thpgw062.pdf Nunan CS (1965) A positron linear accelerator design. Proc Pac IEEE Trans Nucl Sci 12(3):465 Schwinger J (1949) On the classical radiation of accelerated electrons. Phys Rev 75:1912. https:// doi.org/10.1103/PhysRev.75.1912 Scrivens R (2003) Electron and ion sources for particle accelerators. CAS 2003, CERN-2006-002. https://cds.cern.ch/record/941321 Scrivens R (2013) Classification of ion sources. CERN-2013-007. http://cds.cern.ch/record/ 1693319 Sokolov AA, Ternov IM (1986) Radiation from relativistic electrons. American Institute of Physics, New York TIARA (2013) Accelerators for society. http://www.accelerators-for-society.org Tsai Y-S (1974) Pair production and bremsstrahlung of charged leptons. Rev Mod Phys 46: 815–851 Veksler V (1945) Concerning some new methods of acceleration of relativistic particles. J Phys USSR 9:153

8

Accelerator-Based Photon Sources Shaukat Khan and Klaus Wille

Contents A Brief History of Radiation Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Generation of Synchrotron Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Radiation from Accelerated Electrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acceleration of Electrons to Ultrarelativistic Energies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Insertion Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Synchrotron Radiation Sources Worldwide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Applications of Synchrotron Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Diffraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Other Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The New Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Storage Rings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Linac-Based Free-Electron Lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Energy Recovery Linacs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract For about one century, X-rays have been the primary tool to probe the atomic structure of matter. With the advent of synchrotron radiation sources in the 1960s and more recently free-electron lasers, the photon flux, coherence, spectral

S. Khan () · K. Wille Zentrum für Synchrotronstrahlung (DELTA), Technische Universität Dortmund, Dortmund, Germany e-mail: [email protected]; [email protected] © Springer Nature Switzerland AG 2021 I. Fleck et al. (eds.), Handbook of Particle Detection and Imaging, https://doi.org/10.1007/978-3-319-93785-4_8

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brightness, and tunability of short wavelength radiation has improved dramatically. After briefly reviewing the history of X-ray sources, the generation of radiation by accelerating electrons will be addressed. Synchrotron radiation is produced by circular acceleration of relativistic electrons in magnetic fields. Therefore, the discussion in this chapter focuses on linear and circular particle accelerators, on the principles of particle optics as well as on magnetic devices called wigglers and undulators. After giving a brief overview of the applications of synchrotron radiation, the newly emerging radiation sources, in particular novel storage rings and free-electron lasers, will be discussed. It will become clear that X-ray science is far from settling into a routine but is presently undergoing a more rapid development than ever.

A Brief History of Radiation Sources On the evening of the 8th of November 1895, W. C. Röntgen discovered that a discharge tube which he had wrapped in black cardboard caused a faint glow on a nearby fluorescence screen, and he recognized this to be a new kind of radiation, which penetrated opaque material like cardboard or wood, and he could even see the bones inside his hand on the screen (Röntgen 1895). These X-rays, as Röntgen named them (also called Röntgen rays in German), were not bent by electric or magnetic fields (unlike cathode rays, i.e., electrons) but were also not noticeably deflected by a prism (unlike visible light). Röntgen did speculate that they might be ultraviolet light or even “aether waves,” which were believed to exist at that time. The fact that X-rays were indeed electromagnetic radiation with short wavelength became finally clear around 1912, when other scientists like M. von Laue, W. H. Bragg, and his son W. L. Bragg, P. Debye, P. Scherrer, and others started to exploit another stunning property of X-rays, namely, their ability to reveal the structure of crystalline matter on the Ångström scale by diffraction (1 Å = 10−10 m). Much more efficient than Röntgen’s discharge tube is the X-ray tube as we know it today, which was invented in 1913 by W. D. Coolidge at General Electric in New York (Coolidge 1913). Here, electrons are generated by a heated cathode and accelerated toward an anode, where their sudden deceleration produces bremsstrahlung with a continuous spectrum and, in addition, a line spectrum caused by fluorescence. With rotating anodes to provide better cooling, X-ray tubes reached a brightness six orders of magnitude higher than that of Röntgen’s original apparatus. Another recent approach to further increase the brightness by two orders of magnitude is to replace the solid anode by a liquid-metal jet (Hemberg et al. 2003). While X-rays became an indispensable tool in biology and condensed matter physics, the need for higher intensity but also for monochromatic radiation with tunable wavelength and small divergence arose. With the advent of particle accelerators using radiofrequency (closely linked to the progress in radar technology in World War II), electrons could be accelerated to ultrarelativistic energies. When forced on a circular trajectory by a magnetic field, relativistic electrons produce radiation tangentially to their trajectory within a narrow opening angle and over a broad

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spectral range. This type of radiation is called synchrotron radiation. Forty years after its prediction, synchrotron radiation was for the first time directly observed and photographed in 1947 at the General Electric synchrotron in Schenectady, NY, USA, which happened to have a vacuum vessel made of glass (Elder et al. 1947). Even though it gave synchrotron radiation its name, a synchrotron would be a poor radiation source since it ramps the electron energy E up on a macroscopic timescale, while the radiation power increases with E 4 and becomes only significant toward the end of the ramp cycle. Therefore, synchrotron radiation facilities are not really synchrotrons but always electron (or positron) storage rings in which the particle energy is kept constant. As a first generation of synchrotron radiation sources, scientists started in the 1960s to use radiation from synchrotrons or e+ e− colliders parasitically (see, e.g., Madden and Codling 1963). The second generation emerged in the 1970s when electron storage rings dedicated to this purpose were built (Martin 1988). Without counter-propagating positrons, the electron beam emittance (measuring its size in phase space) could be reduced, leading to radiation with smaller source size and divergence. Third-generation synchrotron radiation sources, starting 1992 with the ESRF in Grenoble, France (Laclare 1993), are larger storage rings with even smaller beam emittance and a large number of so-called insertion devices, particularly undulators. The purpose of these devices is to produce more intense radiation compared to the emission from a simple circular path. In undulators, electrons move on a sinusoidal trajectory and act like a dipole emitter moving at relativistic speed in the laboratory system. Thus, the emitted radiation has a reduced opening angle and a line spectrum comprising a fundamental wavelength and possibly harmonics thereof. The label “fourth-generation light source” is nowadays claimed by several types of facilities. In 2009, PETRA III at DESY in Hamburg, Germany, was commissioned and is currently the largest storage-ring-based light source with a circumference of 2,304 m (Balewski 2010). A new design concept has emerged with the construction of MAX IV in Lund, Sweden (Tavares et al. 2014). The ultimate X-ray source based on storage rings should have a high beam energy to reach short wavelengths and a large circumference with a magnetic lattice allowing to reach the diffraction limit, in which the product of rms (root mean square) size and divergence of the radiation is given by λ/2π with λ being the radiation wavelength. Free-electron lasers (FELs) based on linear accelerators have now reached subvisible wavelengths, from 108 nm in 2000 at DESY in Hamburg down to the sub-Å regime, e.g., at SACLA in Harima, Japan (Ishikawa et al. 2012). FELs provide ultrashort and extremely intense radiation pulses, but conventional linear accelerators are limited to pulsed operation with low repetition rate. Superconducting energy-recovery linear accelerators (ERLs), on the other hand, are envisaged as complementary sources in continuous-wave operation and with ultrashort pulse duration but with lower intensity than FELs. Existing ERLs produce radiation in the infrared regime, but several X-ray facilities have been proposed (Bilderback et al. 2009).

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Fig. 1 Peak brilliance of radiation sources (photon rate per source size in mm2 , solid angle in mrad2 and 0.1% bandwidth) from 1895 until today, covering more than 25 orders of magnitude. Schematically shown is an early X-ray tube, a third-generation synchrotron light source and a linac-based free-electron laser

In addition to synchrotron radiation sources based on conventional accelerator technology, “table-top” sources driven by laser-plasma accelerators are now under consideration. Even though these accelerators have not yet reached the required level of stability, remarkable progress has been made in this field, demonstrating the generation of undulator radiation (Fuchs et al. 2009) and reaching electron energies in the GeV range (Leemans et al. 2014). The history of X-ray sources is best illustrated by the increase of their radiation intensity over the years. In Fig. 1, the peak brilliance (defined below in Eq. 5) is shown from the year 1895 until today. The peak brilliance has not only increased by more than 25 orders of magnitude, but the slope has also become steeper with the advent of synchrotron light sources and steepened again with the first X-ray FELs.

Generation of Synchrotron Radiation Radiation from Accelerated Electrons When an electron is at rest or moves with constant speed in free space, the electric field lines point to the electron. Now, let the electron be accelerated for a short

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Fig. 2 Screenshots from running the simulation program Radiation2D, written by Shintake (2003). In the left figure, a charge has been briefly accelerated upward, causing a wave to travel spherically outward at the speed of light. In the right figure, a charge is on a circular orbit, emitting a spiral-shaped wave front

time. If the field lines would instantaneously follow that acceleration, there would be no radiation. Given the finite speed of light, however, a distant observer will see the field lines still pointing to a spot where the electron would be had it not been accelerated. A nearby observer, on the other hand, will see the field lines pointing toward the electron (Fig. 2). The transition between the two regimes takes place in a spherical zone which expands at the speed of light and in which the field lines are distorted. The distortion of the electric field gives also rise to a magnetic field, and observers detecting such a distortion moving at the speed of light will call it “electromagnetic radiation.” The magnitude of the field distortion depends on the acceleration, and since it is much easier to accelerate electrons (or positrons), radiation from heavier particles is usually negligible. Examples of electron acceleration causing radiation are the oscillatory motion of electrons in a radio transmitter antenna, the abrupt deceleration of electrons in an X-ray tube, and the circular acceleration of electrons in a storage ring which gives rise to synchrotron radiation. An electron beam of energy E and current I perpendicular to a magnetic field B radiates the power (Wille 2001) P = AI B

with

A=

ce2 E 3  4 . 3ε◦ me c2

(1)

Here, e is the elementary charge, c is the velocity of light, ε◦ is the dielectric constant, and me is the electron mass. For a given magnetic field, the power is proportional to E 3 , but for a fixed bending radius R, the relation B ≈ E/(ecR) yields the E 4 dependence mentioned above. The radiation spectrum, i.e., the power per time unit and spectral energy width as function of the photon energy Ep , is given by the relation

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Fig. 3 Spectrum of synchrotron radiation from ultrarelativistic electrons. In this example, the electron energy is 3.5 GeV, the beam current is 100 mA, and the magnetic field is 1.5 T. The dot at 12.2 keV indicates the critical energy

dP P = S dEp Ec



Ep Ec



√  ∞ 9 3 with S (ξ ) = ξ K5/3 (u)du , 8π ξ

(2)

where K5/3 (u) is a modified Bessel function. The critical photon energy Ec =

3eh E2B 4π m3e c4

or

Ec [keV] = 0.665 · E 2 [GeV2 ] · B[T]

(3)

with h being Planck’s constant divides the spectrum into two parts of equal power and thus characterizes the typical energy range of photons emitted by electrons in a magnetic field. On a double-logarithmic scale, as shown in Fig. 3, the shape of the radiation spectrum given by S (ξ ) is always the same. For a normal-conducting electromagnet with an iron yoke, saturation limits the magnetic field to below 2 T. Consequently, the generation of photons in the X-ray regime (several keV) requires electron beam energies in the GeV range. As an example, the European Synchrotron Radiation Facility (ESRF) in Grenoble, France, with a beam energy of 6.04 GeV produces photons with a critical energy of 20.6 keV in bending magnets with B = 0.85 T. Contemporary synchrotron light sources have beam energies ranging from below 1 GeV (e.g., the Metrology Light Source in Berlin, Germany, with 630 MeV (Feikes et al. 2011)) to 8 GeV (SPring-8 in Hyogo, Japan (Kamitsubo 1997)). As described in the next paragraph, conventional synchrotron light

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sources comprise an electron accelerator (a synchrotron or a linear accelerator) and a storage ring in which the electrons circulate for hours at constant beam energy.

Acceleration of Electrons to Ultrarelativistic Energies Electrostatic accelerators are limited to energies of a few MeV. For a synchrotron light source with electrons in the GeV range, accelerators driven by radiofrequency (RF) such as linear accelerators (linacs) or synchrotrons are required.

Conventional Electron Linacs Most linear accelerators for high-energy electron beams consist of cylindrical waveguide structures operating in the TM01 mode and providing a strong longitudinal electric field at their center. However, the phase velocity of an electromagnetic wave in a cylindrical waveguide is higher than the velocity of light c. In order to accelerate electrons traveling at a speed slightly below c, it is necessary to reduce the phase velocity of the co-propagating RF wave by adding disks with holes to the waveguide (Fig. 4) at which the wave is partially reflected. The superposition of the reflected part with the main wave results in a phase velocity which matches the electron speed. The largest electron linac until now is the Stanford Linear Accelerator (SLAC) in Menlo Park, USA, with a length of 3 km. Here, the electromagnetic wave has a frequency of 3 GHz (S band) and is produced by pulsed power klystrons of several tens of megawatt. The resulting energy gain is about 15 MeV per meter. In the past, the SLAC linac had reached a maximum energy of 50 GeV and was later employed at lower energy as injector of a B-meson factory. Today, its final third is used to deliver electrons up to 16.5 GeV for LCLS, an X-ray free-electron laser (Emma et al. 2010). For conventional synchrotron radiation sources, however, much smaller linacs are used as injectors.

Fig. 4 Conventional normal-conducting linac structure for the acceleration of electrons. The disks reduce the phase velocity of an electromagnetic wave in a cylindrical waveguide to slightly below the velocity of light

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Fig. 5 Superconducting linac structure, consisting of an array of bell-shaped cavities made of highly purified niobium

Superconducting Linacs and Energy Recovery In order to improve the electric field gradient and the duty factor of linacs, superconducting structures have been developed. The duty factor is the fraction of time, at which the linac contains RF power. Resistive power losses in the walls limit normal-conducting copper structures to duty factors around 1%. Superconducting linacs consist of an array of bell-shaped cavities (Fig. 5) made of niobium. Compared to cylindrical structures, the bell shape eliminates the problem of multipacting (build-up of an electron avalanche) which would limit the gradient to a very low value. A typical frequency is 1.3 GHz (L band), and gradients exceeding 40 MV/m have been achieved for individual cavities. For mass production, however, typical values are around 25 MV/m. In a linac, each electron passes the structure only once and is either injected into a storage ring or directly used, for example, to produce radiation, and then absorbed by a beam dump, where the whole energy is lost. As a consequence for linac-driven radiation sources, a rather high average RF power is required, and most of it is not used to produce radiation. The idea of an energy-recovery linac (ERL) (Tigner 1965) is to guide the bunched beam through the linac structure a second time (Fig. 6). If the phase of the particles in the RF field is shifted by 180◦ with respect to the accelerating phase, the returning beam excites an electromagnetic wave in the linac structure and transfers its energy back to the field. In this case, the external power transmitter only has to compensate the power losses in the system. Since these losses are rather large in normal-conducting structures, the energy recovery principle requires the use of superconducting cavities. Synchrotrons The first machines producing synchrotron radiation were – as the name suggests – synchrotrons, ring-shaped accelerators with a constant electron beam orbit (Fig. 7). Here, bending magnets define a circular trajectory and quadrupole magnets focus the beam. During acceleration by one or several RF cavities operating in the TM010 mode, the field of the magnets increases proportional to the beam energy. A typical

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Fig. 6 Principle of energy recovery. A bunched particle beam is accelerated and subsequently decelerated in the same superconducting linac returning most of its energy to the RF field

Fig. 7 A synchrotron with beam injected from a linac. The beam particles gain energy from an RF cavity at each turn. When reaching their final energy after many turns, the beam is ejected, e.g., to be accumulated in a storage ring. Injection and ejection kickers are fast magnets that are switched on and off within a few revolution times of the synchrotron

cavity provides an accelerating voltage of several 100 kV, and at every turn, the beam particles increase their energy accordingly. At very low beam energy, the remnant field of magnets with iron yokes varies significantly, and a stable beam orbit is not possible. Therefore, a pre-accelerator

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(typically a linac or a microtron) is required to inject electrons with an energy of several 10 MeV into the synchrotron. In order to periodically ramp the fields of the magnets up and down, they are in many synchrotrons driven by a sinusoidal current through the coils. When using a resonant circuit formed by the magnet coils and a bank of capacitors, the frequency of this alternating current may be several 10 Hz. This way, the stored energy alternates between the magnetic field of the coils and the electric field of the capacitors, and only resistive losses have to be compensated. The beam energy achieved by electron synchrotrons ranges from some 100 MeV to many GeV. The very first experiments with synchrotron radiation were performed at electron synchrotrons with photon beamlines installed tangentially to the electron orbit in bending magnets. Apart from the small beam current, the periodically changing beam energy E strongly limited the photon flux, since the radiation power is proportional to E 4 . Consequently, the radiation intensity during the ramp cycle of a synchrotron is most of the time negligible.

Electron Storage Rings The photon flux produced by storage rings at constant beam energy is much higher than that of synchrotrons. Originally designed for high-energy physics with colliding beams, storage rings are very similar to synchrotrons. They are also circular machines with bending magnets and quadrupoles to guide and focus the beam. However, synchrotrons are optimized for varying magnetic fields, which requires, for example, measures against eddy currents, while storage rings are optimized for beam quality and lifetime. Among other issues, this implies a more elaborate vacuum system providing a residual gas pressure of the order of 10−7 Pa. For a beam lifetime of 10 h, for example, the average electron has to avoid fatal collisions over a distance of 1010 km, roughly the circumference of Saturn’s orbit around the Sun. Furthermore, RF cavities are required to keep the beam energy constant by compensating the energy loss due to synchrotron radiation at each turn. For a sufficiently long beam lifetime, additional RF voltage is needed to retain electrons which have lost or gained energy in interactions with residual gas atoms or among themselves. Many storage rings are refilled when the beam current has dropped to, for example, half the initial value, but over the last decade, more and more synchrotron light sources have adopted a “top-up” mode of operation, injecting electrons every few minutes to keep the beam current constant on a subpercent level (Ohkuma 2008). Top-up operation increases the time-averaged photon flux and greatly improves the thermal stability of the storage ring and its X-ray beamlines. On the other hand, the demands on the injection system and on radiation safety are high. A linac or synchrotron is used to accelerate electrons and inject them into the storage ring. The injection process is repeated in order to accumulate a stored beam current of several 100 mA. While a high current yields a high flux of photons, it also gives rise to collective effects, particularly coupled-bunch instabilities (Chao 1993; Khan 2006). Here, each bunch induces electromagnetic fields interacting with the surrounding vacuum chamber. These so-called wake fields act on subsequent

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bunches and thus excite longitudinal and transverse oscillations of the whole beam. Coupled-bunch instabilities limit the storable beam current and increase the average beam size, divergence, and energy spread, which directly influences the quality of emitted synchrotron radiation. In the worst case, sudden beam loss can occur. In order to keep beam instabilities at bay, the vacuum chamber should be large and highly conductive, abrupt changes of its cross section should be avoided, and higherorder modes of the RF cavities should be reduced. In addition, bunch oscillations can be damped by active feedback systems measuring and correcting the position of each bunch at each turn (Teytelman 2016). Apart from beam instabilities, unwanted beam motion over a wide frequency range may arise from power supply ripple at harmonics of the mains frequency (50 or 60 Hz), from mechanical vibrations (around 10 Hz), from ground motion due to traffic (a few Hz), ocean waves (typically 0.2 Hz), diurnal and seasonal temperature changes, and other effects. Slow drifts are compensated by adjusting the settings of corrector dipole magnets every few seconds, while vibrations and power supply ripple are counteracted by sophisticated feedback systems with bandwidths in the kHz range (Hubert et al. 2009). Sudden beam loss may also be induced by positive residual gas ions which are attracted by the negative charge of the electron beam. For sufficiently large rings, a common countermeasure is to leave a gap in the fill pattern of the electron beam, allowing the ions to drift away. In the case of positron beams, positive ions are repelled, but trapped electrons may give rise to instabilities. In summary, electron storage rings are optimized to deliver a high photon flux which either decays smoothly or is kept nearly constant by top-up injection. A lot of effort is put into stabilizing the beam over a frequency range of sub-Hz to GHz (see Fig. 8). Furthermore, electron storage rings are optimized for small beam emittance, which in turn defines the brilliance of the photon beam. These quantities are described in the next paragraph.

Electron Beam Optics In most applications of synchrotron radiation, a high photon flux is preferred, i.e., a large number of photons per unit time and spectral width

Fig. 8 Order-of-magnitude frequencies in electron storage rings. A typical frequency for RF systems is 500 MHz. Revolution frequencies (1/turn) range from 0.13 MHz to several MHz. The frequencies for horizontal and vertical oscillations are slightly different, usually around 10 MHz, while the longitudinal motion is three orders of magnitude slower. Not shown are harmonics and sidebands occurring in the beam spectrum

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 S

 photons , s · 0.1% bw

(4)

where the spectral bandwidth (bw) is usually defined as 0.1% of the photon energy. In addition, a small transverse size of the radiation source and a small divergence are often required, which is expressed by the definition of the “spectral brightness” or “brilliance” S B= 2 4π · σx σy σx  σy 



photons s · 0.1% bw · mm2 mrad

 . 2

(5)

Here, σx,y and σx  ,y  are standard deviations of the horizontal or vertical electron position x and y and of the horizontal or vertical trajectory angles x  ≡ dx/ds and y  ≡ dy/ds. It is common practice to express angles (in rad) as derivatives of the transverse coordinates with respect to the position s along the orbit, denoted by a prime. The rms horizontal or vertical beam size and divergence are functions of s, given by σx,y (s) = εx,y · βx,y (s)

and

σx  ,y  (s) =

εx,y ·

2 (s) 1 + αx,y , βx,y (s)

(6)

where εx,y is the beam emittance, βx,y (s) is the amplitude function, also known as “beta function,” and αx,y (s) ≡ (−1/2) · dβx,y (s)/ds. Thus, a large beta function implies a large beam with small divergence and vice versa, while the constant emittance εx,y represents the area occupied by the beam in the respective phase space (x, x  ) or (y, y  ) spanned by spatial and angular coordinates. According to a common definition, the phase space area π · εx,y contains 39% of the particles in a normal distribution. Liouville’s theorem states that this area is constant under the influence of conservative forces. Due to energy dissipation via synchrotron radiation, this is not exactly true for electron beams, but restoring the energy with RF cavities in a storage ring leads to a constant equilibrium phase space distribution. The smaller the horizontal and vertical emittance, the larger the brightness of the photon beam. Besides bending magnets with homogeneous fields, strong quadrupole magnets with constant transverse field gradients are employed to keep the beam small. Quadrupole magnets comprising four hyperbolic pole faces (Fig. 9) focus the beam in one coordinate and act like defocusing lenses in the other direction. An overall focusing structure is always composed of at least two quadrupole magnets of alternating polarity. The beam optics is mainly defined by quadrupole magnets with their respective strengths and polarities chosen such that the beam is transversely confined at each position along the circumference of the storage ring. Since the beta function is uniquely defined for a given position s, the periodicity conditions

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Fig. 9 Quadrupole magnet with four coils on an iron yoke with hyperbolic pole faces. In this example, an electron beam pointing into the image plane is focused vertically and defocused horizontally

βx,y (s + C) = βx,y (s)

  βx,y (s + C) = βx,y (s)

and

(7)

hold, in which C is the circumference of the storage ring and the prime again denotes the derivative with respect to s. The quadrupole magnets give rise to an attractive potential in which particles oscillate transversely around the ideal trajectory. This motion is known as betatron oscillation. The number of oscillations per revolution around the ring Qx,y is called betatron tune and is typically of the order of 10. At particular tune values (integer, half integer, third integer, etc.), magnetic field errors act repeatedly in the same direction and tend to increase the betatron oscillation. Such a resonance can lead to beam loss or at least reduce the beam lifetime, and therefore tune values being ratios of small integers must be avoided. A particle deviating from the reference energy E of the storage ring travels along a trajectory which is horizontally displaced from the ideal orbit by x = Dx (s) ·

E , E

(8)

where Dx (s) is the dispersion function. In the absence of vertically deflecting dipole magnets, dispersion is caused by horizontal dipoles, and spurious vertical dispersion is usually negligible. Thus, the index x can be omitted. Like the beta functions, the dispersion and its derivative also satisfy periodicity conditions: D(s + C) = D(s) and

D  (s + C) = D  (s) .

(9)

The energy distribution of a circulating electron beam is in good approximation given by a Gaussian distribution with a standard deviation of the order of 0.1%,

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and the maximum dispersion is typically 1 m or less. Since dispersion increases the horizontal beam size significantly, most synchrotron light sources are based on achromatic lattices with dispersion-free straight sections to accommodate wigglers and undulators (see section “Insertion Devices”). Due to the strong focusing in synchrotron light sources, even a small energy deviation causes a significant variation of the tune. A large chromaticity, defined as tune change per energy offset Qx,y /( E/E), causes off-energy particles to hit a resonance and thus reduces the beam lifetime. The chromaticity is reduced by employing sextupole magnets in which the field depends quadratically on the transverse coordinates. However, in the presence of nonlinear fields, the motion of a particle with large transverse deviation becomes chaotic, and there is a distinct boundary beyond which particles are lost. To keep this so-called dynamic aperture large, many relatively weak sextupoles should be distributed around the ring rather than a few strong ones.

Radiation Effects The synchrotron radiation power P emitted by an electron beam with energy E and current I in a magnetic field B is given by Eq. 1. With B = E/ (ecR), the energy loss of a single electron per turn is W =

e2 E4 eP =  4 I 3ε◦ me c2 R

or

W [keV] = 88.5 ·

E 4 [GeV4 ] R[m]

(10)

ranging from below 100 keV to several MeV. The radiated power has to be compensated by the accelerating RF system, and due to the strong dependence on E, it imposes economic limits on the beam energy for electron or positron storage rings. A given energy loss per turn W is restored by a sinusoidal RF voltage with amplitude URF , if the condition W = eURF sin s

(11)

is fulfilled, where s is the so-called synchronous phase. Electrons deviating from

s undergo oscillations in longitudinal direction and in energy. This motion is known as synchrotron oscillation, and the synchrotron tune Qs (defined in analogy to Qx,y as number of oscillations per turn) is of the order of 10−2 , i.e., one longitudinal oscillation takes about 100 turns. Synchrotron radiation has a damping effect on betatron and synchrotron oscillations. The reason for transverse damping is that photon emission from an oscillating electron causes a loss of longitudinal and transverse momentum, while only the longitudinal component is restored by the RF system. The longitudinal damping effect is a consequence of the dependence of the radiated power on electron energy. Radiation damping follows an exponential law with damping constants (i.e., inverse damping times) of

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ax =

W (1 − D) 2ET

199

ay =

W 2ET

as =

W (2 + D) 2ET

(12)

for horizontal, vertical, and longitudinal oscillations, where T is the revolution time and D is a parameter which depends on the magnetic structure and can be neglected for many storage rings. An example with W = 100 keV, E = 1 GeV, and T = 1 μs shows that damping constants are of the order of 100 s−1 . Synchrotron radiation not only damps particle oscillations but, due to its stochastic nature, also excites them. The equilibrium between the two effects determines the horizontal emittance (and thus the beam size and divergence) as well as the energy spread of the beam (which, in turn, determines the bunch length). The horizontal emittance is given by εx =

3 H(s)/R 3 55h 2 H(s)/R = C E2 γ √ γ (1 − D)1/R 2 64π 3m3e c5 (1 − D)1/R 2

(13)

with Cγ = 3.83 · 10−13 m, the Lorentz factor γ = E/(me c2 ), and the other symbols defined as before. Taking the average . . . over the longitudinal coordinate s is only required inside the bending magnets where 1/R is nonzero. The function H(s) is constant between bending magnets and is given by H(s) = γx (s)D 2 (s) + 2αx (s)D(s)D  (s) + βx D 2 (s)

(14)

using the conventional notation 1 αx (s) ≡ − βx (s) 2

and

γx (s) ≡

1 + αx2 (s) . βx (s)

(15)

The horizontal emittance of third-generation light sources is in the range of a few 10−9 rad m. Assuming only horizontally deflecting dipole magnets, the vertical emittance is given by field and alignment errors of the magnetic structure, typically leading to a ratio εy /εx around 10−2 , but values of a few 10−4 were achieved by careful optimization (Aiba et al. 2012). In order to obtain a low emittance, the dispersion should be small inside the bending magnets. The magnetic structure of many synchrotron light sources is derived from the Chasman-Green lattice (Chasman et al. 1975), also known as double-bend achromat (DBA). It comprises a symmetric arrangement of two bending magnets with nonzero dispersion between them and no dispersion elsewhere (Fig. 10). Deriving the horizontal emittance according to Eq. 13 for a DBA lattice is beyond the scope of this chapter (but straightforward). Starting with a given beta function β◦ and its derivative β◦ at the zero-dispersion end of the bending magnets, a remarkably simple result is obtained: The lowest possible emittance is achieved for

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Fig. 10 Beta functions βx,y (s) and dispersion D(s) in one unit cell of a Chasman-Green lattice, comprising two bending magnets and five quadrupoles arranged in three “families”: Q1 and Q3 focus the beam horizontally, Q2 vertically

 β◦ = 2 3/5 L = 1.549 L

and

√ β◦ = −2 15 = −7.746 ,

(16)

where L is the length of each bending magnet and the emittance scales approximately as  3 L , εx ∼ R

(17)

that is, a low emittance is achieved by using many magnets with small bending angle rather than few strong ones. In practice, the values of Eq. 16 are not used because they result in an extremely large chromaticity, but the emittance achieved with other values is only slightly larger. The result of Eq. 17 implies a lower emittance for larger storage rings with large bending radii and a large number of DBA cells. A world record value of εx = 1 nm rad was achieved in 2009 when the 2.3-km PETRA ring in Hamburg, Germany, was converted to a synchrotron light source. However, as already noted in the 1990s (Joho et al. 1994; Einfeld et al. 1995), the emittance can be further reduced by increasing the number of dipoles within each achromat resulting in a lower overall dispersion. A few facilities, namely, the ALS in Berkeley, USA, and the SLS in Villigen, Switzerland, have adopted a triple-bend achromat (TBA), from which an emittance reduction by 0.66 compared to a DBA ring with the same number of dipoles can be expected (Lee 1996). Employing a multi-bend achromat (MBA) with even more dipoles was not attempted until recently when MAX IV in Lund, Sweden, was commissioned (Tavares et al. 2014). Figure 11 shows the optical functions of BESSY in Berlin, Germany, a typical third-generation light source, and of MAX IV.

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Fig. 11 Optical functions of two DBA cells of BESSY in Berlin, Germany, (top) and one MBA cell of MAX IV in Lund, Sweden (bottom): horizontal beta function (red), vertical beta function (blue), rescaled dispersion (black). Dipole magnets are shown in yellow, quadrupoles in green, sextupoles are not shown. (MAX IV data: courtesy S. C. Leemann, J. Breunlin)

Further minimization of H in the numerator of Eq. 13 is achieved by a longitudinal variation of the magnetic field in bending magnets (Guo and Raubenheimer 2002; Nagaoka and Wrulich 2007). In the denominator of Eq. 13, the so-called horizontal partition number 1 − D can be increased by using magnets with a combined dipole and quadrupole field. Both ideas in combination with an MBA lattice are included, for example, in the upgrade plan of the ESRF in Grenoble, France (Revol et al. 2018). Yet another option is to include dipole magnets with opposite bending angle (Streun 2014). In some facilities (e.g., PETRA III), the emittance is further reduced by producing additional radiation in so-called damping wigglers. Wigglers and other insertion devices are described in the next section.

Insertion Devices Synchrotron radiation from bending magnets is limited in several ways. Since the radiation is emitted in a wide fan tangentially to the electron orbit, only a small fraction of the photon flux can be focused onto a sample several 10 meters

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away from the source point. Furthermore, the radiation spectrum is broad, and most of its intensity is not used in experiments requiring monochromatic light. The accessible wavelength range is limited by the beam energy and the maximum magnetic field of ∼ 1.5 T in conventional magnets (see Eq. 3). In order to overcome these limitations, special magnetic structures have been developed, and an important feature of modern synchrotron light sources is to include a large number of free straight sections to accommodate these so-called insertion devices.

Wavelength Shifters and Superbends Since the critical photon energy is proportional to the magnetic field of a bending magnet (see Eq. 3), superconducting magnets can be employed to shift the photon spectrum to shorter wavelengths. Superconducting insertion devices as shown in Fig. 12 with adjacent magnets to cancel the bending angle are known as wavelength shifters. Superconducting magnets replacing conventional bending magnets within the storage ring lattice are called superbends. At the position of such a device, the beta function should be small to minimize its influence on the beam emittance. Wigglers and Undulators Wigglers and undulators consist of a large number of short dipole magnets with alternating polarity arranged along a straight line (Fig. 13). Characteristic parameters are the period length λu (the longitudinal distance between two likesign magnets) and the peak field Bˆ on the midplane axis of the device. For electromagnetic poles, the period length of undulators is usually above 10 cm. In order to reach shorter period lengths, permanent magnets (e.g., SmCo5 or Fig. 12 Wavelength shifter comprising a superconducting high-field magnet and two adjacent magnets to cancel the bending angle

Fig. 13 Wigglers and undulators with alternating magnetic poles. The period length λu is the longitudinal distance between two like-sign poles. The field on the midplane axis depends on the period length and the magnetic gap g

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Nd2 Fe14 B) are commonly used, often combined with steel poles to achieve higher field. For such a hybrid design, the maximum field can be approximated by (Brown et al. 1983)    g g ˆ 5.47 − 1.8 . B [T] = 3.33 T · exp − λu λu

(18)

Evidently, a small gap g between opposite poles allows to reach high field values. Therefore, undulator vacuum chambers often have a very small vertical aperture and thin walls, or the undulator magnets are even placed inside the vacuum vessel (Hara et al. 1998). Assuming a horizontally deflecting device, the vertical field component oscillates periodically along the beam axis according to By (s) = Bˆ sin



2π s λu

 (19)

leading to a sinusoidal beam trajectory with   2π λu K sin x(s) = s 2π γ λu

and

  2π K sin x (s) = s , γ λu 

(20)

where γ = E/(me c2 ) is the Lorentz factor and K≡

λu eBˆ 2π me c

K = 93.4 · λu [m] · Bˆ [T].

or

(21)

is a dimensionless strength parameter. For K  1, the radiation spectrum is similar to that of a bending magnet multiplied by the number of magnetic poles. In this case, the device is called a wiggler. For K of the order of 1 or smaller, the maximum angle of the trajectory in Eq. 20 does not exceed 1/γ , the typical opening angle of synchrotron radiation, and interference of radiation from different poles occurs. Such a device, called undulator, has a line spectrum with a fundamental wavelength of λ=

λu 2γ 2

 1+

K2 + γ 2 2 2

 (22)

and harmonics thereof. In forward direction at angle = 0, only odd harmonics appear. Away from the beam axis, even harmonics show up, and the radiation is redshifted, that is, the wavelength is increased by λu 2 /2. For an undulator with N periods, the linewidth is approximately given by λ 1 ≈ . λ N

(23)

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Therefore and since the opening angle of undulator radiation is proportional √ to N in each dimension, a factor of N 2 is gained in brilliance over radiation from a bending magnet. Undulator design is still an active research topic. Recent developments include superconducting undulators with period lengths of 20 mm or less (Casalbuoni et al. 2006) and cryogenic undulators (Hara et al. 2004) with permanent magnets cooled to 100 K to increase their field. Undulators for synchrotron light sources are several meters long with typically 100 periods. Despite the large forces between opposite magnets, the wavelength of a permanent magnet undulator is tuned by changing the gap g mechanically with a precision on the μm level. For free-electron lasers (see below), the total undulator length can exceed 100 m. So far, “planar” insertion devices were discussed with sinusoidal electron trajectories in their midplane producing linearly polarized light. Radiation from bending magnets contains a circular component above or below their midplane. For planar wigglers, the out-of-plane helicities cancel unless the field strength of opposite poles is different (asymmetric wigglers). A much larger degree of circular polarization is achieved in so-called elliptical undulators with helical beam trajectories (Sasaki et al. 1994).

Synchrotron Radiation Sources Worldwide Presently, about 60 dedicated synchrotron radiation sources in more than 20 countries are in operation, and their number is still growing. Synchrotron light sources commissioned since 1992 are listed in Table 1. Ever since 1997, SPring8 in Japan has the largest beam energy with 8 GeV, and some facilities have reached a beam current of 0.5 A. The facility with the largest circumference is PETRA III at DESY in Germany, where one octant of a former e+ e− collider has been remodeled and other large storage rings may follow this example. The worldwide lowest emittence of 0.33 nm rad at MAX IV may soon be surpassed by the ongoing upgrades of other storage rings. More information on synchrotron radiation sources can be found, e.g., under www.lightsources.org.

Applications of Synchrotron Radiation Soon after their discovery, X-rays became an invaluable tool to probe the structure of condensed matter. Creating images of the shadow of an object (like the human body) is only one of many applications. The major classes of techniques are diffraction, spectroscopy, and imaging. In addition to these classical X-ray applications, the unique properties of synchrotron radiation have given rise to a number of other techniques outlined at the end of this section.

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Table 1 Synchrotron radiation sources since 1992. For ELETTRA, two operation modes are quoted; MAX IV has two rings Facility (first beam) location/country ESRF (1992) Grenoble/France ALS (1993) Berkeley/USA TLS (1993) Hsinchu/Taiwan ELETTRA (1993) Trieste/Italy PLS (1994) Pohang/Korea APS (1995) Argonne/USA MAX II (1996) Lund/Sweden DELTA (1996) Dortmund/Germany SPring8 (1997) Hyogo/Japan BESSY (1998) Berlin/Germany SLS (2000) Villigen/Switzerland ANKA (2000) Karlsruhe/Germany CLS (2003) Saskatoon/Canada SPEAR3 (2003) Stanford/USA SPS (2003) Korat/Thailand INDUS-2 (2006) Indore/India SOLEIL (2006) Gif-sur-Yvette/France DIAMOND (2006) Didcot/UK AS (2006) Melbourne/Australia

Lattice type

Circumference Beam energy [m] [GeV]

Current [mA]

Hor. emittance [nm rad]

DBA

844.0

6.0

200

4

TBA

196.8

1.9

400

4.2

DBA

120.0

1.5

360

22

DBA

259.2

2.0(2.4)

310(160) 7(9.7)

TBA

280.8

2.5

200

19

DBA

1104

7.0

100

3

DBA

90.0

1.5

280

9

triplet

115.2

1.5

130

18

DBA

1436

8.0

100

3

DBA

240.0

1.7

300

5.2

TBA

288.0

2.4

400

5

DBA

110.4

2.5

200

50

DBA

170.9

2.9

250

18

DBA

234.1

3.0

500

16

DBA

81.3

1.2

150

41

DBA

172.5

2.5

300

58

DBA

354.1

2.75

500

3.7

DBA

561.6

3.0

300

2.7

DBA

216.0

3.0

200

16 (continued)

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Table 1 (continued) Facility (first beam) location/country MLS (2008) Berlin/Germany SSRF (2008) Shanghai/China ALBA (2009) Cerdanyola/Spain PETRA III (2009) Hamburg/Germany PLS-II (2011) Pohang/Korea ASTRID 2 (2012) Aarhus/Denmark NSLS II (2012) Upton/USA MAX IV (2015) Lund/Sweden SOLARIS (2015) Krakow/Poland TPS (2015) Hsinchu/Taiwan SESAME (2017) Allan/Jordan

Lattice type

Circumference Beam energy [m] [GeV]

Current [mA]

Hor. emittance [nm rad]

DBA

48.0

0.63

200

25

DBA

432.0

3.5

300

3.9

DBA

268.8

3.0

250

4.5

FODO-DBA 2304

6.0

100

1

DBA

280.8

3.0

400

5.8

DBA

45.7

0.58

200

12

DBA

792.0

3.0

500

0.55

7BA/DBA

528.0/96.0

3/1.5

500/500 0.33/6

DBA

96.0

1.5

500

6

DBA

518.0

3.0

500

1.6

DBA

133.2

2.5

400

26

Fig. 14 X-rays scattered elastically from a crystalline sample form a diffraction pattern which contains information on its microscopic spatial structure

Diffraction Elastic scattering of X-rays from molecules, crystal lattices, or surfaces generates a diffraction pattern which can be recorded by position-sensitive devices like photographic film, drift chambers, or CCD chips (Fig. 14). Since the sample atoms

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are not excited and recoil is negligible, the wavelengths of incident and scattered radiation are the same. Neglecting multiple scattering effects, the diffraction pattern is related to the spatial structure of the scattering object. Usually, the image is enhanced by a lattice sum factor in samples with translational symmetry. Atoms in crystals form a unit cell which repeats itself, and the study of other objects (proteins, in particular) requires to arrange them in a crystal-like fashion. However, when using extremely intense radiation pulses like those generated by X-ray freeelectron lasers, diffraction images from single protein molecules will be possible (Ayyer et al. 2015). The diffraction pattern, that is, the radiation intensity as function of scattering angles, is given by the product of the lattice sum and a complex structure factor, which is directly related to the spatial electron density within a unit cell. Since only the square of this quantity is measured, the phase information of the scattered light waves is lost, but techniques have been devised to get around the phase problem and recover the spatial structure from the diffraction pattern. Spectacular successes of X-ray diffraction were, among others, the studies of deoxyribonucleic acid (Watson and Crick 1953) and the ribosome; see, e.g., Ban et al. (2000). These two examples are almost 50 years apart, and both were awarded a Nobel Prize (1962 and 2009).

Spectroscopy Another important class of applications involves photoelectric absorption of synchrotron radiation (Fig. 15). Here, an electron (photoelectron) is ejected from the atom with a certain kinetic energy, while the atom is left in an excited state. The hole

Fig. 15 Spectroscopic information is obtained by measuring the energy of photons (transmitted, reflected, or emitted by excited atoms), electrons (photoelectrons or Auger electrons) or ionized atoms of the sample

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created in an inner atomic shell is then filled by an outer-shell electron liberating energy by emitting either a photon (fluorescence) or another electron (Auger effect). Spectroscopic information can thus be gained by studying the absorption or transmission of photons as function of wavelength or by observing the spectrum of fluorescent radiation, by measuring the kinetic energies of photoelectrons, or by measuring the Auger electron spectrum. In the case of gas-phase samples, additional information can be gained from measuring the velocities of ionized atoms. The goal of a spectroscopic study may be to either study the energy levels of a particular system, to analyze the chemical content of a sample by known energy levels, or to gain spatial information. As an example of the latter case, extended X-ray absorption fine structure (EXAFS) is a well-established method to determine distances between the absorbing atom and its surroundings; see, e.g., Koningsberger and Prins (1988). When a photoelectron is liberated, the interference between the spherical wave of the outgoing electron and waves reflected by the neighboring atoms leads to wiggles in the absorption spectrum slightly above the absorption edge. These wiggles are visible in the absorption spectrum of an incident monochromatized photon beam as well as in the spectrum of photoelectrons. The distances of neighboring atoms can then be calculated from the frequency content of the respective spectra. Fluorescence spectroscopy offers a destruction-free way to analyze the chemical content of a sample which is nowadays also employed by historians and archaeologists, for example, to reveal hidden layers of a painting (Dik et al. 2008) or the composition of ancient metal artifacts (Young 2012).

Imaging In order to directly image an object, one advantage of X-rays is their large penetration depth; another is their short wavelength which translates into spatial resolution (X-ray microscopy), and yet another advantage is the strong dependence of X-ray absorption on properties like atomic number and magnetic state. The quality of images can be greatly enhanced by subtracting data taken above and below an absorption edge of particular chemical elements. One example is coronary angiography (imaging blood vessels in the vicinity of the heart) by taking pictures above and below the K edge of iodine as contrast material (Dill et al. 1998). The advantage of employing intense synchrotron radiation is that intravenous injection (rather than intra-arterial catheterization) of the contrast material is sufficient. Another imaging technique is tomography, measuring the transmission through an object from several angles and reconstructing the 3-dimensional structure (Bonse and Bush 1996). In most applications, the image contrast is provided by absorption, but phase contrast has also been successfully employed. Microscopy at short wavelengths is possible using Fresnel zone plates (Yun et al. 1999) to focus the X-rays, for example, to study the structure of wet biological samples in the “water window” (photon energy 300 to 500 eV).

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Fig. 16 The structure of a sample is imaged by recording transmitted X-rays or emitted photoelectrons passing through an electron microscope

Apart from X-rays, imaging can also be performed with photoelectrons, as sketched in Fig. 16. In PEEM (photoemission electron microscopy), a sample is illuminated with X-rays, and photoelectrons are passed through the electrostatic lenses of an electron microscope to study, for example, magnetic domains (Stöhr et al. 1993) or the chemical composition of nanostructures.

Other Applications Apart from the applications outlined so far, which constitute the bulk of experiments with X-rays and synchrotron radiation, there is a growing number of additional techniques. The following – certainly incomplete – description is meant to give a flavor of the wide range of scientific opportunities with synchrotron radiation.

Time-Resolved Studies Since synchrotron radiation is pulsed, much of what has been discussed before can be done in a time-resolved fashion. As in laser spectroscopy, time-resolved studies are usually carried out as pump-probe experiments, where the sample is “pumped,” that is, excited in some way by an intense radiation pulse (e.g., from a laser), and the subsequent X-ray pulse is used to probe the state of the sample as function of the delay between the two pulses (Chergui and Zewail 2009). By moving mirrors on the micrometer level, the arrival time of the pump pulse is conveniently controlled on the femtosecond scale. Typically, the pulse duration of synchrotron radiation is several 10 ps, but methods exist to shorten electron bunches (and thus the emitted radiation pulses) to a few picoseconds and even to generate pulses on the 100 fs

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scale. If pulses are as short as 10 fs, which can be the case in free-electron lasers, the timing jitter between the pulses is often the resolution-limiting factor.

Far-Infrared Radiation While the previous discussion was focused on short wavelength radiation, there are several synchrotron radiation sources offering coherently emitted radiation in the far-infrared (THz) regime. This radiation penetrates nonconducting materials, and its absorption coefficient is very sensitive to, for example, the water content of a sample, to different dielectric constants, and to the electric conductivity. Spectroscopy in the THz regime (e.g., Schmidt et al. 2009) addresses collective molecular states (rotation or vibration) and other “fingerprint” properties, making it relevant, for example, in security applications like the detection of explosives. There used to be a “THz gap” due to the lack of bright radiation sources which has been partially filled by laser-based techniques. Nowadays, electron storage rings with reduced bunch length can also create coherent and intense THz pulses with large bandwidth, high repetition rate, and short duration (Holldack et al. 2006; Müller and Schwarz 2016). Dedicated storage rings and linear accelerators to generate THz radiation have been proposed. Very intense and narrowband farinfrared radiation is provided by free-electron lasers. X-Ray Holography Holographic images are created by the interference of a reference wave and coherent laser light passing a sample. As usual, higher spatial resolution requires shorter wavelength. In addition to that, the idea of holography with short-wavelength radiation is attractive because it works without lenses (which are not readily available for X-rays) and preserves phase information. Holographic experiments with synchrotron radiation (Eisebitt et al. 2004) were successfully conducted employing the coherence of synchrotron light restricted in space by a pinhole and in wavelength by a monochromator – at the expense of intensity. The coherence of synchrotron light may also be improved by creating a periodic density modulation of the electron beam at the radiation wavelength. Such a modulation is an intrinsic feature of free-electron lasers. Metrology It is an outstanding property of synchrotron radiation that its intensity and spectrum, for example, from a bending magnet, can be calculated with high accuracy in the framework of classical and quantum electrodynamics once the electron energy, the beam current, and the magnetic field are known. Therefore, synchrotron radiation is ideally suited to serve as a primary standard for the calibration of radiation sources and detectors. There is a great demand for detector calibration in science and industry which the national metrology agencies (e.g., NIST in the USA or PTB in Germany) meet by employing synchrotron radiation sources. For very sensitive detectors, the radiation may even come from a single electron circulating in a large storage ring (Klein et al. 2010).

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X-Ray Lithography Micromechanical devices such as submillimeter gears, nozzles, waveguides, etc. are fabricated by X-ray lithography (Heuberger 1985), usually followed by other process steps like electroplating and molding. In the lithography process, an X-ray-sensitive photoresist is illuminated by synchrotron radiation through a patterned X-ray absorbing mask, and the exposed photoresist is subsequently etched away to form a 3-dimensional structure. The short wavelength of synchrotron radiation yields a high spatial resolution; its low angular divergence creates structures with high aspect ratios and smooth walls with a high degree of parallelism.

The New Generation Storage Rings Third-generation light sources had reached limits which were not easy to surpass. The beam current in storage rings is limited by electron-electron scattering reducing the beam lifetime, by collective instabilities, and by thermal effects. The horizontal beam emittance, the energy spread, and the bunch length are subject to the equilibrium between radiation excitation and damping. The horizontal emittance can be reduced by increasing the circumference or by adding damping wigglers. This had been taken advantage of at PETRA III in Hamburg, Germany, reaching an emittance of 1 nm rad. As stated in section “Acceleration of Electrons to Ultrarelativistic Energies,” multi-bend achromat (MBA) lattices with sub-nm emittance and circumferences of a few 100 m were already devised in the 1990s – e.g., in the case of the SLS in Villigen, Switzerland, and the CLS in Saskatoon, Canada – but were disregarded since the high demand for undulators and wigglers favored conventional DBA or TBA solutions with a large fraction of the circumference usable for these insertion devices. In the case of MAX IV, where an MBA lattice was employed for the first time, size and cost of the magnet structure were reduced by novel technologies in two ways (Ericsson and Johansson 2016): (i) The smaller beta functions and dispersion of the MBA lattice allow to use smaller magnets and a smaller vacuum vessel. The problem of the small vacuum conductance was counteracted by coating the vessel with non-evaporating getter (NEG) material, that is, the whole inner surface acts as a vacuum pump. (ii) Groups of magnet yokes were precisely machined from common steel blocks (bottom and top part) rendering tedious alignment procedures unnecessary and allowing to set up electricity and water connections prior to installation. In addition, the chromaticity (see section “Acceleration of Electrons to Ultrarelativistic Energies”)

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ξx,y

Qx,y 1 =− ≡ E/E 4π



1 k(s)βx,y ds + 4π

m(s)D(s)βx,y ds

(24)

emittance / E 2 (nm/GeV 2) beam energy E (GeV)

is harder to control in MBA lattices, since a high quadrupole strength k(s) increases the natural chromaticity (first term), while the smaller dispersion makes sextupoles with strength m(s) less effective (second term). Nonlinear effects from stronger sextupoles, on the other hand, tend to reduce the beam lifetime and injection efficiency. For MAX IV, the many years of experience with nonlinear optics and new numerical tools allowed to find a robust solution. Following the success of the MAX IV project, several laboratories are building or planning new storage rings based on MBA lattices. At the time of writing (summer 2018), the 5BA ring SIRIUS in Campinas, Brazil, is under construction (horizontal emittance εx = 250 pm rad) (Rodrigues et al. 2018), and the ESRF in Grenoble, France, is shut down for 1 year to install a new 7BA ring (εx = 140 pm rad) comprising three combined dipole/quadrupole magnets and four permanent magnet dipoles with longitudinally varying field (Revol et al. 2018). Other MBA projects are in the design phase. Figure 17 compares the horizontal emittance divided by the beam energy E squared (see Eq. 13) of MBA lattices (red symbols) and the synchrotron light sources listed in Table 1 (blue dots).

101

100

10

102

103

102

103

2

100

10–2

circumference (m) Fig. 17 Beam energy E (top) and horizontal emittance divided by E 2 (bottom) versus ring circumference for the light sources listed in Table 1 (blue). MAX IV (red dot) and other rings under construction or planned are based on MBA lattices. In the order of increasing circumference, the red circles indicate upgrades of ALS, Elettra, SLS, SOLEIL, SIRIUS, DIAMOND, ESRF, APS, SPring8, and PETRA

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The bunch length in storage rings is dictated by radiation effects as well, resulting in radiation pulses with a duration of several 10 ps. If the magnetic lattice is flexible enough, the momentum-compaction factor α = ( L/L)/( E/E) can be reduced to achieve pulses as short as 1 ps (rms) at the expense of bunch charge and emittance (Müller and Schwarz 2016). Laser-based methods allow to extract radiation from a 100-fs long “slice” within a bunch (Khan 2016). Here, the interaction with a femtosecond laser pulse in an undulator results in a periodic modulation of the electron energy. Off-energy electrons are transversely displaced, allowing to extract their radiation emitted in a second undulator using an aperture (“femtoslicing” Zholents and Zolotorev 1996). Alternatively, a small longitudinal displacement leads to a periodic density modulation (microbuncing) which gives rise to coherent emission in an undulator tuned to a harmonic of the initial laser wavelength (“coherent harmonic generation”).

Linac-Based Free-Electron Lasers The free-electron laser (FEL) was invented in the early 1970s by John Madey at the Stanford University in Palo Alto, USA (Madey 2010). It is based on stimulated emission from a beam of relativistic electrons which – in contrast to conventional lasers based on bound electrons – can be tuned continuously in wavelength. The basic process is an exchange of energy dW = −e · E · d s = −e · E · v dt

(25)

between an electron with velocity v and a co-propagating radiation pulse with an electric field E perpendicular to the direction of propagation. A nonzero dot product is enabled by the sinusoidal electron path in an undulator. This interaction modifies the electron distribution such that the radiated power at frequency ω P (ω) = P1 (ω) · Ne + P1 (ω) · Ne (Ne − 1) · g 2 (ω)

(26)

is not just given by the single-electron radiation power P1 (ω) times the number of electrons Ne (first term) as in conventional synchrotron radiation but has a strong coherent component proportional to Ne2 (second term) with a nonzero form factor g 2 (ω). Initially, low-gain FELs produced radiation from the far-infrared to near-visible range between the mirrors of an optical resonator by repeated passages of storage ring or linac beams, as shown in Fig. 18a. In the year 2000, a high-gain FEL generated VUV radiation by a single passage of electrons through a long undulator (Andruszkow et al. 2000): TTF at DESY in Hamburg, Germany (now known as the FLASH facility). A single passage – Fig. 18b, c – is required for short wavelengths at which mirrors with sufficient reflectivity do not exist, which in turn demands a fast increase of radiation power along the undulator. This high-gain condition is fulfilled in electron linacs with high peak current and small emittance. The first

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Fig. 18 Low-gain FELs are either oscillators (a), where a radiation field builds up between mirrors while a train of electron bunches passes through an undulator. In high-gain FELs, a single bunch passes through a long undulator with radiation staring from noise (b) or from an external source (c)

hard-X-ray FEL was LCLS at SLAC in Menlo Park, USA, (Emma et al. 2010) in 2009, producing radiation at a wavelength of 1.5 Å with a peak brilliance exceeding that of conventional synchrotron light sources by nine orders of magnitude. This large factor is partly accomplished by the coherent emission of photons and partly due to a reduction in bunch length and beam emittance. In linear accelerators, the emittance is given by the electron source and – if care is taken to avoid space-charge effects – decreases during acceleration by 1/γ with γ being the Lorentz factor. In this context, the “normalized” emittance εn = ε γ is usually quoted. With εn = 0.5 μm rad as an example and the beam energy of LCLS (16.5 GeV or γ = 3.2·104 ), the absolute emittance would be ε = εn /γ = 15 pm rad, which is significantly smaller than in storage rings. Electron bunches of short duration, and thus high peak current, are provided by a pulsed source, usually a photocathode inside an RF resonator, and further shortening is accomplished by a combination of energy “chirp” (energy variation along the bunch) and dispersive sections with energy-dependent path lengths (so-called bunch compressors). This way, bunch lengths of the order of 10 to 100 fs are achieved. The form factor g 2 (ω) responsible for coherent emission in Eq. 26 is generated by micro-bunching, that is, by modulating the electron density with the periodicity of the radiation wavelength. Most high-gain FELs are based on the SASE (selfamplified spontaneous emission) principle (Kondratenko and Saldin 1980) where spontaneous radiation in the first part of a long undulator acts back on the emitting electrons by periodically modulating their kinetic energy. As these off-energy electrons proceed in the undulator, the electrons with lower energy follow a longer trajectory and fall behind while those with higher energy catch up. This process

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initiates a density modulation which gives rise to coherent emission of radiation, which in turn enhances the modulation. The result of this positive feedback loop is an exponential increase of radiation intensity along the undulator. The distance over which the radiation power increases by Euler’s number is called gain length, in the 1-dimensional theory given by 1 Lg = √ 3



2ε0 γ 3 me c2 λu π K 2 e2 ne

1/3 (27)

with the electron density ne and the other symbols as defined above. The gain length is significantly increased by 3-dimensional effects (Schmüser et al. 2014), hence the requirement of small beam emittance. The FEL process saturates after typically 20 gain lengths when the maximum achievable density modulation is reached. As listed in Table 2, six high-gain FELs based on the SASE process are presently in user operation, and others have been proposed. However, since the amplified radiation starts from noise, the pulses exhibit unwanted fluctuations in intensity as well as in temporal and spectral shape. An alternative route is to “seed” a short wavelength FEL with well-defined radiation pulses, as sketched in Fig. 18c. Starting from laser systems with near-visible wavelengths, different strategies were recently pursued. When intense laser pulses are focused into a gas, the interaction with atomic electrons gives rise to high harmonics which can be used to directly seed an FEL at a short wavelength. Direct seeding has been demonstrated down to a wavelength of 38 nm (Ackermann et al. 2013) but has not reached the stability required for user operation. Alternatively, seeding with a longer wavelength leads to an electron density modulation which allows for coherent emission at harmonics of the seed wavelength. This high-gain harmonic generation (HGHG) scheme (Yu et al. 2000) is employed at the FEL user facilities FERMI near Trieste, Italy, (Allaria et al. 2012) and DCLS in Dalian, China (Wang 2017). While HGHG

Table 2 High-gain FELs producing ultraviolet or X-ray radiation in user operation. These facilities are either based on self-amplified spontaneous emission (SASE) or on external seeding (HGHG, EEHG) Facility (first beam) location/country FLASH (2000) Hamburg/Germany LCLS (2009) Menlo Park/USA FERMI (2010) Trieste/Italy SACLA (2011) Hyogo/Japan PAL-FEL (2016) Pohang/Korea SwissFEL (2016) Villigen/Switzerland DCLS (2016) Dalian/China European XFEL (2017) Hamburg/Germany

Max. beam energy Min. wavelength FEL type [GeV] [nm] SASE 1.2 4 SASE 16.5 0.15 HGHG, EEHG 1.5 4 SASE 8.0 0.1 SASE 10 0.1 SASE 5.8 0.1 HGHG 0.3 50 SASE

17.5

0.1

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reaches roughly the 10th harmonic of the seed wavelength, a double-seeding scheme known as echo-enabled harmonic generation (EEHG) (Stupakov 2009) has been tested at several linac facilities. Presently, the generation of the 75th harmonic has been demonstrated (Hemsing et al. 2016), and the shortest observed wavelength is 2.6 nm (Ribiˇc et al. 2019). Yet another method is “self seeding.” Here, radiation from a SASE FEL is monochromatized and seeds a downstream FEL section. This scheme has first been demonstrated for hard X-rays (Amann et al. 2012) and later in the soft X-ray regime, both at LCLS. Using normal-conducting linacs, the repetition rate of an FEL is restricted to the order of 100 Hz. The recently commissioned European XFEL in the Hamburg, Germany, region is the first superconducting hard-X-ray FEL with a rate of up to 27,000 pulses per second (Madsen and Sinn 2017). In summary, pioneering work has been done in the last two decades to establish a new type of short-wavelength sources with unprecedented properties.

Energy Recovery Linacs With electrons circulating in a storage ring, a beam current of several 100 mA can be obtained which is out of the question for linacs: generating a beam with a current of 100 mA at 3 GeV, for example, would require a DC power of 300 MW. Another advantage of storage rings is that they are multiuser facilities, delivering radiation to many beamlines simultaneously. On the other hand, the equilibrium emittance and bunch length in a storage ring are much larger than what can nowadays be obtained with a low-emittance electron gun and a linac. Using a superconducting accelerating structure, the principle of energy recovery as outlined in section “Superconducting Linacs and Energy Recovery” allows to generate bunches with small emittance and short duration at a high repetition rate for multiple users. Energy recovery linacs (ERLs) to drive infrared FELs are already employed, for example, at the Jefferson Laboratory in Newport News, USA, accelerating 10 mA of beam current to 160 MeV (Hall et al. 2015). ERL-driven X-ray sources do not yet exist, but R&D to this end is underway, for example, at KEK in Tsukuba, Japan, and the Cornell University in Ithaca, USA (Bilderback et al. 2009). According to their conceptual designs, these ERLs will be similar to storage rings but with two orders of magnitude higher brightness, better transverse coherence, and much shorter pulse duration.

Conclusions At the time of writing, more than 120 years after Röntgen’s discovery, for which he was awarded the very first Nobel prize in physics (1901), research with X-rays is still undergoing a rapid and exciting development. Many synchrotron light sources based on storage rings exist worldwide as workhorses for a large number

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of applications in physics, chemistry, biology, and material sciences with steadily improving experimental techniques. Even though the technology of storage rings seemed to be mature, the new paradigm of MBA lattices is presently leading to a significant step toward truly diffraction-limited light sources. Advances in accelerator technology have led to another type of radiation source. Free-electron lasers (FELs) can deliver pulses of extreme brilliance and ultrashort duration, opening up new scientific opportunities such as snapshots of the structure of single proteins with femtosecond resolution. As a first hard-X-ray FEL, LCLS at SLAC was commissioned in 2009, and others have followed. Another challenging and not yet demonstrated technology is that of ERL-based X-ray sources. Their properties will be somewhere between those of storage rings and FELs, addressing scientific questions for which the peak power of FELs is too extreme or the pulse rate too low. It can be expected that these different types of accelerator-based radiation sources (storage rings, FELs, ERLs, and maybe others yet to be invented) will coexist, serving complementary classes of experiments. Finally, first attempts to generate synchrotron radiation with electrons from “table-top” laser-plasma accelerators have been successful (Fuchs et al. 2009). While these novel accelerators are still in their infancy with strong shot-to-shot variation in energy and bunch charge, there has been significant progress over the last decade, and one of the long-term goals is to build table-top (or at least roomsize) synchrotron light sources and FELs.

Cross-References  Accelerators for Particle Physics  Interactions of Particles and Radiation with Matter

References Ackermann S et al (2013) Generation of coherent 19- and 38-nm radiation at a free-electron laser directly seeded at 38 nm. Phys Rev Lett 111:114801 Aiba M, Boege M, Milas N, Streun A (2012) Ultra low vertical emittance at SLS through systematic and random optimization. Nucl Instrum Methods A 694:133 Allaria E et al (2012) Highly coherent and stable pulses from the FERMI seeded free-electron laser in the extreme ultraviolet. Nat Photonics 6:699 Amann J et al (2012) Demonstration of self-seeding in a hard-X-ray free-electron laser. Nat Photonics 6:693 Andruszkow J et al (2000) First observation of self-amplified spontaneous emission in a freeelectron laser at 109 nm wavelength. Phys Rev Lett 85:3825 Ayyer K et al (2015) Perspectives for imaging single protein molecules with the present design of the European XFEL. Struct Dyn 2:041702 Balewski K (2010) Commissioning of PETRA III, Proceedings of the International Particle Accelerator Conference, Kyoto, p 1280. www.jacow.org Ban N et al (2000) The complete atomic structure of the large ribosomal subunit at 2.4 angstrom resolution. Science 289:905

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Bilderback DH et al (2009) Energy recovery linac (ERL) coherent hard X-ray sources. New J Phys 12:035011 Bonse U, Bush F (1996) X-ray computed microtomography using synchrotron radiation. Prog Biophys Mol Biol 66:133 Brown G et al (1983) Wiggler and undulator magnets – a review. Nucl Instrum Methods 208:65 Casalbuoni S et al (2006) Generation of X-ray radiation in a storage ring by a superconductive cold-bore in-vacuum undulator. Phys Rev Spec Top Accel Beams 9:010702 Chao AW (1993) Physics of collective beam instabilities in high energy accelerators. Wiley, New York Chasman R, Green GK, Rowe EM (1975) Preliminary design of a dedicated synchrotron radiation facility. IEEE Trans Nucl Sci 22:1765 Chergui M, Zewail AH (2009) Electron and X-ray methods of ultrafast structural dynamics: advances and applications. ChemPhysChem 10:28 Coolidge WD (1913) U.S. Patent 1,203,495 (application filed 1913) Dik J et al (2008) Visualization of a lost painting by Vincent van Gogh using synchrotron radiation based X-ray fluorescence elemental mapping. Anal Chem 80:6436 Dill T et al (1998) Intravenous coronary angiography with synchrotron radiation. Eur J Phys 19:499 Einfeld D, Schaper J, Plesko M (1995) Design of a diffraction limited light source (DIFL). In: Proceedings of the 1995 particle accelerator conference, Dallas, p 177. www.jacow.org Eisebitt S et al (2004) Lensless imaging of magnetic nanostructures by X-ray spectro-holography. Nature 432:885 Elder FR, Gurewitsch AM, Langmuir RV, Pollock HC (1947) Radiation from electrons in a synchrotron. Phys Rev 71:829 Emma P et al (2010) First lasing and operation of an ångstrom-wavelength free-electron laser. Nat Photonics 4:641 Ericsson M, Johansson M (2016) Integrated multimagnet systems. In: Jaeschke EJ, Khan S, Schneider JR, Hastings JB (eds) Synchrotron light sources and free-electron lasers. Springer, Cham, p 461 Feikes J et al (2011) Metrology light source: the first electron storage ring optimized for generating coherent THz radiation. Phys Rev Special Topics Accel Beams 14:030705 Fuchs M et al (2009) Laser-driven soft-X-ray undulator source. Nat Phys 5:826 Guo J, Raubenheimer T (2002) Low emittance e+ e− storage rings using bending magnets with longitudinal gradient’. In: Proceedings of the 2002 European Particle Accelerator Conference, Paris, p 1136. www.jacow.org Hall CC et al (2015) Measurement and simulation of the impact of coherent synchrotron radiation on the Jefferson Laboratory energy recovery linac electron beam. Phys Rev Spec Top Accel Beams 18:030706 Hara T et al (1998) In-vacuum undulators of SPring-8. J Synchrotron Rad 5:403 Hara T et al (2004) Cryogenic permanent magnet undulators. Phys Rev Spec Top Accel Beams 7:050702 Hemberg O, Otendal M, Hertz HM (2003) Liquid-metal jet anode electron-impact X-ray source. Appl Phys Lett 83:1483 Hemsing E et al (2016) Echo-enabled harmonics up to the 75th order from precisely tailored electron beams. Nat Photonics 10:512 Heuberger A (1985) X-ray lithography with synchrotron radiation. Z Phys B Condensed Matter 61:473 Holldack K et al (2006) Femtosecond terahertz radiation from femtoslicing at BESSY. Phys Rev Lett 96:054801 Hubert N et al (2009) Global orbit feedback systems down to DC using fast and slow correctors. In: Proceedings of the DIPAC 2009, Basel, p 27. www.jacow.org Ishikawa T et al (2012) A compact X-ray free-electron laser emitting in the sub-angstrom regime. Nat Photonics 6:540 Joho W, Marchand P, Rivkin L, Streun A (1994) Design of a Swiss Light Source (SLS), In: Proceedings of the 1994 European Particle Accelerator Conference, London, p 627. www.jacow.org

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Kamitsubo H (1997) First commissioning of SPring-8. In: Proceedings of the 1997 Particle Accelerator Conference, Vancouver, p 6. www.jacow.org Khan S (2006) Collective phenomena in synchrotron radiation sources. Springer, Berlin Khan S (2016) Ultrashort pulses from synchrotron radiation sources. In: Jaeschke EJ, Khan S, Schneider JR, Hastings JB (eds) Synchrotron light sources and free-electron lasers. Springer, Cham, p 51 Klein R, Thornagel R, Ulm G (2010) From single photons to milliwatt radiant power – electron storage rings as radiation sources with high dynamic range. Metrologia 47:R33 Kondratenko AM, Saldin EL (1980) Generation of coherent radiation by a relativistic electron beam in an ondulator. Part Accel 10:207 Koningsberger DC, Prins R (1988) X-ray absorption: principles, applications, techniques of EXAFS, SEXAFS and XANES. Wiley, New York Laclare JL (1993) Commissioning and performance of the ESRF, Proceedings of the 1993 Particle Accelerator Conference, Washington, p 1427. www.jacow.org Lee SY (1996) Emittance optimization in three- and multiple-bend achromats. Phys Rev E 54: 1940 Leemans WP et al (2014) Multi-GeV electron beams from capillary-discharge-guided subpetawatt laser pulses in the self-trapping regime. Phys Rev Lett 113:245002 Madden RP, Codling K (1963) New autoionizing atomic energy levels in He, Ne, and Ar. Phys Rev Lett 10:516 Madey JMJ (2010) Invention of the free electron laser. In: Chao AW, Chou W (eds) Review of accelerator science and technology, vol 3. World Scientific, p 1 Madsen A, Sinn H (2017) Europe enters the extreme X-ray era. CERN Courier 57(6):19 Martin MM (1988) Daresbury SRS. Sync Rad News 1:3:14 Müller A-S, Schwarz A (2016) Accelerator-based THz radiation sources. In: Jaeschke EJ, Khan S, Schneider JR, Hastings JB (eds) Synchrotron light sources and free-electron lasers. Springer, Cham, p 83 Nagaoka R, Wrulich A (2007) Emittance minimisation with longitudinal dipole field variation. Nucl Instrum Methods A 575:292 Ohkuma H (2008) Top-up operation in light sources. Proceedings of the 2008 European Particle Accelerator Conference, Genova, p 36. www.jacow.org Revol J-L et al (2018) Status of the ESRF-extremely brilliant source project. In: Proceedings of the 2018 International Particle Accelerator Conference, Vancouver, p 2882. www.jacow.org Ribiˇc PR et al (2019) Coherent soft X-ray pulses from an echo-enabled harmonic generation freeelectron laser, Nat Photonics 13:555 Rodrigues ARD et al (2018) SIRIUS light source status report. In: Proceedings of the 2018 international particle accelerator conference, Vancouver, p 2886. www.jacow.org Röntgen WC (1895) Ueber eine neue Art von Strahlen (Vorläufige Mittheilung). In: Sitzungsberichte der Würzburger Physik.-Medic.-Gesellschaft Sasaki S et al (1994) First observation of undulator radiation from APPLE-1. Nucl Instrum Methods A 347:87 Schmidt DA et al (2009) Rattling in the cage: ions as probes of sub-picosecond water network dynamics. J Am Chem Soc 131:18512 Schmüser P, Dohlus M, Rossbach J, Behrens C (2014) Free-electron lasers in the ultraviolet and X-ray regime. Springer International Publishing, Cham Shintake T (2003) Real-time animation of synchrotron radiation. Nucl Instrum Methods A 507:89; The program Radiation2D 2.0 can be downloaded from http://www-xfel.spring8.or.jp Stöhr J et al (1993) Element-specific magnetic microscopy with circularly polarized light. Science 259:658 Streun A (2014) The anti-bend cell for ultralow emittance storage rings. Nucl Instrum Methods A 737:148 Stupakov G (2009) Using the beam-echo effect for generation of short-wavelength radiation. Phys Rev Lett 102:074801 Tavares PF, Leemans SC, Sjöström M, Andersson Å (2014) The MAX IV storage ring project. J Synchrotron Rad 21:862

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Teytelman D (2016) Coupled-bunch instabilities in storage rings and feedback systems. In: Jaeschke EJ, Khan S, Schneider JR, Hastings JB (eds) Synchrotron light sources and freeelectron lasers. Springer, Cham, p 605 Tigner M (1965) A possible apparatus for electron clashing-beam experiments. Il Nuovo Cimento 37:1228 Wang G (2017) Commissioning of the Dalian coherent light source. In: Proceedings of the 2017 Particle Accelerator Conference, Copenhagen, p 2709. www.jacow.org Watson JD, Crick FHC (1953) A structure for deoxyribose nucleic acid. Nature 171:737 Wille K (2001) The physics of particle accelerators. An introduction. Oxford University Press, Oxford Young ML (2012) Archaeometallurgy using synchrotron radiation: a review. Rep Prog Phys 75:036504 Yu L-H et al (2000) High-gain harmonic-generation free-electron laser. Science 289:932 Yun W et al (1999) Nanometer focusing of hard X-rays by phase zone plates. Rev Sci Instrum 70:2238 Zholents AA, Zolotorev MS (1996) Femtosecond X-ray pulses of synchrotron radiation. Phys Rev Lett 76:912

Further Reading Wiedemann H (2007) Particle accelerator physics. Springer, Berlin Wiedemann H (2003) Synchrotron radiation. Springer, Berlin Duke PJ (2000) Synchrotron radiation. Oxford University Press, Oxford Als-Nielsen J, McMorrow D (2001) Elements of modern X-ray physics. Wiley, New York Attwood D (1999) Soft X-rays and extreme ultraviolet radiation. Cambridge University Press, Cambridge Pietsch U, Holy V, Baumbach T (2004) High-resolution X-ray scattering: from thin films to lateral nanostructures. Springer, Berlin Schmüser P, Dohlus M, Roßbach J, Behrens C (2014) Free-electron lasers in the ultraviolet and X-ray regime. Springer International Publishing, Cham Falta J, Möller T (eds) (2010) Forschung mit Synchrotronstrahlung (in German). Vieweg+Teubner, Wiesbaden Jaeschke EJ, Khan S, Schneider JR, Hastings JB (eds) (2016) Synchrotron light sources and free-electron lasers. Springer, Cham

9

Calibration of Radioactive Sources Dirk Arnold, Karsten Kossert, and Ole Jens Nähle

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Radioactive Decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Alpha Decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Beta- Decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Beta+ Decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Electron Capture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gamma Decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Internal Conversion (IC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Activity Standards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Decay Counting Methods for Primary Activity Standardization . . . . . . . . . . . . . . . . . . . . . . . Other Methods for Primary Activity Standardization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Secondary Methods for the Calibration of Activity Standards . . . . . . . . . . . . . . . . . . . . . . . . . International Comparability of Activity Standards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract Detector systems for the measurement of radioactivity in various fields of applications need to be calibrated in terms of efficiency by means of radioactive sources of a given radionuclide with known activity. It is the task of national metrology institutes (NMIs) and other calibration laboratories to provide corresponding activity standards which are required in nuclear medicine, environmental radioactivity, industry, and several other research areas.

D. Arnold () · K. Kossert · O. J. Nähle Physikalisch-Technische Bundesanstalt (PTB), Braunschweig, Germany e-mail: [email protected]; [email protected]; [email protected] © Springer Nature Switzerland AG 2021 I. Fleck et al. (eds.), Handbook of Particle Detection and Imaging, https://doi.org/10.1007/978-3-319-93785-4_9

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This chapter describes important methods for primary and secondary activity standardization as well as ways to establish the traceability to primary standards and an international comparability of activity standards.

Introduction Our known world consists of more than 100 different elements. In one of the last issues of the Chart of Nuclides (Magill et al. 2018), more than 4000 nuclides are listed; most of them are radioactive, and only about 10% of them are stable. Most of the radionuclides are short lived and do practically not occur in nature. But about 100 to 200 radionuclides are of interest for research, for medical or industrial applications or in the field of radiation protection and the surveillance of the environment. All these radionuclides have their individual decay parameters. Particle and photon emissions with different energies and emission probabilities as well as half-lives are characteristic for each radionuclide. Therefore, it is necessary to calibrate and provide radioactive standards for a large number of different radionuclides. Due to the large variety of different decay schemes, the methods for the measurement of activity are quite different. They can be divided into secondary and primary methods. A secondary measurement device needs to be calibrated with an activity standard in order to measure the activity of another source of the same radionuclide. In other words, the efficiency of the instrument for the detection of gamma rays and alpha and beta particles must be determined. Typical secondary measurement devices are germanium detectors and scintillation detectors based on NaI(Tl) crystals or ionization chambers. Primary measurement devices do not require activity standards in order to be calibrated. The efficiency of such devices is either known to be 100% or can be determined by measurement of other physical quantities than activity (e.g., from dimensional quantities for a defined solid angle detector), or a method is used where the knowledge of the efficiency is not required. In these cases, only some basic decay parameters of the radionuclide under study must be known in order to determine the activity of a radioactive source. The description of calibration methods in this chapter of the handbook sets its focus to those methods that measure the photons or particles produced within the radioactive decay. Since the number of decaying atoms is related to the number of existing atoms, also methods measuring the number of atoms, e.g., based on mass spectrometry, can be used to determine the activity. However, such methods are not explained in detail in this chapter. Primary methods are typically established at NMIs worldwide. A major task of the NMIs is to establish the traceability and international comparability of standards. Already in 1875, the “Convention of the Meter” was signed by representatives of 17 nations, and the International Bureau of Weights and Measures (BIPM) was founded. The BIPM together with the NMIs is responsible for the equivalence between the national measurement standards and leads to the comparability of the

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calibration of a radioactive source in, e.g., the United States with calibrations in Europe or Japan.

Radioactive Decay The radioactive decay of a nuclide is the phenomenon of the spontaneous conversion of one nuclide into a nuclide of another type. The primary significance of radioactive decay is the disappearance of the original nuclide. The radiations accompanying the decay in the form of photons and particles are characteristic for the decay of the various nuclides of different types and may help to identify special decay paths. Strictly speaking, the activity A(t) of an amount of a nuclide in a specified energy state at a given time t is the expectation value, at that time, of the number dN(t) of spontaneous nuclear transitions in a time interval dt from that energy state: A(t) = −

dN(t) = λN(t) dt

(1)

where λ is a constant. By this definition, zero activity would be equivalent to stability of the nuclide (NCRP 1985). The derived SI-unit (International System of Units) of the activity is the becquerel (Bq). One Bq is one decay per second. It can be shown (Evans 1955) that the decay constant λ is related to the characteristic mean life τ of a radionuclide by τ = 1/λ, which in turn can be expressed by the half-life of that radionuclide T1/2 (see contribution by C. Grupen) by: λ=

ln 2 T1/2

(2)

There exist several different possibilities to release the excess energy during a radioactive decay depending on the number of protons Z and the mass number A of the radionuclide X. Due to the conversion, charged particles, neutrinos, neutrons, gamma rays, or X-rays could be produced and emitted. The main disintegration types are the following.

Alpha Decay A ZX

−4 4 →A Z−2 Y + 2 He

with the special name α-particle for the emitted helium nucleus with a+2 charge (missing its two electrons). The helium nucleus carries two protons and two neutrons. Consequently, the mass number A of the remaining nucleus is reduced by 4, and the atomic number Z is reduced by 2. Typically there are not only one

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but several alpha-transitions of different energy to the daughter nuclide possible. Therefore α-particles with different but discrete energies could be emitted.

Beta- Decay A ZX

→ Z+1A Y + e− + ν e

with the special name β-particle for the emitted electron. In the beta- decay, a neutron in the nucleus is converted into a proton, an electron, and an electron antineutrino. Due to the fact that the decay energy is shared between the electron and the electron antineutrino, the emitted electrons do not have the same discrete energy but show a continuous energy spectrum which is characteristic for a specific nuclide.

Beta+ Decay A ZX

→ Z−1A Y + e+ + νe

In the beta+ decay, a proton in the nucleus is converted into a neutron, a positron, and an electron neutrino. The considerations made for the energy of the emitted particles in beta− decay apply analogously.

Electron Capture A ZX

+ e− → Z−1A Y + νe

The electron capture is another type of beta decay. An electron from the atomic shell (mainly from the inner shell) is captured, and a proton in the nucleus is converted into a neutron and an electron neutrino. After an electron-capture process, the atom Y has a vacancy in its atomic shell. The subsequent atomic rearrangement process leads to the ejection of Auger electrons and X-rays. The abovementioned decay modes change the number of protons and the number of neutrons in the nucleus. Often, the nucleus Y resulting from the decay modes ∗ above is not in his ground state but in an excited state. The excited state Y can reach the ground state Y in several ways. One is the gamma decay.

Gamma Decay A ∗ ZY

→A ZY + γ

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where the emitted gamma ray has the transition energy (difference between ∗ energy levels). Due to the fact that the exited states Y have discrete and nuclide characteristic energy levels, the emitted gamma rays have also discrete energies and can be used to identify a radionuclide. ∗ Another possibility for the transition from the excited state Y to the ground state Y is the internal conversion (IC).

Internal Conversion (IC) A ∗ ZY

− →A ZY + e

with the emission of an electron from the atomic shell. Again, this process leads to an atom Y with a vacancy in its atomic shell. Hence, an atomic rearrangement process is following which leads to the ejection of Auger electrons and X-rays similar as after electron capture. The deexcitation from an excited state to the ground state via a gamma transition or an IC transition can also go via one or more intermediate states. Often various pathways are possible, leading to a complex decay scheme with gamma ray and IC electron emission of various energies. Since the IC electrons are monoenergetic, they are often used as calibration sources. The listed decay modes are the main modes relevant for the calibration of activity standards. In some cases, radionuclides can decay by more than one mode. Radionuclides decaying by beta+ transition can also have an electron-capture branch. In some case (e.g., 64 Cu), even three decay modes are possible. Another decay mode is the spontaneous fission which can occur in the case of nuclei with a high mass number. In this case, the nucleus decays into two daughter nuclei and two or three neutrons. This decay mode has, however, a low probability compared to other disintegration types. It should be noted that most radionuclides do not decay directly to a stable state but to other radionuclides. Hence, a decay can undergo a series of disintegrations until eventually a stable nuclide is reached.

Activity Standards One major task of national metrology institutes (NMIs) is the realization, conservation, and dissemination of the physical units. As part of this task, the NMIs hold the national measurement standards. The national measurement standard (JCGM 200 2012) stands at the top of a calibration hierarchy followed by reference measurement standards and working measurement standards typically used in a laboratory for the calibration or verification of a measuring instrument. A main feature of such a calibration hierarchy is that the measurement uncertainty necessarily increases along the sequence of calibrations.

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For the dissemination of the unit of the physical quantity “activity,” the NMIs produce activity standards traceable to their national measurement standards. Depending on the physical and chemical properties of the elements and the requirements of customers, radioactive standards are produced in various forms, as solid, liquid, or gaseous sources in different geometries as point sources, as extended sources with small or large areas, or as volume sources of various sizes. The large variety of different types of radioactive standards is caused by the needs of the customers to calibrate their measurement instruments in the same geometry and with the same source composition as the source under investigation where the activity needs to be determined. In many cases, the preparation of activity standards starts with a radionuclide solution produced in a nuclear reactor or at an accelerator facility by activation of inactive material with neutrons or charged particles. Typically, the high activity of such a solution is quantitatively diluted in one or more steps using dedicated and calibrated balances. A dilution scheme is established to obtain an activity concentration (activity divided by mass of solution) suitable to prepare sources as required for different measurement devices in order to determine the activity (Sibbens and Altzitzoglou 2007) and in parallel also to produce sources which meet the needs of users for their special measurement arrangements. From a master solution, dozens of daughter solutions could be produced. The major advantage is that the activities of all sources produced from the same master solution can be linked due to the quantitative mass measurements. It is a common approach that several different primary and secondary calibration methods are combined to determine the activity of the set of sources that originates from the same master solution. In this way, the gravimetrically determined dilution factors can be verified, and the whole dilution scheme is checked for consistency. Figure 1 shows a selection of typical calibration standards from a national metrology institute as volume, area, and point sources. The radioactive solutions in the ampoules or in the Kautex bottle can be quantitatively diluted and transferred to any customer-specific laboratory container like, e.g., a Marinelli beaker. Point sources and extended area sources are produced by deposition of weighed aliquots of a radioactive solutions on a source carrier. The area sources shown in the picture are adapted to the size of filters used, e.g., for the measurement of radioactive releases to the air from nuclear power plants.

Decay Counting Methods for Primary Activity Standardization Primary measurement devices (Pommé 2007) do not require activity standards in order to be calibrated. That means that the efficiency of the system can be determined by measurements of other physical quantities than activity. As an example, the geometrical efficiency of a defined solid angle spectrometer can be calculated from measurements of its geometrical dimensions. Depending on the radiation emitted during the decay of a specific radionuclide, different highefficiency counting systems named as 4π counting systems exist.

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Fig. 1 Examples of different types of calibration standards (PTB 2018)

For the measurement of alpha or pure beta particle-emitting radionuclides, a system often used is the 4π proportional counter. Specially designed thin sources with negligible self-absorption are placed in the center of a gas-filled proportional counter. Figure 2 shows dropped sources on a thin VYNS foil as source support. A typical counting gas of the proportional counter is P10 (a mixture of 90% Ar and 10% CH4 ). With such a system virtually 100% of the emitted radiation is detected. However, special correction methods are necessary to determine the non-efficiency and the corresponding uncertainty. For a special group of gamma ray-emitting radionuclides, 4πγ counting can be used for the calibration (Winkler and Pavlik 1983). In this case, the detector is typically a large well-type scintillation detector, e.g., NaI(Tl), with a geometrical acceptance covering a solid angle close to 4π. The method works well for multiphoton-emitting radionuclides, especially in the case that the photons are emitted in coincidence. In this case, the number of photons n emitted per decay may be larger than one, and the overall counting efficiency is given by: ε =1−

n  i=1

(1 − εi )

(3)

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Fig. 2 Specially designed thin sources with negligible self-absorption for 4πβ- and 4πα- counting as well as for 4πβ-γ coincidence counting with proportional counters

where εi is the counting efficiency for a single γ-ray with energy Ei (Ballaux 1983). In such a case, the probability for the non-detection as well as the uncertainty diminishes. Problems may occur if delayed transitions or decay branches with only one single photon emission exist. In the case that a beta decay is accompanied by a prompt gamma transition, the widely used 4πβ-γ coincidence counting method (Bobin 2007) can be used for the activity determination. In the classical approach, a 4π proportional counter for the measurement of the beta particle is combined with a NaI(Tl) detector for the measurement of the gamma ray. Figure 3 shows a schematic drawing of such a coincidence counting system. The counting rates Nβ of the 4π proportional counter and Nγ of the NaI detector are measured as well as the coincidence counting rate Nc of events in both detectors in a defined time interval. Each of the three counting rates Nβ , Nγ , and Nc is proportional to the “unknown activity” A at a given time and the respective counting efficiencies: Nβ = A · β Nγ = A · γ

(4)

Nc = A · β · γ These three equations can be combined to: A=

Nβ · Nγ Nc

(5)

where the unknown activity is defined only by the three measured counting rates. The coincidence counting system has the advantage that the activity of the radioactive source is determined without any explicit knowledge of the counting efficiencies of the two detectors. However, there are requirements that limit the approach in practice. The most important is that the considerations made assume

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Fig. 3 Schematic drawing of a 4πβ-γ coincidence counting system

that the beta detector is not sensitive to gamma radiation, which obviously cannot be realized in the experiment. Compton scattering of gamma rays in the beta detector, for example, can produce a signal in the beta detector. In addition, a gamma transition can also lead to the ejection of electrons from the IC process. Thus, the three simple expressions for the counting rates have to be modified taking these processes into account: 

  Nβ = A · β + 1 − β



Nγ =  Nc = A ·

αT 1 εce + εβγ 1 + αT 1 + αT

A · γ 1 + αT

  β · γ + 1 − β · εc 1 + αT



(6) 

where α T is the total internal conversion coefficient, εce is the detection efficiency for conversion electrons in the beta detector, εβγ is the detection efficiency for gamma rays in the beta detector, and εc is the probability of observing additional coincidences from gamma rays interacting in the beta and in the gamma detector.

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The abovementioned ratio of counting rates Nβ Nγ /Nc does not give the activity directly. However, this ratio is a smooth function of the efficiency of the beta detector, and the ratio Nc /Nγ in many cases is a very good approximation of εβ . This function may be followed by a variation of the efficiency of the beta detector which can be done by successively adding different absorbers around the radioactive source or by variation of the discrimination level in the respective counting chain. From an appropriate extrapolation of the measurement results to unity in Nc /Nγ or, equivalently, to zero in the measured inefficiency (1 - Nc /Nγ ), the activity can be determined. As an example, Fig. 4. shows the result of a measurement series of a 177 Lu source. The coincidence method described above also works for α- and e+ -emitters and even for electron-capture nuclides. It should be mentioned, however, that this method can be very laborious and time-consuming in certain cases and a careful analysis of the decay scheme is a prerequisite to ensure that all decay paths are detectable in the beta detector and that the choice of threshold or window setting in the gamma channel selects suitable decay paths. Otherwise nuclide-dependent correction factors need to be taken into account, which usually require precise nuclear data and information of detector properties that quite often can be only obtained by using a Monte Carlo simulation. The 4πβ-γ coincidence counting technique can also be applied using various detector types in the beta channel. Many proportional counters are operated at ambient pressure, but counting gas can also be used with higher pressure of typically

Fig. 4 Result of a 4πβ-γ coincidence counting measurement of a 177 Lu source with a variation of the efficiency of the beta detector by adding different absorbers. The extrapolation of the fitted curve to (1-Nc /Nγ )/(Nc /Nγ ) = 0 gives the activity of the measured source

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up to 3·106 Pa. Such pressurized proportional counters have significantly higher counting efficiencies at low energies, which is important for nuclides decaying by electron capture and a subsequent gamma transition. Several laboratories make use of a liquid scintillation counter as beta counter (Bobin and Bouchard 2006). In this case, the sample preparation is usually much easier. The efficiency variation can be realized by many methods, e.g., by chemical quenching or by using neutral density filters which absorb parts of the scintillation light. The detection efficiency of gamma rays in the beta detector is significantly higher when using a liquid scintillation counter instead of a gas counter. This influences the slope and the shape of the required extrapolation and might result in higher uncertainties. On the other hand, the increased efficiency for low-energy electrons or X-rays of electron-capture decays reduces the extrapolation range. There are a number of nuclides with delayed states in the decay scheme which require a variation of dead times or coincidence resolving time of the counting channels thus increasing the measuring times needed to determine the activity. Typical radionuclides are 67 Ga and 85 Sr with half-lives of the delayed states of about 9 μs and 1 μs, respectively. One way to overcome these complications is the use of anticoincidence counting (Baerg et al. 1976), because the anticoincidence count rate is less prone to effects of delayed transitions. Especially standardization of these “difficult” nuclides benefits from a full digital approach using digitizers and data taking in list mode. For each signal in the detectors, amplitude and timestamp are recorded, and dead time and coincidence time can be varied in the offline analysis without remeasuring. Modern digitizers can be operated with more than 1 gigasample per second making sure that all signals are captured (Bobin et al. 2014). Other primary methods make use of special liquid scintillation counting (LSC) methods which are based on a theory referred to as the free parameter model (Grau Malonda 1999; Broda et al. 2007). The most important methods are the CIEMAT/NIST efficiency tracing technique and the triple-to-double coincidence ratio (TDCR) method. The latter method will be briefly explained in the following. A TDCR LS counter (Fig. 5) is equipped with three photomultiplier tubes (PMTs). Here, we assume that these PMTs have equal quantum detection efficiencies. We consider a pure beta-emitting radionuclide which emits exactly one electron per decay. Its continuous normalized beta spectrum is S(E). In this case, the counting efficiency for triple coincidences can be calculated according to E max

εT =

 −E·Q(E) 3 S(E) 1 − e 3·M dE,

(7)

0

and the counting efficiency for the logical sum of double councidences is given by E max

εD = 0

 2 3   dE, S(E) 3 1 − e−EQ(E)/3M − 2 1 − e−EQ(E)/3M

(8)

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Fig. 5 Schematic drawing of the triple-to-double coincidence ratio (TDCR) system with three photomultiplier tubes (PMT) and amplifiers around a LSC vial with the radioactive solution and the logical unit to measure triple (T) and double (D) coincidences

where M is an unknown free parameter. The function Q(E) is referred to as the ionization quenching function, which describes a nonlinear relation between the released electron energy E and the number of scintillation photons. Its computation requires information on the electron stopping power dE/dX which depends on the atomic composition of the scintillator. In principle the counting efficiencies for triple and double coincidences could be calculated from the above-stated equations, provided that the free parameter M would be known. Eventually, the free parameter of a given liquid scintillation measurement is defined by the condition εT (M) RT = , εD (M) RD

(9)

i.e., we make use of the fact that the ratio of measured net counting rates must agree with the ratio of corresponding computed counting efficiencies. The activity of the LS sample is then given by A=

RT RD = . εT εD

(10)

A great advantage of the TDCR method is that it can be used for pure beta emitters or pure electron-capture decay, where coincidence counting techniques cannot be applied. The CIEMAT/NIST efficiency tracing method is based on the same free parameter model (Grau Malonda 1999). In this case, however, systems with only two PMTs are used, and the free parameter is determined from a tracer radionuclide with known activity which is measured under the same experimental conditions. In most cases, the low-energy beta emitter 3 H is used as the tracer radionuclide.

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One advantage of both LS methods is that the source preparation is much easier compared to many other methods. The radioactive solution is directly added to a liquid scintillation cocktail, and the self-absorption in the source is negligible. The achievable measurement uncertainties are often comparable and in some cases even superior to those obtained by the classical coincidence counting method. Another method where the efficiency can be calculated is the defined solid angle (DSA) counting for alpha particle-emitting radionuclides (Pommé 2007). The alpha particle source with a typical diameter of 1 cm to 2 cm is placed in a defined distance to a diaphragm of known shape in front of a solid-state detector. The solid angle is therefore well defined by dimensional quantities, and the detection efficiency of the alpha detector is one for all alpha particles passing through the diaphragm.

Other Methods for Primary Activity Standardization In the previous section, several methods were explained which can be summarized as decay counting methods. The determination of the activity can, however, also be realized with other methods. Here, only some basic concepts are presented. When combining Eqs. 1 and 2, we can calculate the activity A at a given time t by: A=

N · ln 2 T1/2

(11)

Hence, the activity can be obtained by determining the number of atoms N of the radionuclide under study provided that the half-life T½ is known. Let us consider a given (constant) number of atoms N. From Eq. 11 we can see that the activity is inversely proportional to the half-life T½ . In other words, for very long-lived radionuclides like 40 K, the resulting activity is very low, and, in many cases, when the amount of radioactive material is limited, an activity determination by means of a counting experiment is not possible or suffering from large statistical uncertainties. In such a case, an alternative can be used to measure the number of atoms N in Eq. 11. Hence, mass spectrometry techniques are being used as supplementary tools for activity determination. Equation 11 also underlines the importance of precise and accurate nuclear decay data. The before-mentioned method to determine the activity via a determination of the number N can only lead to a precise activity determination when the half-life is known with good precision. The radioactive decay of a given radionuclide has a characteristic mean energy which allows us to make use of calorimetry. Let us assume a calorimeter (detector) which absorbs the complete energy of radiation emitted by the radioactive source. The activity A of a radioactive source contained in the calorimeter can be related to the energy (or heat) input, or calorimetric power P, by the basic relation P = A < E >,

(12)

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where is the average energy per decay for the radionuclide. The measurement principle has been extensively used for the primary activity standardization using isothermal microcalorimetry (Collé 2007). A great advantage of such a method is that it can be used for sources with very high activity, for which counting methods would suffer from dead time problems. On the other hand, most calorimetric methods cannot be used for the determination of low activities. Another requirement for such an activity determination by means of calorimetry is the knowledge of the mean energy . For a pure beta-emitting radionuclide, this requires an accurate knowledge of the beta spectrum, from which the average energy can be derived.

Secondary Methods for the Calibration of Activity Standards Most of the primary standardization methods are time-consuming and need sophisticated source preparation. Therefore, the primary methods are often supplemented by secondary methods. The workhorses in metrology institutes are ionization chambers (Schrader 2007). Reentrant pressurized ionization chambers (Fig. 6) are very stable devices, and measurements are reproducible over many years. In addition, the response of an ionization chamber shows a very good linearity with respect to the activity of the source. A standard geometry routinely used is radionuclide solutions in flame-sealed glass ampoules ensuring gas tightness and long-term source stability. The calibration factors derived from primary calibrations can be used to make secondary calibrations under the same measurement conditions. Special caution

Fig. 6 Schematic drawing of a 4π ionization chamber

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must be taken for radionuclides emitting only low-energetic radiation measured in chambers with a rather high efficiency in this energy range, because even small variations in the density of the solution or geometry of the ampoules may induce strong variations in the measured chamber response. Ionization chambers once calibrated with a specific radionuclide are used to preserve the unit of activity for that radionuclide for many years provided that a long-lived reference source is used to monitor possible changes in efficiency or aging of readout electronics. Some commercial electrometer systems tend to show a nonlinear behavior especially when the measuring range is switched due to a change in the current induced in the ionization chamber. Depending on the gas mixture in the chamber, a nuclide-specific upper limit for the activity that can be measured exists but is typically higher than a few GBq. High-purity germanium spectrometers are also widely used as secondary measurement devices for the calibration of activity standards. A set of gamma rayemitting radionuclides is used to calibrate a germanium detector over a wide energy range and to establish an energy-dependent efficiency curve. With such a calibrated detector, the activity of an unknown radioactive source can be determined. This is even possible for radionuclides which were not used for the calibration of the detector, provided that the corresponding photon energies are within the calibrated energy interval and that the photon emission probabilities are known. In addition, the germanium detector has a good energy resolution and can be used to measure not only one but several radionuclides at a time in one source. Gammaspectrometric measurements with germanium detectors are therefore a common tool to measure the “main” radionuclide and potential photon-emitting impurities at the same time. NaI(Tl) detectors are commonly used as secondary measurement devices. The cheap and easy-to-use detector systems are also used to preserve the activity unit for gamma ray-emitting radionuclides for many years. It should be noted that all secondary instruments are suited for activity measurements only if the same measurement conditions are met as for the calibration. Otherwise correction factors have to be established which allow to calculate the activity of a source from measurements under non-calibrated conditions.

International Comparability of Activity Standards A major task of the NMIs is to establish the traceability and international comparability of standards. Already in 1875 the “Convention of the Meter” was signed by representatives of 17 nations, and the International Bureau of Weights and Measures (BIPM) was founded. Based on this convention, the “Système International de Référence (SIR)” (Ratel 2007) was established at the BIPM to compare activity standards from different national metrology laboratories. The system comprises two pressurized ionization chambers. The advantage of the system is that the comparison of the result of two or more laboratories need not be done at the same time. The system measures the ionization current of a standard provided by a NMI together with the activity. The ratio of the measured ionization current to the activity provided

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by the NMI is a measure of the efficiency for the specific radionuclide of interest. These figures can be compared for a variety of radionuclides among the participating laboratories in order to define the degree of equivalence of measurements in the different countries. In 1999 the directors of the national metrology institutes of 38 member states of the BIPM and representatives of 2 international organizations signed a mutual recognition arrangement (CIPM MRA 1999) for national measurement standards and for calibration and measurement certificates issued by NMIs. A number of other institutes have signed since then. This arrangement demands a sophisticated quality management system at the national metrology institutes and a larger number of comparisons in order to validate the claims of the NMIs for their calibration and measurement capabilities (CMC 2010). In principle the NMIs are forced to perform comparison for each radionuclide. However, due to the large number of different radionuclides, a system was established that groups radionuclides together with specific measurement techniques (Karam 2007) in order to limit the number of comparisons to a smaller number. The SIR system together with the regulations of the MRA and the performed key comparisons (KCDB 2010) guarantees the comparability and equivalence of activity measurements between the national metrology laboratories worldwide. In addition the accreditation of calibration laboratories in the different countries guarantees the traceability of activity measurements to the standards of NMIs. As one result of this complex system, a customer who receives an activity standard from a calibration laboratory can retrace how different or equal the activity measurement is done for the same radionuclide in another country.

Conclusions The calibration of radioactive sources is a service offered by national metrology institutes as well as from accredited calibration laboratories. The customer receives standards with traceable activity, with reliable uncertainties, and with the confirmation that the measurement methods and results are comparable to those obtained in other countries. The usage of such radioactive standards is therefore an essential part of the quality system in research institutes. It is one main contribution in order to compare the results of research groups working in different institutes.

References Baerg AP, Munzenmayer K, Bowes GC (1976) Live-timed anti-coincidence counting with extending dead-time circuitry. Metrologia 12:77–80 Ballaux C (1983) High-efficiency γ-ray-detection systems for radionuclide metrology. Int J Appl Radiat Isot 34:493–499 Bobin C (2007) Primary standardization of activity using the coincidence method based on analogue instrumentation. Metrologia 44:S27–S31 Bobin C, Bouchard J (2006) A 4π(LS)β–γ coincidence system using a TDCR apparatus in the β-channel. Appl Radiat Isot 64:124–130

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Bobin C, Bouchard J, Thiam C, Ménesguen Y (2014) Digital pulse processing and optimization of the front-end electronics for nuclear instrumentation. Appl Radiat Isot 87:195–199 Broda R, Cassette P, Kossert K (2007) Radionuclide metrology using liquid scintillation counting. Metrologia 44:S36–S52 CIPM MRA (1999) CIPM Mutual Recognition Arrangement. http://www.bipm.org/en/cipm-mra/ CMC (2010) The BIPM database of the calibration and measurement capabilities. http://kcdb. bipm.org/appendixC/ Collé R (2007) Classical radionuclide calorimetry. Metrologia 44:S118–S126 Evans RD (1955) The atomic nucleus. McGraw-Hill Inc, New York Grau Malonda A (1999) Free parameter models in liquid scintillation counting. Colección Documentos Ciemat Grupen C. Contribution to this handbook JCGM 200 (2012) International vocabulary of metrology – basic and general concepts and associated terms (VIM), 3rd edn Karam L (2007) Application of the CIPM MRA to radionuclide metrology. Metrologia 44:S1–S6 KCDB (2010) The BIPM key comparison database. http://kcdb.bipm.org/AppendixB/KCDB_ ApB_search.asp Magill, J., Dreher, R., Sóti, Zs Karlsruher Nuklidkarte/Chart of the Nuclides, 10th edn. Nucleonica GmbH, Karlsruhe, 2018 NCRP (1985) National Council on Radiation Protection and Measurements; NCRP Report No. 58. A Handbook of Radioactivity Measurements Procedures; Bethesda Pommé S (2007) Methods for primary standardization of activity. Metrologia 44:S17–S26 PTB (2018), Activity standards., https://www.ptb.de/cms/fileadmin/internet/fachabteilungen/ abteilung_6/6.1/6.13/katalog_en.pdf Ratel G (2007) The Système international de Référence and its application in key comparisons. Metrologia 44:S7–S16 Schrader H (2007) Ionization chambers. Metrologia 44:S53–S66 Sibbens G, Altzitzoglou T (2007) Preparation of radioactive sources for radionuclide metrology. Metrologia 44:S71–S78 Winkler G, Pavlik A (1983) Some aspects of activity measurements with NaI(Tl) well-type detectors. International Journal for Applied Radiation and Isotopes 34:547–553

Radiation Protection

10

Claus Grupen

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Units of Radiation Protection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Basic Nuclear Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Basic Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Range of Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Radiation Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Particle Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Photon Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Neutron Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cosmic-Ray Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Radiation Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Safety Standards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Organization of Radiation Protection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Environmental Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Biological Effects of Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Applications of Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Medical Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Metabolism of Plutonium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Radiation-Resistant Organisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Waste Transmutation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Suppliers of Radiation-Protection Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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C. Grupen () Department of Physics, University of Siegen, Siegen, Germany e-mail: [email protected]; [email protected] © Springer Nature Switzerland AG 2021 I. Fleck et al. (eds.), Handbook of Particle Detection and Imaging, https://doi.org/10.1007/978-3-319-93785-4_10

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C. Grupen

Abstract Radiation protection is a very important aspect for the application of particle detectors in many different fields, like high-energy physics, medicine, material science, oil and mineral exploration, and arts, to name a few. The knowledge of radiation units, the experience with shielding, and information on biological effects of radiation are vital for scientists handling radioactive sources or operating accelerators or X-ray equipment. This chapter describes the modern radiation units and their conversions to older units which are still in use in many countries. Typical radiation sources and detectors used in the field of radiation protection are presented. The legal regulations in nearly all countries follow closely the recommendations of the International Commission on Radiological Protection (ICRP). Tables and diagrams with relevant information on the handling of radiation sources provide useful data for the researcher working in this field.

Introduction Radiation is everywhere. Radiation emerges from the soil, it is in the air, and our planet is constantly bombarded by energetic cosmic radiation. Even the human body is radioactive: about 9000 decays of unstable nuclei occur per second in the human body. Since the beginning of the twentieth century, mankind has been able to transform nuclei (Ernest Rutherford) and to artificially create new radioactive nuclei, in particular, since the discovery of nuclear fission in the late 1930s. Since one cannot “see” or “smell” ionizing radiation, one needs measurement devices which can detect it and also a scale by which to judge on its possible dangerous effects. This leads to the definition of units for the activity of radioactive nuclei and quantifications for the effect on humans in terms of absorbed energy and biological effectiveness of different types of radiation. Radiation protection is a truly interdisciplinary field. It concerns, among others, physicists, engineers, lawyers, and health-care professionals. Radioactivity was discovered by Henri Antoine Becquerel in 1896, when he realized that radiation emerging from uranium ores could blacken photosensitive paper. Originally it was believed that this was due to some fluorescence radiation from uranium salts. However, the photosensitive film was also blackened without previous exposure of the uranium ore to light. The radiation spontaneously emerging from uranium was not visible to the human eye. Therefore, it was clear that one was dealing with a new phenomenon. In the context of radiation protection, also the discovery of X-rays by Wilhelm Conrad Röntgen has to be mentioned. This radiation emerged from materials after bombardment with energetic electrons. Actually the discovery by Röntgen in December 1895 had been a factor of stimulating Becquerel to investigate radiation from uranium salts.

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This radioactivity was a phenomenon of the natural environment. Nobody was able to turn inactive materials into radioactive sources by chemical techniques. Not until 1934 Frederic Joliot and Irène Curie managed to produce new radioactive materials artificially using nuclear physics methods. Only a few years later, Otto Hahn and Fritz Straßmann (1938/1939) succeeded in inducing fission of uranium nuclei. The importance of radioactivity and of radiation protection for mankind and the environment is quite substantial.

Units of Radiation Protection The unit of activity is becquerel (Bq). 1 Bq is one decay per second. The old unit curie (Ci) corresponds to the activity of 1 g of radium-226: 1 Ci = 3.7 × 1010 Bq, 1 Bq = 27 × 10−12 Ci = 27 pCi.

(1)

The radioactive decay law N = N0 e−λ t

(2)

describes the decrease of nuclei in time. The decay constant λ is related to the lifetime of the radioactive source as λ=

1 . τ

(3)

One has to distinguish the half-life T1/2 from the lifetime. The half-life is the time after which a half of the initially existing atomic nuclei has decayed: N(t = T1/2 ) =

N0 = N0 e−T1/2 /τ . 2

(4)

Therefore, we have T1/2 = τ ln 2.

(5)

Correspondingly, the decay constant is related to the half-life by λ=

ln 2 1 = . τ T1/2

(6)

The activity A of a radioactive source characterizes the number of decays per second:

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A=−

d dN 1 = − (N0 e−λt ) = λ N0 e−λt = λ N = N. dt dt τ

(7)

The activity in Bq does not say very much about possible biological effects. These are related to the deposited energy by the radioactive source in matter. The energy dose (absorbed energy W per mass unit m), D=

W 1 W = m ρ V

(8)

(ρ – density, V – volume element), is measured in gray (named after the British nuclear physicist Louis Harold Gray) : 1 gray (Gy) = 1 joule (J) / 1 kilogram (kg).

(9)

Gray is related to the old unit rad (radiation absorbed dose, 1 rad = 100 erg/g, which is still in use in the United States), according to 1 Gy = 100 rad = 104 erg/g.

(10)

kg m2 g cm2 (remember: 1 joule (J) = 1 watt second (W s) = 1 s2 = 107 s2 = 107 erg) In terms of deposited energy in units popular in particle physics and medicine, one has 1 Gy = 6.24 × 1012 MeV/kg.

(11)

Gray and rad describe the pure physical energy absorption. These units cannot easily be translated into the biological effect of radiation. Electrons, for example, ionize relatively weakly, while, in contrast, α rays are characterized by a high ionization density. Therefore, biological repair mechanisms cannot be very effective in the latter case. The relative biological effectiveness depends on the type of radiation, the radiation energy, the temporal distribution of the dose, and other quantities. For the radiation field R, one obtains the dose equivalent HR from the energy dose DR according to HR = wR DR ,

(12)

where wR is the radiation weighting factor. This dose equivalent is measured in sievert (named after the Swedish physicist Rolf Maximilian Sievert) (Sv). In the same way, the old energy dose unit rad is converted to roentgen equivalent men, named rem by HR [rem] = wR DR [rad].

(13)

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Table 1 Radiation weighting factors wR Type of radiation and energy range Photons, all energies Electrons and muons, all energies Neutrons En < 10 keV Neutrons 10 keV ≤ En ≤ 100 keV Neutrons 100 keV < En ≤ 2 MeV Neutrons 2 MeV < En ≤ 20 MeV Neutrons with En > 20 MeV Protons, except recoil protons, E > 2 MeV α particles, fission fragments, heavy nuclei

Radiation weighting factor wR 1 1 5 10 20 10 5 2 20

Correspondingly, the relation 1 Sv = 100 rem

(14)

holds. The radiation weighting factors wR , as recommended by the International Commission on Radiological Protection (ICRP), are shown in Table 1. (In the United States, slightly different radiation weighting factors are used. The values of the radiation weighting factors are occasionally changed and subsequently adopted in the various national regulations if new recommendations from the ICRP become available.) In general, the radiation weighting factors take the different biological effects of the various types of radiation into account. For example, α rays are very short-ranged, but they are characterized by a high, local ionization density, which might even produce double strand brakes which cannot be repaired easily, while electrons or γ rays ionize only sparsely, and their effect can be corrected by biological repair mechanisms. Muons, mentioned in the table, are not so familiar in radiation protection. They are short-lived elementary particles which are produced predominantly in cosmic radiation, but they can also be created at accelerators. For detector testing purposes, these omnipresent particles are very useful. Furthermore, dose units for penetrating external radiation (depositing most of their energy in the first 10 mm of tissue) and for radiation of low penetration depth (70 μm skin depth) have been introduced in many national radiation-protection regulations. In personal dosimetry these operative units are denoted with Hp (10), Hp (0.07). In many cases it is necessary to convert a partial-body dose into a whole-body dose. Therefore, a weighting factor wT has to be attributed to the irradiated organs of the body. This effective dose equivalent E is defined as E = Heff =

n  T =1

wT HT ,

(15)

244 Table 2 Tissue weighting factors wT

C. Grupen Organ or tissue Red bone marrow Colon Lung Stomach Breast Gonads Bladder Liver Esophagus Thyroid gland Skin Periosteum (bone surface) Brain Salivary glands Other organs or tissue

Tissue weighting factor wT 0.12 0.12 0.12 0.12 0.12 0.08 0.04 0.04 0.04 0.04 0.01 0.01 0.01 0.01 0.12

Fig. 1 Illustrated tissue weighting factors. The tissue weighting factors are normalized to 1. The “other organs and tissue” item (not shown) has a tissue weighting factor of 0.12

where HT is the average dose equivalent in the irradiated organ or tissue and wT is the weighting factor for the T th organ or tissue. The tissue weighting factors, according to the recommendation of the ICRP, are given in Table 2 and Fig. 1.

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Table 3 Dose-rate constants Γ for some β- and γ -ray emitters (Grupen 2009; Unger and Trubey 1982; Krieger 2002; Sauter 1982)

Radioisotope 32 P 15 60 Co 27 90 38 Sr 131 I 53 204 Tl 81

Radioisotope 40 K 19 60 Co 27 85 Kr 36 99m 43 Tc 131 I 53 137 Cs 55 133 Ba 56

β  dose-rate  constant Sv m2 Bq h 9.1 × 10−12 2.6 × 10−11 2.0 × 10−11 1.7 × 10−11 1.3 × 10−11 γ  constant  dose-rate Sv m2 Bq h 2.2 × 10−14 3.7 × 10−13 4.2 × 10−16 3.3 × 10−14 7.6 × 10−14 1.0 × 10−13 1.2 × 10−13

It is assumed that the inhomogeneous irradiation of the body with an effective dose equivalent Heff bears the same radiation risk as a homogeneous whole-body irradiation with H = Heff . For the general case of partial-body irradiation in a complex radiation field, one has    wT HT = wT wR DT ,R . (16) E = Heff = T

T

R

The determination of the dose-equivalent rate by a point like radiation source of activity A can be accomplished using the following formula: A H˙ = Γ 2 . (17) r In this equation r is the distance from the radiation source (in meters) and Γ a specific radiation constant which depends on the type and energy of the radiation. The dose-rate radiation constants are specific for each radioisotope, and they are different for β and γ radiation. Table 3 lists the dose-rate constants for some commonly used radiation sources.

Basic Nuclear Physics An atomic nucleus of mass number A consists of Z protons and N neutrons: A = Z + N. The atomic number Z of stable nuclei is related to the atomic mass approximately according to

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Zstable =

A . 1.98 + 0.0155A2/3

(18)

For light nuclei (Z ≤ 20, calcium) Z = A/2 holds; for heavy nuclei one has approximately Z = A/2.5. The atomic number Z characterizes the chemical properties of an atom. Nuclei with fixed Z and variable N are called isotopes. If the isotopes are radioactive, they are called radioisotopes. Nuclei with a fixed sum of protons and neutrons, i.e., constant mass number A, are called isobars. Nuclei with fixed neutron but varying proton number are called isotones. Protons and neutrons are approximately of the same mass, mneutron /mproton = 1.00138. The binding energies of nuclei vary around 7 to 8 MeV per nucleon (see Fig. 2). Light elements can be fused to heavier elements, e.g., in stars, supernova explosions or thermonuclear reactors. Heavier elements, like uranium, can be split by neutrons in fission reactors. In both processes mass is converted into energy, albeit with relatively low efficiency. Nuclei with excess neutrons are normally β − emitters. In this nuclear process, a neutron (n) transforms into a proton (p) under emission of an electron (e− ) and an electron antineutrino (ν e ), n - p + e− + ν e .

(19)

Free neutrons have a lifetime of 880 s (Olive 2014). Light nuclei with excess protons are mostly β + emitters. In this case a proton decays into a neutron under emission of a positron (e+ ) and a neutrino (νe ), p - n + e+ + νe .

(20)

Fig. 2 Binding energy per nucleon. Indicated are the processes to generate energy by fusion and fission processes (Grupen and Rodgers 2017)

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Free protons are stable (τp > 1031 years), since there are no lighter baryons into which they could decay. In β + emitters also electron capture can occur: p + e− - n + νe .

(21)

β decays frequently lead to excited nuclear levels of the final-state nucleus (“daughter nucleus”). The excited daughter nucleus de-excites into the ground state under the emission of γ rays. Since the energy difference between the excited nucleus and the ground state is fixed, γ rays, in contrast to decay electrons from nuclear β decay, have a discrete energy. An example for β decay is 137 Cs 55

- 137 Ba∗ + e− + ν e 56 . - 137 Ba + γ

(22)

56

The electron will receive in most cases a maximum energy of 0.51 MeV; (1.17 MeV if the decay proceeds directly into the ground state). The photon from the decay of the excited Ba∗ has an energy of 662 keV. All this information is best summarized in a decay-level diagram (see Fig. 3). Heavy, high-mass nuclei tend to decay under the emission of an α particle, i.e., a helium nucleus. This decay mode is frequently in competition to β + decay, but the proton excess for most heavy nuclei can more easily be reduced by the emission of α particles. Also, there are theoretical reasons (nuclear shell model, strong binding of helium nuclei) why α decay is usually favored. Thus, for example, 238 92 U decays into excited states of the 234 Th isotope. Since the nuclear levels are characterized 90 by fixed energies, the emitted α particles in this two-body decay are monoenergetic. Fig. 3 Decay-level diagram of 137 55 Cs (Grupen 2009)

137 55

Cs

1/2

– 1

(94 %) 137m 56

– 2

Ba

(6 %)

max

137 56

Ba

max

1/2

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Apart from α emission, heavy nuclei (for Z ≥ 90) can also decay by spontaneous fission. As a result of a nuclear transmutation, atomic electrons can also be emitted: an atomic nucleus will normally release its excess energy Eex by γ emission. However, it is also possible that its excitation energy is transferred directly onto an electron in the atomic shell. Such electrons are called conversion electrons. If a vacancy in the atomic shell is produced by electron capture or conversion, the electrons in the atomic shell will try to reach a more favorable energetic state. In this way a vacancy in the K shell can be filled up by an electron from the L shell. The energy difference EK − EL is liberated and can either be emitted as characteristic X-rays with EX = EK − EL or, if EK − EL > EL , it can be transferred directly to another L electron which will leave the atom with the energy EK − 2EL . Such an electron is called Auger electron.

Basic Interactions Charged particles (electrons, positrons, protons, helium nuclei, . . . ) will ionize matter in a direct way, in contrast to neutral particles (neutrons, neutrinos, . . . ) or short-wavelength electromagnetic radiation (X-rays and γ rays), which are ionizing only indirectly. Strictly speaking, radiation is never directly measured; rather it can only be detected via its interaction with matter. A large number of specific interaction processes exists. These interactions are characteristic for each of charged particles, neutrons, neutrinos, X-rays, and γ radiation. For example, charged particles lose their energy essentially by excitation and ionization and by bremsstrahlung. In the field of practical radiation protection, it is sometimes desirable to consider only the local energy deposit, i.e., collisions with relatively low-energy transfer. The idea is that in collisions with large energy transfers, long-range δ electrons are created which are weakly ionizing and therefore have only little biological effect, in contrast to the high ionization density generated by low-energy transfers. It is important to note that the energy spectrum of ionization electrons falls off like 1/ 2 , where is the kinetic energy of the electrons knocked out from the atom. These electrons are also called “knock-on electrons” or δ rays. These δ rays are of low energy, and therefore they are relevant for radiation protection. This led to the introduction of the concept of the linear energy transfer (LET). The linear energy transfer of charged particles is the ratio of the average energy loss E, where only collisions with energy transfers smaller than a given cut-off parameter Ecut are considered, and the traversed distance x,  LET = LEcut =

E x

 .

(23)

Ecut

The energy cut parameter is usually given in eV. A value of LET100 indicates that only collisions with energy transfers below 100 eV are considered. High

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Fig. 4 Energy loss of carbon ions 12 C for various energies per nucleon in water as a functions of depth (Kraft 2000, 2012; Grupen and Shwartz 2008)

linear-energy-transfer radiation corresponds to high biological effectiveness. At the end of their range, charged particles, like protons or heavy nuclei, produce a strong ionization peak (‘Bragg peak’) which is a consequence of the 1/v 2 dependence of the energy loss (v – velocity of the charged particle); see Fig. 4. The interactions of particles and radiation with matter are described in very much detail in the introductory chapter by Eidelman and Shwartz (see also Grupen and Shwartz 2008). Therefore this type of radiation is very important for cancer treatment, like in proton or heavy-ion therapy; see Fig. 5. This kind of application is described in detail in the contribution by Kraft and Weber in the article on tumor therapy with ion beams. There are meanwhile numerous hospitals all over the world where this technique is successfully used. Neutrons are of particular importance for radiation protection because of their high relative biological effectiveness. For neutrons with energies which are typical in the field of radiation protection (Ekin ≤ 10 MeV), the following detection reactions can be considered: n + 63 Li - α + 31 H,

(24)

n + 105 B - α + 73 Li,

(25)

n + 32 He - p + 31 H,

(26)

n + p - n + p.

(27)

In these reactions mostly the lightweight final-state interaction products (α rays, protons and tritons (31 H)) are detected which signalize a neutron scattering process. Just as with neutrons, photons must first produce charged particles in an interaction process, which are then normally detected via processes of ionization, excitation, and scintillation. The interactions of photons are fundamentally different from those of charged particles since in a photon interaction process, the photon

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Fig. 5 Proton therapy treatment gantry at a Proton Therapy Center. (Reproduced with permission from the Roberts Proton Therapy Center at Penn Medicine Hospitals, 2016): The National Association for Proton Therapy (2016)

is either completely absorbed (photoelectric effect, pair production), or scattered through relatively large angles (Compton effect, characterized by the corresponding total attenuation by Compton scattering μc ). Photons are absorbed in matter according to I = I0 e−μx ,

(28)

where I0 is the initial intensity, I the intensity after passing through an absorber of thickness x, and μ is the total mass attenuation coefficient. For the Compton effect, the photon survives the interaction, and consequently one has to distinguish the mass absorption coefficient from the mass attenuation coefficient. For that purpose one defines the Compton scattering coefficient, μcs =

Eγ Eγ

μc .

(29)

In this relation Eγ and Eγ are the energies of the photons before and after scattering in the Compton process. The Compton absorption coefficient is then the difference between the total probability for the Compton effect μc and the Compton scattering coefficient:

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μca = μc − μcs = μc −

Eγ Eγ

 μc = 1 −

Eγ Eγ

 · μc .

(30)

The attenuation or absorption coefficients are frequently normalized to the area density:

μ(cm−1 ) = μ (g/cm2 )−1 ρ

(31)

(ρ – density of the absorber in g/cm3 ). Figure 6 shows the mass attenuation and mass absorption coefficients for photons in lead. Radioactive isotopes are best identified by the full-absorption peak (“photopeak”) which represents a fingerprint of the decaying nucleus. Figure 7 shows the power of photopeak identification in a complex sample of different isotopes.

Fig. 6 Energy dependence of the mass attenuation coefficient μ and mass absorption coefficient μa for photons in lead. μpe describes the photoelectric effect, μpp pair production, μcs Compton scattering, and μca Compton absorption. μa is the total mass absorption coefficient (μa = μpe + μpp +μca ) and μ the total mass attenuation coefficient (μ = μpe +μpp +μc with μc = μcs +μca ) (Grupen 2009)

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Co Cd 241 Am 109

139

203

113

Ce Hg Sn

85

Sr

137

Cs

88

60

Y

Co

60

88

Co

Y

4

10

3

10

2

10

10

1

0

500

1000

1500

2000

E

Fig. 7 Photopeak identification in a mixture of radioisotopes based on the pulse-height spectrum recorded with a high-purity germanium detector. (Reproduced with permission from Oliver Kalthoff, Hochschule Heilbronn; Kalthoff 1996)

Range of Particles Particle from radioactive sources will typically have an energy of a few megaelectron volts. The average energy loss of electrons of these energies in air is approximately 0.25 keV/mm. This means they have a range of less than 10 m in air or 0.3 mm in lead. α particles lose energy much more quickly (about 100 keV/mm in air) because of their stronger charge and higher mass. α particles can be detected, for example, due to their strong local ionization by the track-etching technique, where they produce etch cones which can be made visible (see Fig. 8). The stronger charge (twice the size of the electron’s) increases both the probability of interactions and the energy transferred in each interaction. The higher mass means that at similar energies, the α particle is moving much more slowly, increasing the interaction probability further. This means that α rays are rather short-ranged: just 4 cm in air or approximately 25 μm in aluminum. The great benefit of this short range is that it is almost never necessary to shield against α particles produced outside the body: any clothing or a small distance in air will reduce their impact to a negligible level. The corollary of this is that when α particles are produced inside the body – for example, by inhaled radon gas – they deliver stronger and more concentrated damage than an equivalent β ray would. The α particle gives up all its energy in a small region of

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Fig. 8 Microphotograph of a nuclear-track detector showing etch holes of diameter between 80 and 150 μm due to the impact of α particles from radon decay. (Reproduced with permission from Radonlab, Oslo, Radonlab 2018)

tissue, causing concentrated damage. It is for this reason that the radiation weighting factor for α particles is very high. The fact that particles which move more quickly deposit energy more slowly has a clinically useful consequence. When protons or nuclei are accelerated and fired at the human body, the damage is concentrated at a particular depth, allowing in hadron therapy a tumor to be targeted precisely (see also Fig. 4). Special care must be taken with neutrons, which have a relatively large range because they are electrically neutral. From the point of view of radiation protection, neutrons are very unpleasant because by hitting the nuclei of cells, they can create substantial radiation damage, and that is why their radiation weighting factor is quite large. They often produce charged particles in these interactions, which is how they can be detected. They can also cause some materials to become radioactive themselves (activation). The interactions of photons are fundamentally different from those of the other particles because photons can be created (emitted) and destroyed (absorbed) freely. For other particles it makes sense to talk of the range for each energy they will have in a particular material. Photons, by contrast, have a potentially infinite range, but with an ever-decreasing intensity and clearly, at some point, the intensity is so low as to be irrelevant. The absorption of photons is described by its relevant interaction processes (photoelectric effect, Compton scattering, and pair production) via the mass attenuation coefficient. The absorption of different particle species is demonstrated in Fig. 9. Special absorbers must be used to attenuate or stop α and β particles. X-ray photons or γ rays require absorbers of large atomic number, while in contrast neutrons can only be stopped by lightweight material. Special care must be taken for energetic

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Fig. 9 Typical ranges and absorption techniques for α, β, X rays, γ rays and neutrons. (Reproduced with permission from MIRION Technologies: Types of Ionizing Radiation, MIRION Technologies 2010)

electrons where a good shielding is represented by a sandwich of aluminum followed by a lead layer. A lead layer alone would produce bremsstrahlung which is difficult to shield. The purpose of the aluminum is to slow down the electrons, so that the chance of the formation of bremsstrahlung is reduced.

Radiation Sources One might assume that only radioisotopes are significant sources of radiation. The rapid development in basic physics research and its technical applications have created a variety of possibilities for producing nearly all sufficiently long-lived elementary particles and photons in the form of radiation sources. The energy range from ultracold particles (25 meV) up to energies of 1 TeV can be covered. If, in addition, cosmic rays are considered, also particles and photons with energies in excess of 1 TeV are available albeit at low intensity. In the following subsections, the main methods of production of ionizing radiation are described.

Particle Radiation All charged particles can be accelerated and stored up to very high energies in accelerators. Most accelerators are circular installations in which the particles to

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be accelerated are kept in a vacuum beam pipe by magnetic dipole fields. The particles are then accelerated by high-frequency alternating electromagnetic fields in so-called cavities. For beam focusing quadrupole magnets and magnetic correction lenses are used. Typically electrons, positrons, protons, and antiprotons are accelerated, e+ and − e to, say, 100 GeV in electron synchrotrons and p and p¯ to a maximum of 7 TeV (p) in proton synchrotrons. By extracting the accelerated particles, a large number of secondary particles can be produced by collisions with an external target, which then can also be stored themselves. In the field of experimental high-energy physics mainly pion, kaon, muon, and neutrino beams are produced for this purpose. Beams of negative pions have also been used in the field of medicine for tumor treatment. Heavy ions, which can also be accelerated in synchrotrons up to high energies, are also an excellent tool for tumor treatment in the framework of hadron and heavy-ion therapy. Even though charged pions, kaons, and muons are relatively short-lived (τπ0 = 26 ns, τK0 = 12 ns, τμ0 = 2.2 μs), they can still be used at high energies as secondary radiation because of the relativistic time dilation. Muons can even be stored in circular accelerators. At high energies it makes sense – at least for electrons – to use linear accelerators. A circular movement represents an accelerated motion, and accelerated charged particles suffer an energy loss by synchrotron radiation. This energy loss can be quite substantial for high energies.

Photon Sources X-ray tubes represent a classical photon source. This energetic electromagnetic radiation was discovered by Wilhelm Conrad Röntgen in 1895. In typical X-ray tubes, photons with energies up to several hundred keV can be produced; even the MeV range is accessible. The X-ray spectrum is continuous since it is created by electron bremsstrahlung. It is, however, superimposed by discrete X-ray lines, which are characteristic for the used anode material. The energies of characteristic X-rays can be determined using Moseley’s law:  E(Kα ) = Ry (Z − 1)2

1 1 − 2 n2 m

 .

(32)

In this equation n and m are the principal quantum numbers, and Ry is the Rydberg constant (13.6 eV). For example, for Kα radiation on lead (n = 1, m = 2), one obtains E(KPb α ) = 66.9 keV. The photon energy range which is classically covered by X-ray tubes is also obtained by synchrotron-radiation sources. However, the photon flux of synchrotron-radiation sources is higher by many orders of magnitude. The synchrotron-photon spectrum is continuous just like the bremsstrahlung spectrum of X-ray tubes. Because of the high intensity of the synchrotron-photon spectrum,

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intense monoenergetic photon beams can be produced by monochromators. Such monochromatic X-rays from electron synchrotrons are, for example, used in diagnostics in the field of noninvasive coronary angiography. The coronary arteries are marked with stable iodine as contrast agent. Two digital images, one below and one above the K absorption edge, are taken and subtracted in a computer. This allows to suppress the absorption in the surrounding tissue, thereby yielding an image of the blood vessels of high contrast (“dual-energy technique” or “K-edge subtraction technique”). Decays of neutral pions (π 0 → γ +γ ) or annihilations of electrons and positrons + (e + e− → γ + γ , used in positron-emission tomography (PET)), are sources of energetic photons. For completeness also decays of radioisotopes have to be mentioned, which – after α or β activity – decay frequently by γ emission into the ground state. In these decays photons with energies up to several MeV can be produced. As a consequence of nuclear transformation, also excitations in the electron shell can occur leading to characteristic X-rays. In electron–photon interactions, energetic electrons can produce high-energy photons by the inverse Compton effect. This process plays a dominant role in X-ray and gamma-ray astronomy.

Neutron Sources Neutrons are predominantly produced in strong interactions. In spallation neutron sources, energetic hadrons (mostly protons) produce a large number of neutrons in reactions with heavy nuclei. It is possible to create up to 30 neutrons per reaction by the bombardment of nuclei with hadrons. The spallation neutrons are created over a wide energy range and could ideally be used for the purpose of transmutation of nuclear waste. In dedicated neutron generators, single neutrons can be produced by the bombardment of special targets with protons, deuterons, or alpha particles. In this way neutrons in the MeV range are obtained. A classical technique is the neutron production in (α, n) reactions. α-ray-emitting radioisotopes are mixed with a beryllium isotope. The α rays interact with 9 Be to produce neutrons of around 5 MeV according to the reaction α + 9 Be -

12

C + n.

(33)

As α emitter one can use radium (226 Ra), americium (241 Am), plutonium (239 Pu), polonium (210 Po), or curium (242 Cm, 244 Cm). The neutron yield for these (α, n) reactions is of the order 10−4 per α particle. In fission reactors highly radioactive fission products are generated. Since the fission materials, e.g., 235 U, are relatively neutron rich, the fission products contain too many neutrons. The neutron excess can be decreased by the emission of prompt

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or delayed neutrons. Nuclear fission reactors are therefore a rich source of neutrons. The fission products can also reach a stable final state by successive β − decays. Neutrons are also produced in the Sun and in supernova explosions, but these neutrons are irrelevant from the point of view of radiation protection.

Cosmic-Ray Sources Cosmic rays may present a radiation hazard, in particular, for flight personnel. Radiation-relevant aspects concerning cosmic rays are presented in some detail in the section on environmental radiation (section “Environmental Radiation” in this chapter). Here only the potential of cosmic rays as sources of particles for measurement and calibration of detectors shall be mentioned. Primary cosmic rays consist mainly of protons, α particles, and some heavy nuclei (Z ≥ 3). By interactions of primary cosmic rays with atomic nuclei of the atmosphere, the initial primary particles initiate cascades of secondary and tertiary particles. In this way predominantly pions and kaons are generated. These mesons can either induce further interactions or decay. The competition between interaction and decay depends on the local density of the atmosphere. The soft component of cosmic rays, consisting of electrons, positrons, and photons (initiated by π 0 decay), will be absorbed relatively fast in the atmosphere. In contrast, the decay products of charged pions and kaons, namely, muons and neutrinos, can easily reach sea level. 80% of charged cosmic rays at sea level are composed of muons, which are mainly distributed over an energy range from about 1 GeV up to 1 TeV. Because of their low energy loss (≈2MeV/(g/cm2 )), muons can also reach large depths underground. In the field of radiation protection, cosmic-ray muons will lead to a background in all radiation monitors, in addition to that from terrestrial radiation. A contamination monitor with a horizontal area of 15 × 10 cm2 will measure a background rate of ≈150 particles per minute purely due to cosmic rays. This result should not only be considered as a disadvantage since it represents at the same time a function test of the measurement devices. For such a test, no artificial radiation sources are required. For measurements on radioactive materials, this background rate has to be considered in any case.

Radiation Detectors The necessity for the measurement of radiation exposures originates from the fact that this type of radiation has to be surveyed, controlled, and limited. Humans also have to be protected against unexpected exposures. On the one hand, the surveillance of radiation-exposed workers and the measurement of external radiation exposures, contaminations, and incorporations, in particular, in working areas, are very important. On the other hand, the environment has to be protected against unnecessary exposures. The latter point of view includes the determination of

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radiation exposures of the population, the monitoring of the disposal of radioactive waste into the environment, and the examination of the distribution of radioactive material in the biosphere (atmosphere, soil, water, food). In addition, national radiation-protection authorities also have realized that radiation exposures from natural sources have to be considered. In certain situations natural radiation can increase the radiation level for individuals of the population quite considerably. Therefore, these natural sources cannot be neglected in the framework of radiation protection. The radiation detectors used in the field of radiation protection have to be reliable and robust, and their measurements have to be reproducible. It is important to note that for different types of radiation, adequate detectors must be used. The detailed working principles of standard radiation detectors are described in various articles in this handbook in great detail. Here we only present in the following some general features mostly relevant to the field of radiation protection. Rate measurements are most easily performed with ionization chambers and proportional or Geiger-Müller counters. Proportional counters can also be used for alpha spectroscopy. If gamma spectroscopy for the identification of radioisotopes is required, scintillation counters are a good choice. To obtain the highest resolution, semiconductor counters, like high-purity germanium counters, should be used. For neutron measurements suitably doped scintillation counters or gas counters with boron-trifluoride filling are appropriate. As personal dosimeters directly readable pen-type dosimeters are standard. If exposures have to be documented, one can use film badges or phosphate-glass dosimeters. Thermoluminescence dosimeters are also sensitive, but their information is erased when they are read out. If it is necessary to determine body doses after a radiation accident, and no dosimeter information is available, a so-called accident dosimetry is required: phosphorus in hair or sodium in blood samples are activated by neutrons, and their activity can be measured and can help to estimate the scale of the exposure.

Safety Standards The International Commission on Radiological Protection (ICRP) has proposed safety standards to protect the health of workers and the general public against the dangers arising from ionizing radiation. The recommendations are laid down in a European Directive (Council Directive 96/29/EURATOM) which was presented to the Member States of the European Community. The Directive has defined safety standards for exposed workers in the following way: • the limit on the effective dose is 100 mSv in a consecutive 5-year period, subject to a maximum effective dose of 50 mSv in any single year. In accordance with this, most Member States have defined an annual limit of 20 mSv. • the annual limit on the equivalent dose for the lens of the eye is 150 mSv. • the annual limit on the equivalent dose for the skin is 500 mSv.

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• the annual limit on the equivalent dose for the hands, forearms, feet, and ankles is 500 mSv. The annual limit for the whole-body dose for the general population, e.g., from nuclear power plants, is 1 mSv in most countries. The general recommendation is that reasonable steps must be taken to ensure that the exposure of the population as a whole is kept as low as reasonably achievable (ALARA principle). In contrast, other countries, e.g., the United States of America, have regulations which differ distinctly from the European Directive. For example, according to the Code of Federal Regulations (“Standards for Protection Against Radiation”), the annual whole-body dose limit for workers exposed to ionizing radiation in the United States is 50 mSv (please note that many laboratories in the United States set lower limits) compared to 20 mSv in European countries. Other differences are that in the United States, the old radiation units (rad and rem) are still in use (1 Sv = 100 rem, 1 Gy = 100 rad).

Organization of Radiation Protection The responsibility for the correct integration of the radiation-protection rules in a company, nuclear power plant, research center, or a university lies in the hands of the radiation-protection supervisor. The radiation-protection supervisor has to appoint in a radiation-protection directive an appropriate number of radiation-protection officers for the control and surveillance of the work in question. The radiationprotection officer or, for short, the radiation officer has to be qualified for his work in the field of radiation protection. In contrast to this, the radiation-protection supervisor needs not to be an expert in the field of radiation protection. He transfers the duty to respect the regulations of radiation protection to the radiation officer (Fig. 10). The regulations in the field of radiation protection require that persons who will handle radioactive material, e.g., students in a nuclear physics lab at a university, are instructed about the possible dangers of handling radioactive sources. This instruction must be done annually. Fig. 10 Example of a hierarchy for radiation protection in an organisation (Grupen and Rodgers 2017)

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It is the aim of safety measures in the field of radiation protection to avoid unnecessary radiation exposures, contaminations, and ingestion and inhalation of radioactive material (“incorporations”). To a certain extent, of course, there are radiation exposures which are unavoidable, but it is the aim to reduce these unavoidable radiation exposures, contaminations, or incorporations to a level as low as reasonably achievable. This is the so-called ALARA principle. There are, however, national radiation-protection regulations which require the radiation exposure to be kept as low as possible. Of course, it must be ensured that the exposures stay within the limits given by the regulations. To fulfill these requirements is the main task of the radiation-protection officer. It is interesting to note that in the early days of the study of radioactivity, the concept of “radiation protection” did not even exist, and there was no “radiation officer.” Physicists like Becquerel, Curie, and Hahn handled relatively large quantities of radioactive substances with their bare hands. In addition to this, any radioactive material given off as gas or airborne dust was frequently inhaled. Even today the logbooks of Marie and Pierre Curie are contaminated by radium (halflife 1600 years) and their decay products, and they are on loan in the Bibliothèque Nationale only with special restrictions. One might assume that only radioisotopes are significant sources of radiation. However, as mentioned in the section on “Radiation Sources,” there is quite a variety of possibilities to produce all kinds of particles over a wide energy range. This includes all charged particles, which can be produced in accelerators and tuned by appropriate absorbers; photons by electron bremsstrahlung on a target, where the photon energy can even be flagged by measuring the final-state electron; and neutrons, e.g., in radium-beryllium sources. Regulations for X-ray sources and X-ray facilities are analogous to the normal radiation-protection standards. Many radiation accidents in the fields of medicine and technology are caused by losses and careless disposal of radioactive material. The reason for unnecessary exposures is frequently due to improper storage of disused radioactive sources. Radiation accidents in large manufacturing plants and nuclear-medical sections of hospitals are frequently caused by non-existing elementary safety rules. In the case of existing safety rules, they are often ignored. It is also essential that the maintenance personnel are suitably trained and aware of the radiation risks. Radiation-protection regulations must be meticulously respected; otherwise accidental irradiations or even accidents may occur. The basic rules in the field of radiation protection are (ALARA principle = As Low As Reasonably Achievable): • • • • • •

limit the activity of radioactive material, use shielding whenever possible, limit the exposure time, keep suitable distance to the radioactive material if possible, avoid contamination, and avoid incorporations.

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As far as shielding is concerned, one has to keep in mind that γ rays are effectively absorbed by heavy materials, like lead. In contrast, electrons are best stopped with a sandwich starting with low Z-material followed by lead. In this way one avoids bremsstrahlung by fast electrons which is difficult to shield. When the electrons are slowed down by the low-Z material, they are stopped by a layer of lead. Neutrons are best absorbed by materials which contain many protons, because neutrons can transfer their energy effectively to partners of the same mass. An incorrect shielding might even lead to an increased dose, because behind an inadequately designed shield, the particle rate can increase due to interactions in the shielding. This built-up effect has to be considered. Very recently the German national authorities have proposed to integrate the regulations on protection against ionizing radiation and the regulations for the protection against X-rays into one common legal ordinance (German Strahlenschutzgesetz Radiation Protection Law). Actually the legal limits for ionizing radiation and exposure to X-rays are very similar. An extensive ministerial draft of the ministry for Environment, Nature Protection, and Reactor Safety has been prepared in the form of a “Radiation Protection Law” which was submitted to the parliament. After a suitable consultation with the responsible authorities, this common Radiation Protection Law came into effect by the beginning of 2019 (Rolf Michel 2016).

Environmental Radiation Natural radioactivity from the environment has three components: • cosmic rays (≈0.3 mSv/yr), • terrestrial radiation (≈0.5 mSv/yr), • ingestion (eating, drinking, and breathing) (≈1.5 mSv/yr). Cosmic rays from our Sun and our galaxy and terrestrial radiation from the Earth crust as well as incorporations of radioisotopes from the biosphere represent wholebody exposures. A special role is played by the inhalation of the radioactive noble gas radon which, in particular, represents an exposure for the lungs and the bronchi. In addition to these natural sources, further exposures due to technical, scientific, and medical installations developed by modern society occur. The existence of natural radioactive substances, however, demonstrates that radioactivity and the development of life coexisted since the very earliest times on our planet. Our Milky Way is the dominant source of high-energy cosmic rays. The lowenergy particles predominantly originate from our Sun. Galactic cosmic rays consist largely of protons (≈85%) and helium nuclei (≈12%). Only 3% of primary nuclei are heavier than helium.

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At sea level, cosmic-ray muons, which are created in interactions of primaries in the atmosphere, are the dominant particle species, which present an omnipresent background for radiation detectors. The soil of the planet Earth contains substances which are naturally radioactive and provide natural radiation exposures. The most important radioactive elements which occur in the soil and in rocks are the long-lived primordial isotope potassium (40 K) and the isotopes of radium (226 Ra), thorium (232 Th), and uranium (235 U, 238 U). The radioisotopes 40 K, 226 Ra, and 232 Th also occur in many building materials (such as concrete and bricks). The most important natural isotopes which occur in air, in drinking water, and in food are the isotopes of hydrogen (tritium: 3 H), carbon (14 C), potassium (40 K), polonium (210 Po), radon (222 Rn), radium (226 Ra), and uranium (238 U). These natural radioactive elements accumulate in the human body after being taken in with food, water, and air so that humans themselves become radioactive. The natural radioactivity of the human body is about 9000 Bq and originates predominantly from 40 K and 14 C. The dominant contribution to the natural radioactivity originates from the inhalation of radon isotopes and their decay products. Average and extreme per capita exposures from natural radiation sources are compiled in Table 4. The exposure of humans from X-ray diagnostics, radiology, and radioactive substances from technical installations amounts to about 2 mSv/yr. The dominant source for the per capita exposures is the application of X-rays, β, and γ rays in medicine in diagnostics and therapy. Some examples are given for illustration. Taking an X-ray image of the lungs gives a whole-body dose of about 0.05 mSv. An angiography of the arteries, an X-ray of a kidney, or a computer tomography of the chest can represent an exposure of 10 mSv. In contrast, an X-ray image of the teeth leads to a dose of only 0.01 mSv. The total per capita dose for the population from natural sources and from technical installations (mainly medicine) amounts to about 4 mSv/yr to 5 mSv/yr. The legal limits for radiation-exposed workers and the general population mentioned above do not apply to this unavoidable natural radiation and to exposures from medical diagnostics and therapy. The legal limits only concern exposures additional to environmental radiation and medical exposures. Figure 11 shows the evolution of different contributions to the annual whole-body dose over the last 60 years.

Table 4 Radioactive per capita exposures from natural sources Source Cosmic radiation Terrestrial radiation Incorporation of radioisotopes

Average exposure per year ≈0.3 mSv ≈0.5 mSv ≈1.5 mSv

Highest values 10 mSv (at high altitudes) 260 mSv (Ramsar, Iran) 5 mSv (for extreme diet)

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Fig. 11 Comparison of radiation from the natural environment, exposures from nuclear medicine, legal limits, and exposures from nuclear weapon tests in the atmosphere and from the Chernobyl accident (Grupen 2009)

Biological Effects of Radiation Any radiation exposure might have negative effects on health. This can be considered as the basic principle of radiation protection. It is therefore no surprise that radiation damage due to ionizing radiation was first observed right after the discovery of radioactivity by Becquerel. The biological effect of ionizing radiation is a consequence of the energy transfer by ionization and excitation to body cells. • Early effects: This radiation damage occurs immediately after the irradiation. From a whole-body dose of 0.25 Sv upward, a modification of the hemogram is visible. From 1 Sv on clear symptoms of radiation sickness are to be expected. However, the recovery of the patients is nearly guaranteed. For a whole-body dose of 4 Sv, the chance of survival is 50%. This dose is called the lethal dose. For a dose of 7 Sv, the mortality is nearly 100%. • Delayed radiation damage: A typical late effect is cancer after a period of latency, which can amount to several decades. In contrast to prompt damage, whose effect is proportional to the received dose, delayed radiation damage effects represent a stochastic risk, which means the probability of a damage to occur depends on the dose, but nothing can be said about whether the sickness will

264 Table 5 Risk factors for radiation-induced cancer

C. Grupen Concerned organ or tissue Red bone marrow (leukemia) Periosteum, surface of bones Colon Liver Lung Esophagus Skin Stomach Thyroid gland Bladder Chest Ovaries Other organs or tissue Total radiation-induced cancer risk Genetic risk

Risk factor for 10 mSv whole-body irradiation 50 × 10−6 5 × 10−6 85 × 10−6 15 × 10−6 85 × 10−6 30 × 10−6 2 × 10−6 110 × 10−6 8 × 10−6 30 × 10−6 20 × 10−6 10 × 10−6 50 × 10−6 500 × 10−6 100 × 10−6

be serious or not. The total cancer risk per absorbed dose of 1 Sv is estimated to be to about 5 × 10−2 . Detailed risk factors for specific types of cancer are given in Table 5. It is however problematic and not recommended by the ICRP to work out the theoretical number of deaths due to low-level radiation for large resident groups. For exposures of 100 mSv, not even epidemiological studies can verify an increased cancer risk in large populations (Rolf Michel 2016). • Genetic damage: radiation absorption in germ cells can result in mutations. For the irradiated person, mutations are not recognizable. They will only manifest themselves in the following generations. During the genetically significant age of humans (up to the age of 35), about 140 genetic mutations occur due to environmental factors. A radiation exposure of 10 mSv will add another two mutations; this corresponds only to one or two percent of the natural rate of mutations. The average risk factor for radiation effects, which can be inherited in the first two generations, is estimated to be 10−2 per 1 Sv. Apart from damage due to ionizing radiation, favorable effects after radiation exposures have also been observed. This effect is called hormesis. It is suggested that low doses of nonnatural radiation might increase the lifetime of cells. The idea is that cells are able to repair minor damage as caused by natural radioactivity and that cells become more resistant if they are regularly stimulated to repair themselves by being exposed to additional nonnatural low-level radiation. For the purposes of radiation protection, however, one must assume that any additional irradiation should be avoided if possible.

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Applications of Radiation There is a large variety of applications of radiation and radiation detectors in various fields, like medicine, biology, space science, X-rays, energy production, nuclear waste treatment, homeland security, and many others. In the following a brief list of examples will be given (Grupen and Rodgers 2017).

Medical Applications One of the main fields of radiation and radiation sources is medicine. They are used in diagnosis and therapy. Relatively long-lived isotopes, like 60 Co for γ therapy, can be produced at accelerators and transported to the hospitals. Short-lived isotopes (half-life below 1 hour) are normally produced on the site of the hospitals by various generators: γ sources can also be milked from long-lived isotopes if their decay products decay by γ into the ground state. For example, the long-lived radioisotope 137 Cs (half-life 30.2 years) decays by β − emission dominantly to the metastable state 137m Ba . 137m Ba is obtained after a short time with sufficient yield. This metastable state of barium decays with a half-life of 2.55 min by γ emission with an energy of 662 keV into the ground state 137 Ba. The γ rays from the decay of 137 m Ba are frequently used as calibration radiation for performance tests of radiation detectors. One of the central fields of radiation sources is particle therapy, where deep-seated tumors are treated with particle beams, e.g., protons or ions like 12 C. The number of treatment facilities is substantially increasing worldwide.

Metabolism of Plutonium In the course of the construction of the first nuclear bombs in the United States (the Manhattan Project), the workers building the bombs were exposed to dust particles containing plutonium. Naturally, questions arose about the biological effects of inhaled plutonium. Of the two bombs dropped on Japan at the end of the Second World War, one was made of enriched uranium (mostly 235 U and the other of 239 Pu). There were warnings of potential health risks, and it was suggested that a study be undertaken immediately to understand the metabolism of plutonium. A small fraction of the plutonium that had been produced was allocated for animal studies. The plutonium was injected into different animals, and the excretion and retention rates were studied. Since these rates differed substantially for different species, it was difficult to correlate animal excretion and retention data to humans. As a result, there was a proposal to administer small amounts of plutonium to humans to obtain reliable data. In this context, plutonium was injected into hospital patients at Rochester and Chicago (United States) in the late 1940s. The patients were thought to be either

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terminally ill or to have a life expectancy of less than 10 years either due to age or to chronic diseases. Different quantities between a few μg and about 100 μg were administered, corresponding to activities of up to 220 kBq. After injection, samples of blood, urine, and feces were analyzed at Los Alamos. The physicists and physicians felt reasonably certain that there would be no additional harm to the patients given their preexisting medical conditions. The urinary excretion data showed a rapid initial excretion rate, although much slower than for radium. This rate levelled off to a constant amount per day after a few weeks. It was found that significant quantities of plutonium were retained in the body in the long term, making the problem of chronic plutonium poisoning a matter of serious concern. Because of this retention, and the significant quantities of plutonium used, the patients received doses of hundreds of millisieverts per year for the rest of their lives. Out of the 16 patients tracked, 10 died within 10 years. Four patients survived more than 20 years. Three of the four survivors were examined in 1973, 28 years after the injections had taken place, providing long-term patterns of plutonium retention and excretion. The results of these studies were used as source for estimating permissible limits in the framework of radiation-protection regulations. Naturally, these experiments with radioactive substances on humans raised questions about medical ethics, especially because of the absence of informed consent from the patients selected.

Radiation-Resistant Organisms Different organisms are resistant against ionizing radiation to different extents. For example, the lethal dose – remembering that doses are inherently per kilogram measures – for all mammals is about the same (humans, 4 Sv; dogs, 4 Sv; monkeys, 5 Sv; rabbits, 8 Sv; marmots, 10 Sv). In contrast to that, spiders (with a lethal dose of 1000 Sv) and viruses (2000 Sv) are much more resistant against ionizing radiation. If there were a nuclear holocaust, it would probably only be survived by spiders, viruses, bacteria, and certain types of grass. The idea that cockroaches have an extremely high radiation tolerance is a myth – although higher than that of humans, their resistance is similar to that of many invertebrates. The bacteria Deinococcus radiodurans and Micrococcus radiophilus can even survive a dose of more than 10,000 Sv because of their extraordinary ability to repair radiation damage. They have even been found in the hot reactor cores of nuclear power plants. These bacteria somehow manage to repair DNA damage with the help of a special enzyme system, even if the helix structure of the DNA exhibits about 1 million breaks. Deinococcus radiodurans is able to make chemical changes to highly radioactive waste, which make the process of disposing of it easier and more efficient. For this reason, there is active research into using these bacteria to clean up the radioactively contaminated areas which result from nuclear accidents, military use, and earlier generations of nuclear power plants. Because of the high level of resistance to radiation, and also to extreme temperatures, these organisms

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can survive in meteorites under space conditions over a long time. Consequently they can also propagate over large distances. It is even conceivable that the evolution of life on Earth was initiated by the impact of meteorites containing such organisms (a hypothesis called “panspermia”). The fungus Cryptococcus neoformans appears to exhibit the astonishing ability to transform the energy of ionizing radiation into usable energy. The fungus was described in detail for the first time in 1976. Its special accomplishment became generally known when it was found after the Chernobyl accident in the sealed nuclear reactor. In general, fungi are rather radiation resistant. They can survive radiation doses of more than 10,000 Sv. However, Cryptococcus neoformans goes a dramatic step further: its metabolism increases significantly under irradiation. It appears that the fungus achieves this by using melanin, a class of pigments common in plants and animals, to derive usable energy from the γ radiation, but the mechanism is not well-understood. In principle, this is a similar technique to that of normal plants: plants transform electromagnetic radiation from the visible range into chemical energy (by photosynthesis), and the fungus seems to be doing the same with radiation from the γ energy range. As an aside, Cryptococcus neoformans can be harmful for humans: it can cause meningitis, especially as a secondary infection for AIDS patients.

Waste Transmutation In principle an elegant way for the handling of radioactive waste can be envisaged, namely, the transformation of undesirable long-lived radioactive isotopes into acceptable ones, by neutron or proton irradiation. This process is called transmutation. It is the long-lived radioisotopes that are the main problem in nuclear waste storage, due to the very long storage times required before they are stable: for example, neptunium-237 has a half-life of 2 million years. The drive is to transform these long-lived isotopes into short-lived or even stable ones. Unfortunately, the probability of these transmutation reactions is rather low, so long irradiation times with large numbers of incident particles are required. The amount of nuclear waste generated every year from nuclear power plants and recycling facilities worldwide is estimated to be about 10,000 tons. It is well known how typical fission products, like caesium or strontium, can be dealt with. During the running of a nuclear power plant, some elements heavier than uranium (transuranic elements) are created. The main transuranic elements produced are such as plutonium, neptunium, americium, and curium. Even though the transuranic elements represent only about one percent of the total radioactive waste, the problem arises because of their extremely long half-lives (e.g., 237 Np has a half-life of 2 million years, and plutonium-242 has a half-life of nearly 400,000 years) and their storage appears to be rather problematic (see Fig. 12). These transuranic isotopes are created from the original nuclear fuel (mostly 235 U) by neutron attachment with subsequent β decays.

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Fig. 12 Radiological toxicity of spent fuel as a function of time. (Reproduced with permission from the MIT Energy Initiative: The Future of the Nuclear Fuel Cycle, MIT Energy Initiative 2011)

Indeed, the original aim of Otto Hahn and Fritz Straßmann was to produce elements beyond uranium by neutron bombardment. In this set of experiments, they discovered fission accidentally. These transuranic isotopes would need to be bombarded with fast neutrons. This would either fission the nuclei or transform them into short-lived isotopes. Typical transmutation products are isotopes of ruthenium and zirconium, which are either stable or relatively short-lived, with half-lives up to a year. The safe storage of these isotopes only has to be guaranteed for a period of a few decades. It is believed that salt domes could ensure this. It is hard to imagine a facility which can maintain safe storage for millions of years. A large-scale implementation of this new transmutation technique would require considerable development and implementation effort. The Multipurpose Hybrid Research Reactor for High-tech Applications (MYRRHA) in Belgium, whose construction is expected to start in 2026, is a promising candidate for transmutation studies. It could demonstrate the feasibility and cost-effectiveness of nuclear transformation.

Conclusions Radiation is everywhere. Air, soil, rocks, animals, and plants are radioactive. Life has developed in this environment of natural radiation. Therefore it is good to know about possible biological hazards, if additional radioactive material is

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used in research and technology. Most countries rely on the so-called ALARA principle, which states that by using radioactive material, the effect on humans and the environment should be “as low as reasonably achievable.” Limits for additional radiation have to comply with exposures from natural radiation. In most places these doses are around a few millisieverts per year, sometimes with large fluctuations. Radiation doses from medical diagnosis and treatment on average are comparable to the exposure from natural radiation. The International Commission on Radiological Protection has recommended a limit for the annual whole-body dose of 20 mSv, which has been implemented in most national regulations. To survey and control such limits, suitable detector equipment must be available. The majority of detectors, as described in this chapter and in this handbook, can be used for this purpose. A special point for radiation detection is that these instruments must be robust and reliable. Qualified personnel is required to guarantee that the legal aspects of radiation protection are respected.

Cross-References  Accelerator-Based Photon Sources  Radiation Detectors and Art Acknowledgments It is a pleasure to thank Mrs. Arzu Ergüzel for a very careful reading of the manuscript and Dr. Tilo Stroh for his efficient help in layouting this chapter in a professional way in LATEX.

References German Strahlenschutzgesetz (Radiation Protection Law) (2016) Minesterial Draft, Sept 2016; www.fs-ev.org; see news from 28 Sept 2016. Accessed 23 Apr 2018 Grupen C (2009) Introduction to radiation protection. Springer, Heidelberg/New York Grupen C, Rodgers M (2017) Radioactivity and radiation: what they are, what they do, and how to harness them. Springer, Heidelberg Grupen C, Shwartz B (2008) Particle detectors. Cambridge University Press, Cambridge Kalthoff O (1996) Berechnung der Photopeakeffizienz für koaxiale Reinst-Germaniumdetektoren. Diploma Thesis, Siegen Kraft G (2000) Tumortherapy with ion beams. Nucl Inst Methods Phys Res A 454:1 Kraft G (2012) Tumour therapy with ion beams, and references therein. In: Grupen C, Buvat I (eds) Handbook of particle detection and imaging. Springer, Heidelberg Krieger H (2002) Strahlenphysik, Dosimetrie und Strahlenschutz. Teubner Verlag, Stuttgart MIRION Technologies (2010) https://www.mirion.com/. Accessed Apr 2018 and https://www. mirion.com/introduction-to-radiation-safety/types-of-ionizing-radiation/#. Accessed 23 Apr 2018 MIT Energy Initiative (2011) The Future of the Nuclear Fuel Cycle. http://energy.mit.edu/research/ future-nuclear-fuel-cycle/. Accessed 23 Apr 2018 Olive KA et al (2014) Review of particle physics, Particle data group. Chin Phys C 38(9):090001 Radonlab (2018) Oslo http://www.radonlab.com/. Accessed 23 Apr 2018. see also ‘Integrated Radon Measurements’ by Tuukka Turtiainen. https://www.envir.ee/sites/default/files/radoon_ 2._integrated_radon_measurements.pdf; Accessed 23 Apr 2018, and http://www.radonlab.com/ en/radon-measurements/track-etch-detectors; Accessed Apr 2018 and private communication

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with the manager of Eurofins Radonlab; reproduced with permission from Alexander Birovljev; Eurofins RadonLab, Oslo, 2018 Michel R (2016) Strahlenschutzpraxis, vol 3, pp 13–45 Sauter E (1982) Grundlagen des Strahlenschutzes. Thiemig, München The National Association for Proton Therapy (2016) Roberts Proton Therapy Center at University of Pennsylvania Health System, Penn Medicine Hospitals. http://proton-therapy.org/. Accessed 23 Apr 2018 Unger LM, Trubey DK (1982) Specific Gamma-Ray dose constants for Nuclides important to dosimetry and radiological assessment. ORNL/RSIC-45/R1

Further Reading Allison W (2009) Radiation and reason: the impact of science on a culture of fear. Wade Allison Publishing, Oxford Burchfield LA (2008) Radiation safety, protection and management: for homeland security and emergency response. Wiley-Interscience, New York Charles MW, Greening JR (2008) Fundamentals of radiation dosimetry, 3rd edn. Taylor and Francis, London CTI Reviews (2016) Atoms, radiation, and radiation protection Cram101, 3 edn. Amazon Digital Services LLC Eisenbud M, Gesell TF (1997) Environmental radioactivity. Academic, San Diego Grupen C, Rodgers M (2016) Radioactivity and radiation: what they are, what they do, and how to harness them. Springer, Heidelberg International Atomic Energy Agency, IAEA (2018) Radiation protection of the public and the environment. IAEA, Wien Kraft G (2012) Tumour therapy with ion beams. In: Grupen C, Buvat I (eds) Handbook of particle detection and imaging. Springer, Berlin/Heidelberg Lederer CM, Shirley VS (1979) Table of isotopes. Wiley, New York Martin JE (2006) Physics for radiation protection: a handbook. Wiley-VCH, Weinheim Martin A (2012) An introduction to radiation protection, 6 edn. CRC Press/Taylor and Francis, Abingdon Martin JE (2013) The physics for radiation protection. Wiley-VCH, Weinheim Martin A, Harbison SA (2006) An introduction to radiation protection. Oxford University Press, A Hodder Arnold Publication, New York Mattsson S, Hoeschen C (2013) Radiation protection in nuclear medicine. Springer, Heidelberg Stabin MG (2007) Radiation protection and dosimetry: an introduction to health physics. Springer, Heidelberg The International Commission on Radiological Protection, ICRP (2008) www.icrp.org/. Accessed 24 Apr 2018

Suppliers of Radiation-Protection Equipment Berthold Technologies, Germany. www.bertholdtech.com/ww/en/pub/home.cfm Bicron Radiation Measurement Products, USA. www.bicron.com/ Canberra, USA. www.canberra.com/ EG&G, USA, Germany. https://www.berthold.com Eurofins RadonLab, Norway, Oslo. https://www.eurofins.com/ GRAETZ, Germany. www.graetz.com/englisch/sonden__en.htm

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Nuclitec, Germany. www.nuclitec.de/; c.o. Eckert and Ziegler, Germany. https:// www.ezag.com/home/ Thermo Fischer, Germany. https://www.thermofisher.com/de/de/home/industrial/ radiation-detection-measurement.html Saint Gobain, France. www.bicron.com/ nukepills, USA. https://www.nukepills.com/ LAURUS SYSTEMS, Japan. http://laurussystems.com/Crisis-in-Japan_RadiationInstruments.htm MIRION Technologies; USA, France and Germany. https://www.mirion.com/ All these webpages have been accessed on April 24, 2018

Part II Specific Types of Detectors

Gaseous Detectors

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Maxim Titov

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Basic Principles: Ionization, Transport Phenomena and Avalanche Multiplication . . . . . . . . The Multi-Wire Proportional, Drift, and Time Projection Chambers . . . . . . . . . . . . . . . . . . . . Micro-Pattern Gaseous Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Micro-Pattern Gaseous Detector Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Overview of the CERN-RD51 Collaboration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Future R&D Program for Advanced MPGD Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Summary and Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract Over the course of the last 50 years, the advances and breakthrough in instrumentation, leading to the development of new, cutting-edge technologies, drove the progress in experimental particle physics. A true innovation in detector concepts came in 1968, with the development of a fully parallel readout for a large array of sensing elements – the Multi-Wire Proportional Chamber (MWPC), which earned Georges Charpak a Nobel Prize in Physics in 1992. This invention revolutionized particle detection, which moved from optical-readout devices (cloud chamber, emulsion or bubble chambers) to the electronics era. Since then, radiation detection and imaging with gaseous detectors, capable of economically covering large detection volume with low mass budget, have been playing an important role in many fields of science. Over the past three decades, advances in photo-lithography, microelectronics, and printed-circuit board (PCB) techniques M. Titov () IRFU, CEA, Université Paris-Saclay, Gif-sur-Yvette, France e-mail: [email protected] © Springer Nature Switzerland AG 2021 I. Fleck et al. (eds.), Handbook of Particle Detection and Imaging, https://doi.org/10.1007/978-3-319-93785-4_11

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triggered a major transition in the field of gaseous detectors from wire structures to the Micro-Pattern Gaseous Detector (MPGD) concepts. The excellent spatial and time resolution, high rate capability, low mass, large active areas, and radiation hardness make them an invaluable tool to confront future detector challenges at the frontiers of research. Modern technologies have been also derived from original MPGD structures; hybrid approaches, combining different elements in a single device, gaseous with non-gaseous detectors, as it is the case for optical read-out, or novel concepts, where MPGDs are directly coupled to the CMOS pixel chip, have emerged. Important consolidation of some betterestablished MPGD structures has been reached within the RD51 collaboration, often driven by the working conditions of large collider experiments. The design of the new micro-pattern devices appears suitable for industrial production. This chapter provides an overview of the state of the art in gaseous detectors, various areas of their application, and summarizes some of the future R&D activities for advanced MPGD concepts.

Introduction The single wire proportional counter, invented more than 100 years ago by E. Rutherford and H. Geiger (Geiger and Rutherford 1908), and its high gain successor, the Geiger-Mueller counter first described in 1928 (Geiger and Mueller 1928), can be considered the ancestors of all modern gaseous detectors and were for many decades a major tool for the study of ionizing radiation. A true innovation in detector instrumentation concepts came in 1968, with the G. Charpak’s invention of a fully parallel readout for a large array of sensing elements – the Multi-Wire Proportional Chamber (MWPC) (Charpak et al. 1968), earning him the 1992 Nobel Prize in Physics. Crucially, the emerging integrated-circuit technology could deliver at that time amplifiers small enough in size and cost to equip many thousands of proportional wires. This invention marked the transition from optically readout detectors, such as bubble and cloud chambers, to the electronic era. With its excellent accuracy and modest rate capability, MWPC allowed large areas to be instrumented with fast tracking detectors and a low material budget, and was able to localize particle trajectories with sub-mm precision. Confronted by the increasing demands of particle physics experiments, MWPCs have continuously improved over the years (Sauli 1977, 2004, 2014; Charpak and Sauli 1979, 1984; Grupen 1996; Blum et al. 2008). Gradually replacing slower detectors, numerous advanced concepts with novel geometries and exploiting various gas properties have been developed: Drift Chamber (Walenta et al. 1971), Multi-Drift Module (Bouclier et al. 1988), JET Chamber (Drumm et al. 1980), Time Projection Chamber (TPC) (Nygren and Marx 1978), Time Expansion Chamber (Walenta 1979), Multi-Step Chamber (Charpak and Sauli 1978), Ring-Imaging Cherenkov Counter (RICH) (Seguinot and Ypsilantis 1977), Resistive Plate Chamber (RPC) (Santonico and Cardarelli 1981), and many others. However, limitations have been reached for wirebased devices in terms of maximum rate capability and detector granularity.

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In the late 1980s, advances in photolithography, microelectronics, and printed circuits have favored the invention of novel micro-structured gas-amplification devices. A fundamental rate limitation of wire chambers, due to positive ion accumulation in the gas volume, was overcome with the invention of Micro-Strip Gas Chamber (MSGC) (Oed 1988), capable of achieving position resolution of few tens of microns at particle fluxes exceeding MHz/mm2 (Barr et al. 1998). Developed for the projects at high-luminosity colliders, MSGC’s promised to fill a gap between the high-performance but expensive solid-state detectors, and cheap but rate-limited traditional wire chambers. Despite the impressive progress and a considerable development effort by the RD28 collaboration at CERN, two fundamental weaknesses of the MSGC structure – formation of deposits on the electrodes, affecting gain (“aging effects”), and spark-induced damages of electrodes in presence of highly ionizing particles – could not be resolved (Bagaturia et al. 2002). Nevertheless, MSGC trackers have been operated in the DIRAC (Adeva et al. 2003) and HERAB experiments (Hott 1998). The detailed studies of their properties have led to the development of a family of alternative, more robust structures, collectively named, Micro-Pattern Gaseous Detectors (MPGD), in general using modern photolithographic processes on thin insulating supports (Sauli and Sharma 1999; Sauli 2020). In particular, ease of manufacturing, operational stability, and superior performances for charged-particle tracking, muon detection and triggering have given rise to two main designs: the Gas Electron Multiplier (GEM) (Sauli 1997), and the Micro-mesh gaseous structure (Micromegas) (Giomataris et al. 1996). Recent developments in radiation hardness research with GEM and Micromegas revealed that they might be even less vulnerable to the radiation-induced aging effects than standard silicon micro-strip detectors, if reasonable precautions are taken on the components quality (Titov et al. 2002; Titov 2004). For applications requiring imaging detectors with large-area coverage and moderate spatial resolution (e.g. RICH counters), coarser macro-patterned structures offer an interesting economic solution with relatively low mass and easy construction – thanks to the intrinsic robustness of the PCB electrodes. Such devices are the thick-GEM (THGEM) (Periale et al. 2002; Chechik et al. 2004; Breskin et al. 2009), also referred to in the literature as Large Electron Multipliers (LEM), and patterned resistive thick GEM (RETGEM) (Di Mauro et al. 2007). The consolidation of better-established technologies has been accompanied with flourishing of novel ones, often specific to well-defined applications; among them are Resistive-Plate WELL (RPWELL) (Rubin et al. 2013), Micro-RWELL (μ-RWELL) (Bencivenni et al. 2015), and Micro-Pixel Gas Chamber (μ-PIC) (Ochi et al. 2001). The availability of highly integrated amplification and readout electronics allows for the design of gas-detector systems with channel densities comparable to that of modern silicon detectors. An elegant example is the use of a CMOS pixel ASIC, assembled directly below the GEM or Micromegas amplification structure (Costa et al. 2001; Bellazzini et al. 2004; Campbell et al. 2005; Bamberger et al. 2007). Modern “wafer post-processing technology” allows for the integration of a Micromegas grid directly on top of a Medipix or Timepix chip, thus forming integrated readout of a gaseous detector (“InGrid”) (Chefdeville et al. 2006).

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Using this approach, MPGD-based detectors can reach the level of integration, compactness, and resolving power typical of solid-state pixel devices. By 2008, interest in the development and the use of the novel micro-pattern gaseous detector (MPGD) technologies led to the establishment of the RD51 collaboration at CERN (https://rd51-public.web.cern.ch/welcome). While many of the MPGD technologies were introduced before RD51 was founded, with more techniques becoming available or affordable, new detection concepts are still being introduced and existing ones are substantially improved. The dedication of many groups of MPGD developers has led to rapid progress, crowned by new inventions and understanding of the underlying operation mechanisms of the different detector concepts. Thus, the potentiality of MPGD technologies became evident and the interest in their applications has started growing in high energy and nuclear physics, photon detectors and calorimetry, neutron detection and beam diagnostics, neutrino physics and dark matter detection, X-ray imaging and γ-ray polarimetry. Beyond fundamental research, MPGDs are in use and considered for applications of scientific, social and industrial interest; this includes the fields of medical imaging, nondestructive tests and large-size object inspection, homeland security, nuclear plant and radioactive-waste monitoring, micro-dosimetry, medicalbeam monitoring, tokamak diagnostics, geological studies by muon radiography. Some examples of MPGD applications will be discussed in section “Micro-Pattern Gaseous Detector Applications.”

Basic Principles: Ionization, Transport Phenomena and Avalanche Multiplication The low density of gaseous media sets basic limitations on the detector performance. The process of detection in gas proportional counters starts with the inelastic collisions between the incident particle and gas molecules. These collisions lead to excitation of the medium (followed by the emission of the light, the basis of scintillation detectors) and ionization, the primary signal for tracking devices. The number NP and the space distribution of the primary ionization clusters depend on the nature and energy of the radiation. The primary electrons can often have enough energy to further ionize the medium; the total number of electron-ion pairs NT is usually a few times larger than the number of primaries (NP ). Table 1 provides values of relevant parameters in some commonly used gases at NTP (normal temperature and pressure) for unit charge minimum-ionizing particles (MIPs) (Sauli and Titov 2020). The primary statistics determines several intrinsic properties of gas detectors, such as efficiency, time resolution, and localization accuracy. The actual number of primary interactions follows the Poisson’s statistics; the inefficiency of a perfect detector with a thin layer of gas is given by e−NP . Therefore, in 1 mm of Ar/CO2 (70:30) approximately 6% of all MIPs do not release a single primary electron cluster and therefore cannot be detected. The total energy loss, sum of primary and secondary ionization, follows a statistical distribution described by a Landau

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Table 1 Properties of noble and molecular gases at normal temperature and pressure (NTP: 20 ◦ C, one atmosphere). EX , EI : first excitation, ionization energy; WI : average energy per ion pair; dE/dx|min , NP , NT : differential energy loss, primary and total number of electron-ion pairs per cm, for unit charge minimum ionizing particles. Values often differ, depending on the source, and those in the table should be taken only as approximate. (Sauli and Titov 2020) Gas He Ne Ar Xe CH4 C2 H6 iC4 H10 CO2 CF4

Density(mg cm−3 ) 0.179 0.839 1.66 5.495 0.667 1.26 2.49 1.84 3.78

EX (eV) 19.8 16.7 11.6 8.4 8.8 8.2 6.5 7.0 10.0

EI (eV) 24.6 21.6 15.7 12.1 12.6 11.5 10.6 13.8 16.0

WI (eV) 41.3 37 26 22 30 26 26 34 54

dE/dx|min (keV cm−1 ) 0.32 1.45 2.53 6.87 1.61 2.91 5.67 3.35 6.38

NP (cm−1 ) 3.5 13 25 41 28 48 90 35 63

NT (cm−1 ) 8 40 97 312 54 112 220 100 120

function, with characteristic tails toward higher values. A simple composition law can be used for gas mixtures: for example, the number of primary (NP ) and total (NT ) electron-ion pairs produced by MIP in a 1 cm of Ar/CO2 (70:30) mixture at NTP: NP = 25 · 0.7 + 35 · 0.3 = 28

pairs ; cm

NT =

3350 pairs 2530 · 0.7 + · 0.3 ≈ 97 . 26 35 cm (1)

While charged particles release ionization trail consisting of primary electron clusters, low energy X rays undergo a single localized interaction, usually followed by the emission of the photo-electron, accompanied by the lower-energy photon or Auger electron. For example, a 5.9 keV X ray converts in argon mainly on a K shell (3.2 keV); the emitted photo-electron with energy Eγ − EK ∼ 2.7 keV has a practical range in detector of ∼200 μm. In addition, with 85% probability another (Auger) electron with energy ∼3 keV (∼250 μm range in argon) is ejected; in the remaining cases, a 3 keV K-L fluorescence photon is produced with a mean absorption length of 40 mm. The sum of the energies of photo-electron and Auger electron is responsible for the main 5.9 keV peak, while fluorescence mechanism leads to the Ar escape peak. The total number of electron-ion pairs created by 5.9 KeV X ray absorbed in argon can be evaluated by dividing its energy by the WI : 5900 / 26 ∼ 225. Once released in the gas, and under the influence of an applied electric field, electrons and ions drift in opposite directions and diffuse toward the electrodes. The scattering cross section is determined by the details of atomic and molecular structure. Therefore, the drift velocity and diffusion of electrons depend very strongly on the nature of the gas, specifically on the inelastic cross-section involving the rotational and vibrational levels of molecules. In noble gases, the inelastic cross

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section is zero below excitation and ionization thresholds. Large drift velocities are achieved by adding polyatomic gases (usually CH4 , CO2 , or CF4 ), having large inelastic cross sections at moderate energies, which results in “electron cooling” into an energy range of the Ramsauer-Townsend minimum (located at ∼0.5 eV) of the elastic cross section of argon. The reduction in both the total electron scattering cross section and the electron energy results in a large increase of electron drift velocity (for a compilation of electron-molecule cross sections see https:// fr.lxcat.net/instructions/categories.php). Another principal role of the polyatomic gas is to absorb the ultraviolet (UV) photons emitted by the excited inert gas atoms. The quenching of UV photons occurs through the photo-decomposition of polyatomic molecules. Extensive collections of experimental data (Peisert and Sauli 1984) and theoretical calculations based on transport theory (Biagi 1999) permit estimates of drift and diffusion properties in pure gases and their mixtures. In a simple approximation, gas kinetic theory provides the following relation between drift velocity, ν, and the mean collision time between electron and molecules, τ (Townsend’s expression): ν = eEτ/m. Values of drift velocity and transverse diffusion for some commonly used gases at NTP, computed with MAGBOLTZ program (see https://magboltz.web.cern.ch/magboltz), are given in Fig. 1. Using fast CF4 -based mixtures at fields around kV/cm−1 , the electron drift velocity is around 10 cm μs−1 . Since the collection time is inversely proportional to the drift velocity, diffusion is less in gases such as CF4 that have high drift velocities. In the presence of an external magnetic field, the Lorentz force acting on electrons between collisions deflects the drifting electrons and modifies the drift properties. For parallel electric and magnetic fields, drift velocity and longitudinal diffusion are not affected, while the transverse diffusion can be strongly reduced: σT (B) = σT (B = 0) / \sqrt(1+ ω2 τ2 ). This reduction is exploited in TPC to improve spatial resolution. In mixtures containing electronegative molecules such as O2, H2 O, CF4, electrons can be captured to form negative ions. Capture cross sections are strongly energy-dependent, and therefore the capture probability is a function of applied field. For example, the electron is attached to the oxygen molecule at energies below 1 eV. The three-body electron attachment coefficients may differ greatly for the same addition in different mixtures. As an example, at moderate fields (up to 1 kV/cm) the addition of 0.1% of oxygen to an Ar/CO2 mixture results in an electron capture probability about 20 times larger than the same addition to Ar/CH4 . Carbon tetrafluoride is not electronegative at low and moderate fields, making its use attractive as drift gas due to its very low diffusion. However, CF4 has a large cross section for dissociative attachment in the 6–8 eV electron energy range [Christophorou et al. 1996]. Depending on geometry, some signal reduction and loss of energy resolution can be expected in this gas. The primary ionization signal is very small in a gas layer: in 1 cm of Ar/CO2 (70:30) at NTP only ∼100 electron-ion pairs are created. Therefore, one has to use “internal gas amplification” mechanism to generate detectable signal in gas counters; excitation and subsequent photon emission participate in the avalanche spread processes and can be detected by optical means. If the electric field is

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a

σT [μm for 1 cm]

b 950

Ar Ar-CO2 70:30 Ar-CH4 90:10 CH4 CF4 Ar-CF4-CO2 65:30:5

900 850 800 750 700 650 600 550 500 450 400 350 300 250 200 150 100 50 2

3 4 5 6 7 89

1

2

3 4 5 6 7 89 10

2

3 4 5 6 7 89

E [kV/cm]

Fig. 1 (a) Electron drift velocity computed with the MAGBOLTZ program as a function of electric field in several gases at NTP and B = 0 (Sauli and Titov 2020); (b) standard deviations for transverse diffusion (σT ) are given for 1 cm of drift at NTP and B = 0 and scale with the square root of the drift distance (reproduced with permission from R. Veenhof, 2021)

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increased sufficiently, electrons gain enough energy between collisions to ionize molecules. Above a gas-dependent threshold, the mean free path for ionization, λi , decreases exponentially with the field; its inverse, α = 1/λi , is the first Townsend coefficient. In wire counters, most of the increase of avalanche particle density occurs very close to the anode wires, and a simple electrostatic consideration shows that the largest fraction of the detected signal is due to the motion of positive ions receding from the wires. The electron component, although very fast, contributes very little to the signal. This determines the characteristic shape of the detected signals in the proportional mode: a fast rise followed by a gradual increase. The slow component, the so-called ion tail that limits the time resolution of the counter, is usually removed by differentiation of the signal. In uniform fields, N0 initial electrons multiply over a length x forming an electron avalanche of size N = N0 eαx ; N/N0 is the gain of the counter. Gas amplification of 103 –104 is usually required in order to provide signals with sufficient amplitudes for conventional electronics. Positive ions released by the primary ionization or produced in the avalanches drift and diffuse under the influence of the electric field. Negative ions may also be produced by electron attachment to gas molecules. The drift velocity of ions in the fields encountered in gaseous counters (up to few kV/cm) is typically about three orders of magnitude lower than for electrons. The ion mobility, μ, the ratio of drift velocity to electric field, is constant for a given ion type up to very high fields (McDaniel and Mason 1973; Shultz et al. 1977). For mixtures, due to a very effective charge transfer mechanism, only ions with the lowest ionization potential survive after a short path in the gas. The diffusion of ions, both σL and σT , are proportional to the square root of the drift time, with a coefficient that depends on temperature but not on the ion mass. Accumulation of ions in the gas volume may induce gain reduction and field distortions, especially for long drift distances in TPC.

The Multi-Wire Proportional, Drift, and Time Projection Chambers Single-wire counters that detect the ionization produced in a gas by a charged particle, followed by charge multiplication and collection around a thin (typically 20–50 μm diameter) anode wire, have been used for decades. The invention of the Multi-Wire Proportional Chambers in the late 1960s revolutionized the field of radiation detectors allowing to detect, localize, and measure energy deposit by charged particles over large areas (Charpak et al. 1968; Charpak and Sauli 1984). In the original design, the MWPC consists of a grid of parallel, evenly spaced, anode wires between two large flat planes that serve as cathodes. Figure 2a shows a sketch of this arrangement together with electric field configuration. Typical values for the anode wire spacing range between 1 and 5 mm, and the anode to cathode distance is 5–10 mm. Because of electrostatic forces, anode wires are in equilibrium only for a perfect geometry. Small deviations result in forces displacing the wires alternatively below and above the symmetry plane and making operation increasingly difficult

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Fig. 2 Electric field lines and equipotentials in (a) a Multi-Wire Proportional Chamber and (b) a Drift Chamber. Thin anode wires (running perpendicular to the page) are placed equidistant between two parallel cathode planes and act as a set of independent proportional counters. Over a much volume away from a grid of anode wires, the field is nearly uniform. A high-field region is created in the immediate vicinity of each wire (Charpak and Sauli 1979, 1984)

at smaller wire spacings. For example, the electrostatic repulsion for thin (10 μm) anode wires causes mechanical instability above a critical wire length, which is less than 25 cm for 1-mm spacings. In a MWPC, electrons formed by ionization of the gas drift toward the plane of anode wires, initially in a nearly uniform field. The signal multiplication process,

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which begins a few radii from the anode, is over after a fraction of nanosecond, leaving the cloud of positive ions receding from the wires. A large negative-polarityinduced pulse appears on the anode on which the avalanche is collected, while the neighboring wires show smaller positive amplitude pulses. Detection of charge over a predefined threshold provides the transverse coordinate to the wire, connected to individual preamplifier, with an accuracy comparable to that of the wire spacing. With a digital√readout and s = 1 mm wire spacing, the spatial resolution is limited to: σ = s / 12 ∼ 300 μm. The coordinate along each wire can be obtained by measuring the ratio of collected charge at the two ends of resistive wires. The cathode planes can be fabricated in the form of group of wires or isolated strips, which are often patterned in the orthogonal directions (Sauli 1994). Making use of the positive charge signals induced by avalanches on segmented cathodes, the so-called electronic center-of-gravity (COG) method allows bi-dimensional localization of the ionizing event. Due to the statistics of energy loss and asymmetric ionization clusters, the position accuracy is ∼50 μm for tracks perpendicular to the wire plane, but degrades to ∼250 μm at 30◦ to the normal (Charpak et al. 1979). Drift chambers, developed in the early 1970s, can estimate the position of a track by exploiting the arrival time of electrons at the anodes if the time of interaction is known (Walenta et al. 1971). The distance between anode wires is usually several cm allowing coverage of large areas at reduced cost. In the original design, a thicker wire at proper voltage between anodes (field wire) reduces the field at the middle point between anodes and improves charge collection (Fig. 2b). In some drift chambers design, and with the help of suitable voltages applied to field-shaping electrodes, the electric field structure is adjusted to improve the linearity of spaceto-drift-time relation, resulting in better spatial resolution (Breskin et al. 1975). Drift chambers can reach a spatial resolution from timing measurement of order 100 μm (rms) or better for minimum ionizing particles, depending on geometry and operating conditions. However, a degradation of resolution is observed due to primary ionization statistics for tracks close to the anode wires, caused by the spread in arrival time of the nearest ionization clusters (Breskin et al. 1978). A measurement of drift time, together with the recording of charge sharing from the two ends of the anode wires, provides the coordinates of segments of tracks. The total charge gives information on the differential energy loss and is exploited for particle identification (PID). For an overview of detectors exploiting the drift time for coordinate measurement, see (Grupen 1996; Blum et al. 2008). Introduced in the 1980s, straw and drift tube systems make use of large arrays of wire counters encased in individual enclosures, each acting as an independent wire chamber (Baringer et al. 1987). Techniques for low-cost mass production of these detectors have been developed for large experiments, such as the Transition Radiation Tracker and the Drift Tubes arrays for CERN’s LHC experiments (Virdee 2004). Wire-based drift chambers have become well established in the fertile field of gaseous detectors during the past 50 years and are acknowledged as highly performing tracking devices successfully exploited in many recent experiments (e.g., Belle II Central Drift Chamber [Taniguchi 2017]). An ultra-light weight drift chamber for high precision momentum reconstruction and particle identification is

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under investigation for a Future Circular Collider (FCC-ee) (Abada et al. 2019) and a Circular Electron Positron Collider (CePC) (CEPC 2019). Its design is inspired by the DAFNE’s KLOE large wire chamber as well as by the more recent version of it developed for the MEG2 experiment (Tassielli et al. 2020). Conventionally, drift chambers have been operated with hydrocarbon-based mixtures, which are not trustable for the long-term, high-rate operation (Titov 2004). Hence, a dedicated study might be necessary to find an alternative hydrocarbon-free mixture adapted to the desired drift chamber performance at future colliders. The “ultimate” drift chamber is the Time Projection Chamber (TPC) concept invented in the 1976 (Nygren and Marx 1978), which combines a measurement of drift time and charge induction on the endplates to achieve excellent pattern recognition for high multiplicity environments and moderate rates. It has been a prime choice for large tracking systems in electron-positron colliders at PEP-4 (Nygren et al. 1976), ALEPH (Decamp et al. 1990), DELPHI (Sacquin et al. 1992) and proved its unique resolving power in the heavy ion collisions at NA49 (Afanasev et al. 1999), STAR (Wieman et al. 1997), and ALICE (Antonczyk et al. 2006). A TPC consists of a large gas volume, with a uniform electric field applied between the central electrode and an anode endplate at the opposite side. To be able to measure the position of the particle trajectory as accurately as possible, the electric field has to be very homogeneous in the TPC. This can be achieved by a field cage, which usually consists of conducting rings around the cylinder. These rings divide the potential from the cathode stepwise down to the anode. The ionization trails produced by charged particles drift toward the endplate segmented into 2D readout pads (see Fig. 3); the third coordinate is measured using the drift time information. A good knowledge of electron drift velocity and diffusion properties is required, which has to be combined with the modeling of electric fields in the structures.

Fig. 3 Schematic drawing of the Time Projection Chamber (TPC) (reproduced with permission from O. Schäfer, 2021)

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Additionally, a strong magnetic field parallel to the electric field is used to “bend” the trajectory of the particle on a spiral track due to the Lorentz force. This allows to calculate the momentum of the particle from the knowledge of the curvature and the B-field. The TPC concept provides 3D precision tracking; the gaseous detector volume gives an extremely low material budget; and the high density of space points enables PID through ionization loss (dE/dx) measurement. A further improvement comes from a more accurate description of the ionization energy loss by the socalled Bichsel function. An important major innovation in the design of future TPCs is related to the replacement of MWPCs with Micro-Pattern Gaseous Detectors for the endplate readout detectors. T2K experiment is the first example of the large volume TPC based on Micromegas structure (Anvar et al. 2009). While extensively employed at the LHC and other collider experiments, wirebased devices have limitations in terms of maximum rate capability and detector granularity. The production of positive ions in the avalanches and their slow drift before neutralization result in a rate-dependent accumulation of positive charge in the gas volume. This may result in significant field distortions, gain reduction, and degradation of spatial resolution. As shown in Fig. 4, the MWPC gain starts to drop at particle rates above 104 mm−2 s−1 , leading to a loss of detection efficiency (Breskin et al. 1975). Despite various improvements, basic diffusion processes and space charge effects limit position-sensitive devices based on wire structures to localization accuracies of 50–100 μm (Aleksa et al. 2000). A singlehit spatial resolution of σ ∼ 80 μm has been achieved in the most modern ATLAS Muon Spectrometer, which incorporates 354,000 Monitored Drift Tubes (MDT), assembled in 1172 chambers and covering an active area of more than 5500 m2

Fig. 4 Normalized gas gain as a function of particle rate for Multi-Wire Proportional Chamber (MWPC) (Breskin et al. 1975) and Micro-Strip Gas Chamber (MSGC) (Barr et al. 1998)

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(Aad et al. 2019). Together with the practical difficulty to manufacture large systems with sub-mm wire spacing, this has motivated the development of new generation gaseous detectors for high luminosity colliders.

Micro-Pattern Gaseous Detectors Industrial advances in microelectronics and photolithographic technology on flexible and standard PCB substrates has favored the invention, in the last years of the twentieth century, of novel Micro-Pattern Gaseous Detectors (MPGD) (Sauli and Sharma 1999). By using pitch size of a few hundred microns, an order of magnitude improvement in granularity over wire chambers, these detectors offer intrinsic high-rate capability (>106 Hz/mm2 ), excellent spatial resolution (down to 30 μm), multiparticle resolution (∼500 μm), single photo-electron time resolution in the ns-range, large sensitive area and dynamic range, and superior radiation hardness. The Micro-Strip Gas Chamber (MSGC), a concept invented in 1988, was the first of the microstructure gas detectors (Oed 1988). It consists of a set of tiny parallel metal strips laid on a thin resistive substrate, alternatively connected as anodes and cathodes. The principle of MSGC resembles a multi-anode proportional counter, with fine printed strips instead of wires (see Fig. 5a). Through an accurate and simple photolithography process, the anode strips can be made very narrow (∼10 μm) with a typical pitch (distance between strips) of ∼100 μm. When appropriate potentials are applied to the electrodes, electrons released in the drift volume move toward the strips and start to multiply, as they approach the highfield region. As in the conventional proportional counter, a large fraction of the negative signal on the anodes is induced by moving ions, resulting in a fast rise time. All field lines from the drift volume terminate on the anodes, resulting in full electron-collection efficiency. Owing to the small anode-to-cathode distance, the fast removal of positive ions by nearby cathode strips reduces space charge buildup, and provides a greatly increased rate capability of the MSGC, compared to wire chamber (Barr et al. 1998) (see Fig. 4). Although their primary use has been as position-sensitive detectors for particle tracking, MSGC’s can also provide energy information for spectroscopic measurements. Their energy resolution is enhanced compared to a wire counter, because avalanche fluctuations are minimized due to the sharp gradient in the electric field strength near the anode surface [Miyamoto and Knoll 1997]. Despite their promising performance, experience with MSGCs has raised serious concerns about their long-term behavior. There are several major processes, particularly at high rates, leading to the MSGC operating instabilities: substrate charging-up and time-dependent distortions of the electric field, surface deposition of polymers (“aging”) during sustained irradiation, and destructive micro-discharges under exposure to heavily ionizing particles (Charpak and Sauli 1984; Bouclier et al. 1996). The physical parameters used to manufacture and operate these detectors (substrate material, metal of strips, type and purity of the gas mixture) appeared to

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Fig. 5 (a) Schematic view and field lines in the MSGC: on a resistive substrate, narrow (∼10 μm) anode strips alternate with wider cathodes; typical pitch is ∼100 μm (Sauli and Sharma 1999); (b) microscopic image of the MSGC electrodes. With its very thin metal layers, MSGCs are vulnerable to damage due to discharges induced by heavily ionizing particles (reproduced with permission from F. Sauli, 2019)

play dominant roles in determining the medium- and long-term stability. To avoid surface charging, the substrate must have some finite electrical conductivity, and a number of different recipes for slightly conducting glass and/or coatings on other materials have emerged in the development of these devices. The problem of discharges is the intrinsic limitation of all single-stage MicroPattern Gaseous Detectors in hadronic beams (Peskov et al. 1997; Ivaniouchenkov et al. 1999; Bressan et al. 1999a). Whenever the total charge in the avalanche exceeds a value of 107 –108 electron-ion pairs (Raether limit), an enhancement of the electric field in front of and behind the primary avalanche induces a fast growth of a filament-like streamer followed by breakdown. This has been confirmed under

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a wide range of operating conditions and multiplying gaps (Ivaniouchenkov et al. 1998; Fonte et al. 1999; Iacobaeus et al. 2002; Peskov and Fonte 2009). In the high fields and narrow gaps, MSGC turned out to be prone to irreversible discharges induced by heavily ionizing particles and destroying the fragile electrode structure, as shown in the image in Fig. 5b. Introduced in 1996 by F. Sauli (1997), a Gas Electron Multiplier (GEM) detector consists of a thin-foil copper-insulator-copper sandwich chemically perforated to obtain a high density of holes in which avalanche formation occurs. Originally, the GEM manufacturing method, developed at CERN, was a refinement of the doubleside printed circuit technology. The copper-clad polymer is engraved on both sides with the desired hole pattern; controlled immersion in a kapton-specific solvent opens the channels in the insulator. The hole diameter is typically between 25 μm and 150 μm, while the corresponding distance between holes varies between 50 μm and 200 μm. The central insulator is usually (in original design) the polymer kapton, with a thickness of 50 μm. Application of a potential difference between the two sides of the GEM generates the electric field indicated in Fig. 6a. Each hole acts as an independent proportional counter. Electrons released by the primary ionization particle in the upper drift region (above the GEM foil) are focused into the holes, where charge multiplication occurs in the high electric field (50–70 kV/cm). Most of the avalanche electrons are transferred into the gap below the GEM (Bressan et al. 1999b; Bachmann et al. 1999). Several GEM foils can be placed at short distances (typically 1–2 mm) to distribute the gas amplification among several stages (see Fig. 6b). This allows the triple-GEM detector to operate at overall gas gain above

50 μm

140 μm

Fig. 6 (a) Schematic view and typical dimensions of the hole structure in the GEM amplification cell. Electric field lines (solid) and equipotentials (dashed) are shown (Sauli and Sharma 1999); (b) schematic view of the triple-GEM detector. The original ionization occurs in the region labeled “Drift’,” and the ionization electrons are drawn downward to the GEM foil. The amplified electrons emerging from the first GEM are drifted to the second GEM, where they again multiplied. One more GEM stage provides further amplification, and the output is collected at the readout plane (Sauli 2007) (reproduced with permission from F. Sauli, 2012)

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104 in the presence of highly ionizing particles, while strongly reducing the risk of discharges (105 has been reached in cascaded multi-THGEMs, which together with good photoelectron extraction efficiency, similar to the MWPCs with CsI-PC, small photon feedback and reduced ion backflow ( 0, wk,i = wk (χk,i−1 , Ti ) above, with Ti ≤ Ti−1 defined by the annealing schedule. For T → 0, the Fermi function approximates the Heaviside function, and the assignment turns into a “hard” one (wk = 1 or 0 only). The Multi-Vertex Filter is a generalized DAF, simultaneously fitting m vertices by “soft assignment” of each track to more than one vertex. The extra weights wk of track k w.r.t. vertex  in one iteration are

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2 wk (χk ,T) =  m

λ=1 e

2 /2T −χkλ

+ e−χcut /2T 2

Helix Tracking Coordinates The tracking detector layout is assumed to be approximately rotational symmetric w.r.t. the z-axis, but not necessarily mirror symmetric w.r.t. the origin z = 0. The axes (x, y, z) define a righthanded orthogonal basis. By convention, the x-axis is chosen to be “horizontal,” and the y-axis to point upward. Surfaces are defined as either cylinders of radius R or as planes either normal to the z-axis (“end caps”) or parallel to the z-axis (“prism”) or inclined w.r.t. the z-axis (“pyramid”). They may be real or virtual. Besides Cartesian coordinates, cylindric coordinates and spherical polar coordinates are defined for space points and/or momenta: Space points x = [x, y, z]cart = [R, Φ, z]cyl x = R · cosΦ y = R · sinΦ

 R = x2 + y2 Φ = arc tan(y/x), azimuth angle 0 ≤ Φ < 2π

Momenta p = [px , py , pz ]cart = [P , ϑ, ϕ]sph = [pT , ϕ, pz ]cyl 

px2 + py2 + pz2 =

 pT2 + pz2

px = P · sinϑ · cosϕ

P =

py = P · sinϑ · sinϕ pT = P · sinϑ pz = P · cosϑ

ϑ = arc cos(pz /P ), polar angle 0 ≤ ϑ ≤ π λ ≡ π2 − ϑ, dip angle π2 ≥ λ ≥ − π2 ϕ = arc tan(py /px ), azimuth angle 0 ≤ ϕ < 2π

The magnetic field is assumed to be homogeneous and aligned parallel or antiparallel to the z-axis. It is defined by the flux density B = [0, 0, Bz ]cart . This implies a helix track model, with the helix axis being parallel to z. The following units are most often used: [length] = m (or) cm, [angle] = rad, [momentum] = GeV/c, [B f ield] = T (Tesla), and [charge] = e (elementary charge). For a particle with momentum P and charge Q, the radius of the helix rH and its conveniently signed inverse κ are rH =

1 P · sinϑ · > 0, Kunit | Q · Bz |

κ = − sign(Q · Bz ) / rH

with the unit-dependent constant (here shown for two units of length) Kunit = (10−9

c [length] GeV/c GeV/c GeV/c )· ≈ 0.29979 = 0.0029979 m/s m T · [length] T·m T · cm

The sign convention corresponds to sign(κ) = sign(dϕ/ds) ≡ sense of rotation in the (x, y)projection. Note that in the absence of matter, P and ϑ are constants of motion; in the case of multiple scattering, only P remains constant. The helix equations for a starting point [xS , yS , zS ] and a starting azimuthal direction angle ϕS , as functions of the running parameter ϕ, are: x(ϕ) = xS + (sinϕ − sinϕS ) / κ y(ϕ) = yS − (cosϕ − cosϕS ) / κ z(ϕ) = zS + cot ϑ · (ϕ − ϕS ) / κ,

path length s(ϕ) = (ϕ − ϕS ) / (κ · sin ϑ)

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A fitter’s internal track parameters are often defined as follows: [RΦ, z, ϑ, β, κ], β ≡ ϕ − Φ at R = RS [x, y, cot ϑ, ϕ, κ] at z = zS [x, y, dx/dz, dy/dz, Q/P ] at z = zS

in the radial (“barrel”) region in the forward/backward regions in the extreme fwd/bkwd regions

Examples of popular alternative external track parameters are: [x, y, z, px , py , pz ] [δT , δz , cot ϑ, ΦP , κ]

“6D Cartesian” (RAVE Waltenberger 2011), with the corresponding 6 × 6 covariance matrix being of rank 5 only “Perigee representation”

The perigee point [xP , yP , zP ] of a helix track is defined, in the (x, y)-projection, as the “point of closest approach” (PCA) to a fixed pivot point [x0 , y0 , z0 ]. The track parameters in perigee representation and usual convention are:  δT = ± (xP − x0 )2 + (yP − y0 )2 projected distance between perigee and pivot points (transverse impact parameter), with + or − sign indicating the pivot point sitting to the left or to the right of the helix, respectively; δz = z P − z 0 distance along z between perigee and pivot points; cot ϑ slope of the helix; 0 ΦP = arc tan yxPP −y azimuthal position of perigee point w.r.t. pivot point; −x0 κ inverse helix radius, with the sign defined as before. Beware of subtle differences in the various conventions, e.g., for the units of length and momentum, the sign definitions for δT and κ, replacement of ΦP by the azimuthal direction ϕP = ΦP + sign(δT ) · π2 of the helix at the perigee point, or an assumption about sign(Bz ) with implicit consequences.

Cross-References  Data Analysis  Gaseous Detectors  New Solid State Detectors

References Aaboud M et al (2017) (ATLAS Collaboration) Eur Phys J C 77:673 Abashian A et al (2002) (Belle Collaboration) Nucl Instr Meth A 479:117 Abramowitz M, Stegun IA (eds) (1965) Handbook of mathematical functions, Section 25.5. Dover Publications, Mineola Abreu P et al (1996) (DELPHI Collaboration) Nucl Instr Meth A 378:57 Achenbach P et al (2008) Nucl Instr Meth A 593:353 Adam W et al (2005) J Phys G Nucl Part Phys 31:N9 Adam W et al (2009a) JINST 4 P06009 Adam W et al (2009b) JINST 4 T07001s Adinolfi M et al (2002) Nucl Instr Meth A 478:138

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Adolphsen C et al (eds) (2013) The international linear collider TDR: accelerator baseline design, ILC Report 2013-040, vol 3 Part II. ISBN 978-3-935702-77-5 Adorisio C et al (2009) Nucl Instr Meth A 598:400 Agostinelli S et al (2003) Nucl Instr Meth A 506:250 Alexopoulos T et al (2008) Nucl Instr Meth A 592:456 Alfonsi M et al (2004) Nucl Instr Meth A 518:106 Altunbas C et al (2002) Nucl Instr Meth A 490:177 Anderson M (2003) Nucl Instr Meth A 499:659 Arneodo F et al (2003) Nucl Instr Meth A 498:292 Arrabito L et al (2007) JINST 2 P05004 Avery P (1999) Applied fitting theory vi: formulas for kinematic fitting, Report CBX 98 V-37, University of Florida, Gainesville Bagliesi MG et al (2009) Nucl Instr Meth A. https://doi.org/10.1016/j.Nucl.Instr.Meth.a.2009. 07.006 Beckmann M, List B, List J (2010) Nucl Instr Meth A 624:184 Behnke T et al (eds) (2013) The international linear collider TDR: detectors, ILC Report 2013-040, vol 4. ISBN 978-3-935702-78-2 Beischer B et al (2011) Nucl Instr Meth A 628:403 Beiser A (1952) Rev Mod Phys 24:273 Berggren M (2012) arXiv:1203.0217 Berretti M (2017) (TOTEM Collaboration) Nucl Instr Meth A 845:29 Bethe H, Heitler W (1934) Proc R Soc A 146:83 Bevan AJ et al (eds) (2014) The physics of the B factories. Eur Phys J C 74:3026 (Springer, Berlin, 2015). ISBN 978-3-662-52592-0 Blau M (1963) Methods of experimental physics, vol 5. In: Yuan LCL, Wu C-S (eds) Nuclear physics. Academic Press, New York/London 1961, 1963 Blobel V (2006) Nucl Instr Meth A 566:5 Blobel V (2007) Millepede II: the manual (University of Hamburg 2007) Blobel V, Kleinwort C (2002) Proceedings of conference on advanced statistical techniques in particle physics, Durham Brown DN et al (2009) Nucl Instr Meth A 603:467 Burrows PN et al (eds) (2016) Updated baseline for a staged compact linear collider, CERN-2016004 (CERN, Geneva, 2016) Chabanat E et al (2005) (CMS Collaboration) Nucl Instr Meth A 549:188 Charpak et al G (1968) Nucl Instr Meth 62:262 Chatrchyan S et al (2008) (CMS Collaboration) JINST 3 S08004 Chatrchyan S et al (2014) (CMS Collaboration) JINST 9(10):P10009 Colas P (2004) Nucl Instr Meth A 535:181 De Gerone M et al (2009) Nucl Instr Meth A 610:218 Derré J et al (2001) Nucl Instr Meth A 459:523 Doležal Z, Uno S (eds) (2010) Belle II technical design report, KEK Report 2010-1 (KEK, Tsukuba 2010) Dominguez A (2007) Nucl Instr Meth A 581:343 Eskut E et al (1997) Nucl Instr Meth A 401:7 Evans L, Bryant P (eds) (2008) JINST 3 S08001 Flanagan JW, Ohnishi Y (eds) (2004) Letter of intent for KEK super B factory: accelerator design, KEK Report 2004-4, Part 3 (KEK, Tsukuba 2004) Frühwirth R (1987) Nucl Instr Meth A 262:444 Frühwirth R (1992) Proceedings of international conference on computing in high energy and nuclear physics, Annecy, CERN 92-07, p 323 Frühwirth R (1993) Comput Phys Commun 78:23 Frühwirth R, Nadler M (2011) Nucl Instr Meth A 648:246 Frühwirth R, Regler M (2001) Nucl Instr Meth A 456:369 Frühwirth R, Strandlie A (1999) Comput Phys Commun 120:197

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Fühwirth R, Waltenberger W (2004) CMS conference report CR 2004/062. CERN, Geneva Frühwirth R, Kubinec P, Mitaroff W, Regler M (1996) Comput Phys Commun 96:189 Frühwirth R, Regler M, Bock RK, Grote H, Notz D (2000) In: Regler M, Frühwirth R (eds) Data analysis techniques for high-energy physics, 2nd edn. Cambridge University Press, Cambridge Frühwirth R, Glattauer R, Lettenbichler J, Mitaroff W, Nadler M (2013) Nucl Instr Meth A 732:95 Frühwirth R, Brondolin E, Strandlie A (2020) Pattern recognition and reconstruction. In: Fabjan CW, Schopper H (eds) Particle physics reference library, vol 2: detectors for particles and radiation. Springer, Berlin Giomataris Y et al (1996) Nucl Instr Meth A 376:29 Glattauer R, Frühwirth R, Lettenbichler J, Mitaroff W (2011) Proceedings of international linear collider workshop, Granada. arXiv:1202.2761 Gluckstern RL (1963) Nucl Instr Meth 24:381 Gorbunov S, Kisel I (2006) Nucl Instr Meth A 559:139 Gruber L (2020) (LHCb Collaboration) Nucl Instr Meth A 958:162025 Hartmann F (2017) Evolution of silicon sensor technology in particle physics, 2nd edn. Springer, Berlin. ISBN 978-3-319-64434-9 Highland V (1975) Nucl Instr Meth 129:479 Hillert S (2008) arXiv:0811.4759 ILC software repository. https://www.github.com/iLCSoft/ LCFIVertex Höppner C et al (2010) Nucl Instr Meth A 620:518 Hough PVC (1959) Proceedings of international conference on high energy accelerators and instrumentation. CERN, Geneva Hübner K (2004) Phys Rep 403–404:177 Hyams B et al (1983) Nucl Instr Meth 205:99 Ivaniouchenkov Y et al (1999) Nucl Instr Meth A 422:300 Jackson DJ (1997) Nucl Instr Meth A 388:247 Jacob MRM, Quercigh E (eds) (1997) Symposium on the CERN omega spectrometer: 25 years of physics, CERN-97-02 (CERN, Geneva 1997) Kartvelishvili V (2007) Nucl Phys B Proc Suppl 172:208 Kasieczka G (2015) (RD42 Collaboration). In: Proceedings of international workshop on vertex detectors (Santa Fe, NM 2015), PoS VERTEX2015 033 Ketzer B (2002) Nucl Instr Meth A 494:142 Kim BJ et al (2003) Nucl Instr Meth A 497:450 Kisel I, Ososkov G (1992) Proceedings of international conference on computing in high energy and nuclear physics, Annecy, CERN 92-07, p 646 Kisel I, Konotopskaya E, Kovalenko V (1997) Nucl Instr Meth A 389:167 Klingenberg R (2007) Nucl Instr Meth A 579:664 Kobayashi M (2007) Nucl Instr Meth A 581:265 Kruskal JB (1956) Proc Am Math Soc 7:48 Larsen DT (2009) Nucl Instr Meth A. https://doi.org/10.1016/j.Nucl.Instr.Meth.a.2009.07.002 Li B, Fujii K, Gao Y (2013) arXiv:1305.7300, ILC software repository. http://www.github.com/ iLCSoft/KalTest Mager M (2016) (ALICE Collaboration) Nucl Instr Meth A 824:434 Mankel R (1997) Nucl Instr Meth A 395:169 Mitaroff W, Regler M, Valentan M, Höfler R (2007) Proceedings international linear collider workshop, Hamburg, DESY-PROC-2008-03, p 468 Morley A (2008) Nucl Instr Meth A 596:32 Moser F, Waltenberger W, Regler M, Mitaroff W (2008) Proceedings of international linear collider workshop, Chicago. arXiv:0901.4020 Oed A (1988) Nucl Instr Meth A 263:351 Ortner G, Stetter G (1928) Mittlg. Inst. Radiumforschung No. 228 (Vienna) Prokofiev K (2005) Ph.D. Thesis, University of Zurich, CERN-THESIS-2009-109 Qin ZH et al (2007) Nucl Instr Meth A 571:612 Radon J (1986) (Leipzig 1917) transl. IEEE Trans Med Imaging 5(4):170

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Regler M, Frühwirth R (2008) Nucl Instr Meth A 589:109 Regler M, Mitaroff W, Valentan M, Frühwirth R, Höfler R (2008a) Proceedings of international conference on computing in high energy and nuclear physics, Victoria, 2007, J Phys Conf Ser 119:032034 Regler M, Valentan M, Frühwirth R (2008b) LiC detector toy user’s guide, PUB-863/08. HEPHY, Vienna. http://www.hephy.at/project/ilc/lictoy/UserGuide_20.pdf Reingamum M (1911) Phys Z 12:1076 Riegler W et al (2000) Nucl Instr Meth A 443:156 Sauli F (1997) Nucl Instr Meth A 386:531 Sauli F, Sharma A (1999) Ann Rev Nucl Part Sci 49:341 Sirunyan AM et al (2017) (CMS Collaboration), CERN-LHCC-2017-009 (CERN, Geneva 2017) Speer T, Frühwirth R (2006) Comput Phys Commun 174:935 Strandlie A, Frühwirth R (2010) Rev Mod Phys 82:1419 Thomson M (2009) Nucl Instr Meth A 611:25 Titov M (2007) Nucl Instr Meth A 581:25 Urquijo P, Barberio E (2005) Belle Note 756 (KEK, Tsukuba 2005) Valentan M, Regler M, Frühwirth R (2009) Nucl Instr Meth A 606:728 Waltenberger W (2008) CMS Note 2008/033. CERN, Geneva Waltenberger W (2015) Private software repository. https://www.github.com/ WolfgangWaltenberger Waltenberger W, Frühwirth R, Vanlaer P (2007) J Phys G Nucl Part Phys 34:N343 Waltenberger W (2011) IEEE Trans Nucl Sci 58:434 Widl E, Frühwirth R (2008) Proceedings of international conference on computing in high energy and nuclear physics (Victoria, BC, 2007) J Phys Conf Ser 119:032038 Zerguerras T et al (2007) Nucl Instr Meth A 581:258

Further Reading Frühwirth R, Regler M, Bock RK, Grote H, Notz D (2000) In: Regler M, Frühwirth R (eds) Data analysis techniques for high-energy physics, 2nd edn. Cambridge University Press, Cambridge Frühwirth R, Brondolin E, Strandlie A (2020) Pattern recognition and reconstruction. In: Fabjan CW, Schopper H (eds) Particle physics reference library, vol 2: detectors for particles and radiation. Springer, Berlin Grupen C, Shwartz B (2008) Particle detectors, 2nd edn. Cambridge, Cambridge University Press Hartmann F (2017) Evolution of silicon sensor technology in particle physics, 2nd edn. Springer, Berlin Leroy C, Rancoita P-G (2009) Principles of radiation interaction in matter and detection, 2nd edn. World Scientific Publishing, Singapore Strandlie A, Frühwirth R (2010) Track and vertex reconstruction: from classical to adaptive methods. Rev Mod Phys 82:1419

Photon Detectors

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Samo Korpar and Peter Križan

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . General Properties of Photon Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Vacuum Photodetectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Photomultiplier Tubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Microchannel Plate Photomultiplier Tube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hybrid Photodetectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gaseous Photon Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Solid-State Photon Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Suppliers of Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract This chapter is intended as an overview of techniques for detection of photons, from the infrared to the ultraviolet and extreme ultraviolet. We discuss the vacuum photon detectors, gaseous photon detectors, and semiconductor sensors, as well as recent progress in novel photon detection methods.

S. Korpar Faculty of Chemistry and Chemical Engineering, University of Maribor, Maribor, Slovenia J. Stefan Institute, Ljubljana, Slovenia e-mail: [email protected] P. Križan () J. Stefan Institute, Ljubljana, Slovenia Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana, Slovenia e-mail: [email protected] © Springer Nature Switzerland AG 2021 I. Fleck et al. (eds.), Handbook of Particle Detection and Imaging, https://doi.org/10.1007/978-3-319-93785-4_13

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Introduction A large fraction of detectors in particle, nuclear, and astrophysics, as well as in medical imaging ( Chap. 39, “Radiation-Based Medical Imaging Techniques: An Overview”) is based on the detection of photons in or near the visible range (100 nm < λ < 1000 nm). This includes detection of scintillation ( Chap. 15, “Scintillators and Scintillation Detectors”) and Cherenkov light ( Chap. 19, “Cherenkov Radiation”) as well as the light detected in astronomical observations. In most photosensors, detection of photons proceeds in three steps. First, a primary photoelectron or electron–hole (e–h) pair is generated by an incident photon via the photoelectric or the photoconductive effect. By charge multiplication the number of electrons is increased to a detectable level, so that finally secondary electrons produce an electrical signal. The three steps are best illustrated on the example of the photomultiplier tube (PMT), the most common light sensor with a structure of electrodes enclosed in an evacuated glass vessel (Fig. 1). The photon hits a semitransparent photocathode, in which its energy is transferred to an electron. This photoelectron exits the photocathode and enters an electric field, which leads it to the first dynode. The dynodes serve as an electron multiplier chain; electrons are accelerated in the electric field, strike the next dynode, releasing more electrons. After several amplification stages, the swarm of electrons is collected at the last electrode, the anode, where a detectable current signal is produced.

General Properties of Photon Detectors Photon detectors are characterized by the following properties (Particle Data group 2009):

Fig. 1 Schematics of a transmission-type photomultiplier tube (Hamamatsu 2006). (Reproduced with permission from Hamamatsu Photonics, July 2010)

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Quantum efficiency (QE or q ): the probability that the incident photon generates a photoelectron Collection efficiency (CE or c ): the probability that the photoelectron starts the electron multiplication Gain (G): the number of electrons collected for each generated photoelectron Dark current or dark noise: the electrical signal with no photon at the input Dynamic range: the maximum signal available from the detector (usually expressed in units of the response to noise-equivalent power, or NEP, which is the optical input power that produces a signal-to-noise ratio of 1) Time dependence of the response: this includes the transit time, which is the time between the arrival of the photon and the electrical pulse, and the transit time spread (TTS), which contributes to the timing uncertainty of the pulse, and influences the rise time and duration of a multi-photoelectron signal. Single-photon detection capability: important when measuring very-low-level light intensities Rate capability: inversely proportional to the time needed, after the arrival of one photon, to get ready to receive the next (i.e., recovery time) Stability: essential for long-term operation at elevated counting rates Note that the term photon detection efficiency (PDE) is often used for the combined probability to produce a photoelectron and to detect it (PDE = q c ). Note also that producers often quote the cathode radiant sensitivity Sk , the ratio between the photocathode current to the incoming light power; Sk is related to the quantum efficiency through (Sk = q e/hν), where e is the elementary charge, and hν is the photon energy.

Vacuum Photodetectors In a vacuum photodetector, the photocathode and the electron multiplication stage are in vacuum, enclosed in a vessel made of various combinations of glass, ceramics, and metal. Vacuum photodetectors are of three types: photomultiplier tubes, microchannel plate photomultiplier tubes, and hybrid photodetectors.

Photomultiplier Tubes Photomultiplier tubes (PMTs) (Fig. 1) have been up to very recently the most common photodetector in particle physics experiments and medical imaging (Arisaka 2000). In a transmission-type PMT, the photosensitive material (photocathode) is on the inside of a transparent window through which the photons enter (Fig. 1); in a reflection-type PMT, the photocathode material is deposited on a separate electrode inside the tube. The photosensitive material has a suitably low work function, such that when a photon hits the photocathode, an electron is produced in a photoelectric effect. This photoelectron is then accelerated and guided by the

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electric field to hit the next electrode (dynode), which is covered with a material suitable for high secondary emission. A single electron therefore produces a few (≈5) secondary electrons, and this process is repeated at subsequent dynodes, typically ten altogether. By this electron multiplication process, 105 –106 electrons are generated and collected at the anode. The total gain of a PMT depends on the applied high voltage U as G = AUkn , where k ≈ 0.7 − 0.8 (depending on the dynode material), n is the number of dynodes in the chain, and A is a constant (which also depends on n). The sensitive wavelength range of the PMT is determined by the choice of the photocathode material. These materials are usually Cs- and Sb-based compounds such as CsI, CsTe, bialkali (SbRbCs, SbKCs), multialkali (SbNa2 KCs), as well as GaAs(Cs), GaAsP, etc. From the wavelength dependence of the quantum efficiency for these materials as displayed in Fig. 2, we observe that they cover a wide range of wavelengths, from the infrared (IR) to the extreme ultraviolet (XUV) (Hamamatsu 2006). Note that improved versions of bialkali photocathodes are also available with a considerably higher quantum efficiency. They are known as super-bialkali (SBA) and ultra-bialkali (UBA) photocathodes, with peak efficiencies as high as 35% and 45%, respectively (Nakamura et al. 2010). The low-wavelength cutoff is usually given by the choice of the window material (Fig. 2). Common window materials are borosilicate glass for IR to near-UV, fused quartz and sapphire (Al2 O3 ) for UV, and MgF2 or LiF for XUV. Typical dynode structures used in PMTs are the so called box and grid (Fig. 1), circular cage, linear focused, venetian blind, fine mesh, and metal foil (Fig. 3). The choice of the structure depends on the use. While the linear focused structure allows for a small time jitter, the metal-foil structure is employed in position-sensitive PMTs with multichannel anode granularities as fine as ≈2 × 2 mm2 (Hamamatsu Photonics). The transit time spread is typically a few 100 ps for line-focusing, fine-mesh and metal-foil dynode structures, and a few nanoseconds for PMTs with box-and-grid, circular-cage, and venetian-blind dynodes. Voltages are distributed to the dynodes by a resistive voltage divider chain so that the most negative high voltage is supplied to the photocathode. To improve the linearity and high rate operation, the divider chain includes capacitors in the higher amplification stages, or even active elements, transistors, or diodes. When a photomultiplier is used to detect very low light intensities, it is often advantageous to count single-photon pulses. Because of the nature of the secondary emission process, single-photoelectron pulses show large fluctuations. Some PMT types allow for an efficient single-photon detection, an example of which is shown in Fig. 4, while for some (like fine-mesh PMTs) no single-photon detection is possible because of a low multiplication. PMTs are affected by the presence of magnetic fields. The magnetic field deflects electrons from their normal trajectories and causes orientation-dependent loss of efficiency and gain; these effects are in some cases observed even in the geomagnetic field. In particular PMTs with a long path from the photocathode to the first dynode are very vulnerable. A high-permeability metal shield is often necessary. However, PMTs with the fine-mesh dynode chain can be used even in a high magnetic field

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Fig. 2 Quantum efficiency for different photocathode materials (top), window transmission curves (bottom) (Hamamatsu 2006). (Reproduced with permission from Hamamatsu Photonics, July 2010)

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Fig. 3 Metal-foil dynode structure (Hamamatsu 2006). (Reproduced with permission by Hamamatsu Photonics, July 2010)

Fig. 4 Pulse-height distributions due to single photoelectrons as detected by a multi-anode R5900M16 photomultiplier tube with three different cathode high voltages (Križan et al. 1997)

(≈1 T) if the tube axis is partially aligned with the field, although the gain decreases considerably (Iijima et al. 1997).

Microchannel Plate Photomultiplier Tube In a microchannel plate (MCP) photomultiplier tube , the discrete dynode chain is replaced by continuous multiplication in 6–20 μm-diameter cylindrical holes, or

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“channels” (Fig. 5). These channels are densely packed in an about 1 mm thick glass plate. The inner channel walls are processed to have proper electrical resistance and secondary-emission properties. The multiplication gain depends exponentially on the ratio of the channel length to its diameter. A typical value of this ratio is 40, and typical gains of a single microchannel plate are about 104 . For higher gains, two or more microchannel plates are used in series. MCP PMTs are thin: the gaps between the transmission-type photocathode and the microchannel plates, and between the microchannel plates and the anode plane are only a few mm thick. MCP PMTs offer good spatial resolution, have excellent time resolution (≈20 ps r.m.s.; here and throughout the paper, uncertainties and resolutions will be quoted with their r.m.s. values), and can tolerate random magnetic fields up to 0.1 T and axial fields exceeding 1 T. However, they suffer from a relatively long recovery time per channel and short lifetime. The performance of this sensor type may degrade due to residual gas in the channels, which gets ionized, and the feedback ions and photons hit and gradually destroy the photocathode. Most modern MCP-based photodetectors consist of two microchannel plates with angled channels rotated with respect to each other producing a chevron (v-like) shape, as illustrated in Fig. 5. The angle between the channels reduces ion and photon feedback in the device. In addition, in the last few years, further improvement was achieved in the lifetime of MCPs by improving the vacuum in the vessel and by a protective aluminum foil (Hamamatsu 2006; Flyckt and Marmonier 2002); the best performance is, however, achieved by atomic layer deposition (ALD) of the microchannel plates. While MCPs have been widely employed as image intensifiers, they have not been used in particle physics or astrophysics. Recently, however, the need to perform Cherenkov imaging within magnetic spectrometers, combined with requests of excellent timing, has considerably increased the interest in this sensor type. In the Time-of-Propagation (TOP) counter of the Belle II experiment MCP PMTs are used

Fig. 5 Microchannel plate photomultiplier tube (left), electron multiplication in a channel (right) (Flyckt and Marmonier 2002)

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for the first time on a large-scale (Abe et al. 2004; Inami 2008); another example are the planned Cherenkov detectors of the PANDA experiment (Foehl et al. 2008).

Hybrid Photodetectors Hybrid photon detectors (HPDs) combine the sensitivity of a vacuum PMT with the excellent spatial and energy resolutions of a Si sensor (Braem et al. 2004). The photoelectron is accelerated through a potential difference of U ≈ 10–20 kV before it hits the silicon sensor, as shown in Fig. 6. The electric field is usually shaped in such a way that the entry window is demagnified onto the silicon sensor (Fig. 6); by this, the Si sensor can be kept smaller than the window, and the active area fraction can be very high. Because the silicon sensor is segmented, these devices are naturally of multichannel type, with a very flexible segmentation design. The gain roughly equals the number of e–h pairs as given by the kinetic energy eU of the accelerated electron: G ≈ e(U − Uth )/w, where w ≈ 3.7 eV is the mean energy required to create an e–h pair in Si at room temperature, and eUth is the energy lost by the photoelectron in the insensitive layer of the silicon; this relation is valid for U considerably higher than Uth . Because of the single step multiplication Fig. 6 Hybrid photon detector (HPD) of the LHCb experiment. The outer diameter of the detector is 17 cm (Eisenhardt and LHCb RICH Collaboration 2006; Alves et al. 2008). The large photocathode surface is imaged onto a much smaller Si sensor by a suitably shaped electric field. (Reproduced with permission by Elsevier, July 2010)

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Fig. 7 Pulse-height spectrum of very-low-intensity light pulses recorded with a Geiger-mode APD (left), visual-light photon counter (VLPC, middle), and an HPD (Bross et al. 2002; Buzhan et al. 2003). (Reproduced with permission by Elsevier, July 2010)

the variations of gain are small, and are further reduced due to the Fano effect discussed in  Chap. 18, “Gamma-Ray Spectroscopy”. The excellent single-photon resolution is displayed in Fig. 7. The gain is smaller than in a typical PMT, and low-noise electronics must be used to read out HPDs when counting small numbers of photons. HPDs also require rather high biases, and do not function in a magnetic field. An exception is the proximity-focused device in an axial field; the performance of such a sensor is actually improved if operated in an axial magnetic field because of reduced photoelectron back-scattering effects and reduced influence of electric field inhomogeneities at the edges of the sensor. Large-scale applications include the CMS hadronic calorimeter and the RICH detector in LHCb. Large-size HPDs with sophisticated focusing are also considered for future very-large-scale water Cherenkov experiments. In hybrid APDs (HAPDs) the silicon sensor is operated in the avalanche mode; with this additional multiplication step the gain is increased by a factor of ≈50. This allows for operation at a higher gain or at a lower supply voltage, but also degrades the signal-to-noise characteristics. This sensor type can also have excellent timing, with the time resolution of about 20 ps for a 8 mm diameter photocathode area and 1 mm diameter APD (Fukasawa et al. 2008). A 144-channel proximity-focused HAPD has been developed for a RICH counter of the Belle II experiment (Abe et al. 2004; Nishida et al. 2009) with very good single-photon detection sensitivity.

Gaseous Photon Detectors In gaseous photodetectors, the electron multiplication step happens in an avalanche in the high-field region of a gaseous detector, in the same way as in gaseous tracking detectors such as multiwire proportional chambers, time projection chambers,

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Fig. 8 Gaseous photon detectors: quantum efficiency for photosensitive substances used in gaseous photodetectors (left), typical wire-chamber geometry (right)

micromesh gaseous detectors (Micromegas), or gas electron multipliers (GEM) (as discussed in  Chap. 11, “Gaseous Detectors”). Photoelectrons are generated either on a photosensitive component of the gas mixture or on a solid photocathode material similarly as in a PMT (Fig. 8). Since one of the cathodes of the gaseous photon detector can be structured in pads of few mm size, these devices can be employed as position-sensitive photon detectors. Just like tracking chambers, they can be made to cover large areas (several m2 ). They can operate in high magnetic fields, and are relatively inexpensive. Their drawback is that they are only sensitive in the UV and XUV region (Fig. 8). As a solid photocathode material, a ≈0.5 μm thick layer of CsI is commonly used since it is stable in gas mixtures typically employed in single-electron detection (e.g., CH4 , CF4 ). Among photosensitive gas components, vapors of TMAE (tetrakis dimethyl-amine ethylene) or TEA (tri-ethyl-amine) have the highest thresholds at 230 nm (TMAE) and 165 nm (TEA), and can thus be used for UV and XUV photon detection (Arnold et al. 1992) (Fig. 8). In gaseous photon detectors, special care must be taken to suppress the photonfeedback process, that is, effects due to photons produced in an avalanche. It is also important to maintain high purity of the chamber gas since O2 at concentrations exceeding a few ppm can significantly degrade the detection performance and longterm stability. Note also that TMAE and TEA are chemically aggressive, so that special care has to be taken in the choice of materials for the chambers and supply tubing. Most of the ring imaging Cherenkov (RICH) detectors of the first generation have used gaseous photon detectors for the detection of Cherenkov light. TEA was first used as the photosensitive component in the pioneering RICH experiment E605 (Mangeot et al. 1983). Later, it was considered as the RICH photon detector at B-factories, first as a proximity focusing RICH prototype (Seguinot et al. 1994), and then later successfully employed for the CLEO spectrometer (Artuso et al. 2005), with LiF as the solid radiator and CaF2 as a UV-transparent wire-chamber window. TMAE was employed in the OMEGA, DELPHI, and SLD experiments

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(Apsimon et al. 1986; Arnold et al. 1988; Aston et al. 1989). The RICH counters of COMPASS, Hades, RICH at the JLAB-Hall A and ALICE experiments employ multiwire chambers with a solid CsI photocathode (Fabbietti et al. 2003; Albrecht et al. 2005; Iodice et al. 2005; Di Mauro et al. 2005). Robust gas-based photon detectors remain an attractive alternative for applications where large-area detectors are needed which have to operate in high magnetic fields. For the upgrades of RICH counters of the COMPASS and ALICE experiments, counters were developed that use the thick GEM, THGEM, as the electron amplification component. In both cases, THGEM is made photosensitive by the CsI coating (Breskin et al. 2009). In COMPASS, THGEM is used in combination with Micromegas. We note, finally, that CsI photocathodes are not suitable for very high rate operation because of instabilities in operation and because of photocathode degradation due to the bombardment by ions produced in the avalanche close to the anode wire. An ideal photocathode should be sensitive for visual light rather than in the UV region, but the stability of such visual-light-sensitive photocathodes in a gas atmosphere has been a serious problem. Recently, however, laboratory-produced K2 CsSb, Cs3 Sb, and Na2 KSb photocathodes have been found to be quite stable in a gas chamber (Chechik and Breskin 2008; Lyashenko et al. 2009). In an Ar/CH4 (95/5) gas mixture, K2 CsSb photocathodes yielded quantum efficiency values above 30% at wavelengths between 360 and 400 nm.

Solid-State Photon Detectors In a solid-state photodetector, production and detection of photoelectrons take place in the same thin material (Fig. 9). Solid-state photodetectors are a special sort of semiconductor detector, which is discussed in great detail in  Chaps. 16, “Semiconductor Radiation Detectors”, and  17, “Silicon Photomultipliers”. In a silicon photodiode, photons with wavelengths shorter than about 1050 nm (i.e., with energies exceeding the bandgap of 1.12 eV) can create electron–hole pairs by the photoconductive effect. In its simplest form, the photodiode is a reverse-biased p–n junction (as shown in Fig. 9), and the electrons and holes are collected on the n and p sides, respectively. The same structure is widely used in high-energy physics as particle detectors and in a great number of applications. (Note that a solar cell is a large-area photodiode run with zero external bias). In a PIN diode, intrinsic silicon is doped to create a p–i–n structure. The reverse bias increases the thickness of the depleted region; typically, the full depletion depth is about 100 μm. This has two benefits, decrease of electronics noise due to a lower capacitance, and an improved sensitivity at longer wavelengths where the absorption length is comparable to the thickness of the sensitive region (Fig. 9). The quantum efficiency can exceed 90%, but decreases toward longer wavelengths because of the increasing absorption length of light in silicon. The efficiency is also reduced for small wavelengths when the photon absorption length becomes comparable to the thickness of the insensitive surface layer. Since there is no electron multiplication (G = 1), amplification of the induced signal is necessary. Low-light-level signal detection is limited to a few 100

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Fig. 9 Schematic view of a photodiode (top), photon absorption length in silicon at 77 K (bottom) (Renker and Lorenz 2009). (Reproduced with permission by Journal of Instrumentation, July 2010)

photons even if slow low-noise amplifiers are used. This sensor type can therefore be used where enough light is available, typically for crystal scintillator readout like in the CLEO, L3, Belle, BaBar, and GLAST calorimeters. Compared to traditional vacuum-based photodetectors, solid-state sensors have several advantages. They are compact and robust, do not require high voltages, and are insensitive to magnetic fields. Another advantage is the low cost because of the relatively cheap production methods. They can be pixelized and integrated into large systems. Arrays of tens of millions of pixels, photodiodes at a few μm pitch, have to

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a large degree replaced the photographic film and plates in photography including the applications in astronomy. To read such large arrays, usually the charge-coupled device (CCD) scheme is employed in which the large number of pixels is read out by a much smaller number of electronic channels; the signal charge is transferred from pixel to pixel by using them as shift registers (Janesick 2001). The readout speed can be considerably increased in Active Pixel Sensor (APS) arrays with the first amplifying stage on each pixel. Avalanche photodiodes (APDs) have a similar structure to regular photodiodes, but have a different doping profile and are operated with much higher reverse bias. This allows each photo-generated carrier to get multiplied in an avalanche, resulting in internal gain (typically G = 10–200) within the photodiode (Haitz et al. 1965; McIntyre 1966; Dautet et al. 1993; Perkin-Elmer Optoelectronics). As a result, a detectable electrical response can be obtained from low-intensity optical signals, as low as 10–20 photons. Well-designed APDs, such as those used in the crystal-based electromagnetic calorimeter of the CMS experiment, have achieved a photon detection efficiency of ≈0.7 with sub-ns response time (Deiters et al. 2000). The sensitive wavelength window and the gain depend on the semiconductor used. Stability and monitoring of the operating temperature are important for the linear-mode operation (e.g., when used in calorimeters), and cooling is often necessary. Visible-light photon counter (VLPC) is a special kind of APD. By a very high donor concentration (As-doped Si) an impurity band is created 50 meV below the conduction band (Petrov et al. 1987; Atac and Petrov 1989; Atac et al. 1994). The device is characterized by a high gain (G ≈ 5 × 104 ), high efficiency (q ≈ 0.9), and very good single-photon sensitivity as illustrated in Fig. 7. The small gap makes the sensor, however, sensitive to infrared photons, and requires operation at cryogenic temperatures. The D0 detector at the Tevatron collider at Fermilab was the only experimental apparatus with a large-scale application of this sensor type; 86,000 VLPCs were employed to read out the optical signals from a scintillating-fiber tracker and scintillator-strip preshower detectors (Abachi et al. 1994). Very-low-light-level detection (including single photons) is possible with yet another type of APD, operated in the limited Geiger mode (Buzhan et al. 2001, 2003; Sadygov et al. 2003; Golovin and Saveliev 2004) with gains of G ≈ 106 . This device type is known as silicon photomultiplier (SiPM), but other names are used as well (G-APD for Geiger mode APD, PPD for Pixelated Photon Detector, MPPC for Multi-Pixel Photon Counter). SiPMs typically cover an area of ≈1–10 mm2 and consist of 100–1000 APD cells (Fig. 10). All cells are read out by a single readout channel. Since each cell provides a binary output, the sensor output is a sum of cell outputs, proportional to the number of incoming photons as shown in Fig. 7 (Once the number of detected photons becomes comparable to the number of cells, a correction factor has to be applied to relate the numbers of detected and incoming photons). SiPMs are also fast devices, with a time resolution of 100–200 ps for single photons. Another advantage for practical use is the moderate bias voltage of ≈50 V. However, the single-photoelectron noise of a SiPM is rather large, about 100 kHz/mm2 at room temperature.

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Fig. 10 Silicon photomultipliers (SiPMs): photograph of a 1 mm2 -sized sensor (left), sensitivity scan over 100 × 100 μm cells (right)

SiPMs are particularly well-suited for detector systems where triggered pulses of several photons are expected over a small area, for example, fiber-guided scintillation light. Early large-scale applications include the T2K experiment (Yokoyama et al. 2009) and the CALICE collaboration calorimeter prototype (Danilov and CALICE Collaboration 2007) for the linear-collider detector (Abe et al. 2010). SiPMs are considered as an excellent alternative to the photomultiplier tubes in several other applications including medical imaging, in particular positron emission tomography (PET) ( Chap. 42, “PET Imaging: Basic and New Trends”). SiPMs are in principle also a very promising candidate for detectors of Cherenkov photons in a RICH counter. However, due to the serious disadvantage of a very high rate of noise with a pulse-height distribution equal to the one for single photons, they have up to now not been used in ring imaging Cherenkov detectors, where single-photon detection is required at low noise. Because Cherenkov light is prompt, this problem could in principle be reduced by using a narrow time window (a few ns) for signal collection. To test such a device in a RICH counter, a study was carried out with cosmic rays, and led to the first detection of single Cherenkov photons with this sensor type (Korpar et al. 2008). Light concentrators, gathering light from a larger area and concentrating it onto the SiPM sensitive surface (Fig. 11), could increase the number of detected photons while conserving the dark count rate, and therefore improving the signal-to-noise ratio. A prototype with 64 sensors with light guides as shown in Fig. 11 was indeed successfully employed in a pion test beam (Korpar et al. 2010); un upgraded version with an 8 × 8 array of 3 × 3 mm2 sensors was also successfully tested in the beam (Korpar et al. 2014). When SiPMs are used in the hostile environments of high-energy physics experiments, radiation can produce defects in the silicon bulk or at the Si/SiO2 interface ( Chap. 16, “Semiconductor Radiation Detectors”). As a result, some

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Fig. 11 The photon detector module consisting of 64 1 × 1 mm2 SiPMs (Hamamatsu MPPC S10362-11-100P) without (left) and with (middle) the pyramidal light guides (right) on top of SiPM sensors (Korpar et al. 2010). (Reproduced with permission by Elsevier, July 2010)

parameters of SiPMs may change during irradiation (Renker and Lorenz 2009). For low-level light detection, dark count rate is particularly harmful. Hadrons create defects in the bulk silicon, which act as generation centers, and the dark current, the dark count rate, and the after-pulsing probability will increase during an irradiation. Measurements carried out with SiPMs from different producers showed significantly increased dark currents and dark counts after irradiation with 1010 neutrons/cm2 (the irradiation is normalized to an irradiation with 1 MeV neutrons, and known as neutron fluence). At neutron fluences exceeding 1011 neutrons/cm2 , single-photon counting at room temperatures becomes impossible. To mitigate this problem, sensors can be cooled for operation in high radiation environments. Recently, another solution has been investigated where SiPMs are annealed at higher temperatures with forward bias applied to the sensor (Tsang et al. 2016, Musienko et al. 2020). We finally note that some hybrid devices try to combine the best features of different technologies, an example of which is a vacuum-based device where accelerated photoelectrons hit a fast-scintillating crystal; the resulting scintillation light is detected by a small phototube (as in the QUASAR-370 or XP2600 tubes) or with a SiPM. The advantage of such a sensor is that it can cover a large sensitive area without a complicated dynode structure of a photomultiplier tube. Such devices are considered as photon detectors for large-volume underwater neutrino telescopes.

Conclusion Detection of low light level signals is one of the most important techniques in particle physics, nuclear physics and astrophysics, as well as in medical imaging. The development of novel or dramatically improved light sensors with a higher quantum efficiency and with a better time response is a very active research area; the emphasis is shifting from the vacuum-based photomultiplier tubes to solid-state devices.

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Acknowledgments The authors wish to thank A. Stanovnik and G. Kramberger for useful discussions. A. Stanovnik was also – as usual – kind enough to carefully read and comment the chapter.

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Flyckt SO, Marmonier C (2002) Photomultiplier tubes: principles and applications. Philips Photonics, Brive Foehl K et al (2008) The DIRC detectors of the PANDA experiment at FAIR. Nucl Inst Methods Phys Res A 595:88 Fukasawa A, Haba J, Kageyama A, Nakazawa H, Suyama M (2008) High speed HPD for photon counting. IEEE Trans Nucl Sci 55(2):758–762 Golovin V, Saveliev V (2004) Novel type of avalanche photodetector with Geiger mode operation. Nucl Inst Methods Phys Res A 518:560 Haitz R et al (1965) Mechanisms contributing to the noise pulse rate of avalanche diodes. J Appl Phys 36:3123 Hamamatsu (2006) Photomultiplier tubes, basics and applications. https://www.hamamatsu.com/ resources/pdf/etd/PMT_handbook_v3aE.pdf. Accessed 28 Nov 2019 Hamamatsu Photonics. Photomultiplier tubes. https://www.hamamatsu.com/resources/pdf/etd/ PMT_TPMZ0002E.pdf. Accessed 28 Nov 2019 Iijima T et al (1997) Study on fine-mesh PMTs for detection of aerogel Cherenkov light. Nucl Inst Methods Phys Res A 387:64 Inami K (2008) Development of a TOP counter for the super B factory. Nucl Inst Methods Phys Res A 595:96 Iodice M et al (2005) Performance and results of the RICH detector for kaon physics in Hall A at Jefferson Lab. Nucl Inst Methods Phys Res A 553:231 Janesick J (2001) Scientific charge-coupled devices. SPIE Press, Bellingham Korpar S et al (2008) Measurement of Cherenkov photons with silicon photomultipliers. Nucl Inst Methods Phys Res A 594:13 Korpar S et al (2010) A module of silicon photo-multipliers for detection of Cherenkov radiation. Nucl Inst Methods Phys Res A 613:195 Korpar S et al (2014) Test of the Hamamatsu MPPC module S11834 as a RICH photon detector. Nucl Inst Methods Phys Res A 766:107 Križan P et al (1997) Tests of a multianode PMT for the HERA-B RICH. Nucl Inst Methods Phys Res A 394:27 Lyashenko AV et al (2009) Development of high-gain gaseous photomultipliers for the visible spectral range. J Instrum 4:P07005 Mangeot P et al (1983) Progress in Cherenkov ring imaging Part 2: Identification of charged hadrons at 200 GeV/c. Nucl Inst Methods Phys Res A 216:79 McIntyre R (1966) Multiplication noise in uniform avalanche diodes. IEEE Trans Electron Devices 13:164 Musienko Y et al (2020) Change of SiPMparameters after very high neutron irradiation. Talk given at INSTR20, Novosibirsk, Feb 2020. https://indico.inp.nsk.su/event/20/session/4/contribution/ 167/material/slides/0.pdf Nakamura K et al (2010) Latest bialkali photocathode with ultra high sensitivity. Nucl Inst Methods Phys Res A 623:276 Nishida S et al (2009) Study of an HAPD with 144 channels for the Aerogel RICH of the Belle upgrade. Nucl Inst Methods Phys Res A 610:65 Particle Data Group (2009) Particle detectors for accelerators. http://pdg.lbl.gov/2009/reviews/ rpp2009-rev-particle-detectors-accel.pdf. Accessed 26 Feb 2010 Perkin-Elmer Optoelectronics. Avalanche photodiodes: users guide. https://www.perkinelmer.com/ CMSResources/Images/44-6538APP_AvalanchePhotodiodesUsersGuide.pdf Petrov M, Stapelbroek M, Kleinhans W (1987) Detection of individual 0.4–28 μm wavelength photons via impurity-impact ionization in a solid-state photomultiplier. Appl Phys Lett 51:406 Renker D, Lorenz E (2009) Advances in solid state photon detectors. J Instrum 4:P04004 Sadygov Z et al (2003) Super-sensitive avalanche silicon photodiode with surface transfer of charge carriers. Nucl Inst Methods Phys Res A 504:301 Seguinot J et al (1994) Beam tests of a Fast-RICH prototype with VLSI readout electronics. Nucl Inst Methods Phys Res A 350:430

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Tsang T et al (2016) Neutron radiation damage and recovery studies of SiPMs. J Instrum 11:P12002 Yokoyama M et al (2009) Application of Hamamatsu MPPCs to T2K neutrino detectors. Nucl Inst Methods Phys Res A 610:128

Further Reading Flyckt SO, Marmonier C (2002) Photomultiplier tubes: principles and applications. Philips Photonics, Brive Knoll GF (2000) Radiation detection and measurement. Wiley, New York Križan P (2009) Advances in particle-identification concepts. J Instrum 4:P11017 Križan P, Korpar S (2013) Photodetectors in particle physics experiments. Annu Rev Nucl Part Sci 63:329–349 Leo WR (1994) Techniques for nuclear and particle physics experiments. Springer, Berlin Photomultiplier technical papers from ET-Enterprises. http://www.etenterprises.com/technicalinformation/. Accessed 26 Feb 2010 Renker D, Lorenz E (2009) Advances in solid-state photon detectors. J Instrum 4:P04004 Rieke GH (2003) Detection of light, 2nd edn. Cambridge University Press, Cambridge

Suppliers of Technology AdvanSiD. http://advansid.com/ Broadcom. https://www.broadcom.com/ ET Enterprises. http://www.et-enterprises.com/ Hamamatsu Photonics K.K. http://www.hamamatsu.com/ HZC Photonics. http://www.hzcphotonics.com/ Ketek. https://www.ketek.net/ Photek. http://www.photek.com/ Photonis Technologies S.A.S. http://www.photonis.com/ ON Semiconductor (SensL). http://sensl.com/ Zecotek. http://www.zecotek.com/

Neutrino Detectors

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M. Wurm, F. von Feilitzsch, and Jean-Come Lanfranchi

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Overview of Neutrino Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Important Neutrino Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Reactor Antineutrino Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Reines-Cowan Experiment: Discovery of the Neutrino . . . . . . . . . . . . . . . . . . . . . . . . . Discovery of Long-Baseline Oscillations in KamLAND . . . . . . . . . . . . . . . . . . . . . . . . . . . The Hunt for the Mixing Angle θ13 : Double-Chooz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Very Short-Baseline Searches for Sterile Neutrinos: PROSPECT . . . . . . . . . . . . . . . . . . . . Solar Neutrino Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Early Radiochemical Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pointing at the Sun: Kamiokande . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Neutrino Flavor-Resolved Detection in SNO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Solar Neutrino Spectroscopy with Borexino . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Atmospheric and Accelerator Neutrino Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Atmospheric Neutrinos in Super-Kamiokande . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Search for ντ Appearance in OPERA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A First Glimpse at Leptonic CP Violation in NOvA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Neutrino Telescopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . First Glimpse at Cosmic Neutrinos with IceCube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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M. Wurm () Institute of Physics, Johannes Gutenberg-Universität Mainz, Mainz, Germany e-mail: [email protected] F. von Feilitzsch · J.-C. Lanfranchi Physik-Department, Technische Univeristät München, Garching, Germany e-mail: [email protected]; [email protected] © Springer Nature Switzerland AG 2021 I. Fleck et al. (eds.), Handbook of Particle Detection and Imaging, https://doi.org/10.1007/978-3-319-93785-4_14

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Abstract The neutrino was postulated by Wolfgang Pauli in the early 1930s but could only be detected for the first time in the 1950s. Ever since, scientists all around the world have worked on the detection and understanding of this particle which so scarcely interacts with matter. Depending on the origin and nature of the neutrino, various types of experiments have been developed and operated. In this chapter we will review neutrino detectors in terms of the observed neutrino sources and the associated energy range, aiming to introduce the readers to the variety of techniques employed depending on the specific experimental context. Many of the challenges encountered in neutrino detection are shared by all variants of neutrino experiments. For instance, the low event rates provided by weak interaction make huge active detection volumes a basic necessity. However, there is no one-size-fits-all solution: detector requirements have to be adjusted to the specific neutrino (anti-)flavor, energy, and property that is to be investigated. Therefore, this chapter reviews different classes of detectors ordered by the neutrino sources they observe, highlighting a selection of past, present, and future key experiments for each branch of solar, reactor, accelerator, and cosmic neutrino observation.

Introduction Wolfgang Pauli invented neutrinos to save quantum statistics and energy conservation in nuclear beta-decay. At the same time, he assumed that this particle would not be detectable in experiments as he invented it as an electrically neutral particle with practically no interaction with matter. The first experimental detection of neutrinos was achieved by Frederick Reines and Clyde Cowan only a quarter of a century later in 1956 (Reines and Cowan 1956; Cowan et al. 1956; Reines 1979). Since that time, a continuously growing interest to explore the nature of this particle and to use it for the exploration of nuclear and stellar matter led to numerous developments in the field of neutrino detection. This chapter aims to give a review on neutrino experiments and the key technologies used. Since its early days, the field of experimental neutrino physics has become extremely broad, which complicates any attempt on a complete overview of past and present experiments. Instead, this chapter groups experiments according to the neutrino sources (and hence neutrino energy ranges) they observe. Among the tens of neutrino detectors that have been operated over the last 60 years, only a selection of key experiments will be picked out for a more detailed discussion. The chapter sets out with a short overview of the available neutrino sources (section “Overview of Neutrino Sources”) and their most relevant properties (section “Important Neutrino Properties”). It then proceeds to an account of four distinctive categories of neutrino experiments: for each reactor (section “Reactor Antineutrino Experiments”), solar (section “Solar Neutrino Experiments”),

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accelerator/atmospheric (section “Atmospheric and Accelerator Neutrino Experiments”), and cosmic neutrino detectors (section “Neutrino Telescopes”), the sections describe the historic developments of the respective fields, visiting several key experiments and detection techniques along the way. Finally, the chapter concludes with a short outlook on future experiments (section “Conclusions”).

Overview of Neutrino Sources Neutrinos are emitted by a variety of sources. Figure 1 gives an overview of neutrino fluxes of different origins as a function of their energy: • • • • • • •

solar neutrinos from thermonuclear fusion processes inside the Sun neutrinos from core-collapse Supernova explosions neutrinos from neutron-rich fission isotopes inside nuclear reactors geo-neutrinos from the natural radioactivity of the Earth’s interior accelerator-based neutrino beams atmospheric neutrinos from cosmic-ray interactions in the upper atmosphere high-energy neutrinos from cosmic accelerators (active galactic nuclei, gamma ray bursts, etc.)

While artificial neutrino sources – nuclear power reactors and accelerator beams – are studied primarily to obtain information on neutrino particle properties, neutrinos from celestial bodies are used as probes in both astrophysics and geophysics.

Fig. 1 Energy spectra of neutrinos from different origins (Koshiba 1992): Beyond the solar, reactor, atmospheric, and cosmic neutrinos discussed in this chapter, also the expected signal from a galactic Supernova neutrino burst as well as that of the diffuse Supernova neutrino background is shown; the latter is a remnant of all Supernovae that have exploded over the course of the Universe and has not been detected yet

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Fig. 2 The energy dependence of neutrino cross sections for reactions on the electrons, protons, and carbon nuclei available in a liquid scintillator-based neutrino target

However, many of the most spectacular insights in the nature of the neutrino have been obtained by studying the neutrinos emitted by natural sources. Neutrino detection becomes possible by weak interaction processes with the electrons, nucleons, or whole nuclei of the detector material: depending on neutrino flavor and energy as well as detector materials, different detection reactions become accessible. Neutrino cross sections feature a strong energy dependence. As an example, Fig. 2 illustrates the energy dependence of reaction cross sections available for (anti-)neutrino detection for organic scintillator detectors , featuring interactions on electrons, protons (hydrogen), and carbon nuclei. Neutrino interaction cross sections rise with the neutrino energy; however, neutrino fluxes from the observable natural sources decrease even more steeply. Hence, expected detection rates decrease as well: While solar neutrinos can be observed with rates of one interaction per day and ton of detector material − already requiring large detectors to acquire meaningful statistics − the high-energy neutrino telescope IceCube employs a billion tons of ice to detect a handful of cosmic neutrinos per year. Not only the rates, but also the required detector performance, i.e., event reconstruction capabilities, widely defer for the different energy ranges. As will be laid out in the following chapters, low-energy (MeV) neutrino events produce virtually point-like interactions. Hence, detectors are optimized to reconstruct position, energy, and (in case of Cherenkov detectors) direction of the final state lepton. At PeV (1015 eV) energies, huge detection volumes on the scale of cubic kilometers are required to detect the minute neutrino fluxes; however, the demand on instrumentation density is very limited: tracks of muons produced in chargedcurrent interactions can easily reach lengths of several hundred meters at such energies. The intermediate energy regime centered on GeV energies is usually considered the most challenging for reconstruction, as − mainly due to nuclear effects − interactions on the nuclei of the target atoms can be due to both charged

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and neutral weak currents and may thus produce relevant amounts of secondary particles, muddling the results of both energy and directional reconstruction algorithms.

Important Neutrino Properties The deciphering of the neutrino particle properties has always been closely linked to the detectors employed for their measurement. After establishing the existence of the neutrino by the Reines-Cowan experiment described in section “The Reines-Cowan Experiment: Discovery of the Neutrino,” solar radiochemical experiments returned a deficit in measured neutrino flux that was incompatible to astrophysical expectations (section “Early Radiochemical Experiments”). A similar deficit was observed in atmospheric neutrinos (section “Atmospheric Neutrinos in Super-Kamiokande”). While in the beginning a variety of mechanisms was proposed, neutrino oscillations emerged as the only explanation around the year 2000, supported mainly by the evidence of three experiments: the water Cherenkov detector Super-Kamiokande (section “Atmospheric Neutrinos in Super-Kamiokande”), the heavy-water detector SNO (section “Neutrino Flavor-Resolved Detection in SNO”), and the liquid scintillator detector KamLAND (section “Discovery of Long-Baseline Oscillations in KamLAND”). In the standard model of particle physics, neutrinos are massless, electrically neutral particles that only interact by weak interactions. There are three generations of particles: For instance, the electron e− has two cousins, the muon μ− and the tau τ − , that feature the exact same particle properties with exception of their larger masses. Accordingly, also the neutrino appears in three kinds, commonly known as flavors, that each correspond to a charged lepton: electron-neutrino νe , muonneutrino νμ , and tau-neutrino ντ . When reacting with matter via weak interactions, a νe will convert into an electron, but never into μ or τ . Also the antiparticles of the neutrino appear in three antiflavors, ν¯ e , ν¯ μ , and ν¯ τ , related to the antiparticle counterparts of the charged lepton, e+ , μ+ , and τ + . Neutrino oscillations describe a periodic conversion of neutrinos between the three flavors: An accelerator beam neutrino created as νμ can change its flavor during propagation to the detector, being detected as a νe . This strange effect becomes possible because the neutrino is not massless and there is a mass difference for the three kinds of neutrinos, called mass eigenstates. Peculiarly, quantum mechanics does not require these mass eigenstates to coincide with the flavor eigenstates that take part in weak interaction. In fact, each flavor eigenstate is a superposition of mass eigenstates and vice versa, an effect commonly represented with the help of a 3 × 3 unitary mixing matrix U : ⎞ ⎛ ⎞⎛ ⎞ Ue1 Ue2 Ue3 ν1 νe ⎝ νμ ⎠ = ⎝ Uμ1 Uμ2 Uμ3 ⎠ ⎝ ν2 ⎠ . ντ Uτ 1 Uτ 2 Uτ 3 ν3 ⎛

(1)

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Named after the pioneering neutrino physicists Pontecorvo, Maki, Nakagawa, and Sakata, the PMNS mixing matrix U contains nine interrelated coefficients for the flavor mixing and is fully analogous to the CKM matrix of the quark sector. It is usually described as a product of three 3 × 3 rotation matrices, ⎛

UPMNS

⎞⎛ ⎞⎛ ⎞ 1 0 0 c13 0 s13 e−iδ c12 −s12 0 = ⎝ 0 c23 −s23 ⎠ ⎝ 0 1 0 ⎠ ⎝ s12 c12 0 ⎠ , iδ 0 s23 c23 −s13 e 0 c13 0 0 1

(2)

with the common shorthands cij = cos θij and sij = sin θij . Unitarity demands that there are only four free parameters to describe the mixing: the rotation angles θ12 , θ13 , and θ23 and the complex phase δ (see below). In neutrino oscillations, the coefficients of U govern the probabilities (amplitudes) of conversion between the neutrino flavors. The oscillation frequency depends on the quotient of the distance from the neutrino source to the detector L (aka the oscillation baseline) and the neutrino energy E and the quadratic mass difference between the participating mass eigenstates, Δm2 . It is often possible to treat experimental setups in a two-flavor picture, leading to the two simplified oscillation formula:    2 Δm2j i L 2 P (να → νβ ) = sin 2θij sin (3) 4E P (να → να ) = 1 − P (να → νβ )

(4)

Instead of the PMNS matrix elements Uαi , the mixing angles θij are commonly used to parametrize the conversion probability between flavors, with θ = 45◦ corresponding to maximum mixing. Roughly, θ12 can be ascribed to cause solar neutrino oscillations νe → νμ (section “Solar Neutrino Experiments”), while θ23 has been first observed in atmospheric neutrino oscillations (section “Atmospheric Neutrinos in Super-Kamiokande”). As last of the three, θ13 has been determined by short-baseline reactor antineutrino experiments (section “The Hunt for the Mixing Angle θ13 : Double-Chooz”). The first time the phase of the oscillatory terms reaches 90◦ corresponds to a maximum in flavor transition probability and is hence named the first oscillation maximum. The following oscillation minimum sees a full restoration of the initial neutrino flavor. The corresponding distance is referred to as the oscillation length. As the phase factor holds the neutrino energy in the denominator, the oscillation length is proportional to the neutrino energy, meaning that high-energy neutrinos have to go longer distances for oscillation to occur. More crucial, the oscillation frequency depends as well on the squared mass differences between the neutrino eigenstates, Δm221 , Δm232 , and Δm231 . Today, solar θ12 ≈ 33◦ and atmospheric θ23 ≈ 45◦ mixing angles are known to be large, leading to large-scale conversion and hence dramatic effects observed in the rates of the corresponding neutrino experiments. But even the third mixing angle θ13 ≈ 9◦ has been found to be

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relatively large by short-baseline reactor (section “The Hunt for the Mixing Angle θ13 : Double-Chooz”) and long-baseline accelerator experiments (section “Atmospheric Neutrinos in Super-Kamiokande”). For a relatively recent overview of neutrino oscillations and values of oscillation parameters, we refer the reader to Gonzalez-Garcia et al. (2016). The neutrino PMNS mixing matrix is thus decisively different from its quark sector equivalent that features only minimal weak mixing between quark generations. Also the neutrino mass squared differences are tiny, resulting in long oscillation lengths ranging from about 1 to 103 km in terrestrial experiments. Interestingly, standard oscillation experiments are only able to measure the absolute values of these differences that are by now well determined. However, due to the quadratic sine of the oscillatory term, they are not sensitive to their signs. So while subdominant effects in solar neutrino oscillations do indeed tell us that the sign of the smaller mass splitting Δm221 is positive, the other two signs are still undetermined. Several large-scale neutrino oscillation experiments (section “Conclusions”) are currently in preparation to remedy this ambiguity. Similarly, the complex phase term δ in the PMNS matrix remains still undetermined. Potentially introducing differences in the oscillatory behavior of neutrinos and antineutrinos, a measurement of this parameter would be especially interesting from the point of view of theory, as it may be linked to the still unexplained matterantimatter asymmetry in the present Universe. Again, further neutrino projects on an even larger scale are in preparation in an attempt to measure the potential asymmetry between neutrino and antineutrino oscillations (section “Conclusions”).

Reactor Antineutrino Experiments The natural fluxes of low-energy neutrinos at energies around 1 MeV are far greater than the ones observed for atmospheric or cosmic neutrinos. On Earth, the highest natural flux is provided by the neutrinos from solar fusion (section “Solar Neutrino Experiments”). However, reactor neutrinos provide locally even higher neutrino fluxes if the detector is not positioned too far from the reactor core. In the following, we will give an overview over the experimental techniques used for the detection of these neutrinos, starting from the discovery of the “free neutrino” in the Savannah River reactor experiment. The neutrinos emitted in β-decays of radioactive isotopes feature typical energies in the range of 0.1 to 10 MeV. A strong natural source especially of antineutrinos are the radioisotopes undergoing β − decays in the uranium and thorium decay chains that are embedded in the Earth’s crust and mantle (see below). However, an even stronger source is the neutron-rich isotopes produced in nuclear fission reactors. A single commercial nuclear power plants produces electron antineutrinos (ν¯ e ) at a rate of 1020 ν¯ e per second. The ν¯ e ’s emerges by the decay of neutrons that are part of the atomic nucleus of a neutron-rich fission product: n → p + e− + ν¯ e ,

(5)

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where n is the neutron, p the proton, and e− the electron. This neutrino source became available in the early 1950s with the rise of nuclear energy production. At that time, the only hint for neutrinos came from measurements of the electron energy emitted in β-decays. The observation of an electron energy distribution had led Pauli to the postulation of the neutrino. Now, F. Reines and C. L. Cowan had the goal to give final prove to the existence of this particle by an observation of the “free neutrino” at some distance from the neutrino source (Cowan et al. 1956).

The Reines-Cowan Experiment: Discovery of the Neutrino Reines and Cowan set up their neutrino experiment first at the Hanford (Reines and Cowan 1953a,b) and later on at the Savannah River nuclear reactor (Reines and Cowan 1956; Cowan et al. 1956; Reines 1979). The experiment was designed to detect the low-energy ν¯ e by an inversion of the process described by Eq. (5). This “inverse β-decay” uses the capture of an ν¯ e on a free proton (i.e., hydrogen nucleus), p + ν¯e → n + e+

(6)

producing a neutron and a positron (e+ ) in the end-state. The coincident detection of the emerging positron and the neutron allows for a significant identification power and thus discrimination against natural radioactivity in the detector. A further advantage at that time was that the cross section of this reaction could be calculated accurately from standard weak interaction theory. Originally, Reines and Cowan thought of using a nuclear explosion to yield a pulse of neutrinos intense enough to override the natural radioactive background. For some time this concept was under serious discussion, until it was realized that reaction (6) bore a great rejection power so that the first tentative experiment was performed at the fission reactor at Hanford, Washington. After a few months of operation and after modifying the shielding of their detector several times, Cowan and Reines finally concluded that the reactor-independent background they were facing was overwhelming (Reines 1979). Thereafter, the experiment was dismantled. After a period of reflection and analysis of the data, they decided to place the next experiment underground, based on the conclusion that the background had to be of cosmic origin. They performed their next attempt to detect the neutrino at the Savannah River Power Plant, South Carolina. There, again using the inverse β-decay reaction, a detector was set up which could discriminate more selectively against reactorindependent as well as reactor-associated backgrounds. The new location was particularly well suited since the reactor had a comparably high power (700 MW) and a small physical size. In addition, a well-shielded place was available only 11 m away from the reactor core and protected against cosmic radiation by a “rock” overburden of ∼12 m. The neutrino flux originating from this reactor at that distance was ∼1.2×1013 cm−2 s−1 .

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Cadmium-capture gamma rays

n Capture in cadmium after moderation

n

Target proton

b+ 7,6 cm

H2O + CdCI2 (target)

Annihilation

Liquid scintillation detector 2

Fig. 3 Schematic of the neutrino detection principle re-drawn based on description from C. Cowan and F. Reines (Reines 1979)

The detection principle is illustrated in Fig. 3. A ν¯ e originating from fission products in the reactor is incident on a water target that provides the hydrogen for reaction (6) and contains cadmium chloride as an additive. A positron and a neutron are produced in the water volume. The positron slows down and annihilates with an electron of the detector, emitting two 0.511 MeV gamma rays in opposite directions. The γ rays cross the water and are detected in coincidence by two large scintillation detectors on opposite sides of the target. The neutron is moderated in the water and finally captured by the cadmium, thus producing multiple gamma rays, which are also observed in coincidence by the two scintillation detectors. The cadmium is used for the neutron detection since it has a high neutron absorption cross section. The signature of an ν¯ e capture is therefore a delayed coincidence between the prompt gamma pulse produced by the e+ -e− annihilation and gamma pulses produced microseconds later by the neutron capture on cadmium. Even though the conditions were much more favorable at Savannah River, the whole experiment necessitated a running time of about 100 days over a period of roughly 1 year. In the end, Reines and Cowan succeeded in a definitive observation of ν¯ e in 1956 (Reines and Cowan 1956; Cowan et al. 1956). The couple informed Wolfgang Pauli via telegram about their discovery and that the measured cross

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section agreed well with the theoretically expected one of ∼6 × 10−44 cm2 (Fermi 1934). On receiving the news, he replied by telegram: “Thanks for message. Everything comes to him who knows how to wait. Pauli.” In 1995 the Nobel Prize for physics was attributed to F. Reines (C. Cowan had died already in 1974). Numerous challenges that affect modern neutrino detectors are of the same kind as those faced by Cowan and Reines (Reines 1979): First of all, neutrino searches then and now are ultralow background experiments, employing elaborate experimental schemes to obtain sensitivity to only a handful of neutrino events per day. Similarities go even to a much more technical level: like Reines and Cowan, experimenters today worry about the transparency of the scintillator to transmit its own scintillation light, the reflectivity of the target containers to increase light collection, the chemical stability of the scintillator after addition of the neutron capturer cadmium, the behavior of the photomultiplier tubes, and so on. The experimentalists also realized soon that their new detector designed to detect neutrinos had unusual properties concerning other particles such as neutrons and gamma rays, featuring detection efficiencies near 100%. They recognized that detectors of this type could be utilized to study diverse quantities such as neutron multiplicities in fission, muon capture, muon decay lifetimes, and natural radioactivity of the human body (Reines 1979).

Discovery of Long-Baseline Oscillations in KamLAND Even after their detection, neutrinos were still peculiar particles, inviting for a lot of speculation about properties not accounted for by the standard model of particle physics. The search for nonstandard effects picked up speed in the 1970s, when the solar neutrino experiment conducted by Ray Davis in the Homestake Mine showed a considerable deficit compared to the expected rate (section “Early Radiochemical Experiments”). Again, nuclear reactors were exploited as an intense neutrino source, this time searching for neutrino oscillations that had been proposed by B. Pontecorvo. Compared to solar neutrinos, reactors offered the advantage that ν¯ e offered a clear detection signature and that the baseline to the neutrino source could be freely chosen. Over the next two decades, a series of relatively small-scale experiments was constructed at reactor sites in the USA and Europe, searching for neutrino oscillations. The experimental signature looked for was a deficit in the detected ν¯ e rate in comparison to the neutrino flux emitted by the nuclear reactor, commonly dubbed “disappearance search”: The inverse β-decay (6) is only sensitive to antineutrinos of electron flavor ν¯ e ; instead, ν¯ μ and ν¯ τ are too low in energy to interact in the same way as they would have to create a much heavier μ+ or τ + in the reaction’s final state. While the oscillation baselines from reactor to detectors kept steadily increasing and finally approached 1 km, no sign of ν¯ e disappearance was found. Finally, a liquid scintillator detector of 1,000 tons target mass was deployed in the Kamioka

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Fig. 4 Left: Schematic of the KamLAND detector located in the Kamioka mine in Japan. Right: Experimental results on reactor neutrino oscillations. A clear, energy-dependent suppression in the observed event rate is a telltale sign of ν¯ e disappearance oscillations. (Courtesy of the KamLAND collaboration)

mountain mine in Japan at a depth of 2,700 m water equivalent underground. Observing the ν¯ e signals from a multitude of Japanese nuclear power plants at typical distances from ∼180 km, the KamLAND (Kamioka Liquid Scintillator Anti-Neutrino Detector) was finally able to provide convincing evidence of ν¯ e oscillations. As displayed in Fig. 4, KamLAND consists of an outer and an inner detector. The first is a water Cherenkov detector (∼200 PMTs) acting as an active anticoincidence veto for cosmic muons that potentially produces background events in the central detector. The latter is enclosed by a stainless steel sphere equipped with ∼2,000 PMTs. A nylon balloon suspended in the center of the sphere contains the target scintillator (∼1,000 t) that serves both as target and active detector material. The interspace between PMTs and the nylon balloon is filled with plain mineral oil, shielding the target volume from the radioactivity originating from the surrounding rocks and the PMTs themselves. The design resembles closely that of the Borexino experiment (section “Solar Neutrino Spectroscopy with Borexino”). As in the Savannah River experiment, ν¯ e were detected using the delayed coincidence signature of the inverse β-decay on hydrogen, in this case provided by the hydrocarbon molecules of the organic scintillator. The emerging positron quickly deposits its energy and then annihilates. The remaining neutron thermalizes and is captured some 200 µs later on another hydrogen nucleus, yielding a deuteron and an associated 2.2 MeV de-excitation gamma. Positron and gamma signal again provide a clear signature for the detection of ν¯ e ’s. The energy of the emerging positron is closely related to the one of the incident ν¯ e . In KamLAND, this relation could be exploited to do a spectrally resolved measurement of the reactor neutrinos. The most striking evidence for the

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observation of neutrino oscillations was therefore not only the deficit in the detected neutrino rate but also the deformation of the positron/ν¯ e energy spectrum observed (Fig. 4, right panel) (KamLand Collab 2008). The success of KamLAND depended primarily on the use of low-radioactivity detector materials – natural radioactivity levels are order of magnitudes too large; in addition, the large monolithic volume of liquid provides a self-shielding capability, restricting most of the gamma rays emitted by trace impurities of the outer detector materials to the verge of the target volume. Consequently, single event background rates were so low that the accidental coincidences of otherwise uncorrelated events did not contribute a significant background (Fig. 4). There is a further background at lower energies, originating from ν¯ e produced by the β-decays of natural radioactive isotopes embedded in the Earth’s crust and mantle. These geo-neutrinos originate mainly from the β-decays occurring along the natural uranium and thorium chains. Originally considered a low-energy background to the reactor neutrino analysis, the statistics gathered in KamLAND were finally sufficient to provide a positive evidence of the geo-neutrino signal (KamLAND Collab 2005). Some years later, the Borexino experiment performed a similar measurement but with lower reactor neutrino background, confirming the positive observation result (section “Solar Neutrino Spectroscopy with Borexino”). While the statistics collected by both experiments is not yet sufficient to deduce quantitative results on the Earth’s radiogenic heat production, future detectors will be able to determine the geo-neutrino flux and spectrum much more accurately, shedding light on the otherwise unaccessible chemical composition and heat production in the inner layers of the Earth.

The Hunt for the Mixing Angle θ13 : Double-Chooz In the decade following the discovery of neutrino oscillations by SuperKamiokande, SNO, and KamLAND (sections “Discovery of Long-Baseline Oscillations in KamLAND,” “Neutrino Flavor-Resolved Detection in SNO,” “Atmospheric Neutrinos in Super-Kamiokande”), the focus of reactor neutrino experiments shifted toward the measurement of the last unknown mixing angle, θ13 . A measurement of this kind had to look for the conversion of the ν¯ e emitted by the reactor into ν¯ τ (resp. νμ ). As a search for ν¯ τ appearance was not practical due to the low reactor neutrino energies, the experiments had to look for the disappearance of the original ν¯ e flux. Based on the available data, it was clear that the value of Δm231 governing the ν¯ e → ν¯ τ oscillations was about 30 times greater than Δm221 . This meant that a detector based close to the first oscillation maximum, i.e., a bit more than 1 km from the reactor, would be sensitive solely to the disappearance induced by Δm231 and θ13 . In fact, two earlier reactor experiments, Chooz and Palo Verde, had been measuring at that exact distance, setting an upper limit of sin2 2θ13 < 0.12 to the maximum amplitude of the oscillation (Dwyer 2015). Consequentially, it was clear

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that a very accurate measurement was necessary to achieve a positive result, i.e., a non-zero value for θ13 . After several years of a worldwide prioritization process, finally three projects obtained funding to progress to the experimental level: Double-Chooz in Northern France (Double-Chooz Collab 2012), RENO in South Korea (RENO Collab 2012), and Daya Bay in southern China (Daya-Bay Collab 2012). While the number of reactor cores and detectors involved and details of the detector construction varied, the basic measurement principle of all three experiments was identical: a comparative measurement of the reactor neutrino rates observed at the expected oscillation maximum at 1–2 km to a reference detector at very short distance (∼100 m) from the reactor(s) where no oscillations were expected. Moreover, both far and near detectors were constructed to be functionally identical, avoiding the need for relative corrections in the detection efficiencies for the observed neutrinos. In the following, the Double-Chooz experiment is described as it features the most simple layout of two reactor cores, one near and one far detector (Fig. 5). Finally, it was the Daya Bay experiment that won the price of the first discovery of θ13 discovery, reporting a 5σ evidence in early 2012. Figure 5 illustrates both the basic layout of the experiment and the details of a Double-Chooz antineutrino detector. Note that both near and far detectors are set at slightly different distances from the two reactor cores of the Chooz nuclear power plant. The relative contributions of the two sources are, however, the same. On first glance, a Double-Chooz detector seems likely a smaller version of KamLAND: A central volume containing 8 tons of liquid scintillator for neutrino detection, surrounded by 392 photomultipliers to register the scintillation light and 2 veto detectors to suppress cosmic muon-related backgrounds. However, there are several aspects that should be highlighted as they cater to the need of a very accurate absolute rate measurement: • The separating vessels are made of acrylic, not nylon: In order for an accurate rate measurement, it is important to precisely determine the amount of scintillator

Fig. 5 Left: Setup of the Double-Chooz experiment, featuring two reactor cores, a near and a far detector. Right: Layout of one antineutrino detector

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available for neutrino detection. To achieve this on the sub-percent level, a flexible nylon balloon is less suitable than a rigid acrylic structure. • The addition of gadolinium to the scintillator, like KamLAND and DoubleChooz, employs the inverse beta-decay on protons as the ν¯ e detection reaction. Unlike KamLAND, the delayed neutron signal is not due to capture on carbon but gadolinium dissolved in small quantities (per mill level) in the scintillator. While the solution of gadolinium in organic liquids is chemically challenging, it offers two decisive advantages: Gadolinium features the largest thermal neutron capture cross section of all elements, so even addition on trace level speeds up the capture time considerably to ∼30 µs, improving the signal coincidence tag. Even more importantly, the capture triggers a gamma cascade of a total energy of ∼8 MeV, an energy well above natural background levels. Hence, the achievable signal-to-background ratio is on the level of 10:1 (cf. Neutron Detection). • In order to acquire the complete gamma signal from the capture of gadolinium, it is necessary to integrate the Gd-loaded target in a second, surrounding volume of scintillator that is wide enough to absorb/detect gamma rays leaking out of the target volume. This auxiliary gamma-catcher is filled with plain scintillator of the same light yield and density as the target scintillator. Note that the quoted list of properties would already make for a much more accurate measurement in a single-detector setup, as was demonstrated by Double-Chooz in 2012 (Double-Chooz Collab 2012). However, full sensitivity is only reached in the combined measurement with two detectors where many of the remaining systematic uncertainties (mostly on the underlying reactor neutrino flux and spectrum) cancel in a simultaneous measurement. The power of this relative measurement was impressively demonstrated by both Daya-Bay Collab (2012) and RENO Collab (2012). A corresponding publication by the Double-Chooz collaboration is in preparation.

Very Short-Baseline Searches for Sterile Neutrinos: PROSPECT Triggered by the worldwide reactor neutrino program dedicated to measuring θ13 , groups of nuclear physicists started to refine their predictions on the source energy spectra emitted by the reactors in order to reduce systematic uncertainties in these experiments. The neutrino spectrum observed arises from the superpositions of β − decay spectra by thousands of fission isotopes resulting from 235 U, 238 U, 239 Pu, and 241 Pu. In principle, the sum spectrum can be derived in an ab initio calculation, making use of the vast data bases available for the fission yields of different isotopes and their respective decay spectra. In practice, however, it has been shown that this approach falls short of the actual reactor neutrino flux by about 10%. As a consequence, neutrino predictions rely on the measured β-decay spectra that have been measured separately for each of the four main fission isotopes with electron spectrometers at nuclear reactors. This electron data is converted to a neutrino energy spectrum by a method of spectral inversion. Again, it is not possible to do

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this taking into account thousands of single isotopes; instead, conversion is done on the basis of a few tens to hundred virtual decay branches fitted to reproduce the main features of the reactor spectrum. Despite this very effective approach, spectral and flux predictions obtained in this fashion had proven robust enough for all experiments up to KamLAND. It was only when a new prediction by Mueller et al. appeared in 2011 (Mueller et al. 2011) that doubt was cast on the correspondence between predicted and measured reactor neutrino signals. Given that the new calculations predicted a slightly harder energy spectra, the observed event numbers in reactor experiments were now globally considered to be low by ∼6%. Why this had no impact on the large disappearance signal identified by KamLAND or the relative measurements of the θ13 experiments, it meant that all experiments at shorter baselines (10–1,000 m) in effect showed a too low rate. What if this deficit stemmed not from an inaccurate prediction but a very short-baseline oscillation of the ν¯ e ’s into a new neutrino state (Mention et al. 2011)? Note that it is impossible to explain such a short-wavelength oscillation signal in the standard three-flavor picture. The mass squared difference required for a meter-long oscillation length of reactor neutrinos is of order eV2 , incompatible with the established values of Δm221 , Δm231 , and Δm232 . Instead, a new neutrino mass eigenstate on the eV-mass scale would have to be introduced, providing a corresponding Δm241 . However, four mass eigenstates would require the presence of four flavor eigenstates, a finding in conflict with LEP measurements that put the number of light (mν < 45 GeV) active neutrinos to 3. The only solution to this conundrum is to introduce a fourth, inactive flavor that does not participate in weak interaction. The new oscillation signal could thus be caused by an eV-scale “sterile” neutrino state, a particle clearly outside the standard model of particle physics. In the follow-up, almost a dozen of experimental projects were started to corroborate or reject the hypothesis that sterile neutrino oscillations were the cause of the observed rate deficit. Most of these relied on a antineutrino detector positioned very close (∼10 m) to a nuclear reactor (preferably one of the more compact research reactor cores). To obtain clear proof of neutrino conversion, it was necessary to observe the associated oscillatory behavior. Hence, these detectors were all designed to measure both a spectral distortion as well as the distance dependence expected for oscillations. At the time of writing, the reactor-based experiments already in operation are DANNS, Neutrino-4, NEOS, PROSPECT, SoLiD, and STEREO (Buck). Here, we discuss PROSPECT as a typical proponent of the detector class employed in this very short-baseline experiments (PROSPECT Collab 2016). The basic technology for the detection of reactor antineutrinos is still liquid scintillator, using the inverse beta-decay for an energy-resolved rate measurement. Compared to the detectors described in earlier chapters, PROSPECT features a relatively small target mass of 4 tons. However, given the short distance to the HFIR reactor core (∼7 m), about 160,000 neutrino events are expected in 1 year of measurement.

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In order to increase the spatial resolution of the detector, almost all of the very short-baseline projects feature segmented detectors. As laid out in Fig. 6 for PROSPECT, this segmentation is done in 2 dimensions, structuring a cubic detection volume into 11 × 14 detector “strips” with a quadratic base of about 10-by-10 cm (panel c). PMTs are attached to both ends to the reflective cell to record the scintillation signal (panel d). This segmentation perpendicular to the reactor core allows to measure the neutrino energy spectrum as a function of distance to the core. In the presence of oscillations, the energy spectra acquired in each individual cell should vary with respect to its neighbors (panel b). To maintain the advantages of a close coincidence detection in this highly segmented detector geometry makes it necessary that the inverse beta-decay signal is detected well localized within a single strip. This would be very difficult if the neutron was captured either on hydrogen or gadolinium as the corresponding gamma rays travel several 10 cm before undergoing Compton scattering, potentially crossing the boundaries of several strips. Instead, PROSPECT employs a scintillator loaded with lithium: The isotope 6 Li features a large neutron capture cross section and undergoes the reaction n + 6 Li → 4 He + 3 H.

(7)

The emerging α and triton particles have only a very limited range in liquid scintillator but provide a well-detectable signal. Combined with an excellent energy resolution of 4.5% at 1 MeV of visible energy, PROSPECT will not only be sensitive to a potential sterile neutrino signal but will provide a high-quality reference reactor neutrino spectrum to be used in future experiments (PROSPECT Collab 2016).

Solar Neutrino Experiments In the early 1960s, Ray Davis conceived and constructed an experiment to detect the low-energy neutrinos emitted in solar fusion processes (section “Discovery of Solar Neutrinos in the Homestake Experiment”). His pioneering effort proved to be not only the foundation to neutrino astronomy but also the source of a long-standing conundrum in neutrino particle physics: the long-standing deficit in the observed solar neutrino rate that was finally resolved by the discovery of flavor-changing oscillations in the SNO experiment (section “Neutrino Flavor-Resolved Detection in SNO”). Based on the electromagnetic luminosity and nuclear effects, it was obvious that the Sun should create an intense neutrino flux on Earth. The energy driving the Sun is released by the exothermal thermonuclear fusion of hydrogen to helium: 4p → 4 He + 2e+ + 2νe

(8)

This fusion reaction takes place deep inside the Sun at temperatures of 15 million degrees Kelvin. The energy released per 4 He fusion process is 26.73 MeV. From

Fig. 6 Overview of PROSPECT: expected oscillation signal, experimental layout, and signature of neutrino events (PROSPECT Collab 2016). (With kind permission from IOP Publishing, Ltd; courtesy of the PROSPECT collaboration)

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this total energy, only about 2% are transferred onto the two emerging νe ’s. The remaining energy is set free in the form of thermal energy and takes on the order of 105 years to dissipate to the solar surface. Therefore, using the solar constant S = 8.5 × 1011 MeV/cm2 s, the νe -flux, Φν , on Earth can be estimated to Φν =

S = 6.5 × 1010 /cm2 s 13 MeV

(9)

Inside the Sun, the fusion process from protons to 4 He can take several different avenues: Fig. 7 illustrates the division of the dominating pp chain into several different sub-cycles and indicates their respective branching ratios. Several of these reactions emit neutrinos with different energy spectra depending on the Q-value. These neutrinos are named after these reactions pp, 7 Be, pep, 8 B, and hep neutrinos. In addition, the subdominant CNO cycle (Bethe-Weizsäcker-cycle) provides a minor fraction (∼1%) to the solar neutrino flux. It is important to note that − independent of the specific path of reactions taken − the number of νe ’s released per fusion to a 4 He nucleus is always 2. For a more detailed and accurate description of the solar fusion processes the socalled standard solar models (SSM) have been developed mainly by Bahcall et al. (2005) and Turck-Chièze (2001). These models provide predictions about the energy and abundance of neutrinos originating from different branches of the fusion cycles

Fig. 7 Fusion branches in the Sun. The pp-fusion chain is responsible for ∼98.5% of the energy production in the Sun as calculated by present SSMs (Bahcall et al. 2005). The figure illustrates the various contributing reactions as well as their branching ratios; the names used to identify the neutrinos from the different reactions are marked in red

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Fig. 8 The solar neutrino spectrum as predicted by the standard solar model (SSM) (Bahcall et al. 2005). The solar neutrino flux is plotted versus the neutrino energy in MeV. Depending on the fusion cycle in which the neutrino was generated, i.e., 2- or 3-body process, the energy spectrum is discrete as in the case of 7 Be and pep and continuous in the case of pp-, 8 B and hep-neutrinos. On the top x-axis, the energy detection threshold for different detector types is given

(Bahcall et al. 2005). Figure 8 depicts the solar neutrino spectrum as calculated from SSMs by Bahcall together with thresholds for different detectors.

Early Radiochemical Experiments As laid out above, solar neutrinos are produced in νe flavor only. As a direct consequence for experimenters, these neutrinos cannot be detected via the inverse beta-decay on protons that is only sensitive to ν¯ e . Instead, they have to rely either on the conversion of heavier elements or the elastic scattering off electrons (section “Pointing at the Sun: Kamiokande”). The first approach was followed up by the early radiochemical experiments: By measuring the number of converted atoms in a defined target volume (i.e., containing a known number of target atoms), experimenters were able to calculate the underlying solar neutrino flux. This kind of experiment required a very accurate knowledge of conversions induced by radioactivity − indeed, excessive shielding from cosmic rays proved necessary − but also an intricate scheme for the extraction of a handful of converted atoms from a target measuring tens or hundreds of tons. The extracted atoms were then identified by their radioactive decays.

Discovery of Solar Neutrinos in the Homestake Experiment It was the goal of the Homestake Chlorine experiment, proposed by Ray Davis, to measure solar neutrinos for the first time (Davis 1964; Bahcall and Davis 1976). To this purpose, a steel tank containing 615 tons of perchloroethylene was placed at a depth of 1,400 at the deep levels of the Homestake Mine in South Dakota. Largely

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protected from cosmic rays, this detector became sensitive to solar neutrinos by the conversion reaction: νe + 37 Cl → 37 Ar + e−

(10)

Solar electron neutrinos weakly interact with 37 Cl nuclei, transforming one neutron inside the nucleus into a proton and thus producing the argon isotope 37 Ar. Over a given solar run (starting without any argon in the detector), the 37 Ar accumulated slowly inside the tank, corresponding to a rate of about 1 conversion per day. However, the isotope 37 Ar is not stable and decays via electron capture (EC) back to 37 Cl with a half-life of 35 days: 37

Ar + e− → 37 Cl + νe

(11)

Therefore, an equilibrium of neutrino-induced 37 Ar production and radioactive decay is established on the time-scale of months. Every few weeks, Davis and his team extracted the 37 Ar atoms from the tank by bubbling the liquid perchloroethylene with helium. The exhaust helium carried the argon atoms to a cryofilter were the argon atoms froze out. In the follow-up, these 37 Ar were inserted into gas counting tubes, determining the amount of nuclei produced by the measured number of decays. Astonishingly, while the experimenters were able to detect a positive neutrinoinduced result, the observed rate fell significantly short of the expectation from the standard solar model: In comparison to the predicted neutrino emission, Davis et al. yielded only about one third of the expected event rate (Davis 1994, 1996; Cleveland et al. 1995). Unknown at that time, the underlying reason was the occurrence of solar neutrino oscillations, changing about two-thirds of the solar νe flux into μν and μτ neutrinos to which the detection reaction (10) is not sensitive. These findings gave rise to the solar neutrino problem that hounded the field for more than 30 years. In the end, Ray Davis was awarded the Nobel Prize in Physics in 2002 “for pioneering contributions to astrophysics, in particular for the detection of cosmic neutrinos.”

The Gallium Experiments and the Solar Neutrino Problem In the early days of the solar neutrino problem, the scientific community was widely convinced that the rate deficit observed in the Homestake experiment was either due to systematic uncertainties in the detection efficiency or a wrong prediction by SSM calculations. When the first explanation was excluded by a sequence of painstaking calibration measurements, a miscalculation of the expected 8 B neutrino flux seemed likely. The rate of the corresponding fusion reaction is only weakly linked to other observational parameters of the Sun. This is decisively different for neutrinos emitted by the initial pp reaction that is dominating solar energy production (Fig. 7) and thus closely linked to the well-known electromagnetic energy output of the Sun. An accurate measurement of the pp neutrino flux would yield a very sensitive test of the SSM and neutrino properties.

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Radiochemical gallium experiments proved to be especially attractive: Inheriting the basic experimental technique from the Homestake experiment, they employ the detection reaction νe + 71 Ga → 71 Ge + e− .

(12)

The energy threshold of 233 keV is sufficiently low to become sensitive to the solar pp neutrino rate. Due to the promise of this technique, two radiochemical gallium detectors began their operation in the early 1990s: • the GALLEX experiment at the Gran Sasso underground laboratory in central Italy began measurement in 1991, exposing 30.3 tons of natural gallium in the form of an acidic GaCl3 solution; in 1998, it was upgraded to GNO, the Gallium Neutrino Observatory • SAGE, the Soviet-American Gallium Experiment in Baksan, Russia, based on 50 tons of liquid metallic gallium While the exact procedure for the extraction of the germanium isotope and counting its re-decay to 71 Ga varied, both experiments were able to measure the produced 71 Ge with high (∼95%) efficiency. However, their results fell again short of the SSM prediction, measuring only about 50% of the expected rate (Anselmann et al. 1995; Hampel et al. 1996, 1999). This ruled out an explanation of the deficit based on the SSM, as the solar luminosity constraint imposes a much tighter bound on the pp neutrino flux. As a consequence, nonstandard properties of the neutrinos and especially neutrino oscillations were shifting into the focus of neutrino physicists.

Pointing at the Sun: Kamiokande The Kamioka Nucleon Decay Experiment (KamiokaNDE) (Koshiba 1992) in the Kamioka mine (2,700m.w.e.) 300 km west of Tokyo, Japan, was a water Cherenkov detector containing 3,000 tons of water. The detector was constructed in 1983 and primarily aimed at the search for proton decay. While these decays were not observed, the experiment is today primarily remembered for the detection of the neutrino burst from Supernova SN1987A in the Great Magellanic Cloud; in the follow-up, M. Koshiba received the 2002 Nobel Prize in Physics for pioneering contributions to astrophysics, in particular for the detection of cosmic neutrinos, a prize he shared with R. Davis. In the present context, our interest in Kamiokande is in the first real-time (i.e., event-by-event) measurement of solar 8 B neutrinos. The relevant detection channel in a water Cherenkov detector is the elastic scattering of the neutrinos off an electron in the target volume (in this case, 680 tons): ν + e− → ν + e−

(13)

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The emerging electron is travelling at a velocity greater than the speed of light in the medium: vgroup ≈ vphase = c/n, with n the refractive index. This light is emitted in a cone around the electron track, very much like the Mach cone emitted by a supersonic jet in air. The opening angle of this cone depends on the relative speed of particle and light, cos θc = 1/βn. The total amount of Cherenkov light emitted is roughly proportional to the kinetic energy of the particle; about 350 photons per MeV are emitted, the wavelength spectrum in water peaking in the near UV (cf. Cherenkov Radiation). In Kamiokande, the Cherenkov light was detected by about 1,000 photomultiplier tubes (PMTs) surrounding the water target. Given the relatively low amount of photons produced by the Cherenkov effect in water and the limited coverage and photo-detection efficiency provided by the PMTs, the effective detection threshold was much higher than in the radiochemical experiments. Initially, the energy threshold (for recoil electrons) was ∼9.3 MeV at first and could later be improved to ∼7.5 MeV. Consequentially, the detector was sensitive only to the high-energy part of the solar neutrino spectrum (see Fig. 8), the 8 B, and hep neutrinos. The Cherenkov effect provides the possibility to reconstruct the momentum vector of the recoil electron. Due to kinematics, the electron is mostly scattered in forward direction. Therefore, directional signal events can be discriminated from isotropic background events (mostly radioactive decays) when plotting the angle between the reconstructed direction and the position of the Sun in the sky. As demonstrated in Fig. 9, this allowed to establish beyond doubt the presence of a solar neutrino signal in the detector and allowed for an accurate measurement of the event rate. However, the neutrino flux measured was only (43±6)% of the predicted value by the SSM (Kamiokande-II Collab 1990; Bahcall and Pinsonneault 1995), similar to the results of the Chlorine experiment. Kamiokande thus corroborated the experimental evidence for the solar neutrino problem. The low rate reported for solar neutrinos as well as hints at an asymmetry in the flux of atmospheric muon neutrinos observed in the detector were the main motivations to realize a successor experiment to Kamiokande: In 1996, the Super-Kamiokande detector started data taking, featuring a substantially enlarged

Fig. 9 Reconstructed direction of low-energy electrons in the Kamiokande experiment. While radioactive backgrounds are isotropically distributed, recoil electrons from solar neutrinos show a clear correlation with the direction of the Sun. (Courtesy of the Kamiokande collaboration)

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fiducial volume of 22,500 tons and an energy threshold of ∼5 MeV for solar neutrino detection. A sketch of the detector is depicted in Fig. 13, an inside photograph in Fig. 14. Super-Kamiokande confirmed the earlier results, measuring ∼40% of the predicted solar neutrino rate. Further details are given in Nakahata (2005). More importantly, the experiment discovered the occurrence of neutrino oscillations νμ → ντ in atmospheric neutrinos (section “Atmospheric Neutrinos in Super-Kamiokande”).

Neutrino Flavor-Resolved Detection in SNO The SNO (Sudbury Neutrino Observatory) detector was located at a depth of 2 km (6,000m.w.e) in the Creighton mine close to Sudbury in eastern Canada. Like Kamiokande, SNO relied on the Cherenkov effect for neutrino detection. Different from Kamiokande that employed normal light water (H2 O), SNO used a neutrino target consisting of 1,000 tons of heavy water (D2 O). The layout is shown in Fig. 10: The D2 O target was contained in a transparent acrylic sphere of 12 m diameter and 5 cm wall thickness. Shielding from external radioactivity was provided by filling

Fig. 10 Schematic of the SNO detector. (Courtesy of the SNO collaboration)

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the outside detector cavern with light water. The Cherenkov photons produced by particle interactions were recorded by ∼9,500 8-inch photomultipliers equipped with light-collecting mirrors, positioned on a concentric support structure of 18 m diameter. Due to the good light collection, the corresponding energy threshold for particle detection was only ∼5 MeV, later on lowered to about 3.5 MeV (see Fig. 8). The main difference to Kamiokande was the presence of deuterons (d = 21 H) in the heavy water target. Due to this fact, neutrinos could not only be detected by elastic scattering of electrons but by three different reactions: • A charged-current (CC) reaction on deuterons: νe + d → p + p + e− only accessible for electron neutrinos

• A neutral-current (NC) reaction on deuterons: νx + d → p + n + νx featuring identical interaction cross sections for all neutrino flavors

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• and the well-known elastic scattering (ES) off electrons: νx + d → d + νx for which the cross section is dominated by the interaction with νe ’s.

Based on those three channels, SNO was able to directly test flavor transitions from νe to νμ or ντ , comparing the interaction rates measured by the CC and NC reactions: Since only electron neutrinos are produced in the Sun, the CC channel provides a measurement of the νe → νe survival probability. This was established to be close to 30%. On the other hand, the NC channel providing the sum signal of νe , νμ , and ντ fluxes showed perfect agreement with the prediction of the SSM. This demonstrated beyond doubt that the missing νe were actually undergoing flavor conversion induced by oscillations (Aharmim et al. 2005). This phenomenal result changed the landscape of neutrino physics. In the end, A. McDonald was awarded the Nobel Prize in Physics 2015 “for the discovery of neutrino oscillations,” sharing it with T. Kajita from the Super-Kamiokande experiment (section “Atmospheric Neutrinos in Super-Kamiokande”).

Solar Neutrino Spectroscopy with Borexino Water Cherenkov detectors have proven enormously successful in the detection of the solar neutrino spectrum above 5 MeV. At these comparatively high energies, the solar spectrum is dominated by 8 B neutrinos, while the majority of the solar neutrino flux lies below (Fig. 8). Unfortunately, a further reduction of the detection threshold in water Cherenkov detectors is extremely demanding: Both Super-Kamiokande and SNO were eventually able to lower their thresholds to ∼3.5 MeV (Aharmim et al. 2010). Below, not only the number of detected Cherenkov photons becomes sparse compared to the dark noise of the PMTs but more importantly radioactive background from trace elements in water effectively overwhelm any neutrino signal. However, experiments based on liquid scintillator offer a viable alternative for the detection of low-energy neutrinos. Scintillation produces significantly more light than the Cherenkov effect, typically 104 UV/blue photons per MeV of deposited particle energy. Moreover, the organic solvents forming the base material

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of scintillators can be purified very efficiently from intrinsic contamination with radioactive isotopes, as distillation or column chromatography are purification techniques well-probed by (industrial) chemistry (cf.  Chap. 15, “Scintillators and Scintillation Detectors”). The liquid scintillator experiment Borexino has been designed for spectroscopy of low-energy solar neutrinos. In 2007, the detector started data taking at the Gran Sasso national laboratories (LNGS) under the Gran Sasso mountain range in central Italy, at a depth of 3,500 mwe. A sketch of the experimental setup is shown in Fig. 11. At the heart of the detector, 280 tons of liquid scintillator serves as the neutrino target. The scintillator is based on the organic solvent pseudocumene (PC, 1,2,4-trimethylbenzene), doped with a wavelength shifter at per mill concentration that allows the scintillation light to escape the reabsorption in PC by shifting the light to longer wavelength. The target region is contained in an ultrathin spherical vessel of transparent nylon. It floats in an inactive buffer of pure PC held by a spherical steel tank of 13.7 m diameter. This steel sphere is again enclosed in a domed steel tank (diameter: 18 m) filled with ultrapure water that serves both as shielding from external radioactivity and as an active veto for cosmic muons. It is equipped with 208 photomultipliers distributed on the sphere outer surface and the tank floor that detect the Cherenkov light created by muons traversing the water. Inside the steel sphere, the scintillation light of neutrino events is detected by 2,212 photomultipliers mounted to the inner sphere surface. The individual multipliers are equipped with light-collecting conical mirrors around their photocathode that enhance the light detection area. Altogether, 30% of the sphere surface are photosensitive. Of the 104 photons per MeV originally produced, only about 550 are detected due to the optical coverage, the photomultiplier detection efficiency of about 20%, and self-absorption of the scintillation light in the liquid. Nevertheless, the improvement in light yield compared to water Cherenkov detectors is substantial.

Fig. 11 Left: Schematic of the Borexino detector. Right: Fit to the neutrino (and background) components of the observed electron recoil spectrum; rates for solar pp, 7 Be, and pep neutrinos can be extracted from the fit; for the CNO component, only an upper limit is provided (Borexino Collab). (Creative Commons Attribution 4.0 International license. https://doi.org/10. 1103/PhysRevD.100.082004)

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The detection of solar 7 Be neutrinos at an energy of 866 keV (Borexino Collab 2008) was considered the primary objective of Borexino. Like water Cherenkov detectors, the detection of solar neutrinos in Borexino relies on the elastic neutrino scattering of target electrons. However, as there is no possibility on an eventby-event basis to discriminate recoil electrons from neutrinos from the electrons induced by β and γ decays of radioactive contaminants, purity of the target liquid is the main challenge of the experiment. The expected signal rate from 7 Be neutrinos is of the order of 0.5 interactions per day and ton of detector material. To obtain a similar low rate of radioactive decays, the contamination with elements of the natural decay chains of 238 U and 232 Th must be below 10−16 gram per gram (g/g) scintillator in the target volume. For comparison, the natural uranium content of the Earth’s crust is about 10−4 g/g! A reduction to the required level was only possible by application of strict purity requirements during the construction of the detector, the transportation and the filling of the liquid, and the detector operation. In the end, the radioactivity levels achieved at the start of data taking were even below the specified requirements: (1.6±0.1)×10−17 g/g for 238 U and (6.8±1.5)×10−18 g/g for 232 Th were achieved (Borexino Collab 2008). During construction, radiopurity requirements applied not only to the target scintillator but also for all materials coming in contact with the liquid, as, for instance, the nylon balloon, but also the piping of the liquid handling system that was carefully cleaned prior to filling. Still, γ rays emitted by the outside materials, especially from U/Th contained in trace amounts in the glass of the PMTs, can reach into the active scintillator and pose a formidable background in the outer regions of the target volume. Consequently, a fiducial volume cut has to be applied in a software basis, limiting the volume regarded for solar neutrino detection to the innermost 100 tons of the scintillator target, corresponding to a spherical fiducial volume of 3 m radius. This cut on the spatial event position is possible because the vertex position can be reconstructed based on the nanosecond time-of-flight differences of photons detected in individual photomultipliers. Dependent on event energy, accuracies on the level of centimeters can be reached. Finally, cosmic muons crossing the steel sphere near to its verge can produce low-light signals that can in principle be mistaken as neutrino signals. However, this background is effectively reduced by the passive shielding provided by the Gran Sasso mountain and the active suppression by the external muon veto. It is also possible to reconstruct the muon track by the light arrival time patterns of the inner photomultipliers and the Cherenkov light cones detected in the water tank. Over its 10 years of operation, it became clear that the science case of Borexino is not limited to 7 Be neutrinos. Basically all neutrinos arising from the solar pp fusion chain proved to be within detection reach: The 8 B neutrino spectrum could be determined down to energies of 3 MeV (Borexino Collab 2010), and – though demanding – signals of both pep and eventually pp neutrinos could be spectrally resolved (see Fig. 8). While Borexino is slowly approaching the end of its experimental lifetime, the last and probably most formidable task remaining is a first detection of the faint CNO neutrino signal that would provide relevant

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information on the metal contents of the Sun and is furthermore of considerable interest for the understanding of stars heavier than our Sun in which − due to higher core temperatures − the CNO cycle provides the dominant mechanism for hydrogen burning.

Atmospheric and Accelerator Neutrino Experiments Solar and reactor neutrinos have proven very successful in the investigation of neutrino oscillations connected to the mixing angles θ12 and θ13 (commonly known as the “solar” and “reactor” angles). However, as these experiments operate with neutrino energies in the MeV regime they are limited to disappearance searches of νe and ν¯ e ; the masses of μ and τ leptons potentially created by νμ and ντ in charged-current weak interactions are too large to be produced at these energies. This situation changes at GeV energies: Both atmospheric and accelerator beam neutrinos offer sufficiently intense sources to study the oscillation of νμ ’s in both disappearance and appearance experiments. Atmospheric Neutrinos Atmospheric neutrinos offer a natural source of electron and muon neutrinos at GeV energies. These neutrinos are created by high-energy primary cosmic rays impinging on the Earth’s atmosphere and undergo inelastic collisions, creating a multitude of charged mesons. Especially pions and kaons primarily decay into lepton+neutrino pairs. Most commonly, the decays π + → μ+ νμ

and

π − → μ− ν¯ μ

(14)

provide a flux of muon (anti-)neutrinos. The subsequent decay of the μ± , e.g. μ+ → e+ νe ν¯ μ

(15)

adds additional νμ ’s and νe ’s. The expected ratio of muon to electron flavor neutrinos is such 2:1. As the neutrino energy is directly correlated to the oscillation length, there is a consequent increase in the baselines required to observe neutrino oscillations: In this case, they are on the order of thousands of kilometers. However, depending whether atmospheric neutrinos are created in zenith, nadir, or at intermediate angles, oscillation baselines vary in fact from 20 to 13,000 km, allowing for a broad range of oscillation parameters to be tested. Historically, the first evidence for neutrino oscillations of the type νμ → ντ relied on the disappearance of upward-going atmospheric νμ ’s observed with Super-Kamiokande, a result awarded with the Nobel Prize for T. Kajita in 2015 (section “Atmospheric Neutrinos in Super-Kamiokande”).

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Accelerator Neutrinos From the very early days of neutrino physics, it had been known that there was an artificial way to produce neutrinos at GeV energies. In 1962, L. Lederman, M. Schwartz, and S. Perlmutter directed high-energy protons from the AGS accelerator at Brookhaven at a fixed target, creating multitudes of charged pions (and kaons) in the collisions. As a consequence of kinematics, the mesons were beamed in forward direction when decaying, creating muons and neutrinos. Positioning flavor-sensitive detectors (spark chambers) downstream of the beam target and shielding all particles (including the decay muons) by a several meters thick shield of concrete, the trio was able to demonstrate that the neutrinos produced associated with muons in the pion decays − νμ in modern terms − did produce only muon-like but no electron-like signals in the spark chambers. This demonstrated the different nature of neutrinos produced in nuclear β-decays, νe , from those in pion decays, νμ , a finding that was awarded with the Nobel Prize in Physics in 1988. While in 1962, the production of a muon beam from a high-energy proton accelerator was just a diversion from the main purpose of the machine, today the same technique is employed for the production of high-intensity, high-energy neutrino beams by fully dedicated accelerator complexes. As in the early days, highenergy protons are directed onto a fixed target from light materials (beryllium or carbon), creating large numbers of charged pions at impact. As depicted in Fig. 12, the neutrino yield is improved by focusing the pions with the help of a magnetic field, guiding them into a long evacuated decay tunnel to allow for the process π + → μ+ νμ to happen. As experimenters are usually interested in a “clean” neutrino beam containing only νμ , the length of the decay line is chosen to suppress the subsequent decay of the comparatively long-lived muons that would add other flavors to the beam (usual contamination levels are on the percent level). The advantages compared to atmospheric neutrinos are the very clearly defined oscillation baseline and the possibility to adjust mean energy and shape of the neutrino spectrum by the geometry of target, magnetic horns, and decay line. Moreover, the pulsed structure of the original proton beam is passed on to the neutrinos, allowing to very efficiently reduce uncorrelated backgrounds. Finally, inverting the orientation of the magnetic fields that usually focus π + and divert π − in neutrino mode, it is possible to run the beam in a mode dominated by the production of antineutrinos, ν¯ μ ’s. Therefore, beams are exceptionally well suited to measure the appearance amplitude of non-muon flavor neutrinos induced by oscillations and to study differences in the oscillation probabilities of neutrinos

Fig. 12 Principle components of a modern muon neutrino beam facility

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and antineutrinos expected in case of a non-zero value of the CP-violating phase δ (section “Important Neutrino Properties”). In the following, we describe only a small selection of experiments: In Japan, the J-PARC laboratory produces the T2K beam, a high-intensity νμ beam from Tokai (on Japan’s eastern coast) to Super-Kamiokande (section “Atmospheric Neutrinos in Super-Kamiokande”). With the Booster Neutrino Beam and the Neutrino Main Injector Beam, the Fermi National Laboratory (USA) is currently featuring two neutrino beamlines, providing (among others) neutrinos to the NOvA experiment (section “A First Glimpse at Leptonic CP Violation in NOvA”). A third beamline for the future DUNE project is in preparation (section “Conclusions”). Finally, the CNGS neutrino beam from CERN to Gran Sasso supplied νμ ’s for the OPERA experiment (section “Search for ντ Appearance in OPERA”). Over these setups, average neutrino energies vary from 600 MeV to 20 GeV, while oscillation baselines span from about 1 to 1,000 km.

Atmospheric Neutrinos in Super-Kamiokande As the successor to the Kamiokande experiment (section “Pointing at the Sun: Kamiokande”), the Super-Kamiokande detector is based on a large cylindrical water tank of 39 m diameter and 41 m in height, containing a total of about 50,000 tons of ultrapure water (Figs. 13 and 14). This volume is surrounded by 11,146 photomultipliers of 20 inch diameter each. The photomultipliers are placed at 70 cm distance, corresponding to a fraction of 40% of the detector walls that

Fig. 13 Sketch of the Super-Kamiokande detector. (Courtesy of the Super-Kamiokande collaboration)

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Fig. 14 Picture of the Super-Kamiokande detector during water filling. (Courtesy of the SuperKamiokande collaboration)

is photosensitive. The detector is located 1,000 m underground (2,700 m of water equivalent) in the Kamioka mine in Gifu Prefecture, Japan. Data taking started in 1996 and has been going on to the present day, intermitted by some breaks for detector upgrades. Super-Kamiokande features a wide physics program, ranging from solar neutrino to proton decay and Supernova neutrino searches. In the present context, we are interested in only two of the measurement programs: the study of atmospheric νμ oscillation and the deployment as far detector in the T2K neutrino oscillation beam experiment. In the relevant energy range from hundreds of MeV to several GeV, neutrinos are detected by the Cherenkov light of charged leptons (electrons or muons) that are produced in the interaction with the target material. At the lower end of the indicated energy range, the dominant reaction is on single nucleons of the hydrogen and oxygen nuclei inside the target: νe + n → p + e− ,

ν¯ e + p → n + e+ ,

νμ + n → p + μ− ,

ν¯ μ + p → n + μ+ .

The recoil proton or neutron is below the Cherenkov threshold in water and remains therefore undetected, but the emerging electron or muon will carry away most of the kinetic energy of the incident neutrino. Similar to MeV energies, neutrino events are thus identified based on the final state lepton, either electron or muon. In fact, this detection reaction allows to discriminate between νμ and νe events: While the muon proceeds along a straight track and projects a very sharp image of the cone (i.e., a

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Fig. 15 The flavor recognition in the Super-Kamiokande relies on the “fuzziness” of the observed Cherenkov rings: In quasi-elastic scattering reactions, neutrinos create single electrons (left) and muons (right). As electrons scatter in the detector producing electromagnetic showers, the resulting ring is washed out, while a muon creates a clear signal

Cherenkov ring) on the PMTs, electrons undergo considerably more scattering and produce electromagnetic showers; as a consequence, their ring images are washed out (Fig. 15). This “fuzziness” is quantified and used as a powerful discrimination criterion for electrons and muons (cf.  Chap. 6, “Particle Identification”). While this is true in the low energy range, interaction final states become more complicated for multi-GeV events: Resonant pion production and deep inelastic scattering result in the creation of neutral and charged pions, either along with the lepton in charged-current reactions or without for neutral currents. Unfortunately, neutral pion decays into two gammas cannot always be perfectly discriminated from the electromagnetic showers created by νe CC interactions, resulting in ambiguities in the analysis of results. Despite this partial limitation at higher energies, the Super-Kamiokande collaboration was able to produce a series of outstanding results on neutrino oscillations in the GeV range: Most famously, Super-Kamiokande observed a deficit in the upwardgoing flux of νμ ’s entering the detector from below, while the downward-going νμ flux fully met expectations. As shown in Fig. 16, the flavor ratio between up-going νμ ’s and νe ’s was measured close to 1:1, while the expected 2:1 ratio was observed for down-going events (Super-Kamiokande Collab 1998, 1999). Hints of this effect had been already observed in Kamiokande. Super-Kamiokande now refined this analysis and greatly increased the statistics of the data set, determining both the energy and angular dependence of the νμ flux at high accuracy; note that in this case, the incident angle is closely connected with the distance a neutrino had to travel through the Earth upon creation in the Earth atmosphere (see above). Such, the deficit in ascending νμ is due to the oscillation of νμ → ντ over the comparatively long baselines, while oscillations of type νμ → νe can be largely excluded as the νe signal corresponded to observation. Moreover, Super-Kamiokande was employed as a far detector in a sequence of long-baseline neutrino beam experiments, first from

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Fig. 16 Angular dependence of the atmospheric neutrino events observed in Super-Kamiokande compared to expectation. While good agreement with model predictions is found for down-going neutrinos, a significant deficit is observed for up-going νμ ’s, while νe ’s correspond to expectation. This is a clear sign of neutrino oscillations of type νμ → ντ (Super-Kamiokande Collab 1998). (With permission of APS)

KEK (K2K) and later on from the J-PARC accelerator complex at Tokai (T2K) (T2K Collab 2014): For the later, the average neutrino beam energy was chosen to 600 MeV, aligning the first oscillation maximum corresponding to Δm232 with the baseline to Super-Kamiokande. As a consequence, both the νμ disappearance and the νμ → νe appearance signal can be studied, providing information both on the mixing angle θ13 and the CP-violating phase δ of the PMNS matrix (section “Important Neutrino Properties”).

Search for ντ Appearance in OPERA Super-Kamiokande was able to demonstrate the disappearance of νμ but was originally not able to prove that these oscillations were indeed of type νμ → ντ . This provided the motivation for the European neutrino beam program that focused on an appearance measurement of ντ in a muon neutrino beam. The CNGS (CERN Neutrinos to Gran Sasso) beam was constructed at CERN, pointing an intense νμ beam at the LNGS laboratories, 735 km from the source. As the average neutrino energy of ∼17 GeV was actually at a mismatch with the chosen oscillation baseline, the conversion amplitude νμ → ντ was quite suppressed. However, the high energy favors the production of the large mass charged τ leptons in the final state that provide the signature for ντ appearance. To detect the ντ ’s in charged-current reactions, the OPERA detector was erected at the LNGS underground laboratory. OPERA is a hybrid detector that associates an inactive lead target with nuclear emulsions and electronic detectors. This peculiar configuration was chosen due to the challenge set by the detection of the short-lived τ lepton: A sub-millimeter spatial resolution is required to observe the τ lepton that travels only millimeters in the neutrino target before decaying in lighter particles

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Fig. 17 Picture of the OPERA experiment. (Courtesy of the OPERA collaboration)

and a tau neutrino, resulting a revealing kink signature from the decay. On the other hand, large target mass (order 1,000 tons) is required to collect a sufficient number of ντ interactions. The detection principle relies on ντ ’s interacting in a large mass target made of lead plates, interspaced with nuclear emulsion films acting as high-accuracy tracking devices. This kind of detector is historically called Emulsion Cloud Chamber (ECC). It was successfully used to establish the first evidence for charm in cosmic rays interactions (Niu et al. 1971) and in the DONUT experiment for the first direct observation of the ντ (Kodama et al. 2001). As depicted in Fig. 17, OPERA (Acquafredda et al. 2009) consisted of two super modules aligned in beam direction. Each super module contained a target section holding 75,000 emulsion/lead ECC modules, the so-called bricks: Each brick in turn consisted of 56 lead plates of 1 mm thickness interleaved with 57 emulsion films and weighs 8.3 kg, corresponding to a total of 1,300 tons of lead. A segmented plastic scintillator detector, the target tracker, was positioned in between brick walls and was used to identify and localize neutrino interactions based on the high-energy final state particles leaving the lead bricks. The super modules were preceded by a muon veto (to identify events originating from the rock upstream from the detector) and followed by a spectrometer to measure the momentum of final state muons. Once the target tracker identified a neutrino event, the corresponding brick was physically extracted by an automated system. The bricks were transported from the underground laboratory and analyzed in automatic scanning stations at the LNGS and various laboratories in Europe and Japan. The CNGS facility provided the neutrino beam from 2008 to 2012. In 2010, OPERA reported the first positive identification of a ντ appearance event in OPERA Collab (2010): The corresponding event is depicted in Fig. 18. The short track created of the τ from the neutrino interaction vertex to the particles decay is clearly visible. In the final analysis, 5 (10) ντ candidates were identified, relying on strict

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Fig. 18 Reconstruction of the first ντ appearance event in the OPERA. The characteristic decay kink of the short-lived τ is clearly visible

(soft) quality cuts on the underlying event selection (OPERA Collab 2018). This result demonstrated the νμ → ντ nature of the oscillations beyond doubt.

A First Glimpse at Leptonic CP Violation in NOvA In parallel to the neutrino beam programs of Japan and Europe, a further strand has been developing in the USA: Based on the existing accelerator infrastructure at the Fermi National Lab, the BNB (Booster Neutrino Beam) and NuMI (Neutrino Main Injector) beams have been providing neutrinos to a number of experiments, of which MiniBooNE, MicroBooNE, MINOS, and MINERvA are the most prominent examples. With the advent of the future LBNF beam, Fermilab will be turned into the global center of accelerator-based neutrino programs, comparable to the role of CERN in high-energy physics. Here, we only have space to describe the NOvA (NuMI Off-Axis νe Appearance) experiment (NOvA Collab 2016). At the time of writing, it is the largest of the running US neutrino experiments: The NuMI beam provides a pure νμ beam to the 810 km far detector of NOvA, a 15,000 ton on-surface liquid scintillator detector. Note that the neutrino beam is actually slightly “mis-aligned” with the far detector site. This off-axis configuration kinematically selects a narrower energy range of decaying pions and νμ ’s, leading to a narrower profile of the beam energy that is optimizing the spectrum with regard to the first oscillation maximum located at 1.6 GeV. Differently from the low-energy neutrino detectors that were described before (secs. Reactor Antineutrino Experiments and Solar Neutrino Experiments),

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Fig. 19 Schematic view of the NOva detector: (a) overall detector subdivided in horizontal and vertical scintillator cells; (b) event display of a neutrino interaction; (c) light readout inside a scintillator cell. (Courtesy of NOvA collaboration)

NOvA is a highly segmented detector. As depicted in Fig. 19, the detector is constructed from alternating layers of long scintillator bars. Extruded from highly reflective PVC, each of the 500,000 subvolumes measuring 4 cm × 6 cm × 12 m is filled with liquid scintillator. The scintillation light created by charged particles in the scintillator is collected by a wavelength-shifting fiber that runs in a loop along the whole length of the cell and is read out by avalanche photodiodes. The main purpose of this segmentation is an improved resolution with respect to the tracks of the final state particles resulting from neutrino interactions. As indicated in Fig. 19, for example, neutrino event, particles created inside the detector will “activate” cells along their tracks; given the alternating orientation of the scintillator strips, full 3D information is available. Due to the low stopping power of the low-Z material, muons are easily identified as long extended tracks. Electrons, pions, and even nuclei can be reconstructed based on their differing event topologies. NOvA employs are near detector at short distance from the neutrino beam stop. The main purposes are to perform a high-statistic measurement of the neutrino flux and beam spectrum as well as to determine cross sections and detection efficiencies. These measurements are to provide a reference for the analysis of the far detector data and are essential to reduce systematic uncertainties in the oscillation analyses. Near and far detector employ functionally identical detectors, albeit the near detector containing only 220 tons of liquid scintillator. Note that also T2K employs a system of several near detectors to obtain a similar characterization of the initial neutrino beam. NOvA was originally conceived to provide a very accurate measurement of the mixing angle θ13 should it turn out to be small. However, when it took up data taking in 2014, θ13 was already known to be large and measured with high precision at the

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Daya Bay experiment. Consequentially, the focus of the experiment turned toward the determination of two other oscillation parameters that had just gotten within reach: the CP-violating phase δ and the neutrino mass hierarchy (section “Important Neutrino Properties”). Since 2014, NOvA has performed measurements both in neutrino and antineutrino beam mode, accumulating data that seem to favor a maximum value of CP violation, δ = −π/2, and the normal mass hierarchy, both with a significance of approximately 2σ (NOvA Collab). Under favorable circumstances, this might further increase to the 3 − 4σ level during the remaining run time (up to 2024).

Neutrino Telescopes Since the days of Victor Hess (1912), it has been known that there is a flux of elementary particles that increase with the height over ground. These are mostly secondary particles, created by high-energy cosmic rays (protons, electrons, nuclei) impinging on the outer layers of the Earth atmosphere. At sub-GeV energies, these particles are known to originate from the Sun. It seems very likely that particles with energies up to ∼1015 eV (a PeV) originate from the Supernova remnants within our galaxy, created in the surrounding shock waves by Fermi acceleration. However, the origin of particles at greater than PeV energies is still unclear: Active galactic nuclei (AGNs) and gamma ray bursts (GRBs) are commonly cited as likely sources, but − while plausible − there is no direct evidence. The charged particles (protons) produced by these cosmic accelerators have to travel vast distances. Being subject to the deflecting forces of galactic and intergalactic fields, their direction of motion when detected on Earth is no longer correlated to the source position. Instead, the neutrino telescopes presented in this section aim to observe ultrahigh-energy neutrinos from these cosmic sources. Unlike charged particles, neutrinos are not deflected on their way to Earth and not absorbed by intermediate dust clouds. In fact, they are able to penetrate through the potential outer layers of their sources, providing a direct view of their production process. Much like in an Earth-bound accelerator, it is assumed that cosmic neutrinos would be created in the inelastic collisions of high-energy protons with the surrounding materials, producing charged pions and subsequently νe ’s and νμ ’s in pion and muon decays. An observation of neutrinos from these potential “cosmic accelerators” and their identification based on optical or gamma ray observations is such a telltale sign to identify the sources of high-energy cosmic rays. If the neutrino flavor pattern corresponds to an initial mixture of 1:2:0 for e : μ : τ flavors, it would be a strong hint for pion decay and hence hadronic acceleration as the underlying neutrino source. Finally, a determination of the neutrino flux would allow to determine the source luminosity. However, due to the vast distances involved, the corresponding neutrino fluxes are exceptionally low. As depicted in Fig. 1, the cosmic neutrino flux starts to dominate the atmospheric one only above 100 TeV (1014 eV). Huge target masses on the scale of 109 tons are such required to identify about 10 cosmic neutrino

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events in a year. This corresponds to a cubic water body with an edge length of 1 km! While this scale forbids the construction of an artificial detection volume, experimenters have resorted to the instrumentation of natural water volumes with light sensors. PMTs are arrayed along kilometer-long strings and emerged deep into natural water bodies like Russian Lake Baikal, the Mediterranean, and the Antarctic ice shield. However, instrumentation is sparse, leaving gaps of tens of meters between neighboring PMTs on a string and even more in between. Still, the energies of the charged final state particles created and the associated track lengths and amount of Cherenkov light provide an extended and bright enough signal to be observed by the wide apart PMTs. Note that the main background for neutrino detection at these energies are the tracks of high-energy cosmic muons (inaptly named as they are created in the atmosphere alongside the neutrinos in pion decays). However, the directional resolution of the neutrino telescopes (∼1◦ on an event-by-event basis) allows to distinguish downward-going cosmic muons from upward-going muon tracks created in νμ interactions. The effort toward the creation of a large neutrino telescope of this kind started in the 1970s with the DUMAND project that aimed to deploy strings of PMTs in the Pacific Ocean close to Hawaii. While the conditions at the ocean floor turned out to be unsuitable for a detector deployment several successor experiments based on PMT strings submerged in water succeeded in operation: most noteworthy, ANTARES and NESTOR in the Mediterranean as well as a neutrino telescope in Lake Baikal. Due to their still limited size, these detectors were able to identify the tracks of atmospheric neutrinos but observed none of cosmic origin. In parallel, a second development path investigated the possibility to deploy PMT strings in a large body of natural ice. Close to the geographic South Pole, the AMANDA (Antarctic Muon and Neutrino Detector Array) (Ackermann et al. 2004) detector pioneered this technique: Shafts of km depth were drilled into the ice with the help of hot water, the strings were inserted and the water-filled holes allowed to freeze out. At large depth, the ice proved to be free of air bubbles and very transparent to the Cherenkov light, making the construction of an even larger detector conceivable.

First Glimpse at Cosmic Neutrinos with IceCube IceCube (Abbasi et al. 2010) is the successor experiment to AMANDA. As depicted in Fig. 20, about one cubic kilometer of Antarctic ice has been instrumented with 72 strings of 2.5 km length. Under a shielding layer of 1.5 km of ice, a total of 5,160 digital optical modules (DOMs) has been deployed for the detection of cosmic neutrino interactions. Inside a massive glass sphere to withstand the surrounding pressure, the DOMs contain a downward-facing PMT as well as the necessary infrastructure and electronics for the readout and digitization of the signal that is then sent along the string to the data center on the surface. There, triggers and events are formed based on the pre-digitized signals of individual PMTs.

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Fig. 20 Left: Schematic of the IceCube detector; right: Event display for an upward-going ν-induced muon track

The full array of IceCube strings was completed in 2010. In 2013, the experiment reported the first evidence of a high-energy neutrino flux exceeding the expectation from atmospheric neutrinos in the energy range above 100 TeV (IceCube Collab 2014). However, this was a diffuse flux and could not be associated to individual cosmic sources. Only in 2018, IceCube reported the first observation of a neutrino from a transient source, closely correlated in space and time with the occurrence of a GRB (IceCube Collab 2018). While an important step forward for multi-messenger astronomy and the identification of cosmic accelerators, further such observations will be required to gain understanding of the sources of high-energy cosmic rays and their acceleration mechanisms.

Conclusions For more than 60 years now, neutrino detectors have been successfully operated and in the course have led to profound scientific discoveries. Three Nobel Prizes are directly associated with the observation of neutrinos: the discovery of the muon neutrino, the observation of solar and Supernova neutrinos, as well as the discovery of neutrino oscillations. Experimental neutrino physics profits from the variety of sources available: The combination of different neutrino flavors, energies, and oscillation baselines especially allows to study neutrino oscillations over a versatile range of experimental setups. While many of the experiments presented in this chapter are by now dismantled, a good fraction is still in operation, Super-Kamiokande, Borexino, NOvA, and IceCube being the most prominent examples. Moreover, a next generation of even more sensitive neutrino detectors is currently ongoing:

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• The Jiangmen Underground Neutrino Observatory (JUNO) is a 20,000 ton liquid scintillator detector currently under construction in southern China (JUNO Collab 2016). Located at 53 km from to nuclear reactor complexes at the first solar oscillation maximum (θ12 ), it will be ideally suited to scrutinize the observed oscillation pattern for effects of the neutrino mass hierarchy (section “Important Neutrino Properties”) that appears at this distance in the subdominant oscillation structure driven by θ13 . Moreover, JUNO offers a broad potential for the detection of solar and Supernova neutrinos (JUNO Collab 2016). The detector will become operational in 2021. • With IceCube-Gen2 (IceCube Collab 2016), the collaboration hopes to extend the current IceCube array to a total detection volume of 10 km3 , greatly enhancing the event rates from cosmic neutrinos detected. In the course of this upgrade, a subvolume of the detector will be more densely instrumented, lowering the threshold for neutrino detection to the range of 2 GeV. At these energies, matter effects affecting atmospheric neutrinos crossing the Earth will leave an imprint in the oscillation probabilities that again can be connected to the neutrino mass hierarchy. Meanwhile, a large neutrino telescope of several cubic kilometers volume is planned (and partially funded) under the name of KM3NeT, with ORCA (Oscillation Research with Cosmics in the Abyss) forming a low-energy extension for atmospheric neutrino oscillation studies (KM3NeT Collab 2016). • Finally, two truly large-scale neutrino beam projects for long-baseline oscillations are on the horizon: In the USA, construction work has begun for the Long-Baseline Neutrino beam Facility (LBNF) at Fermilab, directing a 1.2 MW beam toward the Homestake Mine, 1,300 km away in South Dakota. The Deep Underground Neutrino Experiment (DUNE) will observe the neutrinos in a quartet of 10,000-ton liquid argon time projection chambers (DUNE Collab). In Japan, plans toward the 250,000-ton Hyper-Kamiokande water Cherenkov detector are far proceeded. Located close to the Super-Kamiokande site in the Japanese Alps, the detector will receive neutrinos from an upgraded T2K beamline (Hyper-Kamiokande Proto-Collab 2015). Both experiments will offer considerable sensitivity for the discovery of the CP-violating phase δ, with the potential to provide a very accurate measurement if the value was large. All of these experiments are realized by international collaborations, hundreds of physicists working on all different aspects of detector hardware, simulation, and data analysis. This effort is contrasted by a large community of neutrino theorists and phenomenologists, combining the results of oscillation experiments in order to obtain the best constraints on oscillation parameters, carefully looking for signs of deviations from the standard three-flavor oscillation picture and connecting the observed neutrino signals to the properties of their sources. There is good reason to believe that the next decades of neutrino physics will contribute as much to our understanding of both particle and astrophysics as the experiments described above.

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Cross-References  Accelerators for Particle Physics  Cherenkov Radiation  Interactions of Particles and Radiation with Matter  Neutron Detection  Particle Identification  Photon Detectors  Scintillators and Scintillation Detectors

References Abbasi P et al (2010) Astrophys J 710:346 Ackermann M et al (2004) Astropart Phys 22:127 Acquafredda R et al (2009) JINST 4:P04018 Aharmim B et al (2005) Phys Rev C 72:055502 Aharmim B et al (2010) Phys Rev C 81:055504 Anselmann P et al (1995) Phys Lett B 357:237 Bahcall JN, Davis R Jr (1976) Science 191:264 Bahcall JN, Pinsonneault MH (1995) Rev Mod Phys 67:781 Bahcall JN et al (2005) Astrophys J 621:L85 Borexino Collab (2008) Phys Lett B 658:101 Borexino Collab (2010) Phys Rev D 82:033006 Borexino Collab (2019) First Simultaneous Precision Spectroscopy of pp, Be-7 and pep Solar Neutrinos with Borexino Phase-II, Phys Rev D 100 8:082004 Buck C (2016) Proceedings of NuPhys2016 conference Cleveland BT et al (1995) Nucl Phys B (Proc Suppl) 38:47 Cowan CL et al (1956) Science 124:103. https://doi.org/10.1103/PhysRevD.100.082004 Davis R Jr (1964) Phys Rev Lett 12:303 Davis R (1994) Part Nucl Phys 32:13 Davis R (1996) Nucl Phys B (Proc Suppl) 48:284 Daya-Bay Collab (2012) Phys Rev Lett 108:171803 Double-Chooz Collab (2012) Phys Rev D 86:052008 DUNE Collab. FERMILAB-DESIGN-2016-02, arXiv:1512.06148 Dwyer D (2015) New J Phys 17:025003 Fermi E (1934) Z Phys 88:161 Gonzalez-Garcia MC et al (2016) Nucl Phys B 908:199–217 Hampel W et al (1996) Phys Lett B 388:384 Hampel W et al (1999) Phys Lett B 477:127 Hyper-Kamiokande Proto-Collab (2015) PTEP 2015:053C02 IceCube Collab (2014) Phys Rev Lett 113:101101 IceCube Collab (2016) Preprint, arXiv:1412.5106 IceCube Collab (2018) Science 361:1378 JUNO Collab (2016) J Phys G 43:030401 Kamiokande-II Collab (1990) Phys Rev Lett 65:1297–1300 KamLAND Collab (2005) Nature 436:499 KamLand Collab (2008) Phys Rev Lett 100:221803 KM3NeT Collab (2016) PoS ICRC2015:1140 Kodama K et al (2001) Phys Lett B 504:218 Koshiba M (1992) Phys Rep 220:229

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Mention G et al (2011) Phys Rev D 83:073006 Mueller TA et al (2011) Phys Rev C 83:054615 Nakahata M (2005) Nucl Phys B (Proc Suppl) 143:13 Niu K et al (1971) Prog Theor Phys 46:1644 NOvA Collab (2016) Phys Rev Lett 116:151806 NOvA Collab. Preprint: arXiv:1806.00096 OPERA Collab (2010) Phys Lett B691:138–145 OPERA Collab (2018) Phys Rev Lett 120:211801 PROSPECT Collab (2016) J Phys G 43:113001 Reines F (1979) Science 203:11 Reines F, Cowan CL (1956) Nature 178:446 Reines F, Cowan CL Jr (1953a) Phys Rev 90:492 Reines F, Cowan CL Jr (1953b) Phys Rev 90:830 RENO Collab (2012) Phys Rev Lett 108:191802 Super-Kamiokande Collab (1998) Phys Rev Lett 81:1562. https://doi.org/10.1103/PhysRevLett. 81.1562 Super-Kamiokande Collab (1999) Phys Rev Lett 82:1810 Turck-Chièze S (2001) Astro J 555:69 T2K Collab (2014) Phys Rev Lett 112:061802

Scintillators and Scintillation Detectors

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Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Characteristics of Scintillators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Interaction of Radiation with Scintillators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Processes Governing the Generation and Decay of Light Pulses . . . . . . . . . . . . . . . . . . . . . Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Considerations in Matching Scintillators to Photosensors . . . . . . . . . . . . . . . . . . . . . . . . . . Scintillators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Inorganic Crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Organic Scintillators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract Scintillators find wide use in radiation detection as the detecting medium for gamma, x-rays, and charged and neutral particles. Since the first notice in 1895 by Roentgen of the production of light by x-rays on a barium platinocyanide screen, and Thomas Edison’s work over the following 2 years resulting in the discovery of calcium tungstate as a superior fluoroscopy screen, much research and experimentation have been undertaken to discover and elucidate the properties of new scintillators. Scintillators with high density and high atomic number are prized for the detection of gamma rays above 1 MeV, while lower atomic number

Z. W. Bell () Isotopes and Fuel Cycle Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN, USA e-mail: [email protected] © Springer Nature Switzerland AG 2021 I. Fleck et al. (eds.), Handbook of Particle Detection and Imaging, https://doi.org/10.1007/978-3-319-93785-4_15

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and lower density materials find use for detecting low energy gamma rays, beta particles, and heavy charged particles. Hydrogenous scintillators are used for fast neutron detection, and boron-, lithium-, and gadolinium-containing scintillators are used for slow neutron detection. This chapter provides the practitioner with an overview of the general characteristics of scintillators, including the variation of probability of interaction with density and atomic number, the characteristics of the light pulse, a list and characteristics of commonly available scintillators and their approximate cost, and recommendations regarding the choice of material for a few specific applications. This chapter does not pretend to present an exhaustive list of scintillators and applications.

Introduction Scintillators have been used by the radiation detection community since the development of radiation generators and the discovery of radioactivity. Among the conditions of employment at an early nuclear physics laboratory was the requirement of good eyesight. Laboratory assistants were expected to examine zinc sulfide screens under magnifiers to count the number of blue-green flashes they observed when the screens were exposed to alpha particles. Prospective employees sat in a dark room until their eyes acclimated to the darkness and were then presented with screens and sources to determine their visual acuity. Those failing this practicum were encouraged to seek other careers. Today, of course, electronic means of detecting light exist and students and researchers with relatively poor eyesight are free to pursue careers in nuclear physics, high energy physics, medical physics, health physics, and other areas making use of radiation detection. The radiation detection community continues to make heavy use of scintillators; even zinc sulfide continues to be used. In the early days, the discovery of scintillators was often accidental. Roentgen found barium platinocyanide while investigating the effects of different materials on the absorption of x-rays. This material glowed when exposed to a nearby xray tube. Thomas Edison systematically examined crystal and mineral collections to find those that fluoresced when irradiated. Many of the first materials to be evaluated were those that were known to fluoresce under ultraviolet light (carbon arcs lights and gas discharge tubes had been developed by 1880). Most materials discovered in these ways had long decay times and were visible to the naked eye. At the time, these were important characteristics because electronic photosensors did not become available until the 1930s. The first application of photomultiplier tubes to scintillation counting was reported by Curran and Baker (1948) in a confidential report related to the war effort in 1944, but not published until 1948. By 1950, a number of scintillators (NaI:Tl was shown to scintillate in 1948, Hofstadter (1948)) had been demonstrated, and the materials that have been examined since then number in the thousands. Of those thousands, however, approximately 25 inorganic crystals and 20 organic materials are in commercial production and only a few have light yields greater than NaI:Tl, the most recent of those being

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the lanthanum halides, and SrI2 :Eu (Cherepy et al. 2009). Research on the physical processes responsible for scintillation is ongoing as is research to discover new, brighter, more linear scintillators.

Characteristics of Scintillators In this section, a general description of the properties of scintillators is given. The interaction of gamma rays, neutrons, and charged particles with scintillators and the effects of atomic number and mass density are briefly described. The processes governing the generation of light are enumerated and characteristics of the decay of the light pulse are discussed. The section concludes with a brief discussion of the considerations in play when matching a scintillator to a photosensor.

Interaction of Radiation with Scintillators Scintillators depend on the production of charged particles within the scintillating medium to generate excitation resulting in the emission of light. Consequently, they detect radiation capable of producing ionization. Incident electromagnetic radiation typically ionizes atoms to produce fast electrons or creates electron-positron pairs which, in turn, ionize other atoms as they lose energy. Thus, gamma and x-rays are detected by a two-step process (here, step refers to an event leading to energy transferred to the scintillator) in which a scattering or photoelectric event must occur first, and the resulting charged particle (or particles if there are multiple scatterings) then ionizes the scintillator. Light is produced from excitation of the scintillator occurring within microns of the track of the charged particles. On the other hand, incident electrons, positrons, and other charged particles interact directly with electrons in the scintillator, resulting in a one-step process. Neutrons interact only through nuclear interactions and produce gamma rays by capture and inelastic scattering (three steps: capture/scattering, gamma produces electrons, electrons ionize scintillator), charged particles (two steps: neutron scatters a proton or knocks out a proton or alpha particle, charged particle ionizes the scintillator), or, if sufficiently energetic, additional neutrons (at least three steps: (n,xn) first, then neutrons participate in capture, inelastic scattering, and charged particle reactions). The above description applies to what might be called “pure” materials. When a material comprises an inert medium containing particles of scintillator (such as a composite of micro- or nanocrystals of a scintillating compound suspended in a plastic or otherwise non-scintillating material) or a solution of scintillating molecules in an inert carrier (such as diphenyl oxazole dissolved in toluene or polystyrene), an additional step in the production of scintillation light almost always occurs: The inert medium, which can make up more than 90% of the total, will be ionized and that energy must migrate through the inert component to the scintillating component. This step can be important when the light yield of a composite is of

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prime importance because electrons lose energy traversing inert media, leaving less energy for the excitation of the scintillating component. The ranges of ionizing radiations in scintillators differ widely. Between 800 keV and approximately 6 MeV, the mean free path of electromagnetic radiation ranges from 2 to 15 cm. Electrons and positrons with energy of about 1 MeV have ranges that are approximately 1 mm in most scintillators, while heavy charged particles with energies of a few MeV have a range typically less than 15 μm. Neutrons interact via a series of scatterings with nuclei, and since the cross sections (away from resonances) are typically in the range of 1–10 barns (excluding, for the present, possibly high thermal capture cross sections), they tend to travel 10 or more centimeters in many scintillators. These rough order of magnitude figures for mean free path are important to the understanding of the operation of scintillators because they imply that light is generated in close proximity to the track of incident charged particles, whereas it might be generated at multiple, widely scattered points throughout the scintillator in the case of incident neutral radiation. Incident charged particles (α, β–,+ , μ–,+ , π–,+ , etc.) ionize the medium by scattering electrons (the dominant interaction at lower energies) and participating in nuclear reactions. The energy loss due to the collisions of charged particles of mass M with atomic electrons can be estimated with the well-known Bethe formula:     2me β 2 dE 4π z2 e4  − β2  =− nZ ln dx me β 2 I 1 − β2

(1)

where ze is the charge of the incident particle, n is the number density of atoms in the medium, Z is the atomic number of the medium, me is the electron rest mass, β is v/c, and I is the average excitation potential of the medium. Equation 1 is in units of energy per unit length and is valid for me < < M and γ ≈ 1. Equation 1 accounts only for collisions between the incident particles and electrons and does not include shell or density corrections. It is not correct for incident electrons and positrons. However, a similar expression was derived by Bethe and is used in Monte Carlo codes such as Geant4 and MCNP6 for electrons   

 dE 4π e4 me β 2 T 2 − 1 + β2   =− nZ ln 1 − β − ln(2) 2 dx me β 2 2I 2 1 − β 2

2  1  1 − 1 − β2 + 1 − β2 + 8

and for positrons

(2)

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Fig. 1 Stopping powers and range for electrons in CsI

    me β 2 T 4π e4 dE 2   =− nZ ln − ln − 1) (γ dx me β 2 2I 2 1 − β 2    3 γ − 1 1 − 13 (γ − 1)2 (γ − 1) (γ − 1)3 2 −(γ −1) 3 + − − 1− 2γ +1 6 (γ + 1)2 (γ + 1)3 (3) where γ 2 = 1/(1-β 2 ) and T is the kinetic energy of the incident particle. The stopping power and CSDA (continuous slowing down approximation) range for electrons in CsI (4.5 g/cm3 ) as computed by MCNP5 is shown in Fig. 1. Below approximately 12 MeV, collisional losses account for most of the stopping power. However, bremsstrahlung becomes dominant above that, increasing proportionally to the energy. The CSDA range is obtained by integrating Eq. 2 and does not account for deviations from straight-line motion caused by scattering. At energies below the critical energy Ec , the energy at which ionization and radiative losses are equal, ionization dominates. The critical energy is ∼6 MeV in uranium, varies approximately as 610 MeV/(Z + 1.24) in solids and like 710 MeV/(Z + 0.92) in gases. For applications involving natural radioactivity and electrons under ∼10 MeV, bremsstrahlung is not an important energy loss process.

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Fig. 2 Critical energies for electrons

At higher energies, and in applications requiring precise knowledge of the track of an electron or positron, bremsstrahlung must be considered because the mean free path of photons, possibly being much larger than that of charged particles, implies the process may deposit energy relatively far from the actual electron or positron track. The calculated critical energy as a function of atomic number is shown in Fig. 2. Since bremsstrahlung dominates at energies above the critical energy, and the stopping power of this process increases approximately proportionally to the electron’s energy, the energy of an electron after traversing a distance x (in g/cm2 ) is conveniently expressed by E = E0 e

− Xx

0

where X0 is the radiation length (usually measured in g/cm2 ), and E0 is the initial energy of the electron. This characteristic distance is the same as 7/9 of the mean free path for pair production by high energy photons. The radiation length has been parameterized in terms of atomic number and mass as

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Fig. 3 Radiation lengths and Molière radii for elements

X0 =

 716.4 A  g/cm2 287 Z (Z + 1) ln √ Z

and is the appropriate parameter to consider when selecting a scintillator for electrons above the critical energy. Also of interest to designers of detectors for high energy physics experiments is the Molière radius, which is the transverse distance containing 90% of the energy of an electromagnetic shower. It is given by RM = 0.03475 X0 (Z + 1.24), for solids. A small Molière radius, like a small radiation length, is desirable to minimize the size of the scintillator. Calculated radiation lengths and Molière radii for the elements are shown in Fig. 3. Both curves were calculated as if all elements are solids; the reader should recalculate the points for gases. Note that the scale for the Molière radius is linear, while the scale for the radiation length is logarithmic. Photons interact with matter via atomic photoelectric absorption, coherent scattering from atoms (Rayleigh scattering), Compton scattering, and pair production. Each interaction is most important in a different energy regime with photoelectric absorption dominating below ∼500 keV, Compton scattering dominating between ∼800 keV and 3 MeV, and pair production dominating above ∼10 MeV. In units of g/cm2 (i.e., divide by the density to obtain the mean free path in centimeters),

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Fig. 4 Photon mean free path for selected scintillators

the mean free path of photons in several scintillators, calculated with XCOM (NIST 2018), is shown in Fig. 4. A few features of the curves are noteworthy. The K, L, M, etc. edges account for the jagged shapes below 100 keV. The interaction cross section falls until the photon becomes sufficiently energetic to eject an atomic electron from its shell, at which point, the mean free path drops abruptly. As the photon energy rises, the photoelectric absorption cross section falls approximately like E–3.5 , causing the curves to be parallel on the log-log plot. At photon energies much above the highest energy K edge, the Compton cross section takes over, and the curves begin to flatten. At this point and below ∼3 MeV, attenuation is governed primarily by Compton scattering. Since the Compton cross section per atom is proportional to Z, and the number density of atoms is proportional to ρ/Z to the extent that atomic mass is proportional to atomic number, the linear attenuation coefficient is approximately independent of material. This is seen between ∼600 keV and 3 MeV in Fig. 4, where all the curves come together. An energy dependence remains, however, because the Compton cross section has a ln(E)/E dependence. A consequence of this coalescence is that a rough rule of thumb to estimate mean free path in centimeters for photons having energy ∼1 MeV is 15/ρ. Beyond the Compton region, the curves

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take on the characteristics of the pair production cross section and flatten at high energies while separating according to Z and ρ.

Processes Governing the Generation and Decay of Light Pulses We reviewed in the previous section how various particles interact with materials. That discussion covered only the deposition of energy in the scintillator, but not the processes by which that energy is converted into light. That topic is the subject of the present section. In all cases (crystalline and noncrystalline scintillators), the incident particle first transfers energy via collisions with electrons. These electrons typically have energy well in excess of their binding energy and are termed “primary” electrons. Primary electrons leave behind primary holes; both primary electrons and holes are hot in the sense that the temperature corresponding to their average energies is well above that of the remainder of the scintillator. The next step is the “cooling” or relaxation of these primary electrons and holes by additional collisions with atomic electrons, producing secondary electrons, holes, x-rays, plasmons, and other electronic excitations. The third step is the cooling of the secondary excitations until further ionization is not possible (energy has fallen below the band gap), resulting in a final number of electron-hole pairs. The time required to reach this level of thermalization is between 1 and 100 fs. Strictly speaking, electron-hole pairs and band gap are applicable to crystals; however, the concept of a band gap applies to individual organic scintillator molecules which, because of the presence of delocalized electrons (π-electrons) confined to cyclic or polycyclic structures, also exhibit a band structure. Once the energy of the electrons and holes is insufficient to produce further ionization, they begin to interact with the scintillator medium via electron-phonon relaxation (essentially coupling electron and hole motion to vibrations of the lattice or molecules). This process lowers the energies of the electron-hole pairs to the band gap energy, Eg . The number of pairs surviving to this stage is given by E0 /kEg , where k varies between 1.5 and 2.0 for ionic crystals, 3–4 for covalently bonded materials, and 1–2 for noble gas scintillators. The last two steps of the scintillation process are the transfer of energy from thermalized electron-hole pairs to luminescence centers (typically found in inorganic scintillators), and the de-excitation of the excited luminescence centers. Often the energy efficiency, ε, of a scintillator is described as the product of the efficiency for conversion of incident energy to electron-hole pairs (1/k in the previous discussion), the efficiency, S, of the transfer of energy to luminescent centers (typically found in inorganic scintillators), and the efficiency, Q, with which the excited luminescent center generates light. The energy efficiency and the light yield, L, are related by ε=

< hv > nph =< hv > L E0

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where is the average energy of emitted scintillation photons and nph is the number of scintillation photons emitted. For most purposes, the average energy of the scintillation photons can be taken to be the energy of the peak of the emission spectrum. Assuming each electron-hole pair produces S·Q scintillation photons, and knowing the number of electron-hole pairs produced (E0 /kEg ), then the energy efficiency and light yield can be written as ε=

< hv > SQ kEg

SQ L= kEg

(4)

Since SQ can be at most unity, with the band gap expressed in eV, L has an upper bound of about 660/Eg photons/keV for ionic crystals, 330/Eg photons/keV for covalent materials, and 1/Eg photons/keV for noble gases. Thus, CsI:Tl and NaI:Tl could produce no more than about 110 photons/keV. In actuality, under gamma ray or electron irradiation at energies between 500 keV and 1 MeV, CsI:Tl produces approximately 65 photons/keV, and NaI:Tl about 40 photons/keV, implying their energy efficiencies are 14% and 12%, respectively. Energy efficiencies do not track the light yields because the wavelengths of peak emission for the two scintillators are different. The energy efficiency of CdWO4 , which has a spectrum similar to CsI:Tl, but a slightly smaller band gap, is 5.3%, implying the transfer and transport of energy in that intrinsic (requiring no activator) scintillator crystal is somewhat poorer than in CsI:Tl. The time characteristics of the light pulse from a scintillator are determined by the kinetics of the energy transfer, the index of refraction, n, and the oscillator strength of the scintillating transition. The decay time constant of systems with a single type of luminescent center is inversely proportional to the square of the energy of the transition, and also approximately proportional to 10–(n/1.2) with n in the range 1.4–2.5. Although the implication is that higher index of refraction can lead to faster scintillators, the section on matching scintillators to photosensors, below, shows that high indices of refraction lead to light trapping and inefficient transfer of light to the photosensor. Some scintillators have multiple components in their light pulse, and this is a consequence of multiple light-emitting states. Notable among these scintillators are those exhibiting pulse shapes that vary according to the identity of the ionizing radiation. BC501A (an organic liquid scintillator manufactured by SaintGobain Crystals) has three components in its light pulse, with time constants of 3, 30, and 270 ns. The proportion of light emitted in the 270 ns component is measurably larger under heavy ion irradiation (most work has been done with protons scattered by fast neutrons) than under electron or gamma irradiation. The phenomenon occurs because in organic scintillators, ionizing particles produce both spin singlet and triplet excitations of the phenyl rings and transitions between the different spin states are severely suppressed by dipole selection rules. However, collisions between molecules can mediate such transitions, and the increased

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density of excited molecules produced by heavy particles enhances singlet to triplet transitions, while triplet states cannot decay promptly to the singlet ground state and must wait until a second collision transfers energy back to an excited singlet state. Of interest to the detection community has been the elpasolite material Cs2 LiYCl6 :Ce and its variants. This crystal exhibits 1, 50, and 1000 ns decay components, but the 1 ns component disappears when irradiated by neutrons. Neutrons participate in the 6 Li(n,α)t reaction and so produce a 2 MeV α and a 2.7 MeV triton. The 1 ns component has been attributed to CVL (core-valence luminescence, excitation of a core electron to the conduction band of the crystal with a valence band electron subsequently filling the hole in the core), but no theory yet has been proposed to adequately explain why this process is suppressed by high ionization density. Perhaps the high linear energy transfer of the heavy particles, causing a much higher density of ionized electrons than do photons, enhances the probability that the core holes are filled non-radiatively. Much of the previous discussion has revolved around inorganic crystal scintillators. Organic scintillators differ from inorganic crystals in that the periodic structure established by the crystal lattice is established by the organic molecules’ polycyclic structure and delocalized electrons. It is not necessary that organic molecules be arranged as crystals; the process is at the molecular level instead. This property enables the fabrication of organic liquid (toluene, xylene, and mineral oil based) and polymer scintillators (polyvinyltoluene, polystyrene, polysiloxane based), as well as organic crystals (stilbene, anthracene). The generation of light in these materials does not depend on the presence of an activator. Rather, by adjusting the number and arrangement of phenyl rings, the molecule’s structure generates a set of energy levels whose transitions have wavelengths typically ranging from 360 to 500 nm. When organic scintillators are dissolved at the level of 1–10% by weight in a solid polymer or liquid solvent containing many phenyl rings, the composite material continues to exhibit the characteristics of the pure scintillator. This is because of two mechanisms. Most ionization is of the solvent, and benzene-like solvents will fluoresce with the emission of UV light with a time constant of about 16 ns. However, energy transport by resonant dipole-dipole interactions between nearby phenyl rings, first proposed by Förster in 1948, is an efficient transporter of energy over distances of 0.1 nm, which is approximately the average distance between molecules in a scintillating solution (also termed a “cocktail”). There is no charge transported by this process, which occurs in about 1 ns. The decay time constant of the cocktail is significantly shortened by the action of resonant interactions. Organic scintillators typically exhibit multiple decay time constants, with the shortest being that of the scintillating solute and of the order of 3–5 ns.

Resolution A scintillator’s resolution is most often quoted as the ratio of the full width at halfmaximum (FWHM) of the peak in the pulse height spectrum due to the 662 keV

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gamma ray from 137 Cs to the centroid of the peak. That is, R=

F W H M(keV ) 662 keV

In some applications, though, the resolution is quoted at a different energy, usually in the range of interest to the application. Resolution is a function of the number of electrons delivered by the photosensor to the readout and conversion electronics (and, therefore, a function of deposited energy) and the noise in the electronics. We will concentrate on the delivered electrons in this section and include electronic noise as a single term adding in quadrature. Electronic noise can be measured by injecting a precision pulser into the stream of analog data. The number of electrons delivered to the electronics is a stochastic variable that depends on several statistically independent (or nearly so) factors whose variances add in quadrature. The number of electrons, Ne , delivered to the electronics is given by Ne = Nph · εt · G where Nph is the number of scintillation photons, εt is the efficiency for creating photoelectrons in the readout device, and G is the gain of the readout. A silicon PIN photodiode has a gain of unity; a photomultiplier can have a gain of 107 . In the case of a photomultiplier, the gain is, theoretically, the product of the gains of each stage, not all of which need to be equal. However, for convenience G will be taken to be G=

N

gi = g N

i=1

Although in practice the exponent is not the number of stages, but usually closer to N-2, the value N will be retained below. In addition, it is convenient to set all the gi equal. Energy dependence enters via the number of scintillation photons. If the amplitude of the light pulse is sufficiently small, the readout device remains linear and does not saturate, making these processes statistically independent. Consequently, the relative variance associated with Ne is then given (to first order) by  R2 =

σNe Ne

2

 =

σNph Nph

2 +

 σ 2 ε

ε

 σg 2 + N g

(5)

The mean number of scintillation photons in (5) depends on the band gap energy, the efficiency of the transfer of energy to luminescent centers, and the quantum efficiency of the luminescent centers. The variance of the number of scintillation photons comes from the (Poisson) statistics associated with the number of scintillation photons, intrinsic non-proportionality of the scintillator, and non-uniformities

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in the material. The latter is caused, for example, by inhomogeneous distribution of activators (the Tl present in NaI:Tl or the mixing of organic fluors in plastics, for examples), defects in the physical structure of the scintillator (lattice vacancies, inclusions, incomplete polymerization of plastics, phase separations, for examples), and inhomogeneous distribution of unintentional impurities. Non-proportional response is an intrinsic property of the scintillator and is caused by the energy-dependence of the probability of the excitation of luminescent states by electrons. This means that the number of electron-hole pairs created per unit deposited energy, taken to be a constant in the previous section, is actually a function of energy. Birks, noting that the response of scintillators decreased with increasing ionization density along a particle’s track, proposed that the light yield per unit path length can be parameterized by L0 dE dL dx , = dx 1 + kB dE dx where dE dx is given by Eqs. 1–3, and L0 (related to the constant k in Eq. 4) and kB are constants that depend on the scintillator. This equation predicts that for large stopping power (slow electrons, heavy particles), L will be proportional to the range of the radiation in the scintillator, which is not proportional to the energy of the incident radiation. For small stopping power, such as for electrons between ∼400 keV and ∼ 3 MeV (see Fig. 1 for the stopping power of CsI:Tl), L will be proportional to the energy of the radiation. It has been observed, however, that for slow electrons, although the light yield is decidedly nonlinear, it does not follow the Birks equation. In the case of NaI:Tl, when non-proportionality is defined to be the ratio of the light yield at energy E to that at 480 keV (the energy of Compton electrons generated by 137 Cs gamma rays scattered 180◦ ), the ratio rises to 1.2 near 15 keV. This means that a 15 keV electron produces L (15 keV) =

1.20 × L (480 keV ) 32

that is, 20% more light than expected from the ratio of energies (1:32). Since all light production in scintillators is caused by secondary electrons, and these secondary electrons have a continuum of energies, the distribution of electron energies is important. Figure 5 shows Hull’s measurements of the relative light yield of NaI:Tl crystals. The curve rises monotonically to a maximum near 15 keV and appears smooth. This is in disagreement with Dorenbos (1995), who has reviewed measurements of the relative light yield of NaI:Tl, CsI:Tl, CsI:Na, BGO, LSO, CaF2 :Eu, CWO, GSO, YAP, LuAG, and K2 LaCl5 and shows that the relative light yield exhibits local minima near the K-edges of the constituents. Dorenbos also shows that some crystals are less than proportional at lower energies (the relative light yield curve is never greater than unity). The effect of variable relative light

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Fig. 5 Relative light yield of NaI:Tl samples. Reprinted with permission from Hull (2009), © 2014 IEEE

yield is to increase the variance of Nph above what would be expected from Poisson statistics, alone. Payne (2011) presents a theory of the source of nonlinearity in crystals. In addition to the Birks process (formed excitons approaching within a critical distance of each other annihilate without the emission of visible light), he proposes the addition of an Onsager process by which electrons and holes sufficiently near each other either bind to form an exciton that migrates to an activator site, or they arrive sequentially (the order is not important) at the activator site and bind. The exciton collapses at the activator site, and transfers energy to the activator, which then emits light. This process generates an increase of light yield with decreasing energy because as the energy of electrons decreases, their stopping power increases, the distance between them and their corresponding holes decreases, thus increasing the probability of the formation of excitons, and increasing light yield. In some crystals, the Onsager process causes superlinearity (non-proportionality greater than unity), in others, it is not sufficient to overcome the losses incurred due to the Birks process and a sublinear non-proportionality is observed. All crystals eventually become sublinear as electron energy goes to zero. The second term in Eq. 5 accounts for light trapping and collection and is derived from an average over all paths to the exit window from points of scintillations and over all points of scintillation. It accounts for variation in reflectance of materials surrounding the scintillator and the coupling between the scintillator and the entrance window of the photosensor. It also accounts for trapping within the window of the photosensor. The last term in Eq. 5 accounts for the fluctuations in the gain of the photosensor. In a typical photomultiplier, each dynode contributes a

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factor of ∼3.5; in a silicon PIN photodiode, the total gain, G, is between ∼0.35 and 1, depending on the spectrum of the light and the spectral response of the diode. Curves similar to Fig. 5 have been measured for many scintillators. For energies above ∼100 keV, the variation in light yield is small, and the resolution is dominated by terms proportional to the number of scintillation photons, which is approximately proportional to the deposited energy. Practically, this leads to the following relationship between resolution and incident photon energy: R 2 = a + bE where a represents the contribution of the electronics (usually small) and b depends on the scintillator and construction of the detector. Dorenbos (1995) provides a description of the effects of statistics on resolution and provides an expression for the best resolution expected from a scintillator, given the light yield. Figure 6 shows the locus of points for commercially available scintillators and their relation to the best theoretical resolution obtainable for their light yield.

Fig. 6 Best theoretical resolution and observed resolution of scintillators. A photomultiplier quantum efficiency of 20% was used in the theoretical calculation

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Obviously, almost all scintillators lie far from the theoretical line. Notable exceptions are LaBr3 :Ce and YAP:Ce (YAlO3 :Ce). The poorer resolution point is reported by Rodnyi (1997); however, Kapusta (1999) reports a remarkable 4.8% resolution for YAP, which is its theoretical best resolution. Further improvements in the performance of YAP will require improvements in photosensors and electronics. LaBr3 :Ce, which is close to its theoretical limit, has found wide use in the gamma spectroscopy community because of its much higher stopping power.

Considerations in Matching Scintillators to Photosensors All scintillators rely on the energy bands of the constituent materials having transitions with energies ranging from approximately 2 eV to 6 eV. These transitions result in the emission of light with wavelengths between 620 nm and 200 nm, which band is well-matched to the sensitivities of photomultiplier tubes and photoconductors. The relationship between transition energy and emission wavelength is given by λ(nm) =

1240 E(eV )

(6)

where λ is the wavelength in nm and E is the energy in eV. Equation 6 is of importance in the selection of the scintillator and readout device because it is necessary to match the scintillator’s emission band to the sensitive band of the readout to maximize the number of photoelectrons or electron-hole pairs. A photosensor’s sensitivity, S(λ), measured in mA/watt, gives the current liberated per unit incident power at a specified wavelength. The quantum efficiency, QE(λ), gives the average number of photoelectrons generated per photon absorbed by the photosensor, and is easily found from (6) to be QE (λ) =

1.24 S (λ) λ

(7)

Manufacturers often quote the sensitivity of a photosensor at the wavelength of the peak of S; the designer must pay careful attention to this because the response of semiconductors is often heavily biased toward longer wavelengths. For example, the manufacturer of one photodiode quotes S to be 660 mA/W at 960 nm, making the quantum efficiency at this wavelength approximately 0.85. Examination of the device’s data sheet, however, provides the information that S(420 nm), a common wavelength of maximum emission of blue-emitting scintillators, is 200 mA/W, making QE(420 nm) = 0.65. If the designer uses the values at 960 nm to estimate the response at 420 nm, the contribution to the resolution from charge generation statistics would be underestimated by 70%. Ideally, the response of the photosensor closely matches the emission spectrum of the scintillator.

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It is also important to match the scintillator’s index of refraction to that of the photosensor. If there is a significant difference between them, then much of the light can be trapped within the scintillator resulting in loss of light, an artificially lengthened light pulse (because of multiple bounces within the scintillator volume), or both. At normal incidence, the fraction of light energy reflected (R) from, and transmitted through (T) a dielectric interface is given by  R= T =

n1 − n2 n1 + n2

2

4n1 n2 (n1 + n2 )2

where n1 and n2 are the indices of refraction of the two media. For the case of light from a CsI crystal normally incident on a photomultiplier tube’s glass entrance window, nCsI = 1.79, nglass = 1.52, and R = 0.0067. However, for CdWO4 , nCWO = 2.25, and R = 0.037. The reflection coefficient at normal incidence for borosilicate glass-scintillator interfaces is shown in Fig. 7 for a continuum of indices of refraction and the positions of representative, commercially available scintillators are indicated.

Fig. 7 Reflection coefficient at normal incidence

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Although the reflection coefficient at normal incidence does not seem large, the mismatch can have a significant effect on light collection. The critical angle, θ c , the angle of incidence beyond which light is totally internally reflected when going from a scintillator with high index of refraction to a photosensor’s entrance window with lower index of refraction, is given by θ c = sin–1 (nwindow /nscint ), and determines the “cone of acceptance” (termed numerical aperture when referring to a lens) of the interface. Since scintillation light is emitted isotropically, the fraction of the light that is emitted outside the critical angle must scatter inside the scintillator at least once before it exits into the photosensor. This lengthens the path of the light within the scintillator and increases the probability of self-absorption (caused by the overlap of the emission and absorption bands of the scintillator) by trapping light within the scintillator, and, in the case of large blocks of scintillator, can increase the decay time of the light pulse. The latter is generally important only with scintillators with a dimension larger than about 30 cm and having decay times of a few nanoseconds, such as in 10 × 10 × 40 cm polyvinyltoluene-based plastics (PVT). Every meter’s increase of the optical path length increases the apparent decay time by approximately 3 ns. Figure 8 shows the critical angle, in degrees, calculated for a scintillator-glass interface with light entering the glass from the scintillator (left vertical axis), and the

Fig. 8 Critical angle and fraction of scintillation photons emitted outside the cone of acceptance for light exiting a scintillator and entering a borosilicate glass layer with index of refraction 1.52

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fraction of light striking the interface outside the cone of acceptance (right vertical axis). The calculation related to the cone of acceptance is done for an infinite plane interface, which implies that the solid angle subtended by the interface relative to any point of scintillation is 2π. When the scintillator’s index of refraction is less than 1.52, the critical angle is 90◦ . Consequently, some light from CaF2 (n = 1.44) can enter a photomultiplier’s faceplate regardless of the angle of emission from the point of scintillation. However, as the index of refraction rises to that of CsI or NaI, even though only 0.7% of the light is reflected at normal incidence, approximately half the light incident on the interface is totally internally reflected; the remainder has a transmission coefficient that depends on the angle of incidence. The situation rapidly deteriorates as the index of refraction exceeds 2.0. For this reason, diffuse reflectors and indexmatching couplants (such as glycerin and silicone greases) are generally used. The reader is encouraged to consult textbooks on electromagnetic theory for the formulae pertaining to reflection and transmission coefficients as a function of index of refraction and angle of incidence. Photomultiplier tubes are available with different entrance windows. The most common (and least expensive) is the borosilicate glass faceplate; this case has been considered above. Manufacturers, however, list MgF2 as an optional faceplate material, especially for ultraviolet-sensitive photomultipliers. This material is not hygroscopic and has an index of refraction of approximately 1.38 in the visible region, rising to 1.78 at 114 nm. Fused quartz is also used as a faceplate; its index of refraction is 1.46 in the visible region, rising to 1.52 near 230 nm. Sapphire (Al2 O3 ) is available in a more limited number of models of photomultiplier tubes, mostly for solar-blind and aerospace applications. The index of refraction of these faceplates is approximately 1.78 in the visible region, rising to 1.83 near 263 nm. It is a birefringent, non-isotropic material with coefficient of thermal expansion 4.3 × 10–6 /◦ C perpendicular to and 5.4 × 10–6 /◦ C parallel to the c-axis, respectively. This is in contrast with the coefficient of thermal expansion of borosilicate glass (an isotropic material) of 3.2 × 10–6 /◦ C and implies that care must be taken when bonding these materials to avoid cracking due to thermal stresses during normal use. Sapphire-metal brazes are more commonly found than sapphire-glass bonds.

Scintillators It is likely that thousands of materials have been tested for scintillation since the discovery of x-rays. Papers by S. E. Derenzo et al. (1991), Moses et al. (1997), and van Eijk (2001) mention nearly 600 materials, and the book by Shinonoya and Yen (1999) mentions over 1000 materials evaluated as scintillators. Of all of these, only three organic crystals and fewer than 30 inorganic crystals are commonly available. In this section, the properties and representative applications of commercially available materials are described.

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Inorganic Crystals Data in Table 1 are compiled from the Review of Particle Physics, Wilkinson (2004), Rodnyi (1997), Knoll (2000), and the websites of Hilger Crystals (Hilger 2018), RMD, Inc. (RMD 2018), Scintacor (2018), Hitachi Chemical Company, Kinheng Crystals (Kinheng 2018), Berkeley Nucleonics (Berkeley 2018), and Saint-Gobain Crystals, Inc. (Bicron 2018). The data in Table 2 are compiled from the Review of Particle Physics, Wilkinson (2004), Rodnyi (1997), and the websites of Hilger Crystals, RMD, Inc., Scintacor, Hitachi Chemical, Kinheng Crystals, RMD, Inc., and Saint-Gobain Crystals, Inc. The reader should take pricing information below as an approximate guide and must contact a vendor with specific requirements to obtain an accurate quote. Pricing always depends on the size of the crystal, packaging, surface preparation, and quantity ordered. Inorganic scintillator crystals find application is many areas of radiation detection. NaI:Tl, although one of the first discovered scintillators, has been the workhorse of the industry. This is because of its low cost, high brightness, and moderate energy resolution of about 6%. It can be grown in large ingots, routinely seen as single 10 × 10 × 40 cm crystals in detectors used for homeland security applications. It, CsI:Tl and CsI:Na are used for general gamma ray spectroscopy. In thin wafers, NaI:Tl is used in α/β probes in health physics instruments. Both NaI:Tl and CsI:Tl,Na are sensitive to fast and slow neutrons. Thermal neutrons are captured by iodine which results in the production of 128 I, with a halflife of 25 min. This isotope is a β-γ emitter that, when in a scintillator, produces an unexpected background that builds up according to 1–2–t/25 , with t, the irradiation time in minutes. The cross section for thermal neutron capture in Na is sufficiently small, that a large ambient flux is required before its activity is noticed. However, when Na is activated, it produces a beta–gamma continuum with an endpoint of 5.5 MeV and a half-life of 15 h. The activation of Cs by thermal neutrons is not usually a problem because 134 Cs has a half-life of 2 years, making it unlikely that sufficient amounts will be made in most situations. Both these crystals are sensitive to neutrons with energy above 14 MeV because of (n,xn) reactions. In the cases of Cs and I, the products of (n,2n) reactions, 132 Cs and 126 I, are readily made by a D-T generator. Figure 9 shows a spectrum obtained with a HPGe detector from a 10 cm diameter, 2 cm thick CsI:Tl sample exposed to a D-T generator. The sample was placed 5 cm from the anode of the generator (in the air), which was operated at approximately 107 n/s for 3 h. After irradiation, the sample was placed 10 cm from the front face of the HPGe detector and counted for 10 min. The spectrum shows three prominent peaks from four gamma rays from 132 Cs and 126 I; two of the gamma rays are sufficiently closely spaced that they were not resolved by the detector. The remaining unattributed gamma rays are from natural 214 Bi, 214 Pb, 208 Tl, positron annihilation, 228 Ac, and other decay products from the 232 Th and 238 U decay chains. 126 I has a half-life of 13 days, while 132 Cs has a

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Table 1 Properties of Common Inorganic Scintillators

Material NaI:Tl CsI:Tl

Emission maximum ρ(g/cm3 ) (nm) 3.67 415 4.51 550

CsI:Na CaF2 :Eu CLYC 6 LiI:Eu 6 Li - glass BaF2 YAP:Ce YAG:Ce GLuGAG:Ce GGAG:Cee LSO:Ce LYSO:Ce LuAG:Ce LuAG:Pr YSO:Ce GSO:Ce

4.51 3.18 3.31 4.08 2.6 4.88 5.55 4.57 6.8 6.7 7.40 7.10 6.73 6.7 4.55 6.71

420 435 370 470 390–430 315/ 220 350 550 545 520 420 420 530 310 420 440

BGO CdWO4 PbWO4 ZnWO4 LaBr3 :Ce LaCl3 :Ce CeBr3 SrI2 :Eu

7.13 7.90 8.28 7.62 5.08 3.85 5.2 4.59

480 470, 540 420, 425 490 380 350 380 435

Decay time constant 230 ns 600, 3400 ns 630 ns 840 ns 1/50/1000 ns 1400 ns 60 ns 0.63 μs/0.8 ns 27 ns 70, 300 ns 75 ns 53/282 ns 40 ns 40 ns 70 ns 21 ns 37 ns, 82 ns 56 ns, 600 ns 300 ns 20 μs, 5 μs 10 ns, 30 ns 20 μs 16 ns 28 ns 18–20 1–5 μsd

Index of refractiona 1.85 1.79 1.84 1.47 1.81b 1.96 1.56 1.50/1.54 1.94 1.82 1.81 1.82 1.81

1.80 1.85 2.15 2.3 2.20 2.32 1.9 1.9 1.85

Light yield (ph/MeV) 37,700 64,800

Hygroscopic? Yes No

38,500 23,600 20,000 11,000 2,000 10,000/1,400 18,000 19,700 50,000 42,217 30,000 32,000 15,000 17,000 45,000 12,500

Slightly No Yes Yes No No No No No No No No No No No No

8,500 15,000 100, 31 9,500 63,000c 49,000 45,000 80,000

No No No No Yes Yes Yes Yes

a Index

of refraction at the wavelength of maximum emission, unless otherwise noted of refraction at 405 nm c Reports in the literature are as high as 75,000 ph/MeV d Decay constants depend on the size of the crystal because of self-absorption by Eu2+ activator e Data is for Gd Ga Al O 3 3 2 12 b Index

half-life of 6.47 days, implying that an activated detector should not be used for a few months. Cesium and iodine are not the only elements that are susceptible to activation. 186 W comprises 29% of natural tungsten and has a thermal capture cross section of 38 barns. 187 W has a half-life of 23.9 h and is a β-γ emitter. 176 Lu, the radioactive component in LYSO, LuAG, and LSO, comprises 2.6% of natural Lu and has a thermal capture cross section of 2100 barns. 177 Lu has a half-life of 6.71 days and

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Table 2 Additional Properties of Common Inorganic Scintillators Material NaI:Tl CsI:Tl CsI:Na CaF2 :Eu CLYC 6 LiI:Eu 6 Li – Glass BaF2 YAP:Ce YAG:Ce GLuGAG GGAG LSO:Ce LYSO:Ce LuAG:Ce LuAG:Pr YSO:Ce GSO:Ce BGO CdWO4 PbWO4 g ZnWO4 LaBr3 :Ce LaCl3 :Ce CeBr3 SrI2 :Eu a Percent/◦ C

1 dL a L dT

-0.2 ∼0 (fast) 0.39 -0.33

-1.3 (slow) -0.4 -0.27 -0.8 -1.1 -0.2 +0.4 -0.1 -0.9 -0.1 -2.7 -1.2 ∼0 +0.7 -0.25

Neutron sensitiveb ?

Radiation hardness (Gy)c

Radiation length (cm)

Price (US$/cm3 )d

Yes (F) Yes (F, S) Yes (F, S) No Yes (F,S) Yes (F, S) Yes (S) No No No Yes (S) Yes (S) Yes (S) Yes (S) Yes (S) Yes (S) No Yes (S) No Yes (S) Yes (S) Yes (S) Yes (S) Yes (S) No Yes (S)

10 10 10

2.6 1.86 1.86 3.50 3.42 2.55 7.09 2.03 2.67 3.5 1.26 1.54 1.14 1.15 1.45 1.45 2.75 1.38 1.13 1.06 0.89 1.10 1.88 3.12 1.88 1.95

$4–8 $7–12 $7–10 $10–35 $600 ∼$100 $60–70e $45 $125 $125

>105 104

104–5 104–5

104 106 100–1000 10–1000 >105 105 105 >106 ∼6000

$200 $70 $70 $650f $400f ∼$40 $13–30 $13 $20–40 $10 $135–175 $135–175 $140–170 $150–300h

at 20 ◦ C. Light yield of all crystals eventually falls with increasing temperature = sensitive to fast neutrons by (n, 2n), (n,p), (n,α), and x-rays by (γ, n) reactions. S = sensitive to slow neutrons by generating prompt capture gamma rays and/or generating a radioactive product subsequent to capture and/or generating heavy particles c Dose causing significant loss of transmission at the peak emission wavelength d Where provided, pricing estimates are for 2.54 cm Ø × 2.54 cm long crystals. They are provided courtesy of James Telfer of Hilger Crystals, Dr. Alexander Gektin of the Institute for Single Crystals, Kharkiv, Ukraine, Epic Crystal Co, Ltd., Kunshan City, PRC, RMD, Inc., Berkeley Nucleonics, and Ivan Wang of Kinheng Crystals Materials, Shanghai, PRC. The information is current as of June, 2018 e 100 mm × 100 mm × 6 mm plate f LuAG:Ce is quoted for 10 mm Ø × 0.2 mm wafer, LuAG:Pr is quoted for 15 mm Ø × 15 mm cylinder g According to Dr. Alexander Gektin of the Institute for Single Crystals, Kharkiv, Ukraine, production of this material has been cut back since the completion of the Large Hadron Collider h Unit price depends on the size of the crystal bF

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Fig. 9 Spectrum from activated CsI:Tl

is also a β-γ emitter. 139 La, the stable La isotope (99.9% abundance) in LaBr3 and LaCl3 , has a 9.3 barn thermal capture cross section. The reaction product, 140 La, has a 40-h half-life and is also a β-γ emitter. The thermal capture cross section of chlorine, while high, does not lead to significant activation because of the long half-life of 36 Cl. However, the 35 Cl(n,p)35 S reaction is exothermic, with the cross section peaking at 300 mb near 7 MeV. Fast protons from this reaction will generate scintillation light, and 35 S is a β–γ emitter with a half-life of 87.4 days. The thermal neutron capture cross section of 79 Br is sufficiently large that in a high thermal flux, the production of 80 Br (17.6-minute half-life) should be noticed. Reactions with particles capable of ejecting multiple neutrons, and spallation reactions are too numerous to be considered here. Suffice it to say that when a detector is to be used in a neutron field or exposed to energetic particles or x-rays (remember that photonuclear reactions can have the same reaction products as (n,2n) and (n,pn) reactions), the detector designer must consider the possibility and effects of activation. CdWO4 , ZnWO4 , and BGO are also used for general purpose gamma ray spectroscopy and have the characteristic of having extremely low background radioactivity. The latter property, coupled with their high density and average atomic number, make them attractive for use in positron emission tomography (PET).

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However, their relatively slow decay times limit their maximum count rates, and, therefore, the quality of imaging. The speed of LSO and LYSO, on the other hand, more than compensates for their poorer linearity and natural radioactivity in medical instruments. LSO and LYSO are not used for general gamma ray spectroscopy because of the radioactivity of Lu and the crystals’ inferior linearity. The natural radioactivity of Lu is less of a problem in PET because a coincidence is required between a pair of 511 keV gamma rays from the patient, and the coincidence window is sufficiently short to exclude the natural β/γ activity. GSO has also been used in PET because of its high stopping power. In addition to PET, GSO has found application in oil well logging. In this activity, a detector is lowered behind the drilling head in a module containing a strong 137 Cs or 60 Co source and a neutron generator. These sources are used for measurements of rock density and composition, and water, salt, and hydrocarbon concentration at temperatures reaching 200 ◦ C. GSO is extremely radiation resistant, and its light yield remains sufficient for spectroscopy even at high temperature. GSO is also sensitive to thermal neutrons via the 157,158 Gd(n, γ) reactions. In both isotopes, the reaction products are stable and only prompt capture gammas and conversion electrons are emitted. However, the overwhelming majority of neutron capture reactions occurs within 1 millimeter of the surface of the crystal, preventing a peak corresponding to the Q-value of the reactions because half of the capture gammas and electrons exit the crystal. LiI:Eu is used almost exclusively for thermal neutron detection. Thermal neutrons impinging on the crystal are captured by 6 Li which results in the deposition of 4.79 MeV split between an alpha particle and triton. The resulting peak typically occurs at an electron equivalent energy over 3 MeV, which is higher than the vast majority of naturally occurring gamma rays. Since only a thin crystal is needed to capture thermal neutrons, the sensitivity to high energy gammas can be limited by geometry. This scintillator is used in homeland security applications and as an alternative detector to 3 He in polyethylene-moderated neutron detectors, such as Bonner sphere sets. It is rarely, if ever, used as a replacement for 3 He in a mixed γ/n environment because it has a substantial gamma response. CLYC (Cs2 LiYCl6 :Ce) was developed at Delft University of Technology and reported in Combes (1999). As in LiI:Eu, the presence of 6 Li as a constituent of the crystal imparts high sensitivity to thermal neutrons through the 940 b cross section for the 6 Li(n,α)t reaction. The resolution of the first crystals was 7–8%, comparable to NaI:Tl, but as research continued, resolutions as low as 3–4% have been reported. In addition, it was noticed that the shape of the scintillation pulse from neutron interactions was markedly different than that from gammas and x-rays: a fast core-valence luminescence (CVL) process is suppressed when neutrons are captured, causing the pulse to rise much more slowly than when gammas and x-rays impinge. Representative pulses are shown in Fig. 10. The figure shows 4-μs long oscilloscope traces sampling photomultiplier tube anode pulses at 4 GHz. The individual spikes in the traces are from bunches of photoelectrons and show that the light pulse has a relatively long life; the preamble to the pulse shows that

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Fig. 10 Gamma (upper) and neutron (lower) scintillation pulses from CLYC. Reprinted with permission from the 2014 IEEE Nuclear Science Symposium Conference Record, © 2014 IEEE

electronic noise is negligible. Consequently, CLYC is count-rate limited. Hardware or software analysis of the pulse enables pulse shape discrimination. Glodo (2009) reports on the radioluminescence of CLYC. The paper showed that there are three regions in the optical spectrum: 280–325 nm from CVL; the regions from 350 to 400 nm and from 400 to 450 nm which are from Ce3+ emission. Bell (2014) tried to exploit the emission spectrum by viewing a CLYC crystal mounted with two optical windows and viewed through optical filters by two photomultipliers. The scheme failed because the loss of light absorbed by the filters worsened the statistics to the point that PSD failed. However, Bell showed that the application of a Kolmogorov-Smirnov test comparing a sample waveform to average neutron and gamma wave forms could decrease the time needed to classify the identity of the pulse to 44 ns. This does not, however, overcome the limitations imposed by CLYC’s long decay time. The chlorine in CLYC also confers a small sensitivity to fast neutrons via the 35 Cl(n,p) reaction. The Q-value for the reaction is 615 keV, meaning that a proton will be ejected even by thermal neutrons. The cross section for the reaction reaches a peak of 300 mb at 7 MeV, implying that a 2.54-cm thick crystal is at most 1.6% efficient for fast neutrons. This implies that when neutron and gamma pulses can be distinguished, fast neutron spectroscopy is possible with this crystal. Ce-activated Li-glass scintillator is used exclusively for thermal neutron detection. The fact that it is a glass rather than a crystal means it does not have the long-range ordering needed for the efficient transport of electrons and holes to activator sites. Consequently, it develops a continuum gamma ray spectrum. However, a distinct peak is developed in response to the 6 Li(n,α) reaction (Scintacor quotes the resolution at 15–28%), and so neutron events are distinguished from

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gamma events by pulse amplitude. A 7 Li-loaded glass behaves identically to the 6 Li-glass, except for the lack of thermal neutron response, and is used as a “witness” detector whose counts are subtracted from the 6 Li-glass to determine the net neutron flux from a source. CaF2 :Eu finds application in particle detection, and low-energy x-ray detection because of its low atomic number. The crystal is rugged, inert, and not hygroscopic and can be used in more extreme conditions than some other crystals. It is bright, but the relatively long decay time, precludes its use in high count rate applications. BaF2 is also known to exhibit core-valence luminescence, which gives it an extremely fast light component. It is an intrinsic (undoped) scintillator that is prized for its combination of timing resolution and stopping power. It has been proposed for use in PET systems and nuclear and high energy physics coincidence experiments. However, to take advantage of the fast light component, it is necessary to use a photosensor that is sensitive to 200 nm light. According to Knoll (2000), the fast component went unobserved for lack of use of an appropriate photosensor. YAP and YAG find application in particle counting, especially in electron microscopy. Their low atomic number makes them of limited utility for gamma ray spectroscopy at high energies. YAP has excellent proportionality which means resolution is preserved even if gamma rays undergo multiple scatterings prior to photoelectric absorption. Unfortunately, the low Z necessitates the use of a larger crystal, and self-absorption of the light decreases net light yield and worsens resolution. YAP also is a fast crystal (27 ns decay time) and excellent timing resolution can be obtained. YAG is unusual in that the Ce emission is shifted to 550 nm, making it less than optimal for use with photomultipliers; it is a much better match to solid-state readouts. Moszynski (1994) reports that the fraction of light in the fast and slow components changes with the type of incident radiation, making it possible to devise pulse shape discrimination schemes to distinguish between β-γ and ions. In recent years, (Gd,Lu)3 Ga3 Al2 O12 :Ce (GLuGAG) ceramic and Gd3 Ga3 Al2 O12 (GGAG) have become available commercially. Their major use is in medical imaging: ToF-PET, PEM, SPECT, CT, X-radiography. LuAG:Pr has an extremely short decay time constant, making it very useful in medical imaging. However, the Pr activator emits in the near UV region, requiring the PMT readout to have a fused silica, or sapphire window. GGAG:Ce’s decay time constant is a function of temperature, with the main (53 ns) decay time fairly constant up to ∼10 ◦ C and then falling nearly linearly to ∼12 ns at 120 ◦ C (Kamada (2011)). Since 176 Lu is 2.6% of natural Lu, scintillators containing this element are radioactive, and this limits the useful size: a 2.54 cm diameter, 2.54 cm long cylinder would generate ∼1560 disintegrations per second with the major gamma emissions occurring at 88, 202, and 306 keV, and accompanied by a beta spectrum with end-point energy of 593 keV. Lanthanum halides have been reported in the literature since 1999. The crystal contains lanthanum, which is naturally radioactive, and in low background counting

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applications this will limit the useful size of a single crystal. If arrays of crystals are needed, the designer needs to be aware that large amounts of lanthanum will have the effect of raising the local background levels. Kernan (2004) concludes from his measurements of LaCl3 :Ce that the rate of 1435 keV emissions in a 7.62 cm diameter by 7.62 cm thick crystal will be 500/s. The crystal emits light between 350 and 440 nm, which is within the specifications of most photomultipliers. However, if it is desired to use solid state readouts, it is necessary to obtain blue-enhanced devices. The crystal is not cubic and is prone to cracking if not handled carefully or subjected to rapid temperature changes. The good energy resolution, 2–3%, makes these crystals a good choice for highresolution gamma ray spectroscopy and hand-held radioactive isotope identifiers using LaBr3 :Ce are on the market today. The crystals are being considered for space applications and in the oil well logging industry. The latter use is enabled by the small variation of light yield with increasing temperature, dropping by only by 10% between 27 ◦ C and 175 ◦ C. Lanthanum halides are also being considered for medical applications in PET and SPECT imagers. CeBr3 requires no activator because Ce is a major constituent of the crystal. CeBr3 offers high resolution (∼4.5%) and none of the intrinsic radioactivity seen in La halides. There is a small 227 Ac contamination in the crystals, and this contributes up to 0.025/s/cm3 to the count rate. This results in ∼9 counts/s in a 7.62 cm diameter by 7.62 cm thick crystal. CeBr3 is also a fast crystal, offering timing resolution (measured against BaF2 , see Fraile (2013)) of 120 ps. The most common applications of this crystal are high-resolution room temperature gamma ray spectroscopy and spectroscopy applications where timing is important. SrI2 :Eu containing up to 1.6% Eu was patented by Hofstadter in 1968 (Hofstadter (1968)). Cherepy (2008) reports on the properties of a crystal containing 0.5 mole % Eu (∼0.65 wt. %). It had a light yield of 93,000 photons/MeV, and 3.7% energy resolution, and displayed good proportionality at electron energies as low as 6 keV. The decay time of the light pulse is governed by the Eu2+ d → f transition and is 1.2 μs; the emission is relatively narrow and centered at 435 nm. Other Eu2+ -containing scintillators have been reported, but none, other than LiI:Eu, are commercialized, yet. Cherepy (2017) reports on the properties of crystals doped with 1.5–4% Eu. It was noted that Eu2+ traps its own light because of substantial overlap of the emission and absorption spectra of the d ↔ f transitions. This implies that large crystals (optical path lengths > ∼10 cm) and read out from one end of the crystal will not perform as well spectroscopically as crystals up to about 6 cm long. Crystals can be tapered at the end away from the photosensor to improve light collection, and resolution of 3.1% can be achieved. SrI2 :Eu has the important advantage over Ce-activated La halides that it is not radioactive. Therefore, there is no intrinsic radioactivity to interfere with spectrum peaks from a sample under inspection, and weak peaks are more readily observed. Neither is there any danger of nearby crystals irradiating each other and effectively raising the background level. Consequently, these crystal should find use in isotope identifiers as direct replacements for NaI:Tl. Potentially, because its high resolution

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will allow a system to detect lower concentrations of radioactive gamma/x-ray emitting contaminants, the crystal may find use in environmental monitoring. PbWO4 is used almost exclusively by the high energy physics community in particle detectors in calorimeters. It is the material of choice because of its speed, high density, and small radiation length. Melcher (2005) reported that production of PbWO4 was projected to peak in 2005 and be similar to worldwide demand for scintillator crystal for PET, SPECT, and x-ray CT in that year. The light yield is sufficiently small; however, that it is not useful for gamma ray spectroscopy. With the completion of the Large Hadron Collider, commercial production of this material is virtually nil. ZnS was not included in the previous tables because it is not a scintillator commonly used for gamma ray spectroscopy. It is available only as ZnS:Ag or ZnS:Cu powder and is mixed with a binder to form thin sheets. The powder is not transparent to its own light, forcing the sheets to be at most approximately 0.5–1 mm thick with an areal density of 25 mg/cm2 . The decay time constant varies with the incident radiation, being 200 ns for heavy particles, and about 50 ns for electrons. Birks (1964) give a discussion of the early work on this scintillator, which reported a non-exponential decay and decay times for electrons as small as 10 ns. ZnS scintillators have been used exclusively as charged particle detectors in consumer goods (it was the phosphor in the paint in the infamous radium watch dials of the early twentieth century), and detectors for scientific purposes (Hornyak buttons for fast neutrons, mixed with LiF, 235 U, or B2 O3 for thermal neutron detectors). When mixing ZnS with LiF or B2 O3 , it is necessary to optimize the size of the ZnS particles to maximize the escape of light.

Organic Scintillators The data in Table 3 were obtained from the websites of Eljen Technology (Eljen 2018), Saint-Gobain Crystals (Bicron 2018), and Scintacor (2018). In the case of unloaded plastics, the data covers many varieties of scintillator; they are aggregated here because the base plastic is polyvinyltoluene and the phosphors themselves usually only comprise a small fraction of the whole. The data in Table 4 were obtained from the literature, vendors’ websites, and calculation by the author. The reader should take pricing information below as an approximate guide and must contact a vendor with specific requirements to obtain an accurate quote. Radiation hardness information is not readily available for most organics, but would be expected to be similar to non-specialty plastics. Organic scintillators enjoy wide use in homeland security, x-ray detectors, charged particle detectors, heavy ion detectors, fast and slow neutron detection, and electron detectors. They are typically not used for gamma spectroscopy because the primary interaction even at low energies is Compton scattering; no photopeak is generated. The intrinsic resolution of organic scintillators is fairly poor, being only approximately 20% at 662 keV.

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Table 3 Properties of Common Organic Scintillators ρ (g/cm3 ) 1.03

Emission maximum Decay time (nm) constant 375–600 1–300 ns

Index of refraction 1.58

Light yield (ph/MeV) 6,400–10,000

1.096

425

∼1.58

8600

1.02–1.03 425

13, 35, 270 ns 2.2 ns

1.58

7,500–9,200

Plastics (Pb)

1.08

425

2.1 ns

1.58

5,200

Plastics (Li)

1.14

425

Liquids (HC) Liquids (FC) Liquids (DC) Liquids (B) Liquids (MO) Liquids (Dioxane) Liquids (Gd) Liquids (Sn) Stilbene Anthracene p-Terphenyl

0.88–1.0

425

1–300 ns

1.5

12,000

Air sensitive? Slightly (O2 , H2 O vapor) Slightly (O2 , H2 O vapor) Slightly (O2 , H2 O vapor) Slightly (O2 , H2 O vapor) Slightly? (O2 , H2 O vapor) Yes

1.6

425

∼3 ns +

1.4

3,000

Yes

0.95

425

3.5 ns +

1.5

9,200

Yes

0.92 425 0.85–0.87 425

3.7–300 ns 2 ns +

10,000 5,000–10,000

Yes Slightly

1.04

425

3.8 ns +

1.42 1.47– 1.49 1.44

10,000

Yes

0.89

424

3.6 ns +

1.50

10,600

Yes

0.95 1.22 1.25 1.23

425 390 445 420

3.8 ns 3.5 3.0 3.7

1.50 1.64 1.62 1.65

5,300 14,000 20,000 27,000

Yes Yes Yes Yes

Material Plastics (unloaded) Plastics (PSD, blue) Plastics (B)

4,800

Index of refraction is at the wavelength of maximum emission. Li – Lithium loaded. B – Boron loaded. Pb – 5% Lead loaded. Sn – 10% Tin loaded. Gd – 0.25 – 0.5% Gd loaded. HC – Hydrocarbon (toluene, xylene, benzene). FC – Fluorocarbon liquid. DC – Deuterocarbon liquid. MO – Mineral oil. + – There are additional time constants not specified by the vendor

Plastics are easy to form by solvent casting for thin films and thermal casting for larger pieces, easy to machine, are not hygroscopic under laboratory conditions, and can be handled while wearing gloves. They are slightly affected by oxygen and not affected by liquid water in indoor environments. The former is not usually a problem

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Table 4 Additional properties of organic scintillators Material Plastics Plastics (PSD) Plastics (B) Plastics (5% Pb) Plastics (li) Liquids (HC) Liquids (FC) Liquids (DC) Liquids (B)

Neutron sensitivity Fb F F, Sd F S F No No S

Liquids (MO) Liquids (Dioxane) Liquids (Gd) Liquids (Sn) Stilbene Anthracene p-Terphenyl

F, S F S F F F F

Radiation hardness (Gy) 3 × 104

4 × 104 2 × 104 4.5 × 104

Radiation length (cm) 43.2 40.1 43.4 33.2 37.5 50.6 21.7 49.7 48.9 52.5 45.4 48.1 33.3 36.0 35.0 35.6

Price (US$/cm3 )a $0.11–0.40 $5.50c $22e $3 $8 $0.26f $3 $8 $8 (10 B) $2 (nat B) $0.08 $0.50 $0.20 $0.80

a Pricing

data is courtesy of Charles Hurlbut of Eljen Technology, Inc. Solid plastic scintillator is priced for cast sheet up to 50 mm thick (thicker sheet is less expensive). Loaded plastic is priced for 50 mm diameter by 50 mm long cylinders. Liquid scintillator is priced for quantities of 3–10 liters and reflects only the cost of the scintillator, unless otherwise noted. The information is current as of June, 2018 b F = sensitive primarily to fast neutrons c 7.81 cm Ø × 7.81 cm cylinder d S = sensitive to slow neutrons through capture reaction e As a plate 20 cm × 20 cm × 1 cm, boron-loaded plastic can cost as little as $7.00/cm3 . Geometry matters! f ∼$3/cm3 when in a 7.81 cm Ø × 7.81 cm cylindrical cell with mounting flange

unless the scintillator is in a pure oxygen atmosphere for extended periods of time. The base plastic is polyvinyltoluene (PVT) or, for increased temperature stability, polystyrene (PS), and the density is always close to 1 g/cm3 . Cameron observed that after PVT-based scintillator was exposed to high humidity and warm temperatures, and then cooled, a “fog” developed inside the plastic (Cameron et al. 2015). Crack-like defects in scintillators deployed outdoors in uncontrolled environments demonstrably increased the scattering of light in large slabs, decreasing the number of photons collected by the detector’s photosensor. This, in turn, decreased the amplitude of the photosensor’s charge pulse, which decreased the pulse rate from detectors using a fixed threshold discriminator. The net effect was a decrease of the detector’s efficiency. Cameron proposed that the cause of this phenomenon was water vapor saturating the PVT after repeated exposures to high humidity, and then coalescing into microscopic liquid droplets. These droplets behave as a fog in air because the index of refraction of water is 1.33, whereas

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that of the plastic is 1.58. If the temperature is brought sufficiently low, the water freezes, expands, and puts strain on the plastic matrix sufficiently severe to cause a permanent crack. Probably the simplest solution to this problem is to seal the plastic hermetically in a water-vapor-proof container. This is not the same as a water-proof container because surface tension inhibits the infiltration of liquid water. Thus, a polymer bag or hard polymer case may not be sufficient to stop water vapor; a solid metal shield might be preferable. The light yield is a strong function of particle mass. Birks (1964) shows that the light yield from electrons, protons, and alpha particles in anthracene at energies between 10 keV and 10 MeV is in the approximate ratio of 1:0.2:0.06. At energies from 20 MeV to 160 MeV in plastic scintillator, the ratio is approximately 1:0.8:0.4. Consequently, for the same energy, gamma rays produce more light than do a proton (or neutron interacting via (n,p) scattering) and alpha particle. Figure 11 shows the conversion as calculated by Cecil (1979) for NE-213 (identical to the modern EJ301 and BC-501A) over the energy range 0 to 3000 keV. The curve is in general agreement with the results shown by Birks (1964) and is not linear at proton energies below approximately 2000 keV. This conversion must be taken into account when a lower threshold and range of analog and digital electronics is to be established for a detector using organic scintillator. If care is not taken, the system may work perfectly for protons but saturate for gamma rays of interest.

Fig. 11 Proton to electron conversion for EJ-301 (NE-213/BC-501A)

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Some organic scintillators (most of them liquids) also produce different shapes of light pulse, depending on the type of incident particle. The passage of charged particles produces scintillation pulses with fast (3–30 ns decay time, singlet to singlet transitions) and slow (270 ns decay time, ordinarily forbidden triplet to singlet transitions mediated by molecular collisions) components. Light pulses from heavy particles produce a larger fraction of triplet excited states than do electrons, and this is exploited in pulse shape discrimination schemes. Knoll (2000) (in Chap. 17) discusses pulse shape discrimination between neutrons and gamma rays. Note that light pulses from electron interactions (singlet to singlet transitions, mostly) and heavy particle interactions have the same emission spectra because only the excited singlet to ground state singlet transitions produce visible light. This is in contrast to the situation in CLYC in which CVL has both a different decay time constant and a different optical spectrum than does the Ce3+ activator. Zaitseva (2012) reports on work on plastic scintillator exhibiting pulse shape discrimination (PSD). Until 2012, liquid scintillators, and a few organic crystals (trans-stilbene is one) were the only organic scintillators exhibiting this trait. The first commercial versions of PSD plastics (Eljen Technology’s EJ-299, which has been replaced by EJ-276) were inferior to PSD liquids (the old NE-213, and the modern EJ-309). However, after a multi-year effort, Zaitseva (2018) and her colleagues have developed formulations that perform PSD at the same level as organic PSD liquids. The implication of this work is that solid inert plastics can replace flammable liquids thereby enabling safer detectors that require no special containment or precautions against spills, leaks, and fire. Plastic scintillators are, essentially, a solid solution of a base material, usually PVT or PS, in which one or more phosphors are dissolved. Phosphors are chosen for the “cocktail” according to their photoexcitation and photoluminescence spectra. The primary phosphor’s job is to harvest energy from excited base molecules and emit light that is absorbed by a secondary phosphor (if present). A tertiary phosphor is, in turn, excited by emissions of the secondary, and emits its own photoluminescence spectrum. Typically, the concentration of phosphors in the cocktail are 1–10% primary, 0.1–0.2% secondary, with additional phosphors present at ∼10% of concentration of the previous member in the chain. In this way, excitation of the base by ionizing radiation causes sequential excitation and emission from each member of the chain, until the last phosphor’s light exits the scintillator. Zaitseva’s breakthrough was to increase the concentration of primary phosphor from 1–10% to >30%. This increased the probability of molecular collisions between excited solute molecules and enabled triplet to singlet transitions to occur with the same probability in solid solutions as in liquid scintillators. Although the concept of loading PS and PVT with high concentrations of phosphors was patented by Biteman (1992), he makes no mention of PSD. Vendors specify that the temperature variation of the light yield of their scintillators does not vary from –60 ◦ C to +20 ◦ C, but then falls by 5% from +20 ◦ C to +60 ◦ C. Operation above 60 ◦ C typically is not recommended because plastics soften, and liquids are flammable. Some liquids are made with higher flashpoint solvents (xylene or mineral oil in place of toluene), but the flashpoint of these

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scintillators does not exceed ∼100 ◦ C. Some plastics are made with a cross-linked polymer and do not soften until ∼100 ◦ C. The chemistry of hydrocarbons is sufficiently rich to permit the inclusion of boron, tin, lead, and gadolinium compounds in solid and liquid scintillators. In recent years, plastic scintillator incorporating Bi has been reported (see Martinez (2016)); however, this is not yet a commercial product. Addition of lithium is difficult: many lithiated hydrocarbons are pyrophoric. However, Martinez (2016), Cherepy (2015), and Zaitseva (2013) report on stable lithium loadings up to ∼2% 6 Li by weight. Boron, lithium, and gadolinium provide sensitivity to thermal neutrons, while tin and lead enhance gamma sensitivity. However, the addition of heavy metals rapidly reduces the light yield, which limits the weight fraction to 5–30%. This amount of bismuth, tin, or lead does not significantly increase stopping power for gammas between ∼100 keV and the critical energy. As can be seen in Table 4, the radiation length is reduced by 25% by the addition of the few percent of heavy metal. 10 B-loaded scintillator is generally used in small detectors because the thermal neutron capture cross section is 3837 b, the reaction products are ions, and the energy deposited in the scintillator is 2.35 MeV. Consequently, a high concentration of boron is desired and only a small volume is required. When Gd captures a thermal neutron, however, the reaction products are prompt gamma rays, atomic x-rays, and conversion electrons. In a small Gd-based detector it is difficult to distinguish neutron reaction products from photoelectrons and Compton electrons. Lithiumloaded plastic scintillator occupies a similar niche, although the size of detector may be larger because the thermal neutron capture cross section of 6 Li is about 25% of boron’s. In principle, these detectors could be used with pulse shape discrimination since the heavy ions from the capture reactions have larger linear energy transfer than recoil protons and electrons. However, because the amplitude of the pulses from thermal neutron capture are of a magnitude similar to that of pulses from gammas and recoil protons, the standard metric of the ratio of late light to prompt light as a function of amplitude cannot be used alone to distinguish between the three incident radiations. Pulses from thermal neutron capture have an amplitude of ∼300 keVee (electron equivalent) and lie in the region of recoil proton pulses in pulse shapepulse amplitude space. That is, while all thermal neutron pulses have an amplitude of ∼300 keVee and ∼ 13% of their light is in the late components, some pulses having an amplitude of ∼300 keVee and 13% of their light in the late components are not thermal neutron events. A large Gd-based or B-based detector can be made sensitive to fast neutrons by using sufficient loading to make capture by Gd or B far more probable than capture by hydrogen. In such a detector (10–1000 liters, or larger), fast neutrons are thermalized by multiple (n, p) scatterings prior to capture by Gd or B. Each scattering produces a light pulse, and at the end of the sequence of scatterings, a “flash” from the capture occurs. When Gd is the sensitizer, 7.9 MeV (157 Gd) or 8.5 MeV (155 Gd) is released as prompt gamma rays, atomic x-rays, and conversion electrons, and if the detector’s volume is sufficiently large, all the energy is captured and results in an identifiable pulse, generally much larger than any gamma ray

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pulses. Additional discrimination may be achieved by demanding the presence of pulses from (n, p) scattering in some number of microseconds preceding the 8 MeV flash. The same principle can be applied to a boron-based system, with the exception that the flash is much smaller (equivalent to only ∼100 keV electrons) because the reaction products are heavy ions. The interested reader is referred to the section in Knoll (2000) on capture gated neutron spectrometers.

Conclusion Scintillators have been used to detect radiation since the discovery of x-rays and natural radioactivity. Since that time the field has evolved from the trialand-error approach to discovery of new scintillators to computational methods to understand and predict the properties of crystals and compounds. Scintillators have evolved from parlor curiosities (much to their detriment, radium watch dial painters daubed themselves with radium-laced ZnS paint to amuse friends in the dark) to indispensable components in medical equipment, neutron and gamma radiography, detectors for homeland security applications, health physics instruments, and largeand small-scale scientific experiments. They have moved from the laboratory to consumer products with dozens routinely commercially available, and dozens more under active investigation in research projects around the world.

Cross-References  Astrophysics and Space Instrumentation  Gamma-Ray Spectroscopy  Interactions of Particles and Radiation with Matter  Neutrino Detectors  Particle Detectors in Materials Science  Photon Detectors  Semiconductor Radiation Detectors  Technology for Border Security

References Bell ZW, Hornback DE, Hu MZ, Neal JS (2014) Wavelength-based neutron/gamma ray discrimination in CLYC. In: 2014 IEEE nuclear science symposium and medical imaging conference record (NSS/MIC), pp 1–8 Berkeley (2018). https://www.berkeleynucleonics.com/scintillation-crystals-and-detectors, Accessed 5 Apr 2018 Bicron (2018). www.bicron.com, web site of Saint-Gobain Crystals’ scintillator division, a vendor of scintillation crystals, organic scintillator, and Li-glass scintillator. Accessed 18 May 2018 Birks JB (1964) The theory and practice of scintillation counting. Pergamon Press

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Biteman VB et al (1992) USSR patent 818287, Registered Dec. 30, 1992, priority date Nov. 16, 1979 Cameron RJ, Fritz BG, Hurlbut C, Kouzes RT, Ramey A, Smola R (2015) Fogging in polyvinyl toluene scintillators. IEEE Trans Nucl Sci 47:368 Cecil RA, Anderson BD, Madey R (1979) Improved predictions of neutron detection efficiency for hydrocarbon scintillators from 1 MeV to about 300 MeV. Nucl Instrum Meth 161:439 Cherepy NJ, Hull G, Drobshoff A, Payne SA, van Loef E, Wilson C, Shah K, Roy UN, Burger A, Boatner LA, Choong W-S, Moses WW (2008) Strontium and barium iodide high light yield scintillators. Appl Phys Lett 92:083508 Cherepy NJ, Payne SA, Asztalos SJ, Hull G, Kuntz JD, Niedermayr T, Pimputkar S, Roberts JJ, Sanner RD, Tillotson TM, van Loef E, Wilson CM, Shah KS, Roy UN, Hawrami R, Burger A, Boatner LA, Choong W-S, Moses WW (2009) Scintillators with potential to supersede lanthanum bromide. IEEE Trans Nucl Sci 56:873 Cherepy NJ, Sanner RD, Beck PR, Swanberg EL, Tillotson TM, Payne SA (2015) Bismuth- and lithium-loaded plastic scintillators for gamma and neutron detection. Nucl Instrum Meth Phys Res A 778:126 Cherepy NJ, Beck PR, Payne SA, Swanberg EL, Wihl BM, Fisher SE, Hunter S, Thelin PA, Delzer CJ, Shahbazi S, Burger A, Shah KS, Hawrami R, Boatner LA, Momayezi M, Stevens K, Randles MH, Solodovnikov D (2017) History and current status of strontium iodide scintillators. In: Proceedings of the SPIE 10392, hard x-ray, gamma-ray, and neutron detector physics XIX, 1039202 (15 September 2017). https://doi.org/10.1117/12.2276302 Combes CM, Dorenbos P, van Eijk CWE, Krämer KW, Güdel HU (1999) Optical and scintillation properties of pure and Ce3+ -doped Cs2 LiYCl6 and Li3 YCl6 crystals. J Lumin 82:299 Curran SC, Baker WR (1948) Photoelectric alpha-particle detector. Rev Sci Instrum 19:116. The work was reported in 1944 during World War II, but withheld from publication until after the end of the war Derenzo SE, Moses WW, Cahoon JL, DeVol TA, Boatner L (1991) X-ray fluorescence measurements of 412 inorganic compounds. In: IEEE nuclear science symposium conference record 91CH3100-5, vol. 1. pp. 143–147. This paper promised a more comprehensive listing in a future publication, but that manuscript was never submitted to a journal Dorenbos P, de Haas JTM, van Eijk CWE (1995) Non-proportionality in the scintillation and the energy resolution with scintillation crystals. IEEE Trans Nucl Sci 42:2190 Eljen (2018). www.eljentechnology.com, web site of Eljen Technology, a vendor of organic scintillators. Accessed 1 Apr 2018 Fraile LM, Mach H, Vedia V, Olaizola B, Paziy V, Picado E, Udías JM (2013) Fast timing study of a CeBr3 crystal: time resolution below 120 ps at 60 Co energies. Nucl Instrum Meth Phys Res A 701:235 Glodo J, Higgins WM, van Loef EVD, Shah KS (2009) Cs2 LiYCl6 :Ce scintillator for nuclear monitoring applications. IEEE Trans Nucl Sci 56:1257 Hilger (2018). www.dynasil.com/company/hilger-crystals, web site of Hilger Crystals, now a subsidiary of Dynasil, a vendor of scintillation crystals. Accessed 4 Apr 2018 Hofstadter R (1948) Alkali halide scintillation counters. Phys Rev 74:100 Hofstadter R (1968) Europium activated strontium iodide scintillators. U.S. Patent 3,373,279, 12 March 1968 Hull G, Choong W-S, Moses WW, Bizarri G, Valentine JD, Payne SA, Cherepy NJ, Reutter BW (2009) Measurements of NaI(Tl) electron response: Comparison of different samples. IEEE Trans Nucl Sci 56:331 Kamada K, Endo T, Tsutumi K, Yanagida T, Fugimoto Y, Fukabori A, Yoshikawa A, Pejchal J, Nikl M (2011) Composition engineering in cerium-doped (Lu,Gd)3 (Ga,Al)5 O12 . Cryst Growth Des 11:4484 Kapusta M, Balcerzyk M, Moszynski M, Pawelke J (1999) A high energy resolution observed from a YAP:Ce scintillator. Nucl Instrum Meth Phys Res A 421:610 Kernan WJ (2004) IEEE nuclear science symposium conference record, Ergife Palace Hotel, paper N19-6, 16–24 October 2004, Rome

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Kinheng (2018). http://www.kinheng-crystal.com/products.html, Accessed 4 Apr 2018 Knoll GF (2000) Radiation detection and measurement, 3rd edn. Wiley Martinez HP et al (2016) Bismuth and lithium-loaded plastic scintillators for gamma and neutron detection. In: Proceedings of the SPIE 9968 hard x-ray, gamma-ray, and neutron detector physics XVIII, 99680Q. https://doi.org/10.1117/12.2238243 Melcher CL (2005) Perspectives on the future development of new scintillators. Nucl Instrum Meth Phys Res A 537:6 Moses WW, Weber MJ, Derenzo SE, Perry D, Berdahl P, Schwarz L, Sasum U, Boatner LA (1997) Inorganic scintillators for X- and gamma ray detection. Presented at SCINT97 – the international conference on inorganic scintillators and their applications, Shanghai, 22–25 September 1997 Moszynski M, Ludziejewski T, Wolski D, Klamra W, Norlin LO (1994) Properties of the YAG : Ce scintillator. Nucl Inst Meth Phys Res A345:461 NIST (2018). https://www.nist.gov/pml/xcom-photon-cross-sections-database, web site of the U.S. National Institute of Standards and Technology photon cross sections database. Accessed 4 June 2018 Payne SA, Hunter S, Sturm BW, Cherepy NJ, Ahle L, Sheets S, Dazeley S, Moses WW, Bizarri G (2011) Physics of scintillator nonproportionality. In: Proceedings of the SPIE 8142, hard x-ray, gamma-ray, and neutron detector physics XIII, 814210 (28 September 2011). https://doi.org/10.1117/12.895969 RMD (2018). https://www.dynasil.com/product-category/scintillators/, Accessed 4 Apr 2018 Rodnyi PA (1997) Physical processes in inorganic scintillators. CRC Press Scintacor (2018). www.scintacor.com, web site of Scintacor (successor to Applied Scintillation Technologies), a vendor of Li-glass scintillator. Accessed 19 June 2018 Shinonoya S, Yen WM (1999) Phosphor handbook. CRC Press Wilkinson F III (2004) Emission tomography: the fundamentals of PET and SPECT. In: Wernick MN, Aarsvold JN (eds). Elsevier Science, chapter 13 Zaitseva N, Rupert BL, Pawelczak I, Glenn A, Martinez HP, Carman L, Faust M, Cherepy N, Payne S (2012) Plastic scintillators with efficient neutron/gamma pulse shape discrimination. Nucl Inst Meth Phys Res A 668:88 Zaitseva N, Glenn A, Martinez PH, Carman L, Pawelczak I, Faust M, Payne S (2013) Pulse shape discrimination with lithium-containing organic scintillators. Nucl Instrum Meth Phys Res A 729:747 Zaitseva NP, Glenn AM, Mabe AN, Carman ML, Hurlbut CR, Inman JW, Payne SA (2018) Recent developments in plastic scintillators with pulse shape discrimination. Nucl Instrum Meth Phys Res A 889:97

Further Reading Amsler C, Particle Data Group et al (2008) Review of particle physics. Phys Lett B 667:1. 2009 partial update for the 2010 edition. See chapters 27 and 28 Baccaro S, Cecilia A, Mihokova E, Nikl M, Nejezchleb K, Blazek K (2005) Influence of Si – Codoping on YAG:Ce scintillation characteristics. IEEE Trans Nucl Sci 52:1105 Balcerzyk M, Moszynski M, Kapusta M, Wolski D, Pawelke J, Melcher CL (2000) YSO, LSO, GSO and LGSO. A study of energy resolution and nonproportionality. IEEE Trans Nucl Sci 47:1319 Bruekers RD, Bartle CM, Edgar A (2013) Transparent lithium loaded plastic scintillators for thermal neutron detection. Nucl Instrum Meth Phys Res A701:58 Caffrey AJ, Heath RL, Ritter PD, DeW C, VanSiclen DFA, Majewski S (1986) Radiation damage studies on BaF2 and BGO scintillator materials. IEEE Trans Nucl Sci 33:230 Caudel D et al (2016) Radiation damage of SrI2 crystals due to irradiation by 137 Cs gamma rays: a novel approach to altering nonproportionality. Nucl Instrum Meth Phys Res A 835:177

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Chen J, Zhang L, Zhu R-Y (2005) Large size LYSO crystals for future high energy physics experiments. IEEE Trans Nucl Sci 52:3133 Drozdowski W, Dorenbos P, Bos AJJ, Kraft S, Buis EJ, Maddox E, Owens A, Quarati FGA, Dathy C, Ouspenski V (2007) Gamma-ray induced radiation damage in LaBr3 :5% Ce and LaCl3 :10% Ce scintillators. IEEE Trans Nucl Sci 54:1387 Glodo J, Hawrami R, Shah KS (2013) Development of Cs2 LiYCl6 scintillator. J Cryst Growth 379:73 http://scintillator.lbl.gov/. This site contains a summary list of many scintillators, some experimental, some well-established. Accessed 15 Mar 2018 Kraus H, Danevich FA, Henry S, Kobychev VV, Mikhailik VB, Mokina VM, Nagorny SS, Polischuk OG, Tretyak VI (2009) ZnWO4 scintillators for cryogenic dark matter experiments. Nucl Instrum Meth Phys Res A 600:594 Lecomte R, Pepin C, Rouleau D, Saoudi A, Andreaco MS, Casey M, Nutt R, Dautet H, Webb PP (1998) Investigation of GSO, LSO and YSO scintillators using reverse avalanche photodiodes. IEEE Trans Nucl Sci 45:478 Mesquita CH, Fernandes Neto JM, Duarte CL, Rela PR, Hamada MM (2002) Radiation damage in scintillator detector chemical compounds: a new approach using PPO-toluene liquid scintillator as a model. IEEE Trans Nucl Sci 49:1669 Moszyinski M, Kapusta M, Mayhugh M, Wolski D, Flyckt SO (1997) Absolute light output of scintillators. IEEE Trans Nucl Sci 44:1052 Nagornaya L, Apanasenko A, Burachas S, Ryzhikov V, Tupitsyna I, Grinyov B (2002) Influence of doping on radiation stability of scintillators based on Lead tungstate and cadmium tungstate single crystals. IEEE Trans Nucl Sci 49:297 Nagornaya LL et al (2009) Large volume ZnWO4 crystal scintillators with excellent energy resolution and low background. IEEE Trans Nucl Sci 56:994 Pausch G, Stein J (2008) Application of 6 LiI(Eu) scintillators with photodiode readout for neutron counting in mixed Gamma – neutron fields. IEEE Trans Nucl Sci 55:1413 Pepin CM, Berard P, Perrot A-L, Pepin C, Houde D, Lecomte R, Melcher CL, Dautet H (2004) Properties of LYSO and recent LSO scintillators for Phoswich PET detectors. IEEE Trans Nucl Sci 51:789 Pidol L, Kahn-Harari A, Viana B, Virey E, Ferrand B, Dorenbos P, de Haas JTM, van Eijk CWE (2004) High efficiency of lutetium silicate scintillators, Ce – doped LPS, and LYSO crystals. IEEE Trans Nucl Sci 51:1084 van Eijk CWE (2001) Inorganic-scintillator development. Nucl Instrum Meth Phys Res A 460:1 www.hamamatsu.com, web site of Hamamatsu Photonics, K.K. This site has specifications for photomultiplier tubes manufactured by the company. Accessed 1 Apr 2018 Yanagida T et al (2005) Evaluation of properties of YAG(Ce) ceramic scintillators. IEEE Trans Nucl Sci 52:1836 Yanagida T, Fujimoto Y, Kurosawa S, Kamada K, Takahashi H, Fukuzawa Y, Nikl M, Chani V (2013) Temperature dependence of scintillation properties of bright oxide scintillators for welllogging. Jpn J Appl Phys 52:076401 Zhu R-Y (1998) Radiation damage in scintillating crystals. Nucl Instrum Meth Phys Res A 413:297 Zorn C et al (1994) Low dose rate evaluations of long plastic scintillator plates and Bicron G2doped wavelength shifting Fibers. IEEE Trans Nucl Sci 41:746

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Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Energy Band Gap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Charge Carrier Concentration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dopant Impurities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Carrier Mobility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Carrier Lifetime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Material Resistivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Basic Detector Configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pn Junction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pin Junction Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Schottky Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ohmic Contacts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Resistive Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Photoconductive Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gamma-Ray and X-Ray Spectrometers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . X-ray Detectors Based Upon Si . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Detectors Based Upon Ge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Compound Semiconductor Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Charged Particle Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Surface Barrier and Implanted Junction Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Neutron Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Semiconductor Radiation Detector Suppliers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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D. S. McGregor () Semiconductor Materials and Radiological Technologies Laboratory, Mechanical and Nuclear Engineering, Kansas State University, Manhattan, KS, USA e-mail: [email protected] © Springer Nature Switzerland AG 2021 I. Fleck et al. (eds.), Handbook of Particle Detection and Imaging, https://doi.org/10.1007/978-3-319-93785-4_16

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Abstract The basic principles for the design and operation of semiconductor detectors are presented. A summary treatment of pn junction and Schottky junction formation is described. Common semiconductor configurations are discussed, including planar and coaxial detectors for γ -ray spectroscopy and various detectors for α-particle spectroscopy.

Nomenclature A Cdet Ctot E EA EC ED EF EV s 0 FWHM μe μh μs NA NA− ND + ND Ns ni ξe ξh n p q Q Q ρc ρs τe τh φm φs φb V

detector contact area detector capacitance total coupling capacitance energy of radiation quantum acceptor energy conduction band edge donor energy Fermi energy valence band edge semiconductor permittivity free space permittivity full width at half maximum electron mobility hole mobility majority carrier mobility acceptor concentration ionized acceptor concentration donor concentration ionized donor concentration majority impurity concentration intrinsic concentration electron extraction factor hole extraction factor electron concentration hole concentration electron charge charge collected from detector charge excited in detector space charge density semiconductor resistivity electron lifetime hole lifetime metal work function semiconductor work function barrier potential applied detector voltage

16 Semiconductor Radiation Detectors

Vbi ve vh Vin Vw W w χs ψ Z

453

built-in detector potential electron velocity hole velocity detector input voltage signal weighting potential detector active region width average ionization energy semiconductor electron affinity potential atomic number

Introduction Semiconductors are far more desirable for energy spectroscopy than gas-filled detectors or scintillation detectors because they are capable of much higher-energy resolution. The observed improvement is largely due to the better statistics regarding the number of signal carriers (charges) excited by a radiation interaction. On average, it only takes 3 to 5 eV to produce an electron-hole pair in a semiconductor. By comparison, it takes between 25 and 40 eV to produce an electron-ion pair in a gas-filled detector and between 100 eV and 1 keV to produce a single photoelectron ejection from the photomultiplier tube (PMT) photocathode in a scintillation/PMT detector (primarily due to light reflections and poor quantum efficiency at the photocathode). Hence, a semiconductor produces more charge carriers from the primary ionization event and thus reduces the statistical fluctuation in the energy resolution. Semiconductor radiation detectors have many different shapes, sizes, and configurations, yet there are some basic designs that, in some form or another, can be attributed to practically all semiconductor radiation detectors. These basic designs include pn junction diodes, pin junction diodes, Schottky diodes, resistive detectors, and photoconductors. The vast field of semiconductor radiation detectors is much too large to describe in a single book chapter. As a result, only those concepts needed to understand basic detector operations and characteristics are offered here. Much of the material presented here is extracted from a more detailed description in McGregor and Shultis (2021). A selected list of literature is included at the end of the chapter that offers more information on various semiconductor detector configurations, characterizations, and operations. Example performances of some commercial detectors are listed.

Definitions In the following section are listed and described certain basic definitions and concepts used in discussions of semiconductor detectors. For a more detailed discussion regarding these concepts, the reader is directed to the reference literature at the chapter end.

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Energy Band Gap In free space, a single atom has quantized and discrete allowed energy states. The Pauli exclusion principle states that no two electrons can occupy the same four quantum numbers (n, l, ml , ms ), where n is the principle number referring to energy, l is the angular momentum quantum number, ml is the magnetic quantum number, and ms is the spin. However, a solid material, such as a semiconductor crystal, is a matrix of atoms arranged in a lattice such that the various potentials of each of the atoms affect the surrounding neighbors and those electrons associated with them. If two atoms are forced into close proximity, each initially with identical quantum numbers, then something must change such that the exclusion principle is not violated, which is satisfied by the appearance of degenerate energy states. In other words, the original energy levels split such that two states appear where there was only one before (Fig. 1). Consider the issue of a solid, where typical atomic densities range from 1021 to 23 10 atoms cm−3 . The total number of energy states must also split to accommodate

Energy

band of energy states

band gap band of energy states

band gap band of energy states

band gap

band of energy states

Atomic Spacing Fig. 1 As atoms are brought closer together, their allowed energy states split into degenerate states. In a solid medium, the high atomic density causes these degenerate states to form quasicontinua referred to as energy bands

16 Semiconductor Radiation Detectors

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the electron density, which form bands of states in place of what were once individual states for a single atom (Fig. 1). These bands may overlap, may be relatively close to each other in energy with a small energy gap between them, or may form with large energy gaps between the bands (Fig. 2). Electrons in the bands behave almost as though they are in an energy continuum, but it is actually a quasi-continuum, in which there is a defined density of available states in each of the bands. The density of states is still predetermined by the original total number of states of the individual atoms. Each of these energy bands has a certain density of allowed energy states that can be occupied by an electron. The electrical conductivity of a solid is determined by many parameters, which include charge carrier mobility, the density of free charge carriers available in a partially filled energy band, and the availability of unfilled energy states in the partially filled band. As conceptual examples, shown in Fig. 2 are examples of simplistic band diagrams for (a) insulators, (b) conductors, and (c) semiconductors. In Fig. 2a, the valence band, which is active in chemical binding of electrons in compounds, is filled, and the next available energy band is devoid of electrons. In typical notation, the upper energy limit of the valence band is denoted EV , and the lower-energy limit of the conduction band is denoted EC . The energy difference between EC and EV is a forbidden energy region, referred to as the energy band gap and denoted Eg . If the band gap energy is large such that electrons are not thermally excited from the valence band into the conduction band, the material is considered an insulator. Conduction can only take place provided that there are empty states for charge carriers to occupy in lateral energy space. Because the valence band is completely full of charge carriers, there are no empty states, hence no conduction. Further, the conduction band has empty states but no charge carriers; hence again conduction does not take place.

EC EC EC EV overlapping (no band gap)

(a)

EV

EV

EC

partially filled conduction band

(b)

(c)

Fig. 2 Shown are depictions of simple band diagrams for (a) insulators, (b) conductors, and (c) semiconductors. In (b) there are two depictions for conductors, one in which a filled valence band overlaps the conduction band and the other in which the valence band is full with a partially filled conduction band

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D. S. McGregor

In Fig. 2b, there are two examples of conductors. In the first example, the valence band and the conduction band overlap such that electrons can easily move from the filled valence band into the partially filled conduction band without a change of energy. Hence, there are plenty of unfilled states with an overlapping reservoir of electrons (the valence band) that can move to the conduction band, thereby giving rise to free conduction. In the other example, the valence band is filled, and the conduction band is partially filled with a high density of electrons, even at low temperature. Again the conditions exist for free conduction. In Fig. 2c, there is a band gap similar to the insulator example, except the band gap is relatively small. As a result, some electrons are thermally excited from the valence band into the conduction band where they can freely conduct. However, the density of the electrons in the conduction band is determined largely by the band gap energy and the temperature. At low enough temperature, the electrons will all return to the valence band, and the material will behave as an insulator. As the temperature is increased, more and more electrons will cross the band gap into the conduction band, and the material conductivity will continue to increase. Often this class of materials is separated into semiconductors and semi-insulators, roughly defined by the band gap energy. Typically, band gap energies ranging up to approximately 1.4 eV constitute a class of materials commonly designated as semiconductors, while band gap energies ranging from 1.4 eV up to 5 eV are considered semi-insulators. Band gaps exceeding 5 eV form the insulator class of materials. However, these ranges are not rigidly classified, and often semiinsulators and semiconductors are treated as the same, which will be the case in this chapter.

Charge Carrier Concentration The probability distribution of electrons with energy Ee is determined by FermiDirac statistics, F (E) =

1 , Ee − EF 1 + exp kT 

(1)

where k is Boltzmann’s constant (see Table 1), T is the absolute temperature, and EF is the Fermi energy level (Sze 1981). The Fermi energy is the energy level, at 0 K temperature, where all states below it are filled and all above it are empty. Equation (1) can be used to determine the density of electrons in the conduction band, with knowledge that electrons will not be present in the band gap; hence Eq. (1) is valid for Ee ≥ EC and Ee ≤ EV . From Eq. (1), the probability that an electron crosses the band gap to the conduction band will increase with increasing temperature, which should be intuitively obvious. The concentration of electrons in the conduction band is denoted n, and the concentration of empty states in the valence band is denoted p. These empty

16 Semiconductor Radiation Detectors

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states are treated as positive charge carriers called “holes,” which greatly simplifies calculations. For a pure material, the electrons in the conduction band arrive at the expense of leaving an equal density of holes in the valence band. Hence, n = p, which is referred to as the intrinsic case. Typically, the intrinsic concentration of both electrons and holes is denoted ni . It can be shown that, 

∞

n=

EC

  EC − EF , N(E)F (E)dE ≈ NC exp − kT

(2)

where N (E) is the function describing the allowed density of states and NC is the effective density of allowed states in the conduction band. Similarly, describing the unfilled states or holes in the valence band,  p=

EV

−∞

  EF − EV , N(E)[1 − F (E)]dE ≈ NV exp − kT

(3)

where NV is the effective density of allowed states in the valence band (Sze 1981).

Dopant Impurities Dopant impurities are often added to a semiconductor to control the electrical properties. Dopants that add excess electrons to the chemical binding are called donors, because they need only a slight amount of energy to liberate these excess electrons into the conduction band. Dopants that lack an electron to complete the valence bonding are called acceptors, because they need only a slight amount of energy to accept electrons from the valence band into their unfilled states. The simplified energy band structures for intrinsic, n-type, and p-type materials are depicted in Fig. 3. The concentration of donor atoms is denoted ND with energy level ED , and the concentration of acceptor atoms is denoted NA with energy level EA . If donors are added to the semiconductor, then the concentration of holes is reduced. The opposite condition is achieved if acceptors are added to the semiconductor. The general relationship between the free electron concentration and the free hole concentration is np = n2i .

(4)

At room temperature, almost all shallow donors and acceptors are ionized; hence NA ≈ p and ND ≈ n. Combining Eqs. (2), (3), and (4), it is easily shown that the intrinsic carrier concentration is ni =



  Eg . NC NV exp − 2kT

(5)

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D. S. McGregor

electrons

EC

EC

EC

ED EF n-type dopant states (empty)

EF

p-type dopant states (filled)

EF EA

EV

EV intrinsic

holes

EV n-type

p-type

Fig. 3 The simplified energy band structures for intrinsic, n-type, and p-type materials. The electron and hole carrier concentrations are equal for the intrinsic case. Materials doped n-type have an excess of electrons in the conduction band, and materials doped p-type have an excess of holes in the valence band

Equation (5) clearly indicates that the intrinsic charge carrier population ni decreases with increasing band gap energy Eg and decreasing temperature T .

Carrier Mobility The motion of a charge carrier can be influenced by diffusion, magnetic fields, and electric fields. The strength of this influence is characterized by the carrier mobility. The valence and conduction bands have different periodic potentials, and for this reason, electron mobility in the conduction band is different than hole mobility in the valence band. Electron mobility is denoted μe , and hole mobility is denoted μh . The velocity of a charge carrier can be approximated with ve,h = μe,h E,

(6)

where E is the electric field magnitude. Equation (6) is a good approximation provided that the electric field is relatively lower than the saturation field (usually below 2 × 103 V cm−1 ), above which the charge carrier velocities begin to asymptotically approach a saturation limit.

Carrier Lifetime Charge carriers in the conduction band are dynamically dropping back into the empty states of the valence band, while other electrons gain energy to cross the band gap. Overall, a somewhat constant density of electrons and holes remains in the conduction and valence bands, respectively. The time over which a charge carrier

16 Semiconductor Radiation Detectors

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remains in either band is altered by impurity and defect states that appear in the band gap, which increase the probability of either carrier transferring from either band to an intermediate state or eventually to completion of the recombination process. If a charge carrier falls into a defect state, it is referred to as “trapped,” whereas if the charge carrier journey is completed, where an electron falls completely back into a hole in the valence band, it is referred to as having “recombined.” The average time period over which an excited electron remains in the conduction band before being trapped or recombining is the electron lifetime, denoted τe , and the average time period over which a hole remains in the valence band before being trapped or recombining is the hole lifetime, denoted τh .

Material Resistivity The ability of a semiconductor to conduct electrons is referred to as the material resistivity, with units of ·cm. The resistivity of a semiconductor is found with ρ=

1 , q(μe n + μh p)

(7)

where q is the unit electronic charge, μe is the electron mobility, and μh is the hole mobility. In the case that n  p, Eq. (7) reduces to ρ≈

1 , qμe n

(8)

and in the case that p  n, Eq. (7) reduces to ρ≈

1 . qμh p

(9)

The resistance of a right parallelepiped block of semiconductor is described by R=ρ

W , A

(10)

where W is the detector width or length and A is the contact area.

Basic Detector Configurations Semiconductor detectors can be fashioned into many different device configurations, including junction diodes, Schottky barrier diodes, photoconductors, and photoresistors. To select the most appropriate device configuration, one must consider the semiconductor material and the radiation detection application. Some semiconductor materials are composed of substances that are not easily converted

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D. S. McGregor

into junction diodes, such as HgI2 and PbI2 , whereas other semiconductors, such as Si and Ge, are easily fashioned into junction devices. Some materials, such as GaAs, can be fabricated easily into either photoconductors or Schottky barrier devices, whereas limited doping selection and other chemical constraints prevent some materials from being configured easily as either reverse-biased diodes or photoconductors. These fundamental designs are briefly described in the following sections.

pn Junction If two blocks of semiconductor material, one doped with ND donors and the other doped with NA acceptors, are fused together into contact, then the p-type side of the junction boundary has an excess of free hole charge carriers, and the n-type side of the junction has an excess of free electron charge carriers. The concentration gradient across the junction boundary will cause holes to diffuse across the boundary into the n-type side and electrons to diffuse over to the p-type side. The free carriers leave behind the immobile host ions, which produce regions of space charge of opposite polarity, as depicted in Fig. 4. The result is the production of an internal

space charge region

-

p-type

-

+ + + + +

junction

-

+ + + + +

+ + + + +

n-type

EC qVbi EFp

EC EV

EFn

EV xp

0

xn

Fig. 4 In the depiction of a pn junction at equilibrium, the free charge carriers are swept from the space charge or depletion region, leaving behind a polarized zone that produces an internal electric field. Diffusion of charges in one direction is balanced by electric field drift in the other. At equilibrium, the Fermi level is constant across the junction

16 Semiconductor Radiation Detectors

461

electric field with an applied force in the opposite direction of the diffusion force. The presence of space charge distorts the band potentials and causes the bands to bend across the junction boundary. The bands continue to distort and bend until the diffusion force is equal to the electric field force, thereby producing a state of equilibrium. Poisson’s equation is used to determine the space charge region width: ∂ 2ψ ρc (x) q =− = (NA− − ND+ − p + n), 2 s s ∂x

(11)

where ρc is the volumetric charge density, s is the semiconductor permittivity (see Tables 1 and 2), ND is the dopant density on the n-type side, NA the dopant density on the p-type side, and n and p are the electron and hole free carrier densities. Under room temperature conditions, the ionized acceptor concentration NA− ≈ NA , and the ionized donor concentration ND+ ≈ ND . With the assumption of an abrupt junction and uniform dopant distribution, the depletion width solution is  W =

2s (Vbi − V ) q



NA + ND NA ND

 1/2 ,

(12)

where V is an externally applied negative voltage and Vbi is the built-in potential arising from the energy band bending, as shown in Fig. 4 (Pierret 1989). The value of Vbi for common pn junction diodes is approximately 0.7 volts. In the case that one side of the junction is doped much higher than the other side, by at least an order of magnitude, Eq. (12) can be approximated by  W ≈

2s (Vbi − V ) qNs

1/2 ,

Table 1 Some useful physical constants Constant Avogadro’s number Boltzmann’s constant Electronic charge Electron volt Free-electron mass Permittivity of free space Permeability of free space Planck’s constant Velocity of light Thermal energy at 300 K

Symbol N0 k q eV m 0 μ0 h c kT

Magnitude | 6.023 × 1023 molecules mol−1 1.38 × 10−23 J K−1 = 8.62 × 10−5 eV K−1 1.6 × 10−19 C 1.6 × 10−19 J 9.1 × 10−31 kg 8.854 × 10−14 F cm−1 1.257 × 10−8 H cm−1 6.625 × 10−34 J s 3 × 1010 cm s−1 0.0259 eV

(13)

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D. S. McGregor

Table 2 Common semiconductors used as radiation detectors and their properties at 300K

Semiconductor Si SiC(4H) Ge GaAs CdTe Cd0.9 Zn0.1 Te (CZT) HgI2

Atomic number (Z) 14 14/6 32 31/33 48/52 48/30/52 80/53

Semiconductor Si SiC Ge GaAs CdTe CZT HgI2

Intrinsic resistivity ( -cm) >5 × 104 >1015 47 ≈108 109 1011 1013

Density (g cm−3 ) 2.33 3.21 5.33 5.32 6.06 6.0 6.4 Electron mobility (cm2 /V·s) 1500 900 3900 >8000 1050 1350 100

Band gap (eV) 1.12 3.23 0.68 1.42 1.52 1.60 2.13 Hole mobility (cm2 /V·s) 450 120 1900 400 100 120 4

Ionization energy (eV/e-h pair) 3.61 7.8 2.98 4.2 4.43 5.0 4.3

Dielectric constant (s /0 ) 11.9 9.66 16 13.1 10.36 10.63 8.8

Electron lifetime (s) >10−3 4 × 10−7 >10−3 10−9 –10−8 3 × 10−6 10−6 >10−6

Hole lifetime (s) >10−3 6.7 × 10−7 >10−3 10−9 –10−8 2 × 10−6 5 × 10−8 >10−6

where Ns is the doping concentration of the lighter doped side. Note that qVbi is equal to the conduction band energy difference from the p-type side to the n-type side (see Fig. 4), where Vbi

  ND NA kT . ln ≈ q ni 2

(14)

At room temperature, the material resistivity can be expressed as ρs =

1 , qμs Ns

(15)

where Ns and μs are the background dopant concentration and mobility for the lighter doped side of the junction, and Eq. (13) can be rewritten as W ≈ {2s μs ρs (Vbi − V )}1/2 .

(16)

The electric field magnitude across the device is |Ε(x)| ≈

qNs (W − x), s

0 ≤ x ≤ W.

(17)

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463

The active radiation-sensitive volume of the pn junction detector is defined by the space charge region (or depletion region), and the undepleted regions act as series resistances. Detectors based on pn junction diodes are typically operated under reverse bias, which is regarded as a negative voltage but is actually a positive voltage applied to the n-type material with respect to the p-type material. Shown in Fig. 5 is the band diagram of a reverse-biased pn junction. The large energy band barriers prevent electrons on the n-type side from diffusing over to the ptype side and prevent holes on the p-type side from diffusing into the n-type side. As a result, the junction suppresses leakage current that would be present if the semiconductor were operated as a resistor. This necessary condition reduces the electron current such that small charge packets excited in the depletion region by radiation interactions can be measured. There are some sources of leakage current, as depicted in Fig. 5. Although the majority carriers on the p-type side are holes, according to Eq. (4), a small concentration of electrons is still present. These minority charge carriers (electrons) can diffuse into the depletion region, where they are swept across by the electric field and contribute to the leakage current. A similar case is true for holes diffusing from the n-type side into the depletion region. Leakage current can also occur from thermal generation of electrons directly across the band gap into the conduction band, producing electron and hole free carriers. Thermal generation of such charge carriers can be suppressed by cooling the detector while it is operating. Under high voltage bias conditions, charge carriers can also tunnel directly across the band gap, again contributing to the leakage current. Variations about the leakage current can be a significant source of electronic noise (shot noise), which decreases the overall energy resolution of the detector. Basically, pn junctions are employed to minimize leakage currents in semiconductor detectors. The capacitance of a parallel contact pn junction detector is given by Cdet =

s A , W

(18)

minority carrier injection thermal charge carrier generation

EC

tunneling

EF

p-type side

_

Efp

EV

n >> p on n-type side

n-type side Efn

EC EF

p >> n on p-type side

+

EV

Fig. 5 In reverse bias, the density of available carriers, dominated by the minority carrier concentration, determines the leakage current. At higher voltages, bulk generation and tunneling may increase the observed leakage currents.

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D. S. McGregor

where A is the device active contact area. Substituting Eq. (16) into Eq. (18), 

Cdet

s ≈A 2μs ρs (Vbi − V )

1/2 .

(19)

Detector capacitance affects the input voltage pulse height, with a large capacitance diminishing the input voltage from the detector that is measured by the amplification circuit, as Vin ≈

Q , Ctot

(20)

where Ctot is the total capacitance (detector and coupling) and Q is the total charge collected from the radiation detector after a radiation event. Hence, it is important to reduce detector capacitance and coupling capacitance between the detector and the shaping electronics. From Eq. (19), it is seen that increasing the reverse bias voltage decreases the detector capacitance but at the expense of increasing the leakage current.

pin Junction Devices Reverse biased diode detectors need a sizeable depletion region to maximize efficient radiation absorption. As found in Eq. (13), the depletion region width is proportional to the square root of the applied reverse voltage, indicating that excessive voltage would be required to product a sizeable depletion region for a common pn junction diode. The usual remedy is to construct a pin diode, which has an intrinsic or high purity region, between the p-type and n-type contacts. The p- and n-type contacts can produce either blocking barriers or electrically ohmic contacts to the material. The application of p-type contacts to p-type material, or n-type contacts to n-type material, generally produces non-rectifying electrical contacts that follow Ohm’s law. The device may have a truly intrinsic region between the p- and n-type contacts, in which the electron and hole populations are identical, or the high purity region may be a lightly doped material. Lightly doped p-type material is commonly denoted π -type, and lightly doped n-type material is commonly denoted ν-type. Analysis of the diode construction should take into account the “punch-through” voltage, in which the depletion region extends completely across the high purity region, whether the material is i, ν, or π type. Semiconductor pin diode radiation detectors are commonly operated at biases above the punch-through voltage. Intrinsic material either has dopant concentrations below the intrinsic concentration or has compensation dopants that cause the residual free carrier concentration to be below the intrinsic concentration. In either case, the residual space charge is practically zero (ρc ≈ 0), and from Eq. (11), the resulting electric field is constant across the pin diode under reverse bias. Many detectors are fashioned from high

16 Semiconductor Radiation Detectors

465

purity semiconductor materials, yet these actually are not intrinsic behaving, having some residual dopant concentration that is still above the intrinsic concentration. As a result, ρc is nonzero, although small, and the depletion region width is determined by Vbi and the applied voltage. If the lightly doped π or ν regions are relatively thin, the detector might be “fully depleted” without an applied voltage, as depicted in Fig. 6. Usually, such is not the case, and a reverse bias must be applied to extend the depletion region and electric field across the device as determined from Eqs. (13) and (17), respectively.

Schottky Devices The application of a metal to a semiconductor surface acts to bend the semiconductor bands to form an energy barrier qφbn , much like the pn junction diode, as shown in Fig. 7. The Fermi energies, defined by the metal and semiconductor work functions (φm and φs ), must align when the two materials are brought into contact (Henisch 1984). Because the semiconductor work function changes with doping concentration, reference is usually made to the semiconductor electron affinity (qχs ), the difference between the vacuum level at full ionization and the conduction band edge. As a result of the junction formation, a built-in potential qφbi forms, and potential barrier qφbn forms (Sharma 1984; Rhoderick and Williams 1988). Under a reverse bias, this energy barrier serves to reduce leakage current. Typically the barrier height is lower than that for pn or pin junction diodes; hence detectors based on the Schottky barrier diode typically have higher leakage currents than pn or pin diodes. Because the surfaces of semiconductors have defects, interface states, and possible contaminants, the actual barrier height not only depends upon the choice of

xp

xi xn

0

xp x

0

xn

xp

x xn

0

(a) max

p-type region

(b)

intrinsic region

n-type region

p-type region

EC

(c)

-type region

n-type region

p-type region

EC EC EF

EF EV

-type region

n-type region

EC EC EF

EF EV

EV

pin

max

max

EC EF

EF EV

EV

p n

EV

p n

Fig. 6 Electric field (a) and band diagrams (c) of pin, pπ n, and pνn devices. Note that the electric field across the intrinsic region of the pin diode is constant, but the lightly doped pπ n and pνn have a definite slope to their electric fields

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D. S. McGregor

metal

semiconductor

semiconductor

metal

vacuum level s

s

m

EFm

vacuum level

EC EFs EV

q

m

q

EFm

bi

bn

s

s

EC EFs EV

(a)

(b)

Fig. 7 The band configuration depicted for a metal and semiconductor (a) before and (b) after contact, according to the Schottky-Mott model

metal but also on how the surface is prepared. These surface states can effectively “pin” the detector barrier height, thereby predetermining the actual value of qφbn before the metal is applied. The depletion width for a Schottky barrier detector is similar to a one-sided pn junction diode:  W ≈

2s (Vbi − V ) qNs

1/2 ,

(21)

where Ns is the dopant concentration in the semiconductor. Just as Eq. (13) can be rewritten as Eq. (16), Eq. (21) can be rewritten as W ≈ {2s μs ρs (Vbi − V )}1/2 .

(22)

The value of Vbi for common Schottky diodes is 0.3 volts. Note that Schottky contacts can be formed on n-type or p-type semiconductors, as depicted in Fig. 8. Besides being simple to construct, Schottky barrier detectors have a thin entrance region at the contact, unlike most pn and pin diodes, and energy attenuation in this “dead region” is kept to a minimum. As a result, Schottky barrier detectors (sometimes called “surface barrier detectors”) are attractive as charged particle spectrometers.

Ohmic Contacts Efficient charge carrier extraction from a semiconductor detector requires ohmic behaving contacts; hence, it is important in some cases that the metal/semiconductor interface does not form a rectifying potential barrier. For instance, metal contacts to the n and p regions of pn and pin detectors are processed to be non-rectifying,

16 Semiconductor Radiation Detectors

467 vacuum level

vacuum level m

q

Bp

s

EC

Schottky contact

s

qVBi

Efm

s

EC

tunnel contact

Efs

EV

n-type Schottky barrier diode

s

m

e-

Efs

q

Bp

qVBi Schottky contact

EV

Efm

e-

tunnel contact

p-type Schottky barrier diode

Fig. 8 Interface states alter the interface potentials and effectively “pin” the Schottky barrier. Shown are n-type and p-type Schottky barriers, along with n-type and p-type tunneling ohmic contacts

or ohmic, and generally follow Ohm’s law. Unfortunately, due to interface state pinning, a barrier is formed for almost all metals applied to a semiconductor surface. To remedy this problem, a high concentration of dopants is applied with the metal and diffused, typically through thermal treatment, into the semiconductor (Schwartz 1969). The process causes the Schottky barrier to become extremely thin so that electrons can tunnel directly through the barrier; hence the contact has ohmic behavior. Schottky diodes are typically constructed with one (or more) Schottky contact as a rectifying barrier to reduce leakage current and one (or more) opposing ohmic contact to allow for efficient carrier extraction, thereby reducing electronic noise (see depiction in Fig. 8).

Resistive Devices Semiconductor detectors fabricated from wide band gap materials (generally >1.6 eV) have material resistivities high enough to reduce leakage currents to low levels and as a result do not require rectifying contacts to suppress leakage currents. The devices typically have ohmic contacts for electrodes to prevent rectification and the subsequent formation of space charge regions (which can limit the active region volume). Radiation interactions in the detectors excite electron-hole pairs that are swept out of the detectors by an applied electric field. The high resistivity of the device insures that the leakage current is lower than the radiation-excited current. For example, the current from a common 5 mm (width) × 10 mm × 10 mm CdZnTe detector of band gap 1.62 eV has a resistivity of 1011 cm, giving a detector resistance of 5 × 1010 . A bias of 600 volts would produce a 12 nA leakage current. With average excitation energy w of 5 eV per electron-hole pair, a 662 keV gamma-ray will excite approximately 2 × 10−14 C. With a charge sweep out time across the detector of 320 ns, the integrated background charge is 3.8 × 10−15 C, only 19% of the charge excited by the gamma-ray.

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D. S. McGregor

Photoconductive Devices There is a unique class of semiconductor detectors known as photoconductors. In principle, such devices are composed of semiconducting material upon which ohmic contacts have been applied to prevent the formation of a blocking barrier or a space charge region. From Eq. (7), the resistivity of a semiconductor material is inversely proportional to the free carrier concentration. A single radiation absorption event will cause the local conductivity to change spontaneously, yet the small charge cloud is surrounded by higher resistivity material on all sides. Further, the charge cloud is dissipated rapidly by an applied voltage. Suppose instead the semiconductor block is saturated with a radiation pulse such that electron-hole pairs are evenly distributed throughout the crystal bulk. The conductivity of the entire semiconductor block changes because of the macroscopic change in the free carrier concentration. This means that, for any constant applied voltage, the current through the device must increase. The current continues to flow, with well-fabricated ohmic contacts, since Ohm’s law dictates that every electron exiting the device at the anode is replaced by another electron injected at the cathode. This photocurrent continues to flow, decaying away as a function of the charge carrier lifetimes. Hence, the photocurrent is described as  I (t) =



 VA q μe (n + nph e−t/τe ) + μh (p + pph e−t/τh ) , W

(23)

where nph and pph are the excess free carrier concentrations excited by the radiation pulse and n and p are the steady-state free carrier concentrations just before the radiation pulse is produced. This result is important. First, the current decays away as a function of the free-charge-carrier lifetimes, so that the current continues to flow even after the primary charge carriers excited in the semiconductor reach the electrodes. Second, the duration of the detector current pulse can be tailored by changing the freecharge-carrier lifetimes. High-speed photoconductive radiation detectors can be manufactured by purposely adding lifetime shortening dopants or by shortening the lifetimes with intentional radiation damage. These detectors have been used for fasttiming measurements of radiation bursts.

Operation Semiconductor detectors operate on the principle of induced charge, in which mobile charges drifting through the detector cause charge to flow in an externally connected circuit, typically a preamplifier for pulse-mode operation. This concept is important, mainly because the detector produces voltage pulses that depend on the RC time constant of the output circuit, the capacitance of the detector, the coupling capacitance, and the charge-carrier velocities. Further, the voltage pulse induced by the detector begins to form immediately when the charges begin to

16 Semiconductor Radiation Detectors electron-hole pairs

469

-ray V+

A

x x1

0

x2

xi

W

Fig. 9 Planar semiconductor detector configuration

move in the detector. From Fig. 9, N0 electron-hole pairs excited at point xi in a detector with active region of width W will induce a current according to the scaled motion of electrons and holes. The total liberated charge of the electron-hole pairs is represented by Q = qN0 . Consider a semiconductor detector with n number of electrodes where mobile charges are in motion within the device. The induced current on the ith electrode among a set of two or more electrodes is (Shockley 1938) ii =

Q Q dQi dr = − ∇V (r) · = Ε(r) · v, dt Vi dt Vi

(24)

where Qi is the image charge on electrode i, v is the charge-carrier velocity, Ε(r) is the electric field at point r under the condition that the “potential” at electrode i is set at Vi with all other electrodes grounded, and V (r) is the potential at location r within the system. It is useful to normalize V (r) by setting Vi to one volt, i.e., define Vw (r) = V (r)/Vi . This normalized “potential” Vw is called the weighting potential although it is dimensionless. In terms of this normalized potential, Eq. (24) is expressed as ii = −Q∇Vw (r) ·

dr = QΕw (r) · v dt

(25)

and Qi = −QVw (r)

(26)

where the normalized or weighting electric field is Εw = Ε/Vi = −∇Vw . This result can be applied to any one of the electrodes by setting its potential to one volt and grounding all other electrodes (set to zero); see also Jen (1941) and Beck (1953). The results of Eq. (25) are significant and important and are often referred

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to as Ramo’s Theorem (Although Eq. (25) is commonly called Ramo’s theorem, the same result was published by Shockley in 1938 a year before Ramo’s publication in 1939, and it is a straightforward derivation from Green’s theorem. Also, because both Vw and Εw are dimensionless, Eq. (25) is dimensionally correct, although some forget this fact). Hence, for any geometric detector structure, the expected current induction for the electrode tied to the readout circuit can be found with Eq. (25). The weighting potential for a simple planar detector is Vw |planar =

x W

(27)

which is clearly a linear function of position in the detector. Hence, the current induced is directly proportional to the distance charge carriers travel across the detector width W within time t. Suppose electron-hole pairs are created at position xi and the holes are drifted to position x1 while electrons are drifted to position x2 . Using Eq. (27), the solution from Eq. (24) yields the total change in the induced charge from the motion of electrons and holes:    xi − x1 x2 − x1 x2 − xi =Q + =Q . W h W e W 

Q|planar

(28)

From Fig. 9 and Eq. (28), it becomes clear that if the holes and electrons reach their respective electrodes, where x2 − x1 = W , the change in the induced charge Q is the same as Q, a case referred to as complete charge collection. Any condition in which the electrons and/or holes do not completely reach their respective electrodes results in incomplete charge collection, and Q < Q. The induced current is not a linear function of position for detector configurations other than planar devices. Other basic detector configurations include coaxial designs and spherical (hemispherical) designs (see Fig. 10). It can be shown that the weighting potential for a cylindrical detector is  Vw |cylinder = ln

r r2

   −1 r1 ln , r2

(29)

where r2 is the detector outer radius and r1 is the detector inner radius. The weighting potentials for various r1 /r2 cases are shown in Fig. 11. With this result, the solution to Eq. (24) for a coaxial detector configuration is 

Q|cylinder



r2 = Q ln r1

−1

 r2 ln  , r1 

(30)

where r1 and r2 are the drift radii locations for the electrons and holes. Note that the weighting potential is not linear for the cylindrical case and a larger change in the weighting potential is apparent in the vicinity near the inner electrode at r1 ,

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A

V+

rI

rI

r’2

r’2 -ray

r’1

-ray

r’1 r1

A

V+

r1

r2

r2 electron-hole pairs

electron-hole pairs

Fig. 10 Cylindrical and spherical semiconductor detector configurations

Fig. 11 Weighting potentials for various values of r1 /r2 versus the normalized distance from r1 to r2 for a cylindrical detector

and therefore the induced current is much higher for charges moving near the inner electrode than for charges moving near the outer electrode at r2 . Similarly, it can also be shown that the weighting potential for a spherical (or hemispherical) detector is  Vw |sphere =

r1 r2 − r1



 r2 −1 , r

(31)

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D. S. McGregor

Fig. 12 Weighting potentials for various values of r1 /r2 versus the normalized distance from r1 to r2 for a spherical detector

where r2 is the detector outer radius and r1 is the detector inner radius. The weighting potentials for various r1 /r2 cases are shown in Fig. 12. The solution to Eq. (24) for a hemispherical detector is Q|sphere

  r1 r2 r1 − r2 , =Q   r1 r2 r1 − r2

(32)

where r1 and r2 are the drift radii locations for the electrons and holes. Note again that the weighting potential is not linear for the spherical case and a larger change in the weighting potential is apparent near the inner electrode at r1 . The induced current is much higher for charges moving near the inner electrode than for charges moving near the outer electrode at r2 . The weighting potential in detectors with complex geometric shapes can be found by solving Eq. (24) through numerical methods. Because the capacitance of a detector is highly dependent upon the bias voltage, mainly because the size of the depleted active region changes with bias voltage, it is important that the preamplifier circuit used to sense the induced current is properly matched to the detector. Further, the preamplifier should be a chargesensitive preamplifier, in which the pulse height output is largely insensitive to capacitance changes in the semiconductor detector and is instead mainly dependent upon the charge collected from the detector. Commercial detectors generally have specifications with recommended preamplifier characteristics that can serve to optimize the detector performance.

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Gamma-Ray and X-Ray Spectrometers Properties sought for an ideal γ -ray spectrometer include a wide band gap energy, high Z material composition, high atomic density, long charge carrier lifetimes, high resistivity, high electron and hole mobilities, and a small ionization energy. A wide band gap energy (>1.5 eV) and high resistivity allow room temperature operation that otherwise would require cryogenic cooling to reduce electronic noise. High atomic density and high Z components increase the γ -ray interaction probability (see Fig. 13). Long charge carrier lifetimes and high carrier mobilities increase the charge collection efficiency and produce better spectroscopic results. Finally, a small ionization energy causes increased numbers of excited charge carriers, thereby improving statistics and enhancing spectroscopic energy resolution. Unfortunately, no existing semiconductor actually has all of these characteristics; hence the investigator should select a semiconductor detector best suited for the desired application. The basic properties of several semiconductors used for γ -ray and x-ray detectors are listed in Table 2.

X-ray Detectors Based Upon Si Si is a group IV elemental semiconductor with a room temperature band gap energy of 1.12 eV. Its low Z number and low density of electrons cause its γ -ray absorption

Fig. 13 Photon linear attenuation coefficients as a function of photon energy for Si, Ge, CdTe, and HgI2 semiconductor materials

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coefficient to be small. Further, the energy at which the photoelectric effect equals the Compton scattering effect is relatively low at only 60 keV. Hence, Si is a poor choice for high-energy γ -ray spectroscopy. However, its K absorption edge appears at 1.838 keV, meaning that the absorption edge discontinuity does not adversely affect x-ray absorption at higher energies nor does the appearance of x-ray escape peaks cause significant issues in spectra. By comparison, the K absorption edge for Ge is 11.103 keV. The fact that higher-energy γ -rays have less chance of interacting in Si serves to reduce the background effects. Energy resolution is quoted in terms of energy spread at the full width at half the maximum (FWHM) of a spectral full energy peak. Silicon detectors deliver excellent energy resolution, with a FWHM of 

2 1/2 √ F W H M = (F W H Mnoise ) + 2.35 wF E , 2

(33)

where w is the average energy to produce an electron-hole pair, E is the photon energy, and F is the Fano factor (typically 0.1). The Fano factor is a correction factor to account for typically higher-energy resolution than predicted from pure Gaussian statistics. For these reasons, Si does have importance as an x-ray spectrometer for applications such as x-ray fluorescence, x-ray microanalysis, particle-induced xray emission (PIXE), x-ray absorption spectroscopy (XAS), x-ray diffraction, and Mössbauer spectroscopy at energies generally below 50 keV.

Basic Design Highly purified Si can be fashioned into a type of pin diode; yet from Eq. (12), these devices are limited to depleted regions less than 2-mm width, an unsatisfactory thickness for efficient x-ray absorption. The problem is remedied by compensating the remaining impurities in Si with the Li-drifting technique, in which Li ions are electrically introduced deep into the semiconductor under controlled conditions. The resulting devices, denoted as Si(Li) detectors, have active regions ranging from 3 to 5 mm. The basic design is shown in Fig. 14. Although Si(Li) detectors can be operated at room temperature, they perform best when cooled to low temperatures. Various Si(Li) detectors are available coupled to either liquid nitrogen (LN2) dewars or Peltier coolers. The detectors are encapsulated in a protective container with a thin entrance window, typically constructed from Be. The entrance window of the detector affects the low-energy sensitivity limit. Shown in Fig. 15 is the detection efficiency for various Si(Li) detectors with different thicknesses and different entrance windows. Note that thicker detectors increase the efficiency for higher-energy x-rays, while the appropriate choice of entrance window can increase the efficiency for low-energy xrays. An example x-ray spectrum from a fluoresced brass sample taken with a Si(Li) detector is shown in Fig. 16. Si(Li) detectors can be commercially acquired in a variety of segmented patterns, including strips, triangular, and square patterns. The detectors consist of pin diode structures individually fabricated into a single Si substrate, thereby reducing “dead

16 Semiconductor Radiation Detectors n-type region

Au contact

p

e

intrinsic (Li-drifted region)

475 n-type region

Au contact

e p

h

p

intrinsic (Li-drifted region)

p

h Schottky contact

p-type dead layer

Schottky contact

p-type dead layer

Fig. 14 Popular configurations for Si(Li) detectors, showing (left) the inverted T and (right) the etched planar. Copyright (2020). From Radiation Detection: Concepts, Methods and Devices by D. S. McGregor and J. K. Shultis. Reproduced by permission of Taylor and Francis Group, LLC, a division of Informa PLC.

Fig. 15 The absorption efficiency of a Si(Li) detector as a function of x-ray energy, depletion thickness, and entrance window. (Data from Canberra 2003)

zones” between neighboring detectors. These detectors offer high x-ray energy resolution and spatial interaction information. Further, clever designs can actually improve count rate efficiency for ion probe instrumentation, such as PIXE, by surrounding the target region with multiple detectors. Used in conjunction with

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Fig. 16 X-ray spectrum of a brass sample taken with a Si(Li) detector. Copyright (2020). From Radiation Detection: Concepts, Methods and Devices by D. S. McGregor and J. K. Shultis. Reproduced by permission of Taylor and Francis Group, LLC, a division of Informa PLC.

other γ -ray detectors, the segmented Si(Li) detectors can be used for Compton scatter γ -ray cameras.

Detectors Based Upon Ge Presently, the most popular high resolution γ -ray spectrometers are constructed from high purity Ge (HPGe). The material is purified through zone refinement, resulting in a nearly intrinsic material. Although numerous detector configurations exist (see Fig. 17), including special order devices, a standard unit is a coaxial pπ n or pνn design with the rectifying junction on the outer surface. The coaxial design permits large detectors to be fabricated while minimizing the detector capacitance. With the rectifying surface on the outer surface, rather than on the inner surface, the active volume is increased, and the low-energy γ -ray detection efficiency is improved. One difficulty with HPGe detector operation is the need to chill the device while operating. Because of the small band gap energy (0.68 eV), the intrinsic carrier concentration of electrons and holes is much too high at room temperature, and significant leakage current is produced when operated at high voltage, which can damage the detector. For this reason, HPGe detectors are typically attached to a dewar and cooled with LN2, or they are attached to a low noise refrigerator system. To ensure that the damage does not occur from excessive leakage current should the

16 Semiconductor Radiation Detectors

a

477

b

c

d

f

g

h

n-type Li diffused p-type implantation surface barrier passivation

e

Fig. 17 Different commercially available HPGe detector structures with electric field lines depicted: (a) basic planar detector, (b) grooved planar, (c) low capacitance planar, (d) surface barrier planar, (e) truncated pνn blind coaxial, (f) pνn blind coaxial, (g) nπp blind coaxial, and (h) pπ n well configuration. (After Darken and Cox 1995, Canberra 2016 and Ortec 2016)

LN2 be exhausted, most modern systems have a safety shutoff that disconnects the high voltage if the HPGe detector increases to a preset temperature. Portable survey detectors and laboratory units are available with either LN2 dewars or electrically cooled refrigerators. Hybrid LN2/electrical cryostats have become available, where the main cooler is electrical, backed up with LN2 cooling in case of a power outage. The usual standard for quality comparisons of HPGe detectors is to quote the energy resolution for 1.33 MeV γ -rays from 60 Co. The expected energy resolution can be approximated by Eq. (33), where the Fano factor is approximately 0.08. Efficiency, for historical reasons, is quoted most often as a comparison to a 3 in × 3 in (7.62 × 7.62 cm) right cylindrical NaI(Tl) detector with the source placed 25 cm from the face of either detector. For instance, a relative 30% HPGe detector has 30% of the efficiency expected from a 3 in × 3 in NaI(Tl) detector at 1.33 MeV. Although useful as an approximation of detector performance, due to differences in detector geometries and mounting apparatuses, such sweeping generalizations can be erroneous for accurate measurements. It is best to characterize the detector efficiency and resolution, a method described by ANSI/IEEE 325-1996. A calibrated National Institute of Standards 60 Co check source is placed 25 cm from the front of the detector face. The number of counts appearing in the full energy peak for the 1.332 MeV γ -ray is divided by the number of emissions over that same time interval, which yields the absolute efficiency. The relative efficiency is found by dividing the absolute efficiency by 1.2 × 10−3 , which is the standard efficiency for a 3 in × 3 in NaI(Tl) detector under the same irradiation conditions. Comparison

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Fig. 18 Comparison gamma-ray spectra of 60 Co taken with a NaI(Tl) detector and a 20% relative efficiency HPGe detector. Copyright (2020). From Radiation Detection: Concepts, Methods and Devices by D. S. McGregor and J. K. Shultis. Reproduced by permission of Taylor and Francis Group, LLC, a division of Informa PLC.

spectra between a 20% relative efficiency HPGe detector and a 3×3 NaI(Tl) detector are shown in Fig. 18.

Various Designs HPGe detectors are manufactured in various shapes, although most conform to either a planar or coaxial design. Small detectors are commonly manufactured as planar detectors. Relatively large HPGe detectors are manufactured as coaxial devices mainly to keep detector capacitance low. Small HPGe detectors usually have better energy resolution than larger devices, and the larger detectors have better γ -ray detection efficiency. The response functions for ν-type and π -type HPGe detectors are quite different at low energies. High purity π -type detectors are fabricated with Li, an n-type dopant, traditionally diffused at a depth of approximately 700 μm thick around the outer surface. A much thinner implanted junction of p-type dopant (typically boron), approximately 300 nm deep, is formed as the ohmic contact. Consequently, the relatively thick “dead” layer formed by the outer contact significantly reduces the detector sensitivity to low-energy photons (typically below 40 keV). Some commercial units are now offered with thinner n-type contacts to reduce this dead layer. From Eqs. (29) and (30), the reverse bias configuration and geometry cause the average output pulse to be dominated by hole motion. These nπp HPGe detectors

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typically have slightly better energy resolution than pνn HPGe detectors at high γ -ray energies. High purity ν-type detectors are fabricated with p-type dopants implanted and activated at a depth of approximately 300 nm for the outer rectifying contact. A much thicker diffused Li junction up to 700 μm thick is fabricated as the ohmic contact. As a result, low-energy γ -rays and x-rays encounter less “dead” layer in the outer contact, thereby increasing the efficiency for these low-energy photons. To take further advantage of the thin surface contact, these ν-type detectors are typically packaged in a can that has a thin Be window, thereby minimizing γ -ray and x-ray attenuation through the detector container. An additional advantage with ν-type HPGe detectors is their increased radiation hardness to neutron radiation. Neutron damage tends to form hole trapping sites; hence the electron-dominated pulses from ν-type HPGe detectors are somewhat less effected. Examples of efficiency responses for a few HPGe variations are shown in Fig. 19. Notice in Fig. 19 the dip in efficiency at the Ge K absorption edge (11.1 keV). Also note the efficiency reduction below 100 keV for the π -type HPGe detector, which only becomes an issue for the ν-type devices represented in Fig. 19 at energies below

Fig. 19 The absolute detection efficiency for several HPGe detector configurations, showing a (A) 200 mm2 × 10 mm thick low-energy ν-type nominally planar HPGe detector, (B) 10 cm2 × 15 mm thick low-energy ν-type nominally planar HPGe detector, (C) coaxial π -type HPGe detector with 10% relative efficiency, (D) coaxial thin window ν-type 15% relative efficiency HPGe detector, and a (E) broad energy range π -type 5000 mm2 × 30 mm thick nominally planar HPGe detector. (After Canberra 2016)

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10 keV. The drop in efficiency is due to a combination of photon absorption in the detector contact dead region and the container holding the detector. Overall, the decision regarding which HPGe detector is best for an application requires some knowledge of the preferred energy resolution, necessary detection efficiency, and the photon energy range of interest (Table 3).

Compound Semiconductor Detectors Compound semiconductor detectors have become more important in recent years, with commercial units now available. Typically these detectors are somewhat smaller than Si- and Ge-based detectors, mainly due to material imperfections (Schlesinger and James 1995). Regardless, a few materials, namely CdTe, CdZnTe, and HgI2 , have desirable properties for room-temperature-operated devices, an advantage not shared by Si(Li) or HPGe detectors. The reason for this advantageous property is their larger band gap energies that work to reduce their intrinsic carrier concentrations and substantially increase their resistivities at 300 K. Further, CdTe, CdZnTe, and HgI2 all have relatively high Z atomic constituents and hence have larger gamma-ray absorption coefficients over those of Si and Ge. Still, because of their typical smaller size, energy resolution for these compound semiconductor detectors is usually reported relative to 662 keV gamma-rays of 137 Cs instead of 1.33 MeV gamma rays from 60 Co. The total charge collected is usually affected by crystalline imperfections that serve as trapping sites, which are energy states that remove free charge carriers from the conduction and valence bands (Bertolini and Coche 1968). Charge is induced while these charge carriers are in motion; hence, their removal diminishes the output voltage. Although the actual trapping process is complicated, it is typical to describe the relative charge collection efficiency as a simplified function of trapping. For planar shaped detectors, this is induced charge given by Q = ξe (1 − e−x/(ξe W ) ) + ξh (1 − e(x−W )/(ξh W ) ), Q

(34)

where W is the detector active region width, Q is the initial excited charge magnitude, x is the event location in the detector, and  ξe,h =

τe,h ve,h W



 =

 μe,h τe,h V , W2

(35)

where τ is the charge carrier lifetime, v is the charge carrier speed, and V is the applied operating voltage. Note that the relative charge collection is dependent upon the interaction location x and, for low values of ξ , the energy resolution is poor. Typically, good energy resolution is achieved if ξ > 50 for both electrons and holes, where Q/Q has little deviation over the detector width W . Otherwise, the energy resolution suffers for higher-energy γ -rays (more or less >300 keV). The value of ξ

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Table 3 Typically quoted energy resolution performance for some commercial semiconductor detectors Detector Si(Li) Si(Li) Si(Li) Si(Li) Si(Li) Si pin CdTe Schottky CdZnTe hemisphere CdZnTe coplanar implanted Si diode implanted Si diode implanted Si diode p-type SSB p-type SSB p-type SSB HPGe detector p-type coaxial p-type coaxial n-type coaxial

Area (mm2 ) 12.5 20 28–30 80 200 13 25 9 25 ≈100 ≈100 100 225 100

Radiation type γ rays γ rays γ rays γ rays γ rays γ rays γ rays γ rays γ rays γ rays γ rays γ rays γ rays γ rays α particles

450

α particles

900

α particles

50

α particles α particles α particles α particles α particles α particles Radiation type γ rays

Energy (keV) 5.9 5.9 59.6 5.9 5.9 5.9 5.9 5.9 122 122 122 662 662 662 5486 5486 5486 5486 5486 5486 5486 5486 5486 5486 5486 5486 Energy (keV) 122

γ rays

1332

γ rays

122

150 900 Relative eff. (%) 20 50 100 20 50 100 20 50 70

FWHM (keV) 0.155–0.175 0.180 0.450 0.165–0.180 0.175–0.190 0.220 0.18–0.22 0.127–0.230 ≤1.2 ≤1.5 ≤6.1 ≤20 13.2–26.4 16.5–26.4 13 12 17–21 15–19 27–33 22–28 15–17 15–17 16–19 16–18 30–40 30–53 FWHM (keV) 0.715–0.975 0.9–1.2 1.2–1.4 1.8–2.0 1.9–2.1 2.0–2.3 0.69–1.0 0.86–1.2 1.1–1.3

Comments LN2 cooled Peltier cooled Peltier cooled LN2 cooled LN2 cooled LN2 cooled Peltier cooled Peltier cooled Peltier cooled Peltier cooled Room temp Room temp Room temp Room temp W = 100 μm W = 500 μm W = 100 μm W = 500 μm W = 100 μm W = 500 μm W = 100 μm W = 500 μm W = 100 μm W = 500 μm W = 100 μm W = 500 μm Comments LN2 or mech cooled LN2 or mech cooled LN2 or mech cooled LN2 or mech cooled LN2 or mech cooled LN2 or mech cooled LN2 or mech cooled LN2 or mech cooled LN2 or mech cooled

Source M,O B M,O M,O M,O A A K B,K K M,O M,O M,O O O O

Source B,I,M,O B,I,M,O B,I,M,O B,I,M,O B,I,M,O B,I,M,O I,M,O I,M,O I,M,O (continued)

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Table 3 (continued) HPGe detector n-type coaxial

Relative eff. (%) 20 50 70

Radiation type γ rays

Energy (keV) 1332

FWHM (keV) 1.8–2.0 2.1–2.3 2.3–2.5

Comments LN2 or mech cooled LN2 or mech cooled LN2 or mech cooled

Source I,M,O I,M,O I,M,O

A AmpTek, B Baltic Scientific, I Itech, K Kromek, M Mirion, O Ortec (Ametek) These detectors are only a few representative examples and do not account for the numerous variations available nor a complete list of detector sources. Contact vendors to acquire a full listing of detector sizes and performance statistics

can be increased by decreasing the detector size (W ), increasing carrier lifetimes (τ ) through material improvement, or increasing the applied voltage V . Due to practical voltage limitations and the fundamental difficulty with improving materials, most compound semiconductor detectors are manufactured with small active widths to improve detector energy resolution, and hence, the devices are relatively small. The μτ values for electrons and holes are often quoted measures of quality for compound semiconductors used as γ -ray spectrometers. Methods of overcoming the charge carrier trapping problem have been introduced that use electronic correction methods, novel electrode and structural designs to optimize the weighting potentials, or a combination of both. Examples of these single carrier designs include quasi-hemispherical designs, coplanar electrode designs, small pixel effect designs, Frisch effect designs (Frisch collar, Frisch ring), and drift ring designs (McGregor and Shultis 2021; Owens 2019).

CdTe Cadmium telluride (CdTe) is a wide band gap semiconductor of interest as a roomtemperature-operated gamma-ray spectrometer. CdTe has a cubic zinc blende crystal structure and a room temperature direct band gap energy of about 1.52 eV. The average ionization energy is 4.43 eV per e-h pair with a 0.11 Fano factor. The dielectric constant (κ = s /0 ) for CdTe is 10.36 (Strauss 1977). CdTe is relatively soft, rating 54 on the Knoop hardness scale (approximately 2.2 on Mohs scale). The elemental constituents have atomic numbers 48 and 52, and the density of CdTe is 5.86 g cm−3 . Because of the relatively high Z numbers, photoelectric absorption dominates up to approximately 260 keV. Charge carrier mobilities are 1050 cm2 V−1 s−1 for electrons and 100 cm2 V−1 s−1 for holes. Electron and hole mean free drift times are material dependent but often quoted near 3 ×10−6 s and 2×10−6 s, respectively. The wide band gap should yield an intrinsic resistivity of 109 cm. Although the band gap is wide enough for room temperature operation, because of background impurity contamination, resistivities greater than 109 cm are difficult to achieve. As a result, leakage currents are too high to operate CdTe detectors as resistive devices. The detectors are manufactured as pn junction or Schottky junction diodes

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to reduce leakage current to manageable levels. Further, high resistivity is usually achieved through impurity and defect compensation, typically with Cl. Because of material imperfections, mainly impurities, charge carrier trapping compromises the energy resolution performance. Consequently, these devices continue to be manufactured as small detectors, and the detector volumes are usually no more than a few mm thick. Commercial units are available as small gamma-ray spectrometers. Typically, the best energy resolution is achieved with the assistance of small electronic Peltier coolers.

CdZnTe The introduction of Zn in the growth process of CdTe, nominally between 2% and 15%, has led to the production of CdZnTe detectors (This particular semiconductor is denoted CZT (common), (Cd,Zn)Te (less common), Cd1−x Znx Te, or CdZnTe. By adhering to traditional elemental symbols, and because of the many different elemental combinations in use for substrates and detectors, the author chooses to use CdZnTe.). Overall, CdZnTe detectors have the same advantages as CdTe detectors with several added benefits. By adding a small amount of ZnTe to the melt, many important semiconductor properties are drastically improved. The band gap of CdZnTe increases with Zn concentration, with band gap energy of Cd1−x Znx Te at 300 K is well approximated by (Olego et al. 1985) Eg (x) eV = (1.51 ± 0.005) + (0.606 ± 0.01)x + (0.139 ± 0.01)x 2 eV.

(36)

The band gap ranges from 1.52 to 1.64 eV for Zn contents ranging from x = 0.02 to x = 0.2; hence the detectors can operate at room temperature without serious leakage current concerns. With an increased band gap energy, the intrinsic free carrier concentration diminishes, thereby increasing the resistivity while reducing detector leakage current. Butler et al. (1992) report that adding x = 0.2 amount of Zn changes the resistivity of CdTe from 3 × 109 cm to 2.5 × 1011 cm for Cd0.8 Zn0.2 Te. The gamma-ray absorption efficiency of CdZnTe is similar to that of CdTe, with a slight decrease in absorption efficiency with increased concentrations of Zn (Z = 30). The dielectric constant is approximately 10.6 for CdZnTe, although this property is also a function of the Zn concentration. The addition of Zn increases the hardness of CdZnTe over CdTe and decreases the dislocation density (Anand 2013). The ionization energy is approximately 5 eV per e-h pair, although this number changes as a function of band gap energy. The Fano factor of CdZnTe has been measured to be approximately 0.11 (Bale et al. 1999) at 233 K, with at least one research group (Redus et al. 1997) reporting a lower Fano factor of 0.089 also at 233 K. The etch pit density (EPD) is a measure of the dislocation defect density. Butler et al. (1993) show a marked reduction in the EPD as the Zn content was increased, with the densities of 1.5 × 105 cm−2 , 104 cm−2 , and 5 × 103 cm−2 for Zn contents of 0, 0.04, and 0.2, respectively. Further, CdZnTe detectors do not exhibit the polarization phenomenon at low irradiation levels, which are often observed with CdTe detectors. However, Wang et al. (2013) report the observation of polarization

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from CdZnTe detectors under high irradiation conditions. An additional benefit of incorporating Zn is that CdZnTe devices, because of the increased band gap and resistivity, can be operated at higher temperatures than CdTe devices, and they can also resolve lower-energy photon energies (x-rays and gamma-rays) traditionally difficult to observe with CdTe detectors. Due to improved materials properties, they can be manufactured much larger than conventional CdTe detectors, and the detectors can operate at room temperature usually without leakage current problems. Because of the high resistivity, the detectors are typically manufactured with ohmic contacts for the cathodes and anodes and are operated as resistive detectors rather than junction diodes. The detectors have adequate electron transport properties but poor hole transport properties. As a result, conventional planar detectors, similar to the depiction in Fig. 9, seldom produce useful energy resolution for moderate to high-energy γ rays (≥300 keV). Instead, some commercial manufacturers rely upon electronic correction methods, clever electrode contact shapes, and special geometric detector shapes to modify the weighting potential and electronic signal such that electrons dominate signal formation rather than holes (McGregor and Shultis 2021; Owens 2019). Energy resolution below 7 keV FWHM for 662 keV γ -rays can be achieved at room temperature for these single carrier detector designs. CdZnTe detectors are presently used in handheld γ -ray spectrometers, smaller medical imaging apparatuses, and advanced pixelated imaging devices.

HgI2 Attractive for its large Z components, mercuric iodide (HgI2 ) has long been studied as a gamma-ray spectrometer with varying degrees of success [see McGregor and Shultis 2021 and references therein]. HgI2 has atomic numbers of 80 and 53 with a volume density of 6.4 g cm−3 . The α-phase (red) of HgI2 has measured charge carrier mobilities of 100 cm2 V−1 s−1 for electrons and 4 cm2 V−1 s−1 for holes (Ponpon et al. 1975). Thus a substantial voltage is required to ensure acceptably high charge carrier collection. HgI2 has a measured average ionization energy of 4.42 eV per e-h pair with a Fano factor of 0.19 (Ricker et al. 1982). Because of the large atomic number of mercury (80), the photoelectric effect is predominant for gamma-ray energies below 400 keV (see Fig. 13). As a result, HgI2 detectors can be relatively thinner than other common semiconductors and still have comparable efficiencies. For example, the absorption efficiency for 140-keV gamma-rays in a 2mm-thick HgI2 detector is similar to 4.2-mm-thick CdTe or CdZnTe detectors and 1.9-cm-thick Ge or GaAs detectors (McGregor and Hermon 1997). The α-phase of HgI2 has a band gap energy of 2.13 eV and has a resistivity of about 1013 cm. They have fewer commercial applications than CdTe or CdZnTe, mainly because of process and fabrication issues. HgI2 is a layered tetragonal crystal structure (α phase) and is a soft material with a Knoop hardness less than 10 (below 1 on the Mohs scale). HgI2 is also highly reactive, and only a few materials are known to be compatible for electrical contacts, those being carbon (Aquadag® ), Pd, and Pt. HgI2 detectors are usually encapsulated with parylene to prevent decomposition over time. The material is known to polarize over time, which is manifested as the gradual

16 Semiconductor Radiation Detectors 8000

Planar (t = 24 hours) Frisch collar (t = 24 hours) t = Detector bias time at the beginning of counting

7000

Counts per Channel

485

Pulsers FWHMPlanar = 0.3% FWHMFrisch collar = 0.2%

6000 5000

662 keV

4000 Hg X-ray escapes

3000

2.1 x 2.1 mm2 x L = 4.1 mm Counting time (Real): 10 h Preamplifier: eV550 Amplifier gain: 69X Shaping time: 1µs HV = 1500V FWHM = 1.8% ± 0.1%

2000 1000 Source: 137Cs

0 0

500

No electronic corrections

1000

1500

2000

Channel Number Fig. 20 Pulse height spectra taken with a 2.1 × 2.1 × 4.1 mm3 HgI2 device with and without a Frisch collar. A 1.8% FWHM energy resolution was measured with 662-keV gamma-rays from 137 Cs when using the Frisch collar. (From Ariesanti et al. (2010); copyright Elsevier (2010), reproduced with permission)

change in spectral features over time. Charge carrier loss from trapping is also a problem with HgI2 . Combined with the low charge carrier mobilities, HgI2 detectors are usually kept volumetrically small to improve energy resolution. Single carrier detector designs such as pixelated electrode patterns and Frisch collar structures have been used to improve performance. Example spectra from a HgI2 detector, with and without a Frisch collar structure, are shown in Fig. 20. The material has been used for portable x-ray spectrometers for in situ analysis, and modular units are available for specialized room temperature spectroscopy applications.

Charged Particle Detectors Semiconductor charged particle spectrometers offer high-energy resolution for energetic ions. Typically, the devices are operated in vacuum, along with the source, to eliminate energy losses from a charged particle as its passes from the source to the detector. The detectors are typically designed with thin contacts and/or thin pn junctions in order to reduce particle energy loss in the nonsensitive (or dead) region of the contact. Because low Z elements have less problems with ion backscattering, Si is typically the material choice for particle detectors. A simple nomogram representing the depletion width as a function of voltage and impurity concentration can be produced by linearizing Eq. (21) or Eq. (22) (Allcock et al. 1963; Blankenship and Borkowski 1960):

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1 log10 (W ) = log10 2



2s qe



Vbi − V Nb



or log10 (W ) −

 1 1

log10 (2s μ) = log10 (ρ) + log10 (Vbi − V ) , 2 2

(37)

where Nb has been replaced with 1/qe μρ and the applied voltage V is negative (reverse bias). With the properties for Si listed in Table 2, such a nomogram was developed for a silicon surface barrier detector, shown in Fig. 21, in which the depletion width is a function of material resistivity (n-type and p-type). These detectors can be used for a variety of charged particle identification and characterization purposes, including high resolution spectroscopy of α particles, β particles, protons, and heavy ions, continuous air monitoring, and particle telescopes.

Surface Barrier and Implanted Junction Detectors Si surface barrier (SSB) detectors rely upon the production of a thin Schottky barrier for a rectifying junction. A typical SSB detector cross section is shown in Fig. 22. High purity n-type or p-type Si is etched, mounted, and epoxied into a ceramic ring. Afterward, a thin layer of Au or Al, ranging from 80 to 200 nm, is applied to the semiconductor surfaces. The thin contact region minimizes the amount of energy lost by particles that enter the device, a necessary precaution to preserve high-energy resolution. However, these delicate surface barrier detectors can be easily damaged by improper handling and are often difficult to clean. Detectors can be obtained in a variety of sizes, ranging from a few mm to 50 mm diameter. These detectors are usually light sensitive and must be operated in darkness, although commercial companies do offer versions that can operate in ambient light, at the expense of energy resolution. Depletion depths range from approximately 100 microns up to, for special cases, 5 mm. Implanted junction detectors rely upon an abrupt junction pn diode for rectification (see Fig. 22). These devices are commonly fabricated from high purity n-type Si. An oxide is grown on the devices for passivation, followed by etching windows back to the Si surface. Shallow p-type and n-type dopants are implanted on opposite sides of the Si surface and thermally activated (Martini 2017). This process produces dead layer junctions on the order of only 50 nm. Because there is no thin metallization layer over the detector, they are more robust and easier to clean than common SSB detectors. Implanted junction detectors can be used for the same basic detection functions that SSB detectors are used. An example alpha-particle spectrum taken with an implanted junction detection is shown in Fig. 23. SSB and implanted junction detectors can be acquired in numerous shapes, sizes, and configurations, making them a versatile choice for particle detection

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Fig. 21 The depletion region as a function of material resistivity and reverse voltage for Si particle detectors. A straight line will yield material resistivity (n or p type), the depletion depth, and applied voltage, according to Eq. (37). The example shown with the dotted line is for 5 k n-type material at 50 volts reverse bias, which yields W = 282 microns. Copyright (2020). From Radiation Detection: Concepts, Methods and Devices by D. S. McGregor and J. K. Shultis. Reproduced by permission of Taylor and Francis Group, LLC, a division of Informa PLC.

and spectroscopy. Further, the detectors can be acquired as multielement arrays for position sensing and timing purposes. The adaptation of very large-scale integration (VLSI) processing technology to Si detectors allows for detector arrays to be

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ceramic ring epoxy

Au contact

high purity Si (n or p type)

oxide passivation

implanted p-type contact

high purity n-type Si

epoxy Al contact

surface barrier detector

implanted n-type contact

ion-implanted detector

Fig. 22 General configurations for Si surface barrier detectors and implanted junction detectors

Fig. 23 Room temperature alpha-particle differential pulse-height spectrum of a spectroscopic grade 226 Ra source taken with a 24-mm diameter implanted junction Si detector operated in vacuum. Copyright (2020). From Radiation Detection: Concepts, Methods and Devices by D. S. McGregor and J. K. Shultis. Reproduced by permission of Taylor and Francis Group, LLC, a division of Informa PLC.

fabricated in a vast number of detector designs, including custom devices contracted to commercial vendors. The detectors are available as double-sided strip detectors with spatial resolutions as low as 25 μm and pad detectors with spatial resolution as small as 0.4 mm. Large arrays of position-sensitive Si detectors can be used in collider facilities, x-ray scattering, and Compton cameras. Finally, drift diode configurations, a variant design that drifts electronic charge carriers laterally along

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the detector to a small collection contact, offer low capacitances with large sensitive areas (Gatti et al. 1985; Kemmer et al. 1987).

Neutron Detectors Semiconductor radiation detectors used as neutron detectors are typically configured as pn junction or Schottky junction diodes coated with a neutron reactive material. The basic construction of such a detector is shown in Fig. 24, where a Schottky or pn junction diode detector has a coating of neutron reactive material applied to the surface. Typically the devices have either 10 B or 6 LiF as the active coating. The absorption cross sections for both 10 B and 6 Li follow a 1/v dependence. The 10 B(n,α)7 Li neutron reaction yields two possible de-excitation branches from the excited 11 B compound nucleus, namely:

1 10 0n + 5B

−→

⎧ ⎨ 42 He (1.4721 MeV) + 73 Li∗ (0.8398 MeV)

(93.7%)

⎩4

(6.3%),

2 He (1.7762

MeV) + 73 Li (1.0133 MeV)

where the Li ion in the 94% branch is ejected in an excited state, which deexcites through the emission of a 480 keV gamma-ray. Fully enriched 10 B has a microscopic absorption cross section for thermal neutrons of 3840 barns. With a mass density of 2.15 g cm−3 , the solid structure of 10 B has a macroscopic thermal absorption cross section of 500 cm−1 .

neutron reactive film

reaction product

V+

neutron A

reaction product

electron-hole pairs

semiconductor Fig. 24 Cross section of a coated semiconductor neutron detector

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The 6 Li(n,t)4 He neutron reaction yields a single product branch: 1 6 0 n + 3 Li

−→ 31 H (2.7276 MeV) + 42 He (2.0553 MeV).

The reaction products from the 6 Li(n,t)4 He reaction are more energetic than those of the 10 B(n,α)7 Li reaction and, hence, are much easier to detect and discriminate from background radiations. 6 Li has a relatively large microscopic thermal neutron absorption cross section of 940 b, although it is less than that of 10 B. Unfortunately, Li is a chemically reactive metal, and therefore, it is the stable compound 6 LiF, with a macroscopic cross section of 57.51 cm−1 , that is used as the reactive coating. For thermal neutrons, the charged particle reaction products are ejected in opposite directions, meaning that only one reaction product can actually enter the semiconductor detector. Further, the reaction products lose energy as they pass through the neutron absorber to the semiconductor detector, thereby limiting the effective absorber thickness. Detectors of this type are limited to less than 5% thermal neutron detection efficiency (McGregor et al. 2003). These devices are generally not commercially available as independent units; rather they are sold as an active component inside some electronic dosimeter modules. The low efficiency of coated planar diodes led to the development of microstructured semiconductor neutron detectors (MSNDs). These detectors have microscopic structures etched into a semiconductor substrate, subsequently formed into a pin style diode. The microstructures are backfilled with neutron reactive material, usually 6 LiF, although 10 B has also been used (see Fig. 25). The increased semiconductor surface area adjacent to the reactive material and the increased probability that a reaction product will enter the semiconductor greatly increase the intrinsic neutron detection efficiency. Commercial MSNDs backfilled with 6 LiF have quoted thermal neutron detection efficiencies between 30% and 35% with an average operating voltage of 3 volts. Advanced experimental versions of double-sided MSNDs with opposing microstructures on both sides of a semiconductor wafer have been reported with over 69% thermal neutron detection efficiency (Ochs et al. 2020).

6

LiF

p-type contact

neutron

SiO2 isolation Au contacts n-type contact

Fig. 25 The basic structure of an MSND

n-type Si

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Summary Semiconductor materials are attractive as radiation detectors for at least two main reasons. First, due to their low average ionization energy w, semiconductors produce a large number of signal charge carriers per unit energy, thereby decreasing statistical fluctuations beyond that of gas-filled and scintillation detectors, hence producing much better energy resolution. Second, semiconductor materials have energy band structures that allow their electrical properties to be altered through the addition of impurities. These materials can be manipulated to have a majority of negative (n-type) electrical charge carriers, or electrons, or positive (p-type) charge carriers, denoted “holes.” Adjacent n-type and p-type materials can be manipulated to form detectors with rectifying contacts, which work to reduce both leakage current and electrical noise. Semiconductor detectors can be fashioned into various detectors especially designed for x-ray detection, γ -detection, or charged particle detection. Detector performance is optimized by semiconductor choice and device design. Charged particle detectors are generally designed with low Z material, such as Si, to reduce backscattering. Higher Z materials, due to improved absorption efficiency, are generally used for γ -ray detectors. Low-energy x-ray and γ -ray detectors are often fabricated from Li-drifted Si (Si(Li) detectors), although the most commonly used semiconductor for photon detection is high purity Ge (HPGe detectors). Both Si(Li) and HPGe detectors must be cooled to low temperature for best operation. Wide band gap semiconductors, such as CdZnTe, can be used as room-temperatureoperated γ -ray spectrometers. Finally, semiconductor materials can be fashioned into arrays to yield spatial interaction information. These arrays can be arranged from the tiling of numerous individual detectors, or they can be fabricated as pixels upon a single semiconductor substrate. Commercial vendors offer numerous varieties of semiconductor detectors, which include particle, x-ray, and γ -ray detectors, in the form of individual devices or as arrays.

Cross-References  Gamma-Ray Spectroscopy  New Solid State Detectors  Photon Detectors

References Allcock HJ, Jones JR, Michel JGL (1963) The nomogram, 5th edn. Pitman, London Anand KG (2013) Defects in Cadmium Zinc Telluride (CdZnTe) – a review. Int J Eng Manag Sci 4:113–120 Ariesanti E, Kargar A, McGregor DS (2010) Fabrication and spectroscopy results of mercuric iodide Frisch collar detectors. Nucl Instrum Meth A624:656–661

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Bale G, Holland A, Seller P, Lowe B (1999) Cooled CdZnTe detectors for x-ray astronomy. Nucl Instrum Methods A436:150–154 Beck AHW (1953) Thermionic valves. Cambridge University Press, London Bertolini G, Coche A (1968) Semiconductor detectors. Wiley, New York Blankenship JL, Borkowski CJ (1960) Silicon surface barrier nuclear particle detectors. IRE Trans Nucl Sci NS-7:190–195 Butler JF, Lingren CL, Doty FP (1992) Cd1−x Znx Te gamma ray detectors. IEEE Trans Nucl Sci 39:605–609 Butler JF, Doty FP, Apotovsky B, Lajzerowicz J, Verger L (1993) Gamma- and x-ray detectors manufactured from Cd1−x Znx Te grown by a high pressure bridgman method. Mater Sci Eng B16:291–295 Canberra (2003) Silicon (Li) detector systems. Canberra Industries, Inc., Document CSP0157 Canberra (2016) Germanium detectors. Canberra Industries, Inc., Document C39606 Darken LS, Cox CE (1995) High-purity germanium detectors. In: Schlesinger TE, James RB (eds) Semiconductors for room temperature nuclear detector applications, Chapter 2. Part of the semiconductor and semimetals series, vol 43. Academic, San Diego, pp 23–83 Gatti E, Rehak P, Longoni A, Kemmer J, Holl P, Klanner R, Lutz G, Wylie A, Goulding F, Luke PN, Madden NW, Walton J (1985) Semiconductor Drift Chambers. IEEE Trans Nucl Sci NS32:1204–1208 Henisch HK (1984) Semiconductor contacts; an approach to ideas and models. Clarendon Press, Oxford Jen JK (1941) On the induced current and energy balance in electronics. Proc IRE 29:345–349 Kemmer J, Lutz G, Belau E, Prechtel U, Welser W (1987) Low capacity drift diode. Nucl Instrum Meth A253:378–381 Martini M (2017) Introduction to charged particle detectors, ORTEC Technical Note, Oak Ridge McGregor DS, Hermon H (1997) Room-temperature compound semiconductor radiation detectors. Nucl Instrum Methods A395:101–124 McGregor DS, Shultis JK (2021) Radiation detection: concepts, methods, and devices. CRC Press, Boca Raton McGregor DS, Hammig MD, Gersch HK, Yang Y-H, Klann RT (2003) Design considerations for thin film coated semiconductor thermal neutron detectors. Nucl Instrum Methods A500:272– 308 McGregor DS, McNeil WJ, Bellinger SL, Unruh TC, Shultis JK (2009) Microstructured Semiconductor Neutron Detectors. Nucl Instrum Methods A608:125–131 Ochs TR, Bellinger SL, Fronk RG, Henson LC, Hutchins RM, McGregor DS (2020) Improved manufacturing and performance of the dual-sided microstructured semiconductor neutron detector (DS-MSND). Nucl Instrum Methods A954:paper 161696 Olego DJ, Faurie JP, Sivananthan S, Raccah PM (1985) Optoelectronic properties of Cd1−x Znx Te films grown by molecular beam epitaxy on GaAs substrates. Appl Phys Lett 47:1172–1174 Ortec (2016) PROFILE HPGe photon detector product configuration guide. Ametek, Document 012517 Owens A (2019) Semiconductor radiation detectors. CRC Press, Boca Raton Pierret RF (1989) Advanced semiconductor fundamentals. Addison Wesley, Reading Ponpon JP, Stuck R, Siffert P, Meyer B, Schwab C (1975) Properties of vapour phase grown mercuric iodide single crystal detectors. IEEE Trans Nucl Sci 22:182–191 Ramo S (1939) Current induced by electron motion. Proc IRE 27:584–585 Redus R, Pantazis J, Huber A, Jordanov V, Butler J, Apotovsky B (1997) Fano factor determination for CZT. Proc MRS 487:101–107 Rhoderick EH, Williams RH (1988) Metal-semiconductor contacts, 2nd edn. Clarendon Press, Oxford Ricker GR, Vallerga JV, Dabrowski AJ, Iwanczyk JS, Entine G (1982) New measurement of the fano factor of mercuric iodide. Rev Sci Instrum 53:700–701 Schlesinger TE, James RB (1995) Semiconductors for room temperature nuclear detector applications. In: Semiconductors and semimetals, vol 43. Academic Press, San Diego

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Schwartz B (1969) Ohmic contacts to semiconductors. Electrochemical Society, New York Sharma BL (1984) Metal-semiconductor schottky barrier junctions and their applications. Plenum Press, New York Shockley W (1938) Currents to conductors induced by a moving point charge. J Appl Phys 9:635– 636 Strauss AJ (1977) The physical properties of cadmium telluride (1977) Revue de Physique Appliquee 12:167–184 Sze SM (1981) Physics of semiconductor devices, 2nd edn. Wiley, New York Wang X, Xiao S, Li M, Zhang L, Cao Y, Chen Y (2013) Further process of polarization within a pixellated CdZnTe detector under intense x-ray irradiation. Nucl Instrum Methods A700:75–80

Further Reading Dearnaley G, Northrop DC (1966) Semiconductor counters for nuclear radiations, 2nd edn. Wiley, New York Deme S (1971) Semiconductor detectors for nuclear radiation measurement. Wiley, New York Hannay NB (1959) Semiconductors. Reinhold, New York Knoll GF (2010) Radiation detection and measurement, 4th edn. Wiley, New York Lutz G (1999) Semiconductor radiation detectors. Springer, Berlin Martini M, Ottaviani G (1969) Ramo’s theorem and the energy balance equations in evaluating the current pulse from semiconductor detectors. Nucl Instrum Methods 67:177–178 McKelvey JP (1966) Solid state and semiconductor physics. Academic Press, New York Nussbaum A (1962) Semiconductor device physics. Prentice Hall, Englewood Cliffs Owens A (2012) Compound semiconductor radiation detectors. CRC Press, Boca Raton Poenaru DN, Vîlcov N (1969) Measurement of nuclear radiations with semiconductor detectors. Chemical Pub, New York Taylor JM (1963) Semiconductor particle detectors. Butterworth, London

Semiconductor Radiation Detector Suppliers AmpTek-Ametek; www.amptek.com Baltic Scientific Instruments; bsi.lv/en/ Eurorad; www.eurorad.com/detectors.php Itech Instruments; www.itech-instruments.com/ Kromek; www.kromek.com/ Mirion Technologies; www.canberra.com/cbns/ Moxtek; www.moxtek.com/ Ortec-Ametek; www.ortec-online.com/ Radiation Detection Technologies, Inc.; www.radectech.com/ Radiation Monitoring Devices; dynasil.com/rmd Redlen Technologies; www.redlen.com/

Silicon Photomultipliers

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Erika Garutti

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Properties of SiPMs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SiPM Design and Static Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Doping Profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Static Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SiPM Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Signal Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Response to Low Light Intensity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Non-linear Response and Dynamic Range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SiPM Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Photo-detection Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Single-Photon Time Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Radiation Damage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

496 497 498 499 499 500 501 502 503 504 504 506 507 507 509 512 512 513 513

Abstract This chapter is intended as an introduction to a specific type of photon-sensitive device for wavelengths from infrared to near ultraviolet. The basic properties of a silicon photomultiplier are discussed, and a guideline is given on how to choose the appropriate device for a specific application.

E. Garutti () Institute of Experimental Physics, Hamburg University, Hamburg, Germany e-mail: [email protected]; [email protected] © Springer Nature Switzerland AG 2021 I. Fleck et al. (eds.), Handbook of Particle Detection and Imaging, https://doi.org/10.1007/978-3-319-93785-4_48

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Introduction Various research fields in physics, biology, medicine, and increasingly many applications in industry require the detection of single or few photons with: • • • •

wavelengths from infrared to near ultraviolet, high efficiency (more than 50%), excellent time resolution (better than 1 ns), very low noise.

A review of photo-detectors is given by P. Krizan in  Chap. 13, “Photon Detectors.” In the last 15 years, solid-state, mainly silicon-based photomultipliers, in short SiPMs, have replaced other photo-detectors in many applications. SiPMs offer numerous advantages compared to the vacuum technologies: magnetic field insensitivity, compactness, ruggedness, reliability, wide sensitivity range, largevolume production, and low cost. The simplest form of a silicon-based photo-detector is the photodiode, where photons with energy Eγ > Eg are detected via the photo-effect, Eg being the band gap energy of silicon (1.12 eV at 300 K). The photodiode is a reverse-biased p-n junction; the produced electrons and holes are collected at the n- and p-sides, respectively. The photodiode provides no internal amplification of the signal or no gain (G = 1) so that it cannot be used for single-photon detection. For this an amplification of ∼105 is required, which can be obtained either from a combination of medium gain and external electronic amplifier or entirely from the photo-detector. In silicon diodes a gain G > 105 is reached applying a reverse bias voltage above the breakdown voltage level, Vbd . One refers to this operation mode as limited Geiger mode regime. A quenching resistor Rq in series with the diode is necessary to quench the Geiger avalanche and restore the diode to the operation mode after one photon detection. The value of Rq is chosen such that the voltage drops to the level for which the avalanche is no longer self-sustained, the off-voltage Voff . A single-cell photomultiplier is often referred to as Geiger mode avalanche photodiode (GM-APD) or single-photon avalanche diode (SPAD). Arrays of SPADs with maximized fill factor and common signal output are referred to as silicon photomultipliers (SiPMs). The single SPADs in a SiPM are usually called pixels. The usual pixel density in a SiPM is 100–10000 mm−2 , and SiPM sizes between 1 × 1 mm2 and 3×3 mm2 are standard products. Larger sensitive areas are usually obtained by abutting matrices of SiPMs on a common readout board. One distinguishes analogue and digital SiPMs: In analogue SiPMs all SPADs are connected in parallel (Fig. 1); in digital SiPMs every SPAD has its separate readout electronics. This chapter is focused on analogue SiPMs, as they are used in most applications at present. Though thanks to impressive developments of microelectronics and 3D integration, digital SiPMs may well surpass in the future analogue SiPMs in many applications.

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Fig. 1 Photo of a SiPM (left). Visible are 100 pixels in 1 mm2 sensitive area. The arrows indicate photons impinging on the surface of the SiPM. Each photon triggers an avalanche in a pixel. If two photons reach the same pixel, a Geiger avalanche as for one photon is generated. Electrical representation of a SiPM as the parallel connection of Npix SPADs (right). The signal output is the sum of the signal in individual pixels. In this example four photons are counted as three times the charge generated in one Geiger avalanche. (Adapted from Hamamatsu web page)

Applications Today SiPMs are used in fields as diverse as nuclear, astro-, and particle physics, medical imaging, low light intensity detection in biology, spectroscopy, industrial and consumer technology sectors for distance measurements, and LIDAR (light detection and ranging). The future will see SiPMs implemented in many commercial products, for which dedicated optimizations are still ongoing. The magnetic field insensitivity of SiPMs enables, among other applications, the combination of magnetic resonance imaging (MRI), with positron emission tomography (PET). Integrated PET-MRI detectors are still a field of research, but may soon become commercially available. The excellent time resolution of SiPMs and the high granularity achievable with such a compact detector are also advantageous to improve PET performance with time-of-flight information. For SiPMs to be used as sensors for LIDAR applications, e.g., sensors that enable autonomous driving, the excellent time resolution and a high detection efficiency in the near infrared are necessary. First tests with SiPMs not optimized for this application already showed improvements up to 50% in the signal-to-background measurements of aerosols up to a height of 3.35 km (Riu et al. 2012). Optimized SiPMs promise further significant improvements. The development of CMOS SPADs in CMOS integrated circuits with 3D configuration Charbon et al. (2018) opens up many new applications like the selection and control of qubits for quantum computing or processors for deep learning.

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Semiconductor photomultipliers can also be made of III–V semiconductors that work in the near infrared, i.e., in the telecommunications sector. An example is SPAD matrices, which are implemented as InGaAs/InP double layers (Zhang et al. 2015). The rapid progress of long-distance quantum communication using optical fibers is closely associated with the advancement in the development of low-noise single-photon detectors. With InGaAs/InP photomultipliers already in 2004, it has been possible to reliably transfer quantum keys for more than 100 km. These photodetectors were also successfully used in an experiment of “Quantum Secret Sharing” with five partners working on a 50 km telecom network.

Properties of SiPMs Silicon photomultipliers are characterized by the following properties: Abbr. QE PT P DE DCR PCT PAP SP T R Vbd Voff G

Name Quantum efficiency

Description Probability that an incident photon generates an e-h pair Avalanche triggering Probability that a Geiger avalanche is triggered by probability a charge carrier Photo-detection Probability that a photon impinging on the detector efficiency generates a detectable signal Dark count rate Rate of signals with no photon impinging on the detector Cross-talk probability Probability of prompt (PpCT ) and delayed (PdCT ) optical cross-talk between pixels After-pulse probability Probability of signal generated by de-trapping of carriers Single-photon timing The precision of the detection of a single-photon resolution arrival time Breakdown voltage Minimum bias voltage above which carriers generate a Geiger discharge Turnoff voltage Bias voltage for which the Geiger discharge stops Gain Charge in units of electron charges

These parameters are discussed in more details in the following of this chapter. The signal of a SiPM can be directly observed on an oscilloscope, as demonstrated in Fig. 2. Here a SiPM (from Hamamatsu Photonics) is illuminated with low-intensity pulsed light, and the charge signal is amplified by a factor of 10. The response of the SiPM to one, two, three photoelectrons (converted photons in the pixels) are clearly visible and well separated. This is the single-photon counting capability of the device. The other features of the signal are explained in details in section “Noise.”

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Fig. 2 SiPM signal as observed on an oscilloscope after a factor 10 linear amplification. Taken from Hamamatsu Photonics (2019). The x-axis is time and the y-axis is voltage over a 50 Ω resistor

SiPM Design and Static Parameters The doping profile of the SPADs in a SiPM determines its breakdown voltage and P DE. The quenching resistor, Rq ; the pixel capacitance, Cpix ; and the quenching capacitance, Cq , plus the load resistor, determine the time characteristic of the SiPM signal. In this section, the static parameters of SiPMs are discussed, using an exemplary reference structure.

Doping Profile The structure of a SPAD is shown in Fig. 3. The shallow n+ implant is usually only a few hundred nanometers deep and has a very high doping concentration, ND ≈ 1018 − 1019 cm−3 . It forms an abrupt junction with the p-implant, with typical doping concentration NA ≈ 1015 − 1016 cm−3 . The low-doped π region extends few microns in depth and can be, for instance, an epitaxially grown p-layer on a p-substrate. The highly doped p+ at the back of the substrate provides the electrical contact on the anode side. With these high doping concentration, the maximum of the electric field in the abrupt junction is Emax > 3 · 105 V/cm. This is sufficiently high to induce a selfsustained multiplication of electron-hole (e-h) pairs, so that a discharge channel develops. Considering that the multiplication region thickness is of the order of one micron, more appropriate units are Emax > 30 V/μm, meaning that a voltage of about 30 V is sufficient to operate the junction in the Geiger regime. The difference between operating and off-voltage is defined excess bias voltage, or overvoltage, Vex = Vbias − Voff ≈ Vbias − Vbd . The deeper the junction is, the higher is the breakdown voltage of a SiPM. Usual values in commercial devices are between 20 and 70 V. The influence of the doping structure on the P DE is discussed in section “Photo-detection Efficiency.”

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Fig. 3 A possible implementation of the SiPM structure. Photons traverse the anti-reflecting coating (cyan) and interact in the silicon p-n junction. The average depth of the interaction depends on the photon wavelength. The junction in this example is located at 200 nm below the entrance window, and the high-field region extends to about 1 μm in depth. The quenching resistor (Rq ) and the readout aluminum grid are isolated from the silicon by a SiO2 layer. On the right side, the electric field as a function of the depth is sketched. The peak value is higher than the breakdown field (E > 300 kV/cm). Away from the junction the field drops quickly below this value. (Property of Hamburg University)

Static Parameters The extension of the high-field region of a SiPM is small compared to the pixel size, ∼1 μm versus 20–50 μm. In this case the pixel can be approximated by a parallel plate capacitor, Cpix . One quenching resistor Rq , which turns the divergent avalanche off and restores the pixel to the operation condition, is in-series with each Cpix . It may be implemented depositing by a lithographic process a poly-silicon resistive layer on top of an oxide isolation layer. The value of Rq effects the pixel recharge time, also called recovery time, τr = Cpix Rq . The larger the pixel, i.e., Cpix , and the larger the Rq , the longer the recovery time. Typical values are Cpix ≈10–1000 fF for pixel sizes from 10 to 100 μm. As an example, a pixel with Cpix = 100 fF operated at Vex = 5 V, generates a charge ΔQ = C · Vex = 0.5·10−12 C. The value of Rq can be chosen to limit the peak current of the Geiger discharge to Id < 20 μA; the signal duration is Δt = ΔQ/Id = 25 ns. In this example Rq > 250 kΩ is required. It has to be kept in mind that poly-silicon resistors are temperature-dependent, and so is the recovery time. The pixel recovery time affects the design of the readout electronics as the integration or shaping time needed to exploit the large SiPM gain depends on the duration of the signal. To obtain fast signal pulses, i.e., for fast timing applications, an additional quenching capacitor (usually Cq  Cpix ) can be added in parallel to Rq . The effect is demonstrated in Fig. 4.

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Fig. 4 Microphotographs of two SiPMs from KETEK, with (top left) 25 μm and (top right) 50 μm pixel size. The area of the p-n junction is black, (Cpix ). The green lines are lithographically deposited poly-silicon resistors (Rq ), which connect on the one side to the junction and on the other to the aluminum grid of the bias line. In the 50 μm pixel, an additional aluminum line is implemented on top of the SiO2 isolation layer to create a quenching capacitance, Cq . The bottom plots show the waveforms of each SiPM recorded on an oscilloscope with 50 Ω input impedance. The effect of Cq is the spike at the start of the pulse. (Property of Hamburg University)

SiPM Response The SiPM is a photo-detector capable of excellent single-photon detection. At the same time, it offers the possibility to measure light pulses with a large number of photons. The dynamic range of a SiPM can reach 104 photons or higher for dedicated designs, but it is strongly non-linear. In this section we discuss the principle of signal generation in a pixel; we define the gain of the SiPM and describe its response for low light intensity. Then we discuss the non-linear response for high light intensity.

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Signal Formation After a charge carrier triggers a Geiger process, an avalanche of e-h pairs is generated almost instantaneously. The spatial distribution of the avalanche can be described as a narrow micro-plasma tube. The approximation τ = d/vsat = 10−4 cm/10−7 cm/s = 10−11 s, with vsat the saturation electron velocity, indicates that the plasma tube formation takes about 10 ps. According to Knoetig et al. (2014), the lateral extension of the tube is only few micrometers. In addition to diffusion of carriers, also photons generated in the avalanche may contribute to the lateral expansion. Photons absorbed within the pixel generate a second avalanche process and thereby a second tube of current. A pixel provides the same signal charge for one or more photon interactions within the recharge time, due to the quenching mechanism. However, the presence of more than one tube may decrease the signal rise time, if Voff is not affected by the number of plasma tubes. The discharge stops when the voltage drop over the diode reaches Voff . The SiPM signal is given by the recharging of Cpix through Rq from Voff to Vbias . The electrical equivalent circuit of one pixel connected to the bias voltage is given in Fig. 5. The result is an average charge produced by an avalanche process in a pixel

Fig. 5 The equivalent electrical circuit of a single SiPM pixel connected to an external bias voltage. Rpix and Cpix are the intrinsic values of the diode resistance and capacitance. Rq is the quenching resistor and Cq the quenching capacitor often negligible compared to Cpix . An SiPM is the parallel connection of Npix times the pixel circuit. When the switch is open, Cpix is charged to Vbias . At the time of the Geiger avalanche development, the switch is closed, and Cpix discharges over Rpix , generating a current Id , which decreases exponentially. An external current Iext flows from the power supply through Rq and recharges Cpix to Vbias . Once the voltage over Cpix drops below Voff , the Geiger discharge stops (the switch opens). Iext keeps recharging Cpix through Rq with a recharge time constant τr . Note that in some papers the avalanche is modeled as a voltage or current source instead of a switch as shown here

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Qpix  = (Cpix + Cq ) (Vbias − Voff ) with a time constant τr . The charge can be expressed in units of the elementary charge using the pixel gain, Qpix  = q0 G.

Gain The gain of a SiPM is the number of secondary carriers produced in the avalanche, given one or more primary e-h pairs created in a time interval small compared to the recharge time. It is the charge signal generated by the detection of a single photon in units of the elementary charge. The gain is proportional to the sum of the pixel and the quenching capacitance: G=

1 (Cpix + Cq ) (Vbias − Voff ). q0

(1)

The turnoff voltage, Voff , does not necessarily have to be equal to Vbd , but measured differences are usually small. In most of the literature, Vbd is used in Eq. 1, without making a clear distinction between the two processes. The only paper which reports a difference of up to 1 V is Chmill et al. (2017b). Marinov et al. (2007) present a model calculation of a Geiger discharge and derive a formula for Vbd − Voff . Assuming typical values for the SiPM static parameters Cpix = 16 fF, Cq  Cpix , and Vex = 5 V, the gain is G = 16 × 10−15 F · 5 V /1.6 × 10−19 C = 5 · 105 . The linear dependence of the gain on the excess bias voltage is confirmed in Fig. 6, from Eckert et al. (2010). As expected the gain at a given excess bias voltage is larger for devices with larger pixel size, since this corresponds to larger values of the pixel capacitance. The breakdown voltage depends on temperature changes. As Vbd increases for increasing temperatures, the gain, for a fixed Vbias , decreases. Typical values for the breakdown voltage temperature dependence are dVbd /dT ≈ 20 − 50 mV/◦ C, which can be translated to a gain temperature variation using the relation: Cpix dVbd dG =− . dT q0 dT

(2)

The measured charge for one photon detected, i.e., one photoelectron, is Qpix  = q0 G in average. The spread of the measured charge forone photoelectron is given by the spread of G and the electronic noise, σ1pe = σG2 + σ02pe . The electronic noise σ0pe is measured when no photoelectron is detected. The spread of G has two components: the electric field (or excess bias voltage) distribution in a pixel and the variation of Cpix among pixels. The first, namely, the variation δVoff , usually dominates (Chmill et al. 2017b). It means that the fluctuations δQ hardly change with Vbias and the resolution of peaks improves with Vbias . The charge measured in response to Npe photoelectrons can beexpressed as : 2 = (q G σ 2 Q = q0 G Npe , with a variance σQ 0 Npe ) , and σNpe =

Npe σG2 + σ02 .

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Fig. 6 The SiPM gain dependence on the excess bias voltage for various devices with varying pixel size and therefore capacitance. (Adapted from Eckert et al. 2010)

Response to Low Light Intensity If the SiPM is illuminated by low intensity light and the charge is integrated over a time longer than the SiPM recovery time, the signal exhibits the characteristic photoelectron spectrum, shown in Fig. 7. For the determination of the SiPM gain, the single peaks of the low intensity light spectrum are approximated by Gaussian functions, as indicated in Fig. 7. This simplification does not take into account the delayed correlated noise. Using a more complex model as described by Chmill et al. (2017a) allows to fit simultaneously G, DCR, cross-talk and after-pulsing probability, the average number of photons initiating a Geiger discharge, as well as the electronic noise and the gain fluctuations between and in pixels. For a high number of detected photons, the photoelectron peaks are smeared out by statistical fluctuations and by the noise sources; therefore, they are not anymore well separated. Note that to profit from the high SiPM gain, the readout electronics has to be correctly designed to match the signal shape.

Non-linear Response and Dynamic Range A large dynamic range from single to several thousands of photons is often a requirement in SiPM applications, e.g., in calorimetry. The SiPM response for high

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Fig. 7 (Left) Photoelectron spectrum of a SiPM illuminated with low light intensity. The number of counts is plotted against the normalized integrated charge (SiPM gain). Every peak corresponds to a certain number of fired pixels, e.g., 0th peak; pedestal; 1st peak, 1 photon detected; etc. (right) Same spectrum in logarithmic scale. The data (blue histograms) are fitted with a multi-Gaussian function (solid cyan line) and with the model described by Chmill et al. (2017a) (solid red line). (Property of Hamburg University, courtesy of T. Lösche)

light intensity is non-linear and limited by the number of pixels of the device. A precise knowledge of the response function is crucial for energy measurements. The knowledge of the total number of pixels of a device is not sufficient to extract its response function. A major complication is that all the nuisance parameters discussed in section “Noise” affect the dynamic range. If pixels are discharging by noise, they are not sensitive for photon detection. In addition, more than one discharge can be detected in the same pixel, if the light pulse is extended over a time comparable to the pixel recharging time. Therefore, the dynamic range also depends on the time distribution of the photons. The naive formula

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Fig. 8 Non-linear response of various SiPMs using amplitude measurements, adapted from Gruber et al. (2014). Light from a laser with a wavelength of 404 nm and a pulse width of 32 ps has been used. In all cases a significant excess of the number of measured Geiger discharges above the number of pixels in the SiPM, Npix , is seen

Nsat Q = q0 Npix G Npix

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lin  0 sat G

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can be used for the approximation of the response of an SiPM with Npix pixels. The average charge, Qlin , is calibrated for low light intensity assuming Qlin  = Q. The effective number of pixels measured in saturation is usually Nsat > Npix for fast recovery times. Exemplary response functions from various SiPMs are shown in Fig. 8. The response is clearly non-linear over the entire range. Furthermore, it does not saturate at the number of pixels, Npix , but the dynamic range is extended by almost a factor of 2 in some cases. More work is required to reach a complete understanding and modeling of the SiPM response. A review of experimental methods to measure the SiPM response function can be found in Klanner (2019).

SiPM Performance The key requirements for a SiPM are spelled out in the introduction: sensitivity to wavelengths from infrared to near ultraviolet, high efficiency, excellent time resolution, and very low noise. This section explains which SIPM parameters effect the performance in each of these point.

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Photo-detection Efficiency Two basic limitations restrict the sensitivity range of SiPMs. Photons must have an energy larger than Eg , i.e., λ < 1050 nm, to be detected. The minimum wavelength is given by the thickness of the insensitive layer on the surface of the sensor. This depends on the thickness of the anti-reflecting coating and of the undepleted implant near the surface. Figure 3 presents a possible design of a SPAD. The peak of the electric field is at the n+ p-junction. Within the sensitive wavelength range, the photo-detection efficiency can be optimized for a given application by adjusting the peak sensitivity to a specific wavelength. SiPMs are single-photon counting devices, but the probability for a single photon to generate a detectable signal is well below 100%. The photo-detection efficiency, PDE, is described by the product of three factors: P DE(V , λ) = F F · QE(λ) · PT (V , λ).

(4)

The fill factor, F F , is the ratio of active-to-total area in the pixel. It is larger for large pixel size. The wavelength dependence of the quantum efficiency, QE, is explained in Fig. 9. The avalanche triggering probability PT strongly depends on the electric field. In the high-field region, PT has its maximum and falls quickly to zero elsewhere. This is due to the strong field dependence of the impact ionization rates, the average rate of secondary e-h pairs generated by impact ionization per unit of distance traveled by an electron or a hole. Additionally, electrons have higher ionization rate than holes; therefore, electrons crossing the high-field region have a higher PT than holes. This fact can be used to optimize the SiPM design for a specific wavelength range. So, for example, the two designs presented in Fig. 10 are tuned for visible (RGB-HD) or for near-UV (NUV-HD) light detection. More details on the optimization can be found in Acerbi et al. (2019). A more complete overview on the technology of modern SiPMs and the implication on their parameters can be found in Piemonte and Gola (2019). As demonstrated in Fig. 10, SiPMs can reach a P DE ≥ 50%. For a given design and wavelength, the P DE is larger for large pixel size, i.e., larger F F , and larger excess bias voltage.

Single-Photon Time Resolution SiPMs are ideal photo-detectors for fast timing applications. Their timing performance is evaluated with the single-photon timing resolution, or SPTR, i.e., the precision of the arrival time for single-photon determination. The SPTR depends on the SiPM parameters and by the readout electronics. The measured arrival time of photons has a main Gaussian distribution, with tails due to instrumental effects. The sources of Gaussian fluctuations are:

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λ=

hc Eg

Fig. 9 Photo-detection efficiency versus photon wavelength. The F F reduces the ideal value of 100% PDE by a constant factor. The QE introduces a wavelength dependence, which reduces the P DE to zero outside of the sensitivity range. The PT further reduces the P DE and introduces an additional voltage dependence, due to the strong electric field dependence of the impact ionization rates of electrons and holes. (Property of Hamburg University)

Fig. 10 Photo-detection efficiency optimized for different wavelengths and the corresponding SPAD designs. The P DE increases with excess bias voltage (indicated in the plots). The absorption length of near-ultraviolet (NUV) light is only about 0.1 μm. The e-h pairs are created close the surface. For the p+ n diode, the electric field in high-field region points in the direction of the p+ -doping. The avalanches are triggered by e generated inside the p+ implant and drifting to the n+ implant. For red, green, blue (RGB) photons (450 < λ < 780 nm), the absorption length is 0.5 < λabs < 3 μm, comparable to the depth of the high-field region. The highest P DE is for the n+ p design, when the electric field points toward the epi-layer so that again electrons trigger the discharge. (Reprinted with permission of Acerbi et al. 2019)

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• timing jitter of the avalanche build-up (Spinelli and Lacaita 1997); • non-uniformity of the electric field within a SPAD and among SPADs; • time spread in the charge collection from the absorption point to the high-field region; • time delay dependent on pixel position on SiPM; • time jitter caused by front-end electronic noise (Acerbi et al. 2014). The first three points are related to the design of a single SPAD and should be optimized in the design phase. The spread due to the SiPM size increases for larger SiPMs. Values of SPTR of about 40 ps FWHM are reported by Tosi et al. (2014) for a single SPAD, whereas a 3×3 mm2 SiPM with the same SPAD layout reached a SPTR of 180 ps. As a guideline, the time resolution improves for smaller SiPMs; for smaller pixel size, i.e., smaller pixel capacitance; and for higher gain. In the optimization of system for fast timing, the front-end electronics must be designed appropriately to minimize jitter.

Noise In the absence of an external source of photons, processes other than photoabsorption can also contribute to the creation of e-h pairs in silicon. One distinguishes between uncorrelated and correlated noise sources. Once an e-h pair is produced, it can undergo the same avalanche formation process and produce exactly the same output signal as a photon detected. The SiPM noise is often quoted as rate of events generated by noise sources, since each event contributed the same charge. As we will see, this statement is not always correct for delayed noise.

Dark Count Rate The processes responsible for uncorrelated or dark noise are thermal generation and band-to-band tunneling excitation (Fig. 11). Also diffusion from the undepleted regions below and above the high-field region may contribute to DCR, but this process is usually suppressed by design. The thermal energy of a charge carrier at room temperature (kT = 25 meV) is considerably smaller than the band gap energy. The thermal generation is determined by states in the band gap or by crystal defects (traps). Well below the breakdown field, the thermal generation rate of carriers by states in the band gap can be modeled using Shockley-Read-Hall (SRH) statistics, Sze and Ng (2006), and can be approximated as: Ea

DCRth ∝ T 2 e− kT

(5)

For the activation energy, Ea a value of 0.605 eV is found by Chilingarov (2013). From the exponential dependence, one sees that the thermal noise approximately doubles for an increase in temperature of eight degrees. Cooling significantly reduces thermal generation.

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Fig. 11 Sketch of the two main processes contributing to dark noise in a SiPM. Left) thermal generation. Right) band-to-band tunneling excitation. Electrons in the valence band (EV ) are excited to the conduction band (EC ), either via thermal energy or via tunneling effects. The presence of impurities in the depleted region enhances these processes by reducing the energy required for the transition. (Property of Hamburg University)

The second effect contributing to DCR is the excitation of charge carriers induced by the electric field, in short “tunneling.” Electrons can be described by their wave function giving them a certain probability for tunneling through the band gap to a state in the conduction band with the same energy. For high electric field strengths, direct band-to-band tunneling contributes to the generation of e-h pairs, as reported by Hurkx et al. (1992). Also the generation due to defects in the depletion region is enhanced by a high electric field leading to the mechanism of trap-assisted tunneling, or Poole-Frenkel effect. Tunneling effects increase with the increase of the electric field, or applied voltage, and cannot be reduced by cooling. The only temperature dependence of tunneling effects is introduced by the variation of the band gap. Which of these effects dominates the primary noise depends on the characteristic doping profile, the operating voltage of the SiPM, as well as the operating temperature. SRH and field-enhanced SRH generation can be significantly reduced by cooling. Finally tunneling remains as only noise source at low temperature. In modern SiPMs the DCR is below 500 kHz/mm2 at room temperature to a few kHz/mm2 at −20◦ C. A dark noise pulse produces a charge Q = q0 G. The probability of two pixels to be simultaneously fired by the processes described above is negligible, though noise with charge Q = q0 G n (with usually n < 5) is also observed. The effect responsible for this is discussed next.

Correlated Noise In addition to primary DCR, SiPM noise can also be triggered as a consequence of the avalanche development in a pixel. These correlated noise events develop with the same process as a primary avalanche, but have a different origin. Sources of correlated noise are optical cross-talk and after-pulsing.

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Fig. 12 Cross section of a SiPM without trenches for optical isolation (Reprinted with permission of Acerbi et al. 2019). Different sources or correlated noise are indicated: direct or prompt cross-talk (DiCT occurring with a probability PpCT ), delayed cross-talk (DeCT occurring with a probability PdCT ), and after-pulse due to electron diffusion from the undepleted region (APdiff occurring with a probability PAP ). Prompt cross-talk can also occur if a photon generated within an avalanche reaches the neighbor pixel via external optical paths, i.e., reflections on the package material

Optical cross-talk between pixels occurs if a photon generated within the photons are produced per one charge carrier crossing the junction. But contradicting numbers were also reported by Mirzoyan et al. (2009). Also the production mechanism of these photons is not completely certain; they may be consequence of Bremsstrahlung or of e-h recombination. Optical cross-talk can furthermore be instantaneous or delayed. Figure 12 summarized the various possibilities for a photon to reach a neighboring pixel. Prompt cross-talk yields an instantaneous avalanche in a different pixel than the one with the primary avalanche, adding the same total charge as a primary event. A delayed cross-talk, where the photon creates a e-h pair in the non-depleted region, may be only partially integrated by the readout electronics, yielding smaller charge. Optical tranches between pixels can be etched in the fabrication process. They can be as deep as few μm. This technique is very effective to stop direct photon propagation in the depleted volume, but cannot prevent neither the reflection on the surface nor the delayed cross-talk process. Typical cross-talk values for SiPMs without trenches are between 5 and 30% with a strong dependence on the excess bias voltage, i.e., on the number of electron-hole pairs produced in the avalanche. Devices with trenches have in standard operation conditions optical cross-talk below 2–3% and maintain values below 10% even for an excess bias voltage above 5 V. Cross-talk reduces for larger pixel size (Eckert et al. 2010), as photons with longer absorption length are required to reach into neighbor pixels. The second source of correlated noise is after-pulsing. Carriers generated in the high-field region during the avalanche may be trapped by trapping centers (defects

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in the silicon lattice) and re-emitted after a given trapping time. After-pulse events occur in the same pixel as the primary. After an avalanche the voltage in the pixel is reduced to the breakdown value and the gain is zero. During the recovery the pixel voltage increases to the bias voltage; thus, the gain in the pixel increases with time after the primary discharge. Therefore, the charge produced by an after-pulsing event is dependent on its time difference to the primary event. After-pulsing can be minimized by minimizing the impurities/defects in silicon. Irradiation of SiPMs by charged particles generates defects in the band gap and increases the after-pulsing effect. Both cross-talk and after-pulse increase for increasing gain, as more photons and more carriers, which can be trapped, are generated in the avalanche.

Radiation Damage As SiPMs detect single charge carriers, radiation damage is a major concern when operating these devices in harsh radiation environments. Most of the experiments at lepton colliders or at lower energy machines as well as detectors for space and medical applications will receive fluences below 1012 particles/cm2 throughout their lifetime. New detectors for the upgrade of the Large Hadron Collider experiments or for proposed future colliders demand the operation of SiPMs up to fluences of ∼1014 particles/cm2 . The most critical effect of radiation on SiPMs is the increase of dark count rate, which makes it impossible to resolve signals generated by a single photon from the noise. Due to the increased DCR, the single photoelectron separation from noise is lost already at relatively low fluences Φeq ∼ 1010 cm−2 . This limit depends on many factors related to the SiPM design and the operation conditions, so it should be tested for each specific application. The DCR also affects the pixel occupancy, which if no longer negligible leads to a P DE reduction. Once single photoelectrons can no longer be resolved, many characterization methods used for the investigation of nonirradiated SiPM parameters fail. Some recently developed characterization methods are presented by Garutti and Musienko (2019). An optimization of the SiPM design for operation in high radiation environment is not yet available and lacks dedicated experimental input. Further effort in this field is strongly encouraged.

Conclusion Silicon photomultipliers are well-established, robust and relatively cheap, photoncounting detectors. Their photon detection efficiency can exceed 50% in a wide wavelength interval; they count single photons with a time resolution in the 20 ps (FWHM) range, operate at voltages of a few tens of volts, are insensitive to magnetic fields, are robust, and do not deteriorate, even if exposed to strong light intensity. However, their size is limited to about 40 mm2 , their dynamic range is limited by the number of pixels, and they have dark count rates of tens to

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Fig. 13 Optimal parameter space for SiPM performance as a function of pixel size and number of pixels per unit of area of an SiPM. (Property of Hamburg University)

hundreds of kHz/mm2 at room temperature. Their photon-counting resolution is influenced by optical cross-talk and after-pulsing. Thanks to intensive research and development, it was possible to substantially improve their key characteristics over the past years. Given their excellent performance, they now replace vacuum photomultipliers in many applications. Figure 13 attempts to summarize the scaling of the key SiPM performance parameters with number of pixels and pixel size. Best timing resolutions can be achieved with small pixel sizes and small overall SiPM dimension. Conversely to obtain the highest detection efficiency, a large pixel size with reduced fill factor is preferable. A large dynamic range requires a large number of small pixels per unit of area; on the contrary, noise can be reduced by reducing the number (less primary noise) and increasing the size (less crosstalk) of pixels. As one can see, these requirements are often conflicting, and users will need to accept compromises in performance when optimizing for a specific application.

Cross-References  Photon Detectors

References Acerbi F, Ferri A, Gola A, Cazzanelli M, Pavesi L, Zorzi N, Piemonte C (2014) Characterization of single-photon time resolution: from single spad to silicon photomultiplier. IEEE Trans Nucl Sci 61(5):2678–2686. https://doi.org/10.1109/TNS.2014.2347131 Acerbi F, Paternoster G, Capasso M, Marcante M, Mazzi A, Regazzoni V, Zorzi N, Gola A (2019) Silicon photomultipliers: technology optimizations for ultraviolet, visible and near-infrared range. Instruments 3(1):15. https://doi.org/10.3390/instruments3010015 Charbon E, Bruschini C, Lee MJ (2018) 3d-stacked cmos spad image sensors: technology and applications. In: 2018 25th IEEE international conference on electronics, circuits and systems (ICECS). https://doi.org/10.1109/ICECS.2018.8617983

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Chilingarov A (2013) Temperature dependence of the current generated in Si bulk. JINST 8(10):P10003 Chmill V, Garutti E, Klanner R, Nitschke M, Schwandt J (2017a) On the characterisation of SiPMs from pulse-height spectra. Nucl Instrum Meth A 854:70–81. https://doi.org/10.1016/j. nima.2017.02.049, 1609.01181 Chmill V, Garutti E, Klanner R, Nitschke M, Schwandt J (2017b) Study of the breakdown voltage of SiPMs. Nucl Instrum Meth A 845:56–59. https://doi.org/10.1016/j.nima.2016.04.047 Eckert P, Schultz-Coulon HC, Shen W, Stamen R, Tadday A (2010) Characterisation studies of silicon photomultipliers. Nucl Instrum Meth A 620(2):217–226. https://doi.org/10.1016/j.nima. 2010.03.169 Garutti E, Musienko Y (2019) Radiation damage of SiPMs. Nucl Instrum Meth A 926:69–84. https://doi.org/10.1016/j.nima.2018.10.191, 1809.06361 Gruber L, Brunner S, Marton J, Suzuki K (2014) Over saturation behavior of sipms at high photon exposure. Nucl Instrum Meth A 737:11–18. https://doi.org/10.1016/j.nima.2013.11.013 Hamamatsu Photonics (2019) Multi-pixel photon counters. https://www.hamamatsu.com/eu/en/ product/optical-sensors/mppc/index.html Hurkx G, Klaassen D, Knuvers M (1992) A new recombination model for device simulation including tunneling. IEEE Trans Nucl Sci 39(2):331–338. https://doi.org/10.1109/16.121690 Klanner R (2019) Characterisation of sipms. Nucl Instrum Meth A 926:36–56. https://doi. org/10.1016/j.nima.2018.11.083, silicon Photomultipliers: Technology, Characterisation and Applications Knoetig M, Hose J, Mirzoyan R (2014) SiPM avalanche size and crosstalk measurements with light emission microscopy. IEEE Trans Electron Devices 61:1488–1492. https://doi.org/10. 1109/TNS.2014.2322957 Marinov O, Dean JJ, Jimenez Tejada J (2007) Theory of microplasma fluctuations and noise in silicon diode in avalanche breakdown. J Appl Phys 101:064515. https://doi.org/10.1063/1. 2654973 Mirzoyan R, Kosyra R, Moser HG (2009) Light emission in si avalanches. Nucl Instrum Meth A 610(1):98–100. https://doi.org/10.1016/j.nima.2009.05.081, new Developments In Photodetection NDIP08 Piemonte C, Gola A (2019) Overview on the main parameters and technology of modern silicon photomultipliers. Nucl Instrum Meth A 926:2–15. https://doi.org/10.1016/j.nima.2018.11.119, silicon Photomultipliers: Technology, Characterisation and Applications Riu J, Sicard M, Royo S, Comerón A (2012) Silicon photomultiplier detector for atmospheric lidar applications. Opt Lett 37(7):1229–1231. https://doi.org/10.1364/OL.37.001229 Spinelli A, Lacaita A (1997) Physics and numerical simulation of single photon avalanche diodes. IEEE Trans Electron Devices 44:1931–1943. https://doi.org/10.1109/16.641363 Sze SM, Ng KK (2006) Physics of semiconductor devices. Wiley, Hoboken. https://doi.org/10. 1002/0470068329 Tosi A, Calandri N, Sanzaro M, Acerbi F (2014) Low-noise, low-jitter, high detection efficiency InGaAs/InP single-photon avalanche diode. IEEE J Sel Top Quantum Electron 20(6):192–197. https://doi.org/10.1109/JSTQE.2014.2328440 Zhang J, Itzler MA, Zbinden H, Pan JW (2015) Advances in ingaas/inp single-photon detector systems for quantum communication. Light Sci Appl 4(e):286

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Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Detector Response Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gamma-Ray Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gamma-Ray and x Ray Spectral Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Spectral Response Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Qualitative Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Quantitative Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Area Under an Isolated Peak . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Model Fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . General Linear Least-Squares Model Fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nonlinear Least-Squares Model Fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Spectrum Stripping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Library Least-Squares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Symbolic Monte Carlo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Compton Suppression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . More About Spectroscopy Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Channel Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Spectroscopy Quality Metrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Detectors for Gamma-Ray Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Scintillation Spectrometers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Semiconductor Spectrometers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cryogenic Spectrometers (Microcalorimeters) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Crystal Diffractometers (Wavelength-Dispersive Spectroscopy) . . . . . . . . . . . . . . . . . . . . .

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W. L. Dunn · J. K. Shultis Mechanical and Nuclear Engineering, Kansas State University, Manhattan, KS, USA e-mail: [email protected]; [email protected] D. S. McGregor () Semiconductor Materials and Radiological Technologies Laboratory, Mechanical and Nuclear Engineering, Kansas State University, Manhattan, KS, USA e-mail: [email protected] © Springer Nature Switzerland AG 2021 I. Fleck et al. (eds.), Handbook of Particle Detection and Imaging, https://doi.org/10.1007/978-3-319-93785-4_17

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Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Radiation Spectrometer Suppliers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract The common methods of analyzing gamma-ray spectra obtained from detectors capable of energy discrimination are discussed. Gamma-ray spectra generally are in the form of detector response versus discrete channel number. The methods considered for gamma-ray spectroscopy are somewhat general and can be applied to other types of spectroscopy. The general objective of spectroscopy is to obtain, at a minimum, the qualitative identification of the source (e.g., source energies or radionuclides present). However, most spectroscopy applications seek quantitative information also, as expressed by, e.g., the source strength or the radionuclide concentration. Various methods for qualitative and quantitative analysis are summarized, and illustrative examples are provided. A review of detectors used for gamma-ray spectroscopy is included.

Nomenclature Most of the symbols used in this chapter are briefly identified here. More complete descriptions of the symbols are provided within the text. A Aes Aj Ap b(h) bn B(n) c c(n) C(n) Ch d  E Ebs E Ed Ees Ej

source activity escape peak counts net peak counts peak counts background density function background counts in channel n background in channel n speed of light response rate function response cumulative function heat capacity spacing between crystal planes channel width photon energy backscatter photon energy apparent energy energy deposited in detector escape peak energy j th discrete energy emitted by source

18 Gamma-Ray Spectroscopy

Ep es I peak ηrel f F FWHM g G h h0  j j J k k K λ M me m μe,h n˜ n N n˜ n No ν ξk ξe,h PCR PVR PTR q Q Qo R R(h) r(h) Rn (E) R(h|E) s(E)

peak energy escape peak efficiency total intrinsic efficiency peak efficiency HPGe relative efficiency function that relates h to Ed Fano factor Sj full width at half maximum Gaussian density function dynode gain pulse height centroid of pulse-height peak detector efficiency subscript for discrete energy subscript for discrete energy number of discrete energies subscript for nuclide Boltzmann’s constant number of nuclides photon wavelength subset of N electron rest mass number of overlapping peaks charge mobility (electrons, holes) continuous channel number discrete channel number number of channels continuous channel number discrete channel number initial number of charge pairs number of degrees of freedom nuclide concentration carrier extraction factor peak-to-Compton ratio peak-to-valley ratio peak-to-total ratio unit electronic charge total induced charge initial excited charge detector resolution cumulative counts with pulse height < h count rate with pulses about h detector response function detector response kernel source density function

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sc sj Ej σ Tcs Tpe t T T τe,h u ve,h w Wn Wd χν2 y z Xk

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continuum emission rate emission rate at energy emission rate over time T standard deviation Compton electron kinetic energy photoelectron kinetic energy live time counting time absolute temperature charge carrier lifetime detector response function charge carrier velocity average ionization energy weight factor detector width reduced chi-square function response model composite detector kernel basis vector

Introduction Gamma rays and x rays are photons of electromagnetic radiation that are capable of causing ionization. Technically, x rays differ from gamma rays in their source of origin, but for practical purposes, this is irrelevant, and photon spectra can be analyzed by the same methods whether the source photons are x rays or gamma rays. As a practical matter, photons of energy less than about 10 keV are difficult to detect because they are easily absorbed by the detector housing. The concepts that are discussed here can be applied, in principle, to spectra from photons of energy less than 10 keV and also to spectra generated by other particles, such as electrons. For instance, x-ray photoelectron spectroscopy (XPS) and electron scattering for chemical analysis (ESCA) lead to electron spectra that can be analyzed by the methods discussed here. Thus, it is understood that reference to “gamma-ray spectroscopy” is an oversimplification and many of the methods discussed here can be applied to spectra generated by x rays, gamma rays, or other types of radiation. Gamma-ray spectroscopy is a general area of study within which spectra are analyzed in order to determine qualitative and, if possible, quantitative information about a sample under investigation. Spectra generally refer to collections of data for which the independent variable is channel number (or a related quantity such as pulse height, energy, or wavelength) and the dependent variable is a detector response that depends on the independent variable. Spectra are generated in various processes, such as energy-dispersive x ray fluorescence (EDXRF), neutron activation analysis (NAA), prompt gamma neutron activation analysis (PGNAA), XPS, and general counting of unknown radioactive sources. Often, spectroscopy

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is directed at the quantitative objective of identifying concentrations of specific elements or isotopes (henceforth, the generic term “nuclides” is used) that are present in samples, but it also can be employed in a qualitative manner to identify whether specific gamma-ray-emitting nuclides, such as those in special nuclear materials, are present in samples. In general, a sample that is under investigation emits photons whose energies are characteristic of the nuclides present in the sample. The photons may be excited by an external source or the sample may emit these photons spontaneously. A careful spectroscopic investigation generally seeks to determine either the energies emitted and their intensities or the nuclides present and their concentrations. In the remainder of this chapter, attention is given to photon spectra that are generated from samples interrogated by any of a number of means, active or passive, to determine information about the constituents of the sample. Much of the material presented here is extracted from McGregor and Shultis (2020).

Basic Concepts Many photon detectors can produce responses that are proportional to the energy deposited in the detector. These include proportional counters, scintillation detectors, and semiconductor detectors. Regardless of the detector, a voltage pulse is created whose amplitude h, generally called the pulse height, is a function of the energy deposited Ed in the detector, i.e., h = f (Ed ),

(1)

where f is some function. For many detectors, f is linear and h = α + βEd ,

(2)

where α and β are constants unique to a detector. However, scintillation detectors, in particular, can exhibit nonlinearities, especially at low photon energies, and this nonlinearity should be taken into account. Linearity of a detector is often expressed in terms of the pulse height per unit energy as a function of the deposition energy, a quantity which is constant for a linear detector. In any event, a good spectroscopist should know f, the functional relationship between pulse height and deposited energy, for any spectroscopic detector used. In gamma spectroscopy, the pulse height h is measured, and the deposited energy Ed is obtained by inversion of Eq. (1), namely, Ed = f −1 (h), or if the spectrometer is linear, then

(3)

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Ed =

h−α . β

(4)

Moreover, the pulse heights produced by repeated deposition of energy Ed in a detector are not exactly the same; rather, they are distributed about a mean value h0 = f (Ed ) by some kernel g(h|Ed ) such that g(h|Ed )dh is the probability an event that deposits energy Ed in the detector results in a pulse with an amplitude in dh about h. In gamma-ray spectroscopy, this spreading kernel has a shape similar to a Gaussian shape although, in practice, it is usually skewed slightly toward lower amplitudes as a consequence of different collection times of charge carriers produced in different regions of the detector and the different amount of recombination and trapping they experience as they are collected. Shallow angle Compton scattering also contributes slightly to this asymmetry. An example of this amplitude kernel for an HPGe detector is shown in Fig. 1. In effect, the detector systems that produce the voltage pulses operate on the energy deposited Ed with an energy kernel z(Ed , E  ) that transforms Ed into a range of “apparent” energies E  , which are centered on Ed . The resolution of a spectrometer is determined by the degree to which pulse amplitudes are spread out around h0 or around Ed and is quantified by the full width at half maximum (FWHM) either as a percent or in energy units. Often the amplitude spreading kernel is approximated by the Gaussian probability distribution g(h|h0 , σ ) = √

1 2π σ

exp[−(h − h0 )2 /(2σ 2 )],

(5)

g(h|Ed )

Fig. 1 A pulse-height spreading kernel for an HPGe detector as measured for the 1173-keV 60 Co gamma ray [IEEE-325 1996]. Note the peak is not quite symmetric about the centroid hmax

FWHM

h0

h

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where h0 is the mean value or centroid and σ is the standard deviation. The √ peak value of the Gaussian PDF occurs at the centroid and is given by g = 1/( 2π σ ). max √ Note that for a Gaussian distribution FWHM = 2 2 ln 2σ  2.355σ . It is worth noting that the energy resolution of semiconductor detectors is, in general, significantly better than that for scintillation detectors or proportional counters. McGregor (2016) gives a good comparative description of the resolution of various detector types. Each type of detector has its advantages and disadvantages. Several chapters in this book on the various detector types provide useful information on the characteristics of each type of detector. The pulse heights are scaled to be within a finite interval [hmin , hmax ]. Typically, these limits are hmin = 0 and hmax = 10 V. In any case, the variables Ed and h are continuous variables. Whatever the pulse-height limits are, the response of a detector is typically binned into discrete “channels.” If n denotes an individual discrete (integral) channel number and N is the total number of channels, then the channel width is =

hmax − hmin . N

The channel numbers are related to the detected magnitudes of the voltage pulses (pulse heights) by the relations n = 1, if hmin < h ≤ hmin +  = 2, if hmin +  < h ≤ hmin + 2 .. . = N, if hmin + (N − 1) < h ≤ hmin + N.

(6)

Thus, the measured continuous pulse heights are converted into discrete channels, and each pulse registers a count in one and only one channel. NIM multichannel analyzer systems confine voltage signals or pulse heights to be within 0–10 volts. Hence, a binary system may be subdivided with 2N voltage bins over the 10-volt range. For N = 10, there are 1024 bins, or channels, over the 10-volt range having, in this case, 9.8 × 10−3 volts per channel. Typical spectroscopic systems now often operate with N = 13 where 213 = 8,192 channels, with some having N = 14, or 16,384 channels. Although there are a finite number of discrete channels, corresponding to the pulse-height intervals specified in Eq. (6), the peak centroid can occur at any continuous value of h. Thus, it is customary to specify a linear relationship between the continuous values of h and a continuous channel number n, ˜ given by n˜ =

h − hmin , 

(7)

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which varies continuously between 0 and N. Henceforth, the term channel number is used to mean either the discrete integer channel number n or the continuous channel number n; ˜ the context can be used to infer the intent.

Detector Response Models Consider a source that emits photons at a rate with some energy distribution s(E) and a spectrometer that detects the photons and produces a pulse-height spectrum. The basic spectroscopic relationship in its continuous form can be written r(h) =

dR(h) = dh



∞

s(E)R(h|E)dE + b(h),

h ∈ [hmin , hmax ],

(8)

0

where • r(h) is the detector response such that r(h)dh is the expected number of counts within dh about h per unit time. • s(E) is the source strength, in photons per unit time, such that s(E)dE is the number of source photons emitted within dE about E. • R(h|E) is the detector response kernel such that R(h|E)dh gives the probability that a particle of energy E interacting in the detector produces a pulse whose height is within dh about h. Here, R(h|E) = p(E, Ed )g(h|Ed ) where p(E, Ed )dEd is the probability that a source gamma ray of energy E interacts in the detector and deposits an energy in dEd about Ed in the detector. • b(h) is the background count rate such that b(h)dh is the expected number of counts within dh about h, per unit time, that are due to background radiation. h Note that R(h) = 0 r(h )dh is the cumulative number of counts per unit time due h to pulses whose heights are less than h and that R(h2 ) − R(h1 ) = h12 r(h)dh is the total number of counts, per unit time, whose pulse heights are between h1 and h2 . Note also that R(h|E)dh accounts for the probability of transport of source photons to and within the detector, deposition of energy Ed in the detector, and spreading of the deposited energy into an apparent energy E  that produces a pulse whose pulse height is within dh about h. In general, a source can emit photons at J discrete energies and also over a continuum of energies. For such sources s(E) =

J 

sj δ(E − Ej ) + sc (E),

(9)

j =1

where sj is the emission rate of photons of energy Ej from the source, δ(E − Ej ) is the Dirac delta function, and sc (E) is the source emission rate of the photons with a continuum of energies such that sc (E)dE is the expected number of photons emitted

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within dE about E per unit time. For a detector that sorts counts into discrete channels, one can substitute Eq. (9) into Eq. (8), integrate over each channel width, and write the discrete form of the pulse-height spectrum in the form c(n) =

J 



∞

sj Rn (Ej ) +

sc (E)Rn (E)dE + bn ,

n = 1, 2, . . . , N,

(10)

0

j =1

where c(n) is the count rate recorded in channel n, bn is the expected background radiation count rate recorded in channel n, and Rn (E) is the detector response function that is the probability that a particle of initial energy E that is emitted by the source produces a count within the nth channel. Here  Rn (E) =

n

R(h|E) dh.

(n−1)

In general, spectra are accumulated over a counting time T , in order to increase the number of recorded counts and, hence, improve the statistical precision of the measurements. In this chapter, it is assumed that the source strength S(E) is constant in time. If the photon source is from the decay of a radionuclide, then the measurement time T must be much less than the half-life of the radionuclide; otherwise, corrections must be made to correct for the decrease in photon emission rate. The total counts obtained over counting time T per channel can be obtained by integrating Eq. (10) over the counting time. The continuum source term can be due to photons emitted from the source over a continuum of energies and/or to photons emitted at discrete energies from the source that scatter into the detector from material around the detector. Because the primary objective of spectroscopy is to find the Ej and sj , for j = 1, 2, . . . , J , it is customary to combine the continuum and background terms into a generalized background. Doing so and integrating over the counting time T , corrected for dead time effects, one obtains

C(n) =

J 

Sj Rn (Ej ) + B(n),

n = 1, 2, . . . , N,

(11)

j =1

where C(n) ≡ Cn = c(n)T is the detector response in channel n, Sj = sj T , and 

∞

B(n) =

 sc (E)Rn (E)dE + b(n) T .

(12)

0

A plot of C(n) versus n is called a pulse-height spectrum. Summation over any range of channels gives the total counts within those channels.

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Equation (11) describes an inverse problem, in which the specific Ej and Sj , j = 1, 2, . . . , J are sought given J ≤ N measured pulse-height responses C(n). The generalized background Bn is typically not known explicitly and, thus, further complicates the inversion process. There are different methods that can be used to approach this inverse problem, and the number M of channels, M ≤ N, used depends on the method chosen. Because most spectrometers have thousands of channels, most spectroscopy inverse problems are overdetermined in the sense that there are considerably more responses available than unknowns. It is noted that a variant of this inverse problem often is posed in terms of the k = 1, 2, . . . , K nuclides present in a sample, each of which can emit photons at one or more discrete energies. Rather than look for the J discrete energies and their intensities, one looks for the K nuclides and their concentrations. The form of this inverse problem is similar to the form of Eq. (11) and is defined later more precisely by Eq. (53).

Gamma-Ray Spectroscopy

Frequency C(E)

Suppose that the energy deposition in the detector is that shown in Fig. 2. A simple counter records events in the detector that produced a signal exceeding the lower (a)

Energy

Counts

integral pulse height spectrum

LLD

Ei Ei+1

Energy

C(n i)

Ei Ei+1 energy distribution

(b)

(c) differential pulse height spectrum

Channel Number

Fig. 2 Shown in (a) is the continuous energy distribution recorded with a radiation spectrometer. If a counter is connected to the detector, shown in (b) is the resulting count rate as a function of the lower-level discriminator setting, called the integral pulse-height spectrum, superimposed on the radiation energy distribution. Shown in (c) is the resulting discrete differential pulse-height spectrum from (b). Copyright (2020). From Radiation Detection: Concepts, Methods and Devices by D.S. McGregor and J.K. Shultis. Reproduced by permission of Taylor and Francis Group, LLC, a division of Informa PLC

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level discriminator (LLD). In the hypothetical case with no electronic noise or background, all events interacting in the detector within measurement time T are recorded if the LLD is set to zero. As the LLD is increased, those lower-energy events in Fig. 2a are excluded from the measured count rate, and the total number of recorded counts within time T decreases. This function can be plotted as shown in Fig. 2b, where the total integrated counts above the energy equivalent LLD setting are plotted as a function of LLD setting. This plot is called the integral pulse-height spectrum. There are notable features in the integral pulse-height curve that can be interpreted as follows: Flatter features indicate energy regions where few events appear, usually from valleys in the energy spectrum. Steeper features indicate energy regions where many counts are located and produce a large change in counts as a function of LLD, often caused by energy maxima or peaks in the energy spectrum. Although an experienced spectroscopist might be able to interpret the data of an integral pulse-height spectrum, it is usually the derivative of this spectrum that is used in spectroscopy, mainly because interpretation is more straightforward. Suppose the energy spectrum of Fig. 2b is divided into n number of channels, each channel having width of E; then the total number of channels describing the spectrum is n = (Emax − E0 )/E,

(13)

where Emax is the highest energy recorded as a function of channel number and E0 is an experimentally determined zero offset. Ideally, the value of E0 is zero, but in practice usually is not. Suppose that each energy bin is defined by the energies between two adjacent boundaries, i.e., by Ei+1 − Ei = E. Then the number of counts within each boundary, or channel n, is described by  Ci =

∞



C(E)dE −

0

Ei

C(E)dE −

0



∞

 C(E)dE =

Ei+1

Ei+1

C(E)dE.

(14)

Ei

This result is the same as that found by taking the difference between the counts at Ei and Ei+1 in Fig. 2b. If this change in the recorded counts from the integral pulse-height spectrum is plotted as a function of the channel number (or energy), then a discrete differential pulse-height spectrum is produced C(ni ) =

−(CEi+1 − CEi ) −Counts , = Ei+1 − Ei E

(15)

as depicted in Fig. 2c. Figure 2c is a histogram called the differential pulse-height spectrum, which mimics the energy distribution seen by the detector, i.e., that of Fig. 2a. For a good spectrometer, the measured energy distribution is very similar to the actual distribution of energy deposited in the detector. However, for detectors that have nonlinear effects, recombination, or charge carrier-trapping problems, the energy deposited in the detector and the output signal are not necessarily proportional.

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Although a spectrum such as that depicted in Fig. 2c can be developed with a singlechannel analyzer by sequentially moving the energy window E from zero up to 10 volts, it is a multichannel analyzer that is generally used to display the energy spectrum.

Gamma-Ray and x Ray Spectral Features There are various ways that photons interact in a material and, for the present application, in radiation detectors. The three main mechanisms are the photoelectric interactions, Compton scattering, and pair production. Although Raleigh (coherent) scattering can be significant at low energies, the photoelectric effect dominates (in the same energy region), usually by more than an order of magnitude. Consequently, Rayleigh scattering is usually ignored in practical gamma-ray spectroscopy. Likewise, binding effects become apparent only at low energies and are also usually ignored.

Photoelectric Effect Features Photons of relatively low energy (less than a few hundreds of keV) interact with the ambient medium mostly through photoelectric absorption in which all of the photon energy is transferred to a bound electron, producing a photoelectron that has kinetic energy Tpe = Eγ − Eb ,

(16)

where Eb is the binding energy of the electron which depends on its electron shell of origin. The liberated photoelectron moves through the detector medium causing more ionization through Coulombic interactions. Ultimately, an average number of electrons per unit energy are liberated (or excited) in the detector medium. For scintillators, the important quantity is the average number of excited electrons that produces fluorescent light. For gas detectors, the important quantity is the average energy required to produce an electron-ion pair. Similar to gas detectors, in a semiconductor, it is the average energy required to produce an electron-hole pair that is important. Ultimately, the number of information carriers is a function of the average energy w required to produce the carriers and the absorbed photon energy. The photoelectric effect is observed as a photopeak in the differential pulse-height spectrum.

Compton Scattering Features At higher photon energies, ranging between tens of keV and several MeV, depending on the material, the Compton scattering effect becomes dominant compared to the photoelectric effect. The energy of a Compton-scattered electron is

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Tcs =

Eγ2 (1 − cos θs ) me c2 + Eγ (1 − cos θs )

,

(17)

where θ is the photon scatter angle and me c2 = 511.0 keV is the rest-mass energy equivalent of an electron. The scattered gamma rays have a continuum of energies from zero up to the maximum possible energy transfer to a Compton electron (for a single scatter at θs = π ), namely Tcs =

2Eγ2 me c2 + 2Eγ

.

(18)

A simple example is the case in which there is a single Compton scatter and the scattered gamma ray escapes the detector. Under such a condition, the energy absorbed by the detector is given by Eq. (17). Consequently, the pulse-height spectrum is a continuum of energies, termed the Compton continuum, from zero up to the energy described by Eq. (18). The high-energy limit of the Compton continuum is called the Compton edge. If a considerable fraction of photons are Compton-scattered multiple times, ultimately terminating with photoelectric absorption, then the total initial photon energy is represented by the energy peak in the pulse-height spectrum. Because more than one type of interaction contributed to the energy absorption, the proper term for this peak is the full-energy peak. A gap appears between the full-energy peak and the Compton edge, termed the Compton gap. Multiple Compton scatters that still result in some energy escaping the detector produce a small continuum in the Compton gap. Ultimately, the Compton continuum is more prominent in small detectors than large detectors, mainly because more Compton-scattered photons escape the smaller detector.

Backscatter Features Compton scattering of source photons in the surroundings and shielding of a detector can result in some of these scattered photons reaching the detector and being absorbed in it. Theoretically, this backscatter spectrum can have energies described by Ebs =

me

c2

Eγ m e c 2 , + Eγ (1 − cos θ )

(19)

where θ is the scattering angle needed for the scattered photon to reach the detector. The minimum energy of these scattered photons that reach the detector occurs when θ = π and is Ebs =

Eγ m e c 2 . me c2 + 2Eγ

(20)

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Forward scattering of gamma rays becomes more probable with increasing gammaray energy. Hence, the differential backscatter cross section actually decreases with higher gamma-ray energies. However, photons that scatter with angle greater than about 100◦ emerge with nearly the same energies.

Pair Production Features If the gamma-ray energy is greater than 1.022 MeV, then pair production is possible. When this photon interaction occurs in a detector, 1.022 MeV of the photon energy is converted into the masses of the electron-positron pair and the remaining energy shared as kinetic energy between the two particles. The particles produce ionization in the detector just like photoelectrons and Compton electrons. After the electron loses almost all its initial energy, it is absorbed in the material and returns to an allowed state. However, when the positron comes to rest, it combines with an electron and annihilates, producing two 511-keV photons emitted in opposite directions to preserve the zero linear momentum condition. If both of the annihilation photons are reabsorbed in the detector, the initial gamma-ray energy is represented in the full-energy peak. If multiple events result in one 511-keV annihilation photon escaping the detector, then an energy peak forms in the pulseheight spectrum at Eγ − 511 keV, named a single-escape peak. If multiple events result in both 511-keV annihilation photons escaping the detector, then an energy peak forms in the pulse height spectrum at Eγ − 1.022 MeV, named a doubleescape peak. Single- and double-escape peaks can be identified by (1) noticing that no Compton edge forms and (2) noting their energy location with respect to the full-energy peak. Escape peaks are more prominent in small detectors than large detectors, mainly because a larger fraction of annihilation photons escape the smaller detector. Fluorescent X Ray Features As described previously, the initial liberated electrons, be it by photoelectric, Compton scattering, or pair production, lose energy through Coloumbic interactions which produce secondary electron ionization (delta rays). Some electrons are completely liberated, while others are excited to various higher-energy levels. During this energy transfer process, it is possible for de-exciting electrons to release characteristic x rays. If interaction events occur near the surface of a detector, then these characteristic x rays may escape and produce what is called an “x ray escape peak” correlating to the detector material. In a similar fashion, gamma rays can also fluoresce the shielding and detector surroundings, producing a background of characteristic x rays that appear as peaks in the pulse-height spectrum. Often common shielding materials, such as Pb and Cu, will introduce characteristic x ray peaks into the lower-energy region of a pulse-height spectrum. Summary To summarize, consider a radiation source that emits monoenergetic photons of energy Eo . A source photon that enters the detector may experience any of several outcomes, including the following:

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1. It may be completely absorbed by photoelectric absorption, in which case the deposited energy is the photon energy, i.e., Ed = Eo . 2. It might undergo a sequence of one or more scatters within the detector and then be absorbed within the detector by photoelectric absorption. Full-energy absorption again leads to Ed = Eo . 3. It might scatter one or more times in the detector and then escape with an energy Er . Because not all of the gamma-ray energy is deposited, the recorded energy will be Ed = Eo − Er . 4. If Eo > 1.022 MeV, it might undergo pair production in the detector, producing an electron-positron pair that usually leads to the production of two 0.511-MeV photons by positron annihilation. If both annihilation photons deposit all of their energy in the detector, then Ed = Eo . If one of the annihilation photons escapes and the other is absorbed, the energy deposited is Ed = Eo − 0.511 MeV. If both annihilation photons escape the detector, the deposited energy is Ed = Eo − 1.022 MeV. If either or both annihilation photons scatter within the detector and then escape, an intermediate energy within the range Eo − 1.022 < Ed < Eo is deposited. 5. It might not interact at all in the detector and so Ed = 0. Note that outcomes 1 and 2 both contribute to a “full-energy” peak. Voltage pulses will result whose pulse heights are distributed from zero up to a maximum determined by the energy Ed and the energy resolution of the detector. Thus, a monoenergetic source produces a pulse-height spectrum that is distributed over the many channels. These features can be combined to produce the expected features that appear in a gamma-ray pulse-height spectrum. Depicted in Fig. 3 are differential pulse-height spectra for monoenergetic gamma rays with energies below and above 1.022 MeV. An example pulse-height spectrum obtained from a scintillation spectrometer exposed to the photons from a 22 Na source, which emits 1.28-MeV photons and 0.511-MeV annihilation photons, is shown in Fig. 4. The features in the spectrum, from right to left, include a full-energy peak centered about the channel corresponding to E1 = 1.28 MeV, a Compton edge and a continuum extending from about channel 1250 downward, a full-energy peak due to 0.511-MeV annihilation photons, a Compton edge and Compton continuum for the annihilation photons, and a backscatter peak. The maximum amount of energy that a photon can give up in a Compton scatter occurs in a “backscatter” through an angle of π radians, and so the Compton edge occurs over those channels that represent Compton scatters in the detector through angles near π . Photons that are emitted by the source and backscatter (within either the source or the material behind the source) have energies that are near the energy given by Compton scatter through π radians. The backscatter peak in the spectrum of Fig. 4 is caused by source gamma rays that scatter, in or near the sample, through angles close to π and then deposit full energy in the detector. This peak typically has an FWHM that is larger than the FWHM of a full-energy peak for monoenergetic photons. The larger FWHM occurs because source photons can backscatter in or near the source over a range of angles near π

C(E)

Compton continuum

Compton edge

E

x-ray escape peak

Compton gap

full energy peak

x-ray

C(E) 511 keV

511 keV

full energy peak

511 keV

Compton edge single escape peak

Compton Compton continuum

511 keV

escape peak

backscatter peak double

(b)

E

x-ray escape peak

Compton gap

Fig. 3 Composite pulse-height spectra for monoenergetic gamma rays formed from the features described in this section, with (a) Eγ < 1.022 MeV and (b) with Eγ > 1.022 MeV. Copyright (2020). From Radiation Detection: Concepts, Methods and Devices by D.S. McGregor and J.K. Shultis. Reproduced by permission of Taylor and Francis Group, LLC, a division of Informa PLC

backscatter peak x-ray

(a)

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Fig. 4 The pulse-height spectrum obtained by an NaI(Tl) scintillation detector exposed to a 22 Na source. The source emits photons at 0.511 MeV, as a result of positron annihilations, and at 1.28 MeV, emitted as the product 22 Ne transitions from the excited state to the ground state [McGregor 2016]

radians, and thus these scattered photons that reach the detector do not all have the same energy.

Spectral Response Function A spectrum such as that in Fig. 4, normalized to unit concentration, is called the spectral response function for a given radionuclide. Each nuclide has a characteristic detector response function for each spectrometer for a specified source-detector geometry. Let the subscript k refer to a specific nuclide. Then the detector response function unk is the expected response (number of counts) of the spectrometer in channel n per unit concentration of nuclide k. Detector response functions also can be associated with monoenergetic photons. If a source of monoenergetic photons of energy Ej , in some specific sourcedetector geometry, irradiates a detector, then the detector response function unj gives the expected response in channel n per source particle of energy Ej emitted from the source. In either case, it is not only the full-energy peaks that are of interest; the entire spectrum contains information about the source. Ways to exploit this fact are considered later.

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Qualitative Analysis For some purposes, it is necessary to identify only whether or not a sample emits photons at certain discrete energies Ej . This may be the case, for instance, if one wants to know if a sample contains a particular radionuclide. Alternatively, a procedure such as EDXRF, NAA, or PGNAA can be used to excite characteristic photons from a sample under investigation. If the element of interest is present, the characteristic photons emitted from the sample should create full-energy peaks in a pulse-height spectrum collected from the sample. Photons of energy Ej that are emitted by the source produce full-energy pulses whose magnitudes are distributed about a mean value of hj = f (Ej ).

(21)

A pulse of magnitude hj produces a count in discrete channel nj if hmin + (nj − 1) < hj ≤ hmin + nj . For purposes of energy determination, it is useful to consider the continuous, noninteger, channel number nj corresponding to the pulse-height hj of the full-energy peak. Then the gamma-ray energy can be estimated by determining the continuous or fractional channel number n˜ j centroid of each peak. It is then straightforward to obtain the corresponding hj from hj = hmin + n˜ j .

(22)

For the usual case, where hmin = 0 and hmax = 10 V, this reduces to hj =

10 n˜ j . N

(23)

The expected source energy is then easily obtained from Ej = f −1 (hj ).

(24)

For a linear detector whose response is given by Eq. (2), then Eq. (24) is simply Ej =

hj − α . β

(25)

If a nuclide emits several characteristic-energy photons, then one can gain confidence in the conclusion that the element is present if peaks occur at all energies for which the photon abundance and the detection efficiency would lead one to suspect that a peak should occur.

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Fig. 5 An example of visual inspection to yield the channel numbers corresponding to the centroids of two peaks in a spectrum. The vertical lines are used to connect the apparent peaks to their centroid channel numbers

The simplest way to estimate the channel corresponding to the peak is by inspection of the plotted spectrum. This technique often is adequate. One merely estimates the continuous channel number n˜ j that corresponds to the apparent centroid of the full-energy peak due to photons of energy Ej . For instance, in the spectrum shown in Fig. 5, one can obtain estimates of the fractional channel numbers of the centroids of the two peaks shown. It should be apparent that this procedure is subjective (different researchers may estimate slightly different centroids) and, thus, has limited accuracy. Nevertheless, this procedure may suffice for some applications. When estimation of the centroid by inspection is deemed insufficient, other methods must be employed. The wavelet transform has been used in various spectroscopic applications, including nuclear magnetic resonance (Barache et al. 1997) and Raman spectroscopy (Xu et al. 1994). However, this approach is not commonly employed in gamma-ray spectroscopy and, thus, is not further considered here. Rather, it is common that the centroids of the peaks present are identified as part of a fitting process that can determine quantitative information about both the characteristic energies Ej and their relative abundances. Alternatively, such methods may seek to identify particular radionuclides and their concentrations in a sample. Such methods are discussed in the next sections.

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Quantitative Analysis The model of Eq. (11) identifies a general inverse problem in which many channels contain information about the source distribution. One typically seeks to determine not only the characteristic energies Ej emitted by the source but also the individual source strengths sj from the measured responses. Alternatively, one may use the spectral responses to identify the nuclide k and its concentration ξk in a sample. Quantitative analysis refers to the determination of quantities such as sj and ξk . There are several approaches to quantitative analysis in spectroscopy, including the following: 1. 2. 3. 4. 5.

Area under isolated peaks Model fitting Spectrum stripping Library least-squares Symbolic Monte Carlo

Summaries of how these methods are typically implemented are given in the following sections. In general, one seeks to obtain both the Ej , j = 1, 2, . . . , J , and the net areas under each of the J peaks. For spectra that are linearly related to the source strengths, the net area Aj under the j th full-energy peak is related to Sj , the number of gamma rays emitted by the source during the counting time T , by Sj =

Aj , ηj

where ηj is the detector efficiency, presumed known, at energy Ej ,

Aj =

n2  [C(n) − B(n)],

(26)

n1

and n1 and n2 are channel numbers over which the peak is spread. Similarly, in linear systems, the concentration ξk of nuclide k is directly related to the net peak area. A gamma-ray spectrum, generally, consists of a series of peaks atop a continuum produced by sources emitting a continuum of energies and Compton plateaus from scattered photons. Ideally such a spectrum can be described by a sum of K Gaussian peaks plus a continuum as

y(n) =

K  k=1

gk (n, μk , σk ) + B(n),

(27)

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where gk (n, ˜ μk , σk ) = √

Ak 2π σk

exp [−(n˜ − μk )2 /(2σk2 )] = Bk exp [−((n˜ − μk )/τk )2 ].

(28) √ √ Here, Ak = π τk Bk is the number of counts in peak k and σk = τk / 2 is the standard deviation of the peak. Usually, the continuum is represented by a (piecewise) polynomial of n˜ of low order. The principal purpose of quantitative analysis of the spectrum is to determine values of Ak and μk from which radioisotope identification and concentrations can be determined. Also in calibrated MCA spectrometer systems, the continuous channel number n˜ is replaced by the photon energy E and the channel number n by the energy En at the channel midpoint.

Area Under an Isolated Peak For isolated peaks, i.e., those that do not overlap with other peaks, a simple approach can be used to estimate the net peak area. Generally, the peak is superimposed on a generalized background, as shown, for an ideal case, in Fig. 6. To obtain the net area A, one identifies the channel numbers, n1 and n2 , at which the peak disappears into the background. Then, the net peak area is estimated as   n2  C(n1 ) + C(n2 ) . (29) A= C(n) − (n2 − n1 ) 2 n=n 1

The net area is the total number of counts between channels n1 and n2 minus the area under an (assumed) linear background between C(n1 ) and C(n2 ). For instance, for the spectrum shown in Fig. 6, one might choose n1 = 833 and n2 = 861. The total area between these channels is the sum of the counts in each channel, and the background is the area under the straight line connecting C(833) and C(861); thus, the net area A is the area beneath the peak and above the background line in the figure. This simple procedure cannot be applied to overlapping peaks and gives only approximate net areas because the background may not be linear under the peak and identifying the channels n1 and n2 is subjective, especially when the standard deviations of the responses, σ (C(n1 )) and σ (C(n2 )), are large relative to the values C(n1 ) and C(n2 ).

Model Fitting A second technique, which can be used to obtain both the peak centroid and the area under the peak, is to fit a model to the data. Each peak is modeled as consisting of a peak function and a background function. In most gamma-ray spectroscopy applications, the peak function is assumed to be the product of a magnitude and a Gaussian PDF. Because the integral of the Gaussian PDF is unity, the magnitude

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Fig. 6 The net area A under the peak but above background

is just the desired net peak area. The background can be assumed to have any functional form but most often is assumed to be a polynomial. As a rule of thumb, there is little extra work in treating the background function as quadratic (or even cubic) as opposed to linear, and better results are generally obtained if this is done. If the best fit occurs for a linear background function, the coefficients of the higherorder terms are determined to be zero (or very small); if not, then appropriate coefficients for the higher-order terms assume appropriate values. Note that the background model is not physically based but is empirical. Nevertheless, this modelfitting approach works quite well, for both isolated and overlapping peaks.

General Linear Least-Squares Model Fitting Here is considered the problem of fitting a linear combination of M basis functions Xk (x) to a set of data points (xi , yi ), i.e., y(x|a1 , . . . , aM ) ≡ y(x|a) =

M 

am Xm (x),

(30)

m=1

where Xm (x) can be highly nonlinear in x. The term “linear” refers to the linear dependence of the model on the parameters am . This problem is a more general

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problem of fitting a straight line to a set of data in which X1 (x) = 1 and X2 (x) = x. As before, one seeks values of the parameters am that minimize the merit function: χ2 =

N   yi −

M

m=1 am Xm (xi )

2

i=1

(31)

.

σi

First define an N × M design matrix A with elements Xj (xi ) . σi

Aij =

(32)

In general N ≥ M because there must be at least as many data points as there are model parameters. Also define a vector b with components bi =

yi , σi

i = 1, . . . , N,

(33)

and a vector a whose components are the parameters am , m = 1, . . . , M. The minimum of χ 2 occurs when ∂χ 2 /∂am = 0 or when 0=

  N M   1 y − a X (x ) i j j i Xm (xi ), σ2 i=1 i j =1

m = 1, . . . , M.

(34)

This is a set of M linear algebraic equations in the M unknown am . These so-called normal equations can be written compactly as M 

αmj aj = βm ,

m = 1, . . . , M,

(35)

j =1

where αmj =

N  Xj (xi )Xm (xi ) i=1

σi2

or equivalently

α = AT · A,

(36)

and βm =

N  yi Xm (xi ) i=1

σi2

or equivalently

β = AT · b.

(37)

Equations (35) can be solved by any standard linear equation solver such as Gauss-Jordan or Cholesky decomposition techniques. However, these normal equations are susceptible to roundoff errors, and often these simple solution methods

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fail, and more sophisticated methods such as the singular value decomposition technique should be used. Formally, the solution of Eq. (35) can be written as aj =

M 

[α −1 ]j m βm =

m=1

M 

Cj m

 N

m=1

i=1

 yi Xm (xi ) , σi2

(38)

where C = α −1 . However, finding the model parameters is not the end of the data-fitting problem. The standard errors for the estimated parameters must also be estimated. With the usual formula for the propagation of errors, the variance of a fit parameter is estimated as σ 2 (aj ) =

N 

 σi2

i=1

∂aj ∂yi

2 .

(39)

Because Cj m is independent of yi , differentiation of Eq. (38) with respect to yi gives M  ∂aj = Cj m Xm (xi )/σi2 , ∂yi

(40)

m=1

so that 

∂aj ∂yi

2 =

  N M M 1  C C X (x )X (x ) jm jk m i k i . σi2 m=1 k=1 i=1

(41)

Substitution of Eq. (41) into Eq. (39) produces σ 2 (aj ) =

M  m=1

Cj m

M  k=1

Cj k

 N i=1

 Xm (xi )Xk (xi ) = Cjj . σi2

(42)

The last simplification in this result arises because the term in square brackets is αkm (see Eq. (36)), and because α −1 = C, one has M  k=1

Cj k

 N i=1

  M Xm (xi )Xk (xi ) −1 = Cj k Ckm = [C · C−1 ]j m = δj m . σi2 k=1

(43)

Hence, the diagonal elements of the C matrix are the variances of the estimated parameters. Not surprisingly, the off-diagonal elements of C are the covariances covar(aj , am ). Computer programs and subroutines for performing linear least-squares fits are provided by Press et al. (1992), Bevington (1969), and Moré et al. (1980). An

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application of this fitting procedure for an isolated peak is given in the following example. Example 1. Consider a full-energy peak produced in an HPGe spectrometer from 350-keV gamma rays emitted by the naturally occurring 214 Pb radionuclide. The measured data in the spectrum around this peak are listed in Table 1. Fit the data to a Gaussian distribution and determine the area of the peak.

Solution 1. From Fig. 7, the data appears to consist of a single Gaussian on top of an almost linear background. Thus, the general model of Eq. (27) reduces to y(E, Eo , σ ) = √

A 2π σ

exp[−(E − Eo )2 /(2σ 2 )] + a1 + a2 E.

(44)

It is this model that is to be fitted to the data in Table 1. However, to use the general linear least-squares fitting method described in this section, the peak energy Eo and its standard deviation σ must be known a priori so that the fitting function depends only linearly on A, a1 , and a2 . Because the radioisotope is given as 214 Pb, then the energy of the decay gamma ray shown in Table 1 is Eo = 351.9 keV, which, for this example, is rounded to 352 keV. The variances of the counts are taken as the number of counts, i.e., σi2 = yi . From past experience with the spectrometer used to obtain the data of Table 1, the value of σ  0.47 keV. Thus, it is decided to look at two cases, one in which σ = 0.45 keV and another in which σ = 0.50 keV. The results of the fits for the two choices of σ are shown in Fig. 7. Clearly, σ = 0.50 kev is a better choice. To determine the number of counts in the peak, the method described in section “Area Under an Isolated Peak” could be used. By inspection, n1 = 9 and n2 = 20. Then the area is

Table 1 A portion of a spectrum around the 351.93-keV 214 Pb full-energy peak i 1 2 3 4 5 6 7 8

Ei (keV) 348.3 348.5 348.8 349.1 349.4 349.6 349.9 350.2

yi cnts 2626 2574 2594 2588 2558 2579 2658 2650

i 9 10 11 12 13 14 15 16

Ei (keV) 350.4 350.7 351.0 351.3 351.5 351.8 352.1 352.4

yi cnts 2651 2969 3669 4952 6388 7701 7931 6735

i 17 18 19 20 21 22 23 24

Ei (keV) 352.6 352.9 353.2 353.4 353.7 354.0 354.3 354.5

yi cnts 4927 3561 2888 2461 2417 2399 2550 2405

i 25 26 27 28 29 30 31

Ei (keV) 354.8 355.1 355.3 355.6 355.9 356.2 356.4

yi cnts 2303 2457 2388 2433 2310 2477 2385

Fig. 7 Two linear least-squares fits of Eq. (44) to the data of Table 1 for two assumed values of σ

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area1 =

20 

541

c(n) − trapezoid area

n=9

1 = 56, 833 − [c(9) + c(20)][11] = 28, 717. 2 From the linear least-squares fit (with Eo = 352 keV and σ = 0.50), it is found that A = 7161.79±62.19 keV, a1 = 15819±1316, and a2 = −37.75±3.73 keV−1 . The energy width per channel is E =

E(31) − E(1) = 0.2700keV/ch. 31 − 1

Thus, the least-squares area of the Gaussian peak is estimated as area2 = [A ± σ (A)]/E =

7161.79 ± 62.188keV = 26, 525 ± 230. 0.2700keV

Nonlinear Least-Squares Model Fitting Often the model y(x|a) to be fitted to the data yi , i = 1, ..., N depends both linearly on some of the parameters in a and nonlinearly on the remaining M parameters. As before, in the least-squares method, values of the parameters are determined by choosing parameter values that minimize the merit function: χ 2 (a) =

 N   yi − y(xi |a) 2 . σi

(45)

i=1

The normal equations (similar to Eq. (34)) are no longer linear in the parameters a and so cannot be solved directly. Rather, iterative techniques must be used to find the minimum of χ 2 (a). Equation (45) describes a hypersurface in the M-dimensional hyperspace whose axes are the M parameters in a. One must incrementally traverse this hypersurface in some methodical fashion to find its minimum. Such searches range from bruteforce grid searches, in which one moves incrementally along each axis to find a local minimum before searching along another axis, to more sophisticated searches, in which each incremental step is taken in a direction opposite to the gradient of χ 2 (a). However, the hypersurface often has many local minima in which an incremental search can become trapped and thus miss the sought-for global minimum. Moreover, these searches can often venture into regions of the hyperspace with physically unrealistic parameter values, such as those producing negative Gaussian distributions. Such a problem is frequently encountered if a search is begun far from the global minimum. Consequently, it is often necessary to do a

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constrained search to prevent the search path from entering unrealistic regions of the hyperspace. In the analysis of gamma-ray spectroscopic data (xi , yi ), xi is either the channel number n or the channel midpoint energy En , and yi is the measured number of counts in a channel. Typically, data in a gamma-ray spectrum or, more often, a portion of the spectrum are fit to a sum of Gaussian peaks plus a polynomial to represent the continuum upon which the peaks sit. For this case, the fitting model is y(x|a) =

K 

 Bk exp −

k=1



x − Ek τk

2  + a0 + a1 x + a2 x 2 + . . . + an x n .

(46)

The model parameters B1 , E1 , τ1 , ..., BK , EK , τK , a0 , a1, ..., an are the components of a. However, other models are easily treated with the nonlinear leastsquares technique described below. There are several ways to search the M-dimensional hyperspace to find amin that minimizes χ 2 (a) of Eq. (45). One such method is the Leverberg-Marquardt (LM) method, such as that presented by Press et al. (1992). McGregor and Shultis (2020) also describe the method as applied to gamma-ray spectroscopy. The reader is referred to these two citations for a review of the technique.

Isolated Peaks To assure that the entire isolated peak is completely fit, it is suggested that the portion of the spectrum extend to at least ±3σ about the centroid channel. These limits are chosen because the area under a Gaussian over the range μ ± 3σ is 0.997 of the total area under the Gaussian, and thus the parameter Ak in Eq. (28) is a very good approximation to the total area under the Gaussian for the kth peak. For the portion of the spectrum containing an isolated peak, the appropriate fitting model y(x|a) is that of Eq. (27) with K = 1 and a polynomial of low order n to describe the background upon which the peak sits. The merit function to be minimized in this case is χ 2 (a) =

 N   yi − y(xi |a) 2 σi i=1

=

 2  

  N n  1 xi − μ 2 m y + − B exp − a x , i m i τ σ2 i=1 i m=0

(47)

where the components of the parameter vector a are B, μ, τ, a0 , ..., an . To use the LM method, the derivatives of y(x|a) with respect to each parameter are needed. Here one has dy(x|a) = f (x, μ, τ ), dB

dy(x|a) 2(x − μ) = Bf (x, μ, τ ) , dμ τ2

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2(x − μ)2 dy(x|a) = f (x, μ, τ ) , dτ τ3

dy(x|a) = xj , daj

and

j = 0, 1, ..., n. (48)

To illustrate this analysis approach, the data of Table 1 for a 214 Pb peak are fit to a Gaussian plus a linear function (n = 1) in Example 2. Example 2. For the portion of a spectrum containing an isolated peak, as given by the data in Table 1, the fitting model y(x|a) is given by Eq. (46) with K = 1 and a linear background function, so n = 1 in Eq. (46). This is the same model used in Example 1, but now estimate the centroid of the peak and its standard deviation by including them in the fitting parameters. Solution 2. The merit function to be minimized is that of Eq. (47) with n = 1. The initial guess of the parameter values was B = 3000 MeV, a0 = 1000,

μ = 0.350 MeV,

a1 = −200 MeV

−1

τ = 0.002 MeV,

.

After 23 LM steps through 5-dimensional parameter hyperspace, the χ 2 (a) was reduced from an initial value of 16,653 to 72.55, the minimum of χ 2 (a). The bestfit parameters at the χ 2 (a) minimum were B = 5583.6 ± 58.4,

μ = 351.960 ± 0.0051 keV,

a0 = 14062 ± 1331

and

τ = 0.74146 ± 0.00744 keV,

a1 = −32823 ± 3776 MeV−1

√ The normalization of the Gaussian is A = π τ B = 7338.0 ± 70.64 keV counts/ channel, which, upon dividing by the energy width per channel of 0.2700 keV/ channel, gives the total counts in the peak as area3 = 27, 178 ± 262. This result is midway between the two estimates area1 = 28, 717 and area2 = 26, 525 ± 230 √ obtained in Example 1. Finally, the standard deviation of the peak is σ = τ/ 2 = 0.52429 ± 0.00526 keV. The resulting model fit and its two components are shown in Fig. 8. Of note is the estimated gamma-ray energy of 351.960 keV for this peak. This value compares very favorably to the accepted NUDAT value of 351.9321(18) keV. The small difference is easily accounted for by inevitable small errors in the energy calibration of the channels of the spectrometer system.

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Fig. 8 The LM fit to the data of Table 1. Also shown by dashed lines are the Gaussian peak component and the linear background

Overlapping Peaks Sometimes two or more peaks overlap. In situations where a peak is asymmetric or has an FWHM larger than expected, one can try to fit multiple peaks to the data locally. In such cases, one might try a fitting model of the form (see Eq. (27))

y(x|a) =

K 

Bj gj (x, μj , τj ) + a0 + a1 x + a2 x 2 ,

j =1

   x − μj 2 , where g(x, μj , τj ) = exp − τj

(49)

and K is the number of peaks one suspects might be overlapping. Values of the model parameters a = (B1 , μ1 , τ1 , . . . , BK , μK , τK , a0 , a1 , a2 ) are found as those values that minimize the merit function:

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 N   yi − y(xi |a) 2 χ (a) = σi 2

i=1

   2

   N K 2  1 xi − μk 2 j yi − + = Bk exp − aj xi . τk σ2 i=1 i k=1 j =0

(50)

As a practical matter, you might try K = 2 first and see if you obtain reasonable results. If not, try larger values of K. Of course this model introduces new nonlinear model parameters for each additional peak. The fitting of multiple overlapping peaks, with asymmetric peak models, to XPS spectra is considered in detail by Dunn and Dunn (1982). Generally, the yi are either gross counts Ci in channel i or, for backgroundsubtracted spectra, net counts Ni in channel i. (Note that background subtraction removes only part of the generalized background, the Bn of Eq. (12).) If the C(i) are gross counts, then one presumes that Poisson statistics apply and σ 2 (yi )) ≡ σi2 = C(i). If the spectrum is background-subtracted, then σ 2 (yi ) = C(i) + Bi . If the C(i) result from some other process, then one should use the appropriate variances in Eq. (50). For the nonlinear least-squares approach followed here, values of the model parameters a are chosen that minimize the merit function χ 2 (a). To use the LM minimization method, partial derivatives of χ 2 (a) with respect to each parameter are needed and for the above model are given by Eqs. (48). An example of fitting two overlapping peaks is given in Example 3. In this example and in many nonlinear least-squares fitting analyses, the incremental path through the χ 2 (a) hypersurface may often lead to physically unrealistic values of some of the parameters. This is particularly true for overlapping peaks. Unless one starts the minimizing search with very good guesses for the μk for each peak, often a broad positive Gaussian (B1 > 0) with a negative Gaussian (B2 < 0) results. Such is the case for Example 3. One way to avoid these unrealistic parameter values is to start the search very near the minimum of χ 2 (a), which is seldom known a priori or to perform a constrained search along the hypersurface. In such a constrained search, the current values of the parameters are examined after each step, and if outside some preset range, an offending parameter is reset to the nearest range limit. Example 3. Fit the model of Eq. (49) with K = 2 to the count data given in Table 2. Solution 3. The LM method was used to find values of the best-fit parameters. The derivatives needed for this method are dy(x|a) = f (x, μi , τi ), dBi

i = 1, 2

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Table 2 A portion of a spectrum giving channels and gross counts. The data points (xi , yi ) to be fit are xi = i the channel number and yi = c(i) the counts in channel i

i 117 118 119 120 121 122 123 124 125 126

C(i) 2210 2253 2333 2487 2763 2869 2984 3312 3629 4077

i 127 128 129 130 131 132 133 134 135 136

C(i) 4756 6176 9761 17,016 26,462 30,846 28,392 26,822 32,667 42,618

dy(x|a) 2(x − μi ) = Bf (x, μi , τi ) , dμi τi2

i = 1, 2

dy(x|a) 2(x − μi )2 = f (x, μi , τi ) , dτi τi3

i = 1, 2

i 137 138 139 140 141 142 143 144 145 146

C(i) 45,568 36,698 23,773 14,669 10,054 7666 6284 5387 4792 4224

dy(x|a) = xj , daj

i 147 148 149 150 151 152 153 154 155 156

C(i) 3827 3416 3156 2896 2713 2448 2335 2119 1957 1754

j = 0, 1, 2. (51)

The search for the minimum of +χ 2 (a) began with the following dimensionless starting values: μ1 = 130.

σ1 = 2.200

B1 = 22, 000.

a0 = −177,000.

a2 = 2680

μ1 = 140.

σ2 = 2.800

B2 = 38, 000.

a2 = −9.8400

After 15 steps, the initial value of χ 2 (a) was reduced from 80,978. to 2034.92. Further iterations did not change χ 2 (a). Values of the Best-fit parameters are μ1 = 131.664 ± 0.015 μ2 = 136.734 ± 0.0120 a0 = −166,321. ± 1970.

σ1 = 2.1298 ± 0.0157 σ2 = 2.8700 ± 0.0138 a1 = 2517.03 ± 29.22

B1 = 23, 403.4 ± 137.7 B2 = 38,538.5 ± 129.0 a2 = −9.2409 ± 0.10771

The areas of the two Gaussians are A1 =

√ π τ1 B1 = 88,348.1 ± 552.78

A2 =

√ π τ2 B2 = 196,039. ± 761.10

and the standard deviations of the peak are √ σ1 = τ1 / 2 = 1.5060 ± 0.01108

√ σ1 = τ1 / 2 = 2.0295 ± 0.009724.

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Fig. 9 A fit of two overlapping peaks with a quadratic background. The solid line is a weighted √ least-squares fit with σi = c(i), and the dotted line is an unweighted least-squares fit with σi = 1

The fit function is shown in Fig. 9. It is seen that the model fits the data quite well. One would expect that a good model would be within the error intervals for about 68% of the data points, and this seems to be the case here. The uncertainty in each of the model parameters is small, relative to the parameter value, which also indicates a good fit. It is noted that the values of i1 = 117 and i2 = 156 are well beyond the 3σ range for the σ1 and σ2 obtained. Thus, the A1 and A2 values should be good estimates of the net areas under the two peaks.

Spectrum Stripping If response functions can be collected or generated for all the sources (or radionuclides) that are expected to be present in an unknown sample and if the dependence of the response model is linearly related to the source strengths or radionuclide concentrations, then the method of spectrum stripping can be applied. This procedure is as follows: • Collect a spectrum from the unknown sample. • Identify the highest-energy peak in the spectrum.

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• Subtract the response function for that energy peak, weighted by a constant, such that the peak is effectively removed. • Proceed down the spectrum while subtracting other weighted response functions until all peaks are removed. If the residuals are randomly distributed about zero or about some smooth background, then the specific response functions stripped from the spectrum for the unknown identify the radionuclides present, and the weighting constants estimate the source strength or concentration of each radionuclide.

Library Least-Squares Because a detector produces a spectrum, even for a monoenergetic input, one can try to utilize the entire spectral response, or at least a significant part of it, rather than just the response values near each peak or set of overlapping peaks. The library least-squares approach, originally introduced by Marshall and Zumberge (1989), asks the following question: Why focus on only the peaks since other parts of the spectrum also contain information related to the abundances of the radionuclides that produce the peaks? One approach for using all of the information in a spectrum is the library least-squares (LLS) method, as implemented, for instance, by Gardner and Sood (2004) and Gardner and Xu (2009). The LLS method is based on a library that contains detector response functions for all radionuclides that might possibly be present in the sample whose spectrum is to be analyzed in order to determine the abundances of specific radionuclides. Then some fitting technique, such as leastsquares or weighted least-squares, is used to fit the library spectra to the spectrum from a sample whose radionuclide abundances are sought. This approach was not possible many years ago because one could not experimentally measure good spectra from all candidate radionuclides or a sufficient number of monoenergetic gamma rays. However, Monte Carlo modeling has become sufficiently robust that detector response functions can be calculated for almost any radionuclide. When Monte Carlo is used to generate detector response functions, the method often is referred to as Monte Carlo library least-squares (MCLLS). In this method, one calculates monoenergetic detector response functions Rn (E) for a wide range of discrete energies that can be emitted by sources of interest. Examples of such MC calculated detector response functions are shown in Fig. 10 and were calculated by special MC software and empirical resolution functions (Gardner and Sood 2004). The response function Rn (E) is the probability that a photon of energy E emitted by the source produces a count in channel n. This response function, as before, includes the probability a source photon reaches the detector, a probability which depends on the specific source-detector geometry, but it, generally, does not include photons scattered into the detector by material around the detector, i.e., the so-called roomshine. To determine the concentrations of various radioisotopes present in a sample, response functions, per unit activity concentration, for each possible radioisotope

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Fig. 10 Examples of library response functions Rn (E) for a 6 in × 6 in cylindrical NaI detector for monoenergetic photons normally and uniformly incident on the circular end of the crystal. No contribution from scattering in material around the detector is included as indicated by the absence of backscatter and annihilation peaks although several annihilation escape peaks from the crystal are evident. These response functions are a small part of the library for a 512-channel spectrum over the photon range 0–11.38 MeV. (Courtesy of Robin Gardner, NCSU)

likely to be in the sample must first be constructed. A library of such radioisotopic response functions Rkn where k = 1, 2, . . . , K can be constructed from the monoenergetic response functions Rn (E), for a given source-detector geometry, as Rkn =

I 

fik Rn (Eik )ξˆ k ,

(52)

i=1

where fik is the frequency a photon of energy Eik , i = 1, ..., I is emitted per decay of radionuclide k, and ξˆ k is the decay rate of a unit activity concentration of the radionuclide. Then the expected number of counts y(n) recorded in channel n in a measurement time T produced by a sample of K possible radioisotopes is y(n|ξ ) = T

K  k=1

Rkn ξk ,

n = 1, ..., N,

(53)

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where ξk are the radioisotopic activity concentrations being sought. Again it is assumed all the activity concentrations remain constant over the measurement time T . If C(n) are the observed number of counts in channel n from the sample, then the vector ξ , whose components are the concentrations ξk , can be determined as those values that minimize the merit function:

χ 2 (ξ ) =

N 

Wn [c(n) − y(n, |ξ )]2 ,

(54)

n=1

where Wn is a weight factor, often taken as Wn = 1/σ 2 (C(n)) = C(n). Because the response functions do not include background and roomshine, the counts C(n) must first be corrected for these contributions. If a fitted ξk value is negative or near zero for one or more k, then the corresponding radionuclides might not be present in the sample. In this case, it is a good practice to remove the detector response functions for these radionuclides and repeat the analysis to see if a good fit is obtained. The process just described assumes the response model is linear in the radionuclide concentrations and, thus, can be referred to as the linear LLS approach. This approach is very similar to the previous linear weighted least-squares process used to fit Gaussian distributions to spectral peaks. But here more features of the spectrum other than just the full-energy peaks are used. There are instances, however, in which the model is not linear in the radionuclide concentrations. Such cases arise in prompt gamma neutron activation analysis (PGNAA) and energy-dispersive x ray fluorescence spectroscopy (EDXRF).

Nonlinear Spectra Generally, the samples used in a neutron activation analysis (NAA) are small, and their masses can be accurately measured, and because one is usually seeking concentrations of trace elements, an NAA analysis is well approximated as a linear process, and application of linear LS technique is appropriate. However, for bulk samples, a prompt gamma neutron activation analysis (PGNAA) is nonlinear, primarily for the following reasons: • Sample mass, which often is not known, affects the flux density and the macroscopic capture cross section of the sample. • The composition of the sample, which is unknown in advance, affects the spectrum. In particular, moisture content strongly affects the thermal-neutron flux density, which is what gives rise to the prompt gamma rays. Also, neutron absorbers affect the thermal flux density. Thus, nonlinear models are needed for a PGNAA. Such models are iterative in nature and require the need to calculate spectral responses. Usually, Monte Carlo methods are used for such calculations. The general Monte Carlo library leastsquares (MCLLS) approach in the nonlinear case proceeds as follows:

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1. Assume values for the concentrations and use Monte Carlo to generate a complete spectrum for a sample of this assumed composition. 2. Keep track of the individual spectral responses for each element within the Monte Carlo code, so as to provide library spectra unk for each radionuclide. 3. Use linear LLS to estimate the radionuclide concentrations ξk , k = 1, 2, . . . , K from the sample spectrum. 4. If the calculated ξk , k = 1, 2, . . . , K match the assumed composition closely enough, you are done. If not, pick a new composition, based on the calculated concentrations, and repeat the process. 5. Iterate until you converge to the actual composition, to within a desired tolerance. Results of this general procedure are given, for instance, by Gardner and Xu (2009).

Symbolic Monte Carlo In x ray fluorescence, the responses are due to the elements present, but each element is composed of radionuclides, and the convention was introduced earlier to refer only to radionuclides. Hence, in the discussion below, elemental concentrations are called nuclide concentrations. Nonlinear matrix effects lead to absorption and enhancement in EDXRF. For instance, the characteristic x rays of nuclide a can be absorbed by elements with lower atomic numbers, which reduces the signal from nuclide a and enhances the signals for the lower atomic number nuclides. This effect means that the models in EDXRF also are not linear in the nuclide concentrations. Another implementation of Monte Carlo has been used in the EDXRF case. The method, originally called inverse Monte Carlo (IMC) (Dunn 1981), was applied to EDXRF by Yacout and Dunn (1987) for primary and secondary x rays. Mickael (1991) extended the work to include tertiary fluorescence. The term IMC has been used for other purposes, e.g., to solve inverse problems by iterative Monte Carlo simulations in which the unknown parameters are varied until simulated and measured results agree sufficiently. The acronym IMC also has been used for “implicit Monte Carlo” (Gentile 2001). Thus, Dunn and Shultis (2009) recently proposed renaming the version of IMC that is non-iterative in the Monte Carlo simulations symbolic Monte Carlo (SMC) because the method proceeds by using symbols in the Monte Carlo scores for the unknown parameters. SMC is a specialized technique in which the inverse problem of estimating the k and ξk is solved by a system of algebraic equations generated by a single Monte Carlo simulation. For purposes of illustration, a ternary system (one that contains three elemental nuclides) is considered. In essence, SMC creates models, with symbols for the unknown concentrations ξk , for the areas under all of the various x ray peaks (e.g., Kα and Kβ ) in a single simulation. The models depend on the detector efficiency as a function of energy; the nuclide concentrations; the primary, secondary, and tertiary fluorescence produced in the sample; and the background. For a ternary system, three equations result. The equations are rather complex (see Yacout and Dunn 1987 and Mickael 1991) but can be developed using only a single

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Monte Carlo simulation. The advantage of this approach is that there is no need to iteratively run full Monte Carlo simulations as the assumed concentrations are varied. The disadvantage is that development of the model is involved and the algebraic equations are quite complex. Nevertheless, the method has been shown to work well in x ray spectroscopy and can, in principle, be applied to other spectroscopic applications, such as PGNAA, in which the responses are nonlinear functions of the concentrations.

Compton Suppression Because prompt gamma rays tend to be of high energy (most are between 1 and 12 MeV), there is a large Compton component to the spectra, especially for thin semiconductor detectors. There are ways to reduce the Compton continuum. One is to partially surround a high-resolution germanium detector with scintillators, such as BGO, which has high efficiency because of its high density. The basic idea is that a photon that Compton scatters in the germanium detector has a reasonable chance of interacting in the scintillation crystals. These interactions occur at essentially the same time as the Compton scatter in the germanium and can thus be suppressed by an anticoincidence gate (the gate only accepts pulses in the germanium that are anticoincident with the scintillators). Fairly dramatic results can be achieved (Molnar 2004).

More About Spectroscopy Measurements The purpose of radiation spectroscopy is to identify energetic emissions from radioactive materials. Such emissions are reported with several metrics, mainly the confidence in the identified energy or the energy resolution and the source activity (a function of the detector efficiency). The choice of detector is determined by the application and required spectroscopic performance. Detectors needed for field applications with sufficient spectroscopic performance to identify common isotopes may be best performed with lower-resolution scintillation detectors. Measurements requiring high-resolution spectroscopy generally require more expensive semiconductor spectrometers. No matter the type of spectrometer, it must undergo an energy calibration before any measurements can be made.

Channel Calibration Calibration of the spectrometer channels in energy units is relatively simple, particularly if a linear energy/channel response is assumed. Typically two particle energies are chosen with relatively wide separation. For instance, 60 Co and 57 Co might be chosen. The peak channel n˜ H for the higher-energy EH and the peak channel n˜ L for the lower-energy EL are observed, and a simple linear fit between

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these two channels provides a channel energy calibration, i.e.,  E(n) ˜ = n˜

EH − EL n˜ H − n˜ L

+ E0 ,

(55)

where E0 is the energy offset at channel n˜ = 0.0, which is found from  E0 = EH − n˜ H

EH − EL n˜ H − n˜ L

.

(56)

For simplicity, the continuous n˜ is often taken as the channel number n which equals n˜ at the midpoint of a channel. The term in parentheses in the above equations is the energy width per channel E and is an important spectrometer parameter because it defines the minimum energy resolution possible with the spectrometer. Semiconductor materials usually show good signal linearity with energy deposition, but there are many scintillators that exhibit a nonlinear output with energy, especially at lower energies. Example scintillators include NaI(Tl) and CsI(Tl) in the energy region below 500 keV. For such nonlinear detectors, several energies in the nonlinear region should be used to fit a polynomial function to the channel energy calibration.

Spectroscopy Quality Metrics Several quality metrics have been established, some official and others less so, that depend on the system and type of detector. These metrics are used to give the user an idea of the expected detector performance under different measurement conditions. Metrics include measurements of detection efficiency, energy resolution, channel width corrections, figure of merit, noise resolution, energy rate limit, and peak-toCompton ratio. Many of these metrics are described in the IEEE Std 325–1996 document for HPGe detectors.

Detection Efficiency There are multiple methods for defining and measuring the efficiency of a gammaray spectrometer. The efficiencies of most interest and utility are the absolute efficiency, the intrinsic efficiency, and the escape peak efficiency. Total Intrinsic Detection Efficiency The total intrinsic detection efficiency is defined by

I =

N  i

Asp , Af tBi

(57)

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where Asp are the recorded counts from the entire detector spectrum, t is the live time of the counts, A is the source activity, f is the fractional solid angle subtended by the detector, and Bi are the branching ratios of the radiation emissions. For instance, 60 Co emits two gamma rays per decay (B = 2), while only 85% of decays from 137 Cs result in the emission of a 661.7 keV gamma ray (B = 0.85). This metric I yields some information about the overall detector counting efficiency, but does not give information on the energy resolution performance. Further, this particular metric is subject to changes with the LLD setting, and background contamination can skew the results. Intrinsic Peak Efficiency The intrinsic full-energy peak efficiency is defined by peak =

Ap , Af Bt

(58)

where Ap are the recorded counts from the detector in the full-energy peak, t is the live time of the counts, A is the source activity, f is the fractional solid angle subtended by the detector, and B is the branching ratio of the emission under investigation. The intrinsic peak efficiency is similar to the intrinsic detection efficiency, except that Ap pertains only to those counts located in the background subtracted full-energy peak. It is notable that the intrinsic peak efficiency may be difficult to determine accurately for several detector types. For instance, the size and shape of an HPGe detector may be difficult to assess because the actual crystal is much smaller than the apparent cryogenic packaging. A similar situation exists with scintillation counters whose crystal is hermetically packed in a light-tight reflecting canister. The practical outcome of the intrinsic peak efficiency is a function of the packing canister, the absorbing material (NaI(Tl), HPGe, CdTe, etc.), the type of electrical contacts, the detector size, and the detector shape. Energy absorption in the detector encapsulation and contact dead layer affect the low-energy efficiency, while the atomic number and volume of the detector determine the high-energy efficiency. An example of the efficiency variation is shown in Fig. 11 for a 25% relative efficient, bulletized coaxial n-type HPGe detector (Kis et al. 1998). A variety of gamma-ray sources can be used to measure the intrinsic peak efficiency over the energy region of interest. Afterward, a curve fit can be used as a predictive measure of efficiencies at other energies within the measured span (Kis et al. 1998). Although there are several curve-fitting functions offered in the literature, many examples listed in Kis et al. (1998), modern commercial curvefitting computer programs are available that can provide high-fit r 2 values (>0.999). Escape Peak Efficiency The escape peak efficiency, mainly the single- and double-escape peaks from pair production, is a measure of the detector’s ability to effectively recapture 511-keV annihilation photons. Larger escape peaks are indicative of larger losses. Although there are multiple definitions of this metric in the literature, a generally accepted

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Fig. 11 Measured intrinsic peak efficiency for a 25% relative efficient n-type HPGe detector. The sources used for the calibration were 241 Am, 133 Ba, 152 Eu, 137 Cs, 60 Co, 188 Ta, 56 Co, 49 Ti, and 36 Cl. (Data acquired from Kis et al. 1998)

definition for the intrinsic escape peak efficiency is that described by Cline (1968) and Nafee (2011): es =

Aep , Af Bt

(59)

where Aep pertains to the number of counts in either the single-escape peak or the double-escape peak. To determine the number of counts in either escape peak, the subtraction method of Eq. (29) is employed. Equation 59 can be rewritten as es = peak

Aep , Ap

(60)

where the escape peak under investigation is for the corresponding full-energy peak. It is notable that escape peaks can be used to identify the initial gammaray energies. Escape peaks do not have a Compton gap or Compton edge, and the apparent lack of these features can assist with their identification. Although gamma rays equal to or greater than 1.022 MeV can be absorbed through pair production, escape peaks usually do not become apparent for gamma-ray energies below approximately 1.5 MeV.

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Energy Resolution A method to determine the energy resolution of a gamma-ray spectrometer is prescribed by the IEEE Std 325–1996 and was developed for an HPGe detector and a 60 Co check source. The method makes no use of statistical uncertainties in the spectral count data (unlike the weighted least-squares fitting methods used earlier). Rather it depends on a very high number of counts in the full-energy peak so statistical uncertainties are of little consequence. The one unique feature of this standard, however, is that the method makes no Gaussian symmetry assumption about the shape of the full-energy peak and it is capable of treating asymmetric peaks that are wider at energies below the peak energy than above— a feature observed in many spectrometers. In essence, the method relies solely on manipulations of the observed channel counts C(n) ≡ Cn to estimate the FWHM. McGregor and Shultis (2020) describe the analysis method with examples. Perhaps, however, the most used method for determining energy resolution is to determine the FWHM of the energy peak under investigation directly from the data. This determination must be preceded by removing the background counts, as described earlier. When reporting the FWHM in terms of energy, the channel width is directly converted to energy (keV) using the channel energy calibration. When reporting the FWHM in terms of percent, the FWHM (whether in terms of energy or channels) is divided by the most probable energy (also in either energy or channel number) in that full-energy peak. Hence, the energy resolution in energy units and as a percent are FWHMenergy = E keV

and

FWHM% = 100

E , Eγ

(61)

where E is FWHM width in energy units (typically keV) and Eγ is the energy of the gamma ray. The usual standard for reporting energy resolution is to quote scintillator detector energy resolution in terms of percent and semiconductor detector energy resolution in terms of energy with units of keV. However, with many compound semiconductor detectors, there has been an unofficial departure from this standard, where many times the energy resolution is quoted in terms of percent. Peak-to-Compton Ratio Another metric specified for HPGe radiation spectrometers is the peak-to-Compton ratio (PCR). As described in the ANSI/IEEE standard 325–1996, the measurement of the PCR is performed with the 1332.5 keV gamma-ray energy from 60 Co. The PCR is defined as PCR =

Cmax N

,

(62)

where Cmax = CP is the number of counts in the peak channel for the 1332.5-keV gamma ray and N is the average number of counts per channel between the channels represented by 1040 and 1096 keV. The energy range between 1040 and 1096 keV

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Fig. 12 The peak-to-Compton ratio (PCR) is calculated by dividing Cmax by N . In this example for a 20% relative efficiency HPGe coaxial detector, the measured PCR is 31.3. Copyright (2020). From Radiation Detection: Concepts, Methods and Devices by D.S. McGregor and J.K. Shultis. Reproduced by permission of Taylor and Francis Group, LLC, a division of Informa PLC

appears in the Compton gap of the 1173.2-keV gamma ray of 60 Co; therefore, it is almost entirely associated with the Compton continuum of the 1332.5-keV peak (see Fig. 12). The environmental background B should be subtracted from the measurements before calculating the PCR. The PCR metric is analogous to a sort of signal-to-noise ratio because the PCR is a measure of the spectrometer’s ability to discern lower-energy and lower count rate gamma-ray peaks in the presence of higher-energy gamma-rays and their corresponding spectral features. As the energy resolution of an HPGe detector improves, the number of counts in the 1332.5-keV peak channel increases. Also, as the size of the HPGe detector increases, so do counts in the 1332.5-keV peak channel because fewer scattered gamma rays can escape the detector. Hence, improved energy resolution and improved efficiency both tend to increase the PCR. PCR values can range from 30:1 for smaller HPGe detectors up to over 90:1 for relatively large detectors (Gilmore 2008). It is notable that prior versions of the IEEE ANSI standard 325 also included a PCR for 137 Cs in which the maximum counts for the peak channel at 661.7 keV is divided by the average counts per channel in those channels between 358 and 382 keV. Although the 137 Cs-based PCR is generally not used to characterize HPGe detectors, it still has utility as a benchmark for comparing PCR values for

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much smaller semiconductor spectrometers, such as those with CdZnTe or HgI2 detectors whose peak efficiency at 1332.5 keV can be small compared to that of a HPGe detector. However, this particular definition does not appear in the most recent version ANSI 325–1996. Peak-to-Valley Ratio Another, less official, metric is the peak-to-valley ratio (PVR), which is measured with a 137 Cs source. This metric is defined as the number of counts in the peak channel divided by the number of counts in the middle of the Compton gap at 569 keV. This metric is seldom used for HPGe detectors; rather, it is more often used for compound semiconductor detectors and (rarely) used for experimental scintillation detectors. This metric provides a measure of the detector efficiency, energy resolution, and for semiconductors a measure of the charge carrier-trapping effects. Peak-to-Total Ratio The peak-to-total ratio (PTR) is the ratio of the total counts in a full-energy peak to the number of counts in the entire spectrum. The metric is useful with monoenergetic gamma-ray sources, such as 137 Cs and 54 Mn, but is not well defined or interpreted for polyenergetic gamma-ray sources. The peak-to-total ratio is proportional to the intrinsic full-energy peak efficiency peak because  peak = I

peak counts total counts

= I PTR,

(63)

where I is the total intrinsic counting efficiency. By carefully selecting monoenergetic gamma-ray sources, the detector intrinsic peak efficiency can be calibrating over a broad energy range (Heath 1967). Unfortunately, there are a limited few practical monoenergetic gamma-ray sources to conduct such a measurement. Another method to accomplish this same task is to use two detectors in coincidence, with the detector under investigation receiving the scattered gamma ray. The method entails capturing a Compton-scattered gamma ray that escapes from a high energy resolution primary (first) detector. The residual energy deposited in the second detector is determined by subtracting the energy deposited in the first detector from the known emission energy. Collimation and pulse-height discrimination can be used to select and allow only scattered gamma rays of a specific energy, thereby producing a pulse-height spectrum, at the energy under investigation, from the second detector.

Detectors for Gamma-Ray Spectroscopy Typical methods of gamma-ray and x ray spectroscopy can be categorized as either energy-dispersive or wavelength-dispersive. Energy-dispersive spectroscopy (EDS) is perhaps the more popular technique, in which the energy of photons is preserved and recorded. Energy deposition indicators in the detector include light emission,

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electrical current, and thermal changes. Wavelength-dispersive spectroscopy (WDS) is a technique in which a specific photon wavelength is measured by a witness detector. The witness detector position is translated in space so as to accumulate a spectrum of different photon wavelengths. There are numerous detectors that can be used for radiation spectroscopy, which include versions of gas-filled, scintillation, and semiconductor detectors. However, only those commercial devices commonly used as analytical tools for gamma-ray and x ray spectroscopy are described in this chapter. EDS devices include scintillation, semiconducting, and cryogenic spectrometers. Diffractive spectrometers are classified as WDS devices and typically use gas-filled proportional counters as witness detectors.

Scintillation Spectrometers Scintillators are generally separated into two classes: those being inorganic and organic. The method by which either produces scintillation light is physically different, hence the distinction. Inorganic scintillators can be found as crystalline, polycrystalline, or microcrystalline materials. Organic scintillators come in many forms, including crystalline materials, plastics, liquids, and even gases. However, organic scintillators, being composed of low Z materials, are ineffective as gammaray spectrometers and, thus, are not covered here. The scintillation principle is quite simple. Radiation interactions occurring in a scintillator cause either atomic or molecular structure in the scintillator to become excited such that electrons are increased in energy. These excited electrons will deexcite, some of which will radiate light energy. The light emissions can then be detected with light-sensitive instrumentation. A typical scintillation spectrometer consists of a scintillating material hermetically sealed in a reflecting canister. Typical canisters are cylindrical, with one end of the cylinder being an optically transparent window with all remaining surfaces being Lambertian reflectors. The optically transparent window is coupled to a light collection device, such as a photomultiplier tube (PMT), with an optical compound. The optical compound helps match the indices of refraction between the scintillation canister and the light collection device so as to reduce reflective losses. The PMT provides a voltage output that is linear with respect to the light emitted from the scintillator. Hence, the voltage “spectrum” is a linear indication of the radiation energy spectrum deposited in the detector. It is typical for commercial vendors to provide the scintillation canister and the PMT as one complete unit, although they can be acquired separately.

Inorganic Scintillators Inorganic scintillators depend primarily on the crystalline energy band structure of the material for the scintillation mechanism. Shown in Fig. 13 is an energy band diagram for an inorganic scintillator. A lower-energy band, referred to as the valence energy band, has a reservoir of electrons. It is this band of electrons that participates in the binding of atoms. The next higher band is commonly referred to as the

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Upper Band

Forbidden Band

Conduction Band

Ec Exciton Band

Exciton Band

Eg

Et1a Et1b

Exciton

Exciton

Eg

Band Gap

Et0

Ev Valence Band Forbidden Band Tightly Bound Band

(A)

(B)

Fig. 13 Shown are two basic methods by which an inorganic scintillator produces light: (a) is the intrinsic case, and (b) is the extrinsic case. Copyright (2020). From Radiation Detection: Concepts, Methods and Devices by D.S. McGregor and J.K. Shultis. Reproduced by permission of Taylor and Francis Group, LLC, a division of Informa PLC

conduction band, which for inorganic scintillators is usually devoid of electrons. Between the two bands is a forbidden region where electrons are not allowed to exist, typically referred to as the energy band gap. If a radioactive energy quantum, such as a gamma ray or charged particle, interacts in the scintillation material, it can excite numerous electrons from the valence band and the tightly bound bands up into the conduction bands (see Fig. 13a). These electrons rapidly lose energy and fall to the conduction band edge, EC . As they de-excite and drop back into the valence band, they can lose energy through light emissions. Unfortunately, because the radiated energy of the photons is equivalent to the band gap energy, these same photons can be reabsorbed in the scintillator and again excite electrons into the conduction band. Hence, the scintillator can be opaque to its own light emissions. There are exceptions in which intrinsic scintillators work well. For example, bismuth germanate (BGO) releases light through optical transitions of Bi+3 ions, which release light that is lower in energy than the band gap and hence is relatively transparent to its own light emissions.

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However, if an impurity or dopant is added to the crystal, it can produce allowed states in the band gap, as depicted in Fig. 13b. Such a scintillator is referred to as being activated. In the best of cases, the impurity atoms are uniformly distributed throughout the scintillator. When electrons are excited by a radiation event, they migrate through the crystal, many of which drop into the excited state of the impurity atom. Upon de-excitation, an electron will yield a photon equal in energy to the difference between the impurity atom excited and ground states. Hence, it will most likely not be reabsorbed by the scintillator material. Careful selection of the proper impurity dopant can allow for the light emission wavelength to be tailored specifically to match the sensitivity of the light collection device. NaI(Tl) Scintillation Detectors The most used inorganic scintillator current with the writing of this handbook is NaI(Tl), meaning that the scintillator is the salt NaI that has been activated with the dopant Tl. NaI(Tl) yields approximately 43,000 photons per MeV of energy absorbed in the crystal. Light is emitted from NaI(Tl) in a continuous spectrum, yet the most probable emission is at 415 nm, which matches well to typical commercial photomultiplier tubes. The decay time of NaI(Tl) is 230 ns, which refers to the time required to release 63.2% of the scintillation photons. It is the availability of large sizes and the acceptably linear response to gamma rays that make NaI(Tl) important. Many different sizes are available, ranging in size from cylinders that are only 0.5 inch diameter to almost a meter in diameter. Yet, the most preferred geometry remains the 3 × 3 inch (7.62 × 7.62 cm) right circular cylinder. It is the most characterized NaI(Tl) detector size with extensive efficiency data in the literature. Further, it is the standard by which all other inorganic scintillators are measured. Because of its high efficiency for electromagnetic radiation (see Fig. 14), NaI(Tl) is widely used to measure x rays and gamma rays. x ray detectors with a thin entrance window containing a very thin NaI(Tl) detector are often used to measure the intensity and/or spectrum of low-energy electromagnetic radiation. NaI(Tl) detectors do not require cooling during operation and can be used in a great variety of applications. Compact spectrometers with NaI(Tl) coupled to an SiPM array are commercially available. The bare NaI(Tl) crystal is hygroscopic and fragile. However, when properly packaged, field applications are possible because they can operate over a long time period in warm and humid environments, resist a reasonable level of mechanical shock, and are resistant to radiation damage. Basically, for any application requiring a detector with a high gamma-ray efficiency and a modest energy resolution, the NaI(Tl) detector is clearly a good choice. Other Inorganic Scintillation Detectors Since the discovery of NaI(Tl) in 1948, the search has continued for a better scintillator for higher-energy resolution gamma-ray spectroscopy. There has been some limited success, which includes those scintillators listed in Table 3. For instance, CsI(Na) is similar in performance to NaI(Tl) but has a longer decay time. CsI(Tl) has much higher light output than NaI(Tl), but the emission spectrum

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Fig. 14 Intrinsic peak efficiency for NaI(Tl) detectors

maximizes at 560 nm, which does not couple well to PMTs. However, CsI(Tl) has been coupled to Si photodiode sensors and silicon photomultipliers (SiPM) quite successfully. Bismuth germanate (BGO) has lower light output but is much denser and a better absorber of gamma rays. As a result, BGO is used for medical imaging systems, which helps to reduce the overall radiation dose that a patient receives during the imaging procedure. Over the past 10 years, lutetium oxyorthosilicate (LSO(Ce)), another heavy element scintillator, has become a popular alternative for medical imaging instrumentation, especially for PET scanning systems. LiI(Eu) is a scintillator that is primarily used for neutron detection, relying upon the 6 Li content in the crystal. In recent years, LaBr3 , a relatively new scintillator with exceptional properties for gamma-ray spectroscopy, has become available, demonstrating lower than 3% FWHM for 662- keV gamma rays. LaBr3 (Ce) has much higher light yield and a much shorter decay constant than NaI(Tl). Further, it is composed of higher Z elements and hence is a better gamma-ray absorber than NaI(Tl). However, it is extremely hygroscopic and fragile and hence is difficult to produce and handle. Although it has recently become commercially available, it is relatively expensive compared to NaI(Tl). A performance comparison between NaI(Tl), BGO, and LaBr3 (Ce) is shown in Fig. 15. Also, the various elpasolite scintillators have become

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Table 3 Widely used inorganic scintillator materials with some of their properties Density Scintillator (g/cm3 ) NaI(Tl) 3.67 BGO 7.13 CaF2 (Eu) 3.18 CeBr3 5.2 CsI(Na) 4.51 CsI(Tl) 4.51 CLYC(Ce) 3.31 CLLB(Ce) 4.2 CLLBC(Ce) 4.08 GSO(Ce) 6.71 LaBr3 (Ce) 5.29 LaCl3 (Ce) 3.86 LiI(Eu) 4.08 LSO(Ce) 7.4 LuAP(Ce) 8.34 LuAG(Pr) 6.71 SrI2 (Eu) 4.55 YAP(Ce) 5.35 YAG(Ce) 4.55

Wavelength of maximum emission (nm) 415 480 435 371 420 540 372, 400 420 420 440 380 350 470 420 365 310 435 370 550

Decay time (ns) 230 300 900 17 680, 3340 460, 4180 600, 6000 180, 1100 120, 500, 1500 56, 400 16 28 1400 47 16.5, 74 20–22 1200 27 88, 302

Light yield in photons/MeV 43,000 8200 24,000 68,000 ∼45,000 ∼57,500 9565, 18,400 43,000 45,000 9000 63,000 49,000 15,000 25,000 11,400 ∼18,000 115,000 18,000 17,000

Relative PMT response compared to NaI(Tl) 1.00 0.13 0.50 ND 1.10 0.49 ND 1.15 ∼0.70 0.20 1.30 0.70–0.90 0.23 0.75 ND ND ND 0.45 0.50

commercially available, the most common being CLYC(Ce), CLLB(Ce), and CLLBC(Ce). These elpasolite scintillations perform with good energy resolution and have added value as neutron detectors. Overall, there are numerous inorganic scintillators available for special radiation detection purposes. A review article on various inorganic scintillators can be found in the literature (McGregor 2018).

Light Collection The light produced from a scintillation detector is collected by a photosensitive device, such as a photomultiplier tube, a photodiode, a microchannel plate, or a SiPM. The light is then converted to a measureable voltage pulse. Photomultiplier Tubes The photomultiplier tube (PMT) is commonly used to measure the light output from a scintillation detector. Referring to Fig. 16, the basic PMT has a photocathode which is located so as to absorb light emissions from a light source such as a scintillating material. When light photons strike the coating on the photocathode, they excite electrons which can diffuse to the surface facing the vacuum of the tube. A fraction of these excited electrons will escape the surface and leap into the vacuum tube. A voltage applied to the tube will guide the liberated electrons to an adjacent electrode named a dynode. As an electron approaches the dynode, it

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Fig. 15 Comparison of normalized spectral performance for a 2 × 2 NaI(Tl) detector, a 2 × 2 LaBr3 (Ce) detector, and a BGO detector of similar size. The source used was 137 Cs. Copyright (2020). From Radiation Detection: Concepts, Methods and Devices by D.S. McGregor and J.K. Shultis. Reproduced by permission of Taylor and Francis Group, LLC, a division of Informa PLC window

photocathode

dynodes

scintillator

anode

γ-ray

current output

reflector scintillation photons

coupling compound

photoelectron

vacuum tube

Fig. 16 The basic mechanism of a photomultiplier tube (PMT). An absorbed γ ray causes the emission of numerous light photons which can strike the photocathode. A scintillation photon that strikes the photocathode excites a photoelectron. The photoelectron is accelerated and guided to the first dynode with an electric field, where it strikes the dynode and ejects more electrons. These electrons are accelerated to the next dynode and excite more electrons. The process continues through the dynode chain until the cascade of electrons is collected at the anode, which is used to produce a voltage pulse (McGregor 2016)

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gains velocity and energy from the applied voltage and electric field. Hence, when it strikes the dynode, it will again cause more electrons to become liberated into the tube. These newly liberated electrons are then guided to the next dynode where more electrons are liberated and so on. As a result, the total number of electrons released is a function of the number of dynodes in the PMT and the photoefficiency of the photocathode and the dynodes. The total charge released in the PMT is Q = qN0 Gn ,

(64)

where q is the charge of an electron, N0 is the initial number of electrons released at the photocathode, G is the number of electrons released per dynode per electron (the gain), and n is the total number of dynodes in the PMT. For instance, suppose that a PMT has 10 dynodes each operated with a gain of 4. An event that initially releases 1000 electrons (N0 ) will cause over 109 electrons to emerge from the PMT. The photomultiplier tube is an important tool in radiation detection, as it is the device that allowed scintillation materials to be used as practical detectors. It can take a minute amount of light produced in a scintillator from a single radiation absorption and turn it into a large electrical signal. It is this electrical signal, typically converted to a voltage pulse, that is measured from the scintillation detector system. PMTs are stable and electronically quiet (low noise). Modern varieties have exceptional photocathode and dynode efficiencies, often referred to as quantum efficiency, with gains that can exceed 30. However there is a drawback. PMT materials used as photocathodes are generally fabricated from alkaline metals, which are most sensitive to light in the 350 to 450 nm range. Scintillators emitting light outside of these boundaries can still be used under some circumstances, yet their effectiveness can be severely compromised. Microchannel Plates Microchannel plates are an alternative method of amplifying signals from a scintillator. Microchannel plates are glass tubes with the insides coated with secondary electron-emissive materials. A voltage is applied across the tube length which causes electrons to cascade down the tube. Every time an electron strikes the tube wall, more electrons are emitted, much like with dynodes in a PMT. Hence, a single electron can cause a cascade that can eventually produce 106 electrons emitted from the other end of the tube. Typically, hundreds of these microchannels are bonded together to form a plate of channels running in parallel. The microchannel plate can be fastened to a common scintillator, whether organic or inorganic, which operates in a similar fashion as a PMT. Light photons entering the microchannel plate cause the ejection of primary photoelectrons, which cascade down the microchannels to liberate millions more electrons. The main advantage of a microchannel plate is its compact size, in which a microchannel plate only 1 inch thick can produce a signal of similar strength as a common PMT. The main problem with microchannel plates is the signal produced per monoenergetic radiation event is statistically much

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noisier than that produced by a PMT; hence, the energy resolution for spectroscopy is typically worse than provided by a PMT. Photodiodes Photodiodes are actually semiconductor devices formed into a pn or pin junction diode. When photons strike the semiconductor, usually Si- or GaAs-based materials, electrons are excited. A voltage bias across the diode causes the electrons to drift across the device and induce charge much like a gas-filled ion chamber. The quantum efficiency of the semiconductor diode varies with device configuration and packaging. For instance, various different commercial Si photodiodes have peak efficiencies at wavelengths ranging between 700 and 1000 nm. Regardless, they are typically more sensitive to longer wavelengths than common commercial PMTs. As a result, CsI(Tl) emissions match better to Si photodiodes than PMTs. Photodiodes operate with low voltage; are small, rugged, and relatively inexpensive; and hence offer a compact method of sensing light emissions from scintillators. However, they typically do not couple well to light emissions near the 400 nm range (blue-green) and have low gain, if any at all. Consequently, the signals from photodiodes need more amplification than signals from PMTs, and scintillator/photodiode systems generally produce worse energy resolution than do scintillator/PMT systems. Silicon Photomultipliers Junction breakdown of semiconductors can be used as another means of radiation counting and spectroscopy. For any pn junction operated with a reverse bias voltage, there is a voltage above which the junction “breaks down” and continues to conduct current across the semiconductor. This phenomenon is initiated by three different means, namely (1) thermal instabilities, (2) tunneling current, and (3) avalanche breakdown. The avalanche process is solely dependent upon what occurs within the diode depletion region Wd . Hence, an event that excites a charge carrier within the active depletion region may trigger an enormous, continuous avalanche from impact ionization with gains exceeding 106 . This interesting mode of operation is usually not preferred for avalanche photodiode operation (APD) operation, the effects of which were studied by McIntyre (1961) and Haitz (1961). However, there are particular applications in which the breakdown mode of operation is beneficial, mainly realized with the single-photon avalanche diode (SPAD), so-named because of its ability to detect low light levels, one photon at a time. The leading edge of an avalanche signal marks the arrival time of the interacting photon within the depletion region. After the avalanche is triggered, the self-sustained current continues to flow unless quenched. Often a series resistance is included in the design that serves to quench the avalanche, much like an externally quenched GM counter. As a matter of fact, APDs designed and operated in this mode are often said to operate in “Geiger mode” (Renker 2006). As the avalanche current flows through the quenching resistance, it draws voltage from the source, thereby causing the voltage across the APD to drop below the breakdown voltage, causing the avalanche to cease. As a result, the output current and collected charge are nearly the same for each avalanche regardless of energy deposition in the device, statistical

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fluctuations notwithstanding. Consequently, if two or more photons interact in the device simultaneously, the total charge liberated from the quenched avalanche is roughly the same as if a single photon caused the avalanche, again much like a GM counter. Silicon photomultipliers (SiPM) use the breakdown condition with thousands of tiny silicon APDs arranged into a compact array, presently on the order of 6 × 6 mm area or less. The individual APDs in silicon photomultipliers (SiPM) have linear dimensions usually between 20 and 100 μm; a common size is 35× 35 μm per APD pixel. Hence, a single SiPM array may have more than 104 APD pixels. Each APD is electrically decoupled from adjacent APDs with polysilicon resistors fabricated on the same substrate. Typical operational bias voltage is 10% to 15% above the breakdown voltage. SiPMs are commercially available and in some applications are replacing the traditional PMT. A scintillator may be fastened to the SiPM face, much like a conventional PMT, and light from radiation interactions within the scintillator triggers the APDs. Each APD provides information that is ultimately limited to recognizing the excitation of an initial electron-hole pair within the avalanche region. Because each pixel produces an avalanche of relatively the same magnitude per event, the total photon count can be determined by dividing the total measured charge by the avalanche gain. Hence, the device operates mainly as a photon counter, and the total measured current is proportional to the total number of photons. The enormous gain per pixel, when the pixel counts are added together, can produce more than 109 free electrons per event. A particular advantage of SiPMs is the high quantum efficiency of Si for photons with wavelengths between 350 and 950 nm. The photon detection efficiency of an SiPM can be much higher than a common PMT. However, many commercial SiPM units are designed with peak sensitivity near 420 nm, similar to conventional bialkali PMTs. SiPMs are compact and rugged, perhaps one of the most useful features of SiPMs. They need only modest power, usually requiring no more than a few tens of volts for operation. SiPMs are also insensitive to magnetic fields, thereby making them an attractive choice for applications in areas where high magnetic fields may arise.

Factors Affecting Energy Resolution The energy resolution achievable from a scintillation spectrometer is determined by a number of factors, including brightness, reflector efficiency, light collection efficiency, PMT quantum efficiency, activator uniformity, and scintillator light yield linearity. Simplistically, the energy resolution can be described as R2 = Rs2 + Rp2 ,

(65)

where Rs is the energy resolution contribution relating to the scintillation crystal and encapsulation and Rp is the energy resolution contribution relating to the photon detection device. The term Rs can be described by

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Rs2 = Rn2 + Ri2 + Rt2 + Rd2 ,

(66)

where Rn is resolution broadening from statistical fluctuations in the number of electrons excited by monoenergetic absorption events, Rt is resolution broadening from variations in light transfer to the light detection device, Ri is resolution broadening from inhomogeneity, and Rd is the nonproportionality of response. The variance Rn2 can be expected to follow a somewhat Gaussian distribution, corrected with the appropriate Fano factor to correct energy band structure. The distribution of dopants in the scintillator may not be homogeneously distributed in the material, causing spatially dependent variations Ri2 in the number of electrons diffusing to the photon-producing activator sites. Although reflectors around scintillator detectors can be quite efficient, the angle at which photons strike the light collector (PMT, for instance) may cause variations Rt2 in the number of photons that actually enter the light detector. Other factors affecting the light transfer variation include nonuniform clarity of the scintillator, imperfections in the reflector, and nonuniformity of the coupling compound between the scintillator and the light detection device. Most scintillators have a nonlinear light yield as a function of absorbed photon energy, which is especially true in the energy range between a few keV up to 1 MeV. As a result, there will be a variation Rd2 in the number of photons produced for monoenergetic gamma rays, depending on if the photon was absorbed through a single photoelectric event or numerous Compton scatters. The light collection terminates at the photodetection device, typically a PMT or SiPM, in which the light is converted into an electron signal. The conversion efficiency and variance Rp2 of the light collection efficiency are affected by the wavelength of light striking the device and uniformity of the collecting layers. For instance, scintillators emit a spectrum of photon wavelengths, which may or may not match well to the quantum conversion efficiency of the PMT photocathode or the SiPM material. Further, the photocathode layer will have some amount of variance in thickness, which affects the variance in the number of electrons ejected from the photocathode per initial gamma-ray interaction event. With SiPMs, it is possible that two or more photons simultaneously strike the same pixel, resulting in only one of the photons being recorded. As the photon flux increases (brighter scintillator or higher gamma-ray energy), this effect increases, and more scintillation photons are not recorded, causing nonlinearity in the pulse-height spectrum.

Semiconductor Spectrometers In some way, the operation of a semiconductor detector combines the concepts of the charge excitation method in a crystalline inorganic scintillator and the charge collection method of a gas-filled ion chamber. Referring to Fig. 17, gamma rays or charged particles that are absorbed in the semiconductor will excite electrons from the valence and tightly bound energy bands up into the numerous conduction bands. The empty states left behind by the negative electrons will behave as positively

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Upper Band

Forbidden Band

negative voltage reference

Conduction Band

Ec Band Gap

Ev Valence Band

+

“electrons”

Eg

positive voltage reference

“holes ”

Forbidden Band Tightly Bound Band

γ-ray

Fig. 17 Absorbed radiation energy excites electrons from the valence and tightly bound bands up into the higher conduction bands, in a similar manner as excitation occurs in a crystalline inorganic scintillator. The empty states left behind, referred to as holes, behave as positive charges. The electrons quickly de-excite to the lowest conduction band edge, EC , and the holes rapidly deexcite to the top of the valence band, EV . A voltage applied to the detector causes the electron and hole charge carriers to drift to the device contacts, much in the same manner as electron-ion pairs drift to the electrical terminals in a gas-filled ion chamber (McGregor 2016)

charged particles generally referred to as holes. The excited electrons will rapidly de-excite to the conduction band edge, EC . Likewise, as electrons high in the valence band fall to lower empty states in the valence and tightly bound bands, it gives the effect of holes moving up to the valence band edge, EV . A single major difference between a semiconductor and almost all scintillators is that the mobility of charge carriers in semiconductors is high enough to allow for conduction, whereas scintillation materials are mostly insulating materials that do not conduct. As a result, a voltage can be applied across a semiconductor material that will cause the negative electrons and positive holes, commonly referred to as electron-hole pairs, to drift in opposite directions, much like the electron-ion pairs in a gas-filled ion chamber. In fact, at one time semiconductor detectors were referred to as “solid-state ion chambers.” As these charges drift across the semiconductor,

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Table 4 Common semiconductors and properties

Semiconductor Si SiC(4H) Ge GaAs CdTe Cd0.8 Zn0.2 Te HgI2

Atomic numbers (Z) 14 14/6 32 31/33 48/52 48/30/52 80/53

Density (g cm−3 ) 2.33 3.21 5.33 5.32 6.06 6.0 6.4

Band gap (eV) 1.12 3.23 0.72 1.42 1.52 1.60 2.13

Ionization energy (eV per e-h pair) 3.61 7.8 2.98 4.2 4.43 5.0 4.3

Fano factor ≈0.10 – ≈0.08 ≈0.18 ≈0.15 ≈0.09 ≈0.19

they induce a current to flow in an external circuit which can be measured as a current or stored across a capacitor to form a voltage. Semiconductors are far more desirable for energy spectroscopy than gas-filled detectors or scintillation detectors because they are capable of much higher-energy resolution. The observed improvement is largely due to the better statistics regarding the number of charges produced by a radiation interaction. Typically, it only takes 3–5 eV to produce an electron-hole pair in a semiconductor (Table 4). By comparison, it takes between 25 and 40 eV to produce an electron-ion pair in a gas-filled detector and between 100 eV to 1 keV to produce a single photoelectron ejection from the PMT photocathode in a scintillation/PMT detector (primarily due to light reflections and poor quantum efficiency at the photocathode). Hence, statistically, semiconductors produce more charge carriers from the primary ionization event, which determines the statistical fluctuation in the energy resolution. Most semiconductor detectors are configured as either planar or coaxial geometries, as shown in Fig. 18. Small semiconductor detectors are configured as planar devices and can be used for charged particle detection and gamma-ray detection. Large semiconductor gamma-ray spectrometers are often configured in a coaxial form to reduce the capacitance of the detector (which can affect the overall energy resolution). There are three basic methods generally used to reduce leakage currents through semiconductor detectors. Most commonly the semiconductors are formed into reverse biased pn or pin junction diodes, which are the case for Ge, Si, GaAs, and InP detectors. Alternatively, highly resistive semiconductors, such as CdTe, CdZnTe, and HgI2 , need only to have ohmic contacts since the bulk resistance of the material is high enough to effectively reduce leakage currents. Finally, large detectors, such as high-purity Ge detectors and lithium-drifted Si detectors, are chilled with liquid nitrogen (LN2) or a mechanical refrigerator to reduce thermally generated leakage currents.

Ge Detectors Although Li drifting allowed Ge-based semiconductor gamma-ray spectrometers, denoted Ge(Li)detectors, to be realized, it came with problems. Li is highly mobile

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γ-ray

semiconductor

holes

electrical contact

+ ++ +

++ + +

---

- --

electrons

holes electrons

+ electrical contact

Planar Design

γ-ray

electrical contact

+

electrical contact

Coaxial Design (cross section)

Fig. 18 The most common designs for semiconductor detectors are the planar and coaxial configurations (McGregor 2016)

in Ge and must be locked into place by immediately freezing the Ge crystal with LN2 after the drifting process is finished. Further, if Ge(Li) detectors were ever allowed to warm up, the Li would diffuse and redistribute, hence ruining the detectors. As a result, Ge(Li) detectors had to constantly be kept at LN2 temperatures, a major inconvenience. Zone refinement of Ge materials now allows for impurities to be removed from the material such that Li drifting is no longer necessary. Hence, Ge(Li) detectors have been replaced by high-purity Ge detectors, denoted HPGe detectors. However, HPGe detectors must still be chilled with LN2 when operated in order to reduce excessive thermally generated leakage currents. HPGe detectors have exceptional energy resolution compared to scintillation and gas-filled detectors. The dramatic difference in the energy resolution between NaI(Tl) and HPGe spectrometers is shown in Fig. 19, where there is a spectroscopic comparison of measurements made of a mixed 152 Eu, 154 Eu, and 155 Eu radiation source. HPGe detectors are standard high-resolution spectroscopy devices used in the laboratory. Their high-energy resolution allows them to easily identify radioactive isotopes for a variety of applications, which includes impurity analysis, composition analysis, and medical isotope characterization. Portable devices with small LN2 dewars are also available for remote spectroscopy measurements, although the dewar capacity allows for only 1 day of operation. Hence, a source of LN2 must be nearby for such an apparatus. Much improvement has been realized with small mechanical refrigerators, and commercial HPGe detectors with portable refrigerator units are available, thereby largely mitigating the need for an LN2 source. The gamma-ray absorption efficiency for Ge (Z = 32) is much less than that for the iodine (Z = 53) in NaI(Tl). Due to the higher atomic number and generally larger size, NaI(Tl) detectors often have higher detection efficiency for high-energy gamma rays than do HPGe detectors (but much poorer energy resolution). When first introduced, Ge detector efficiency was commonly compared to that of a

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Fig. 19 Comparison of the energy resolution between a NaI(Tl) and an HPGe detector. The gamma-ray source is a mixture of 152 Eu, 154 Eu, and 155 Eu [McGregor 2008]

3-inch-diameter × 3-inch-long (3×3) right circular cylinder of NaI(Tl) for 1332 keV gamma rays from 60 Co. Even today, the relative efficiency of a Ge detector is quoted in terms of a 3×3 NaI(Tl) detector. For instance, a 60% efficient HPGe detector will have 60% of the efficiency that a 3 × 3 NaI(Tl) detector would for 1332 keV gamma rays from 60 Co. HPGe detectors are much more expensive than NaI(Tl) detectors and hence are best used when gamma-ray energy resolution is most important for measurements. If efficiency is of greatest concern, it is often wiser to use a NaI(Tl) detector. Still, although expensive, modern manufacturers do produce larger HPGe detectors with 200% efficiency (as compared to a 3 × 3 NaI(Tl) detector).

Si Detectors The problem with Li redistribution does not apply to Si, hence Si(Li) detectors are still manufactured and available. Since Si(Li) detectors have a much lower atomic number than HPGe, their relative efficiency per unit thickness is significantly lower for electromagnetic radiation. However, for x ray or gamma-ray energies less than about 30 keV, commercially available Si(Li) detectors are thick enough to provide performance which is comparable to HPGe detectors. For example, a 3–5 -mm-thick detector with a thin entrance window has an efficiency of 100% near 10 keV. Si(Li) detectors are preferred over HPGe detectors for low-energy x ray measurements, primarily due to the lower-energy x ray escape peak features that appear in a Si(Li)

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detector spectrum as opposed to an HPGe detector spectrum. Further, background gamma rays tend to interact more strongly with HPGe detectors than with Si(Li) detectors, which also complicates the x ray spectrum. Based upon the fact that a majority of the applications require a thin window, Si(Li) detectors are often manufactured with thin beryllium windows. Typically, Si(Li) detectors are chilled with LN2 to reduce thermal leakage currents, improving performance. High-purity Si detectors, which do not incorporate Li drifting, are also available but are significantly smaller than HPGe and Si(Li) detectors. Such devices are typically only a few hundred microns thick and are designed for charged-particle spectroscopy. They range in diameter from one cm to several cm. The detectors are formed as diodes to reduce leakage currents and use either a thin metal contact or a thin implanted dopant layer contact to produce the rectifying diode configuration. The devices are always operated in reverse bias to reduce leakage currents. Heavy charged particles, such as alpha particles, rapidly lose energy as they pass through a substance, including the detector contacts. In order to preserve the original energy of charged particles under investigation, the detector contacts and implanted junctions are relatively thin, typically being only a few hundred nanometers thick to reduce energy loss in the contact layer. Further, the measurements are typically conducted in a vacuum chamber to reduce energy loss otherwise encountered by the alpha particles in air. Since the detectors are not very thick, they do not have much thermal charge carrier generation and consequently do not need to be cooled during operation.

Compound Semiconductor Detectors Although HPGe and Si(Li) detectors have proven to be useful and important semiconductor detectors, the fact that they must be chilled with either LN2 or a refrigerator is a considerable inconvenience. Hence, much research has been devoted to the search for semiconductors that can be used at room temperature. The main requirement is that the band gap energy (Eg ) be greater than 1.4 eV, which seriously limits the field of candidates. Further, the material must be composed of high atomic numbers for adequate gamma-ray absorption. As a result, there are only a few candidates, all of which are compound semiconductors, meaning that they are composed of two or more elements. Hence, the issues regarding crystal growth defects and impurities become far more problematic. Still, there are several materials that show promise, three of which are briefly mentioned here. HgI2 , CdTe, and CdZnTe Detectors Mercuric iodide (HgI2 ) has been studied since the early 1970s as a candidate gamma-ray spectrometer and has been used for commercial x ray spectrometry analysis tools. The high atomic numbers of Hg (Z = 80) and iodine (Z = 53) make it attractive as an efficient gamma-ray absorber, and its large band gap of 2.13 eV allows it to be used as a room temperature gamma-ray spectrometer. However, the bright red crystals are difficult to grow and manufacture into detectors. The voltage required to operate the devices is excessive, usually 1000 volts or more for a device

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only a few mm thick. HgI2 detectors degrade over time, an effect referred to as polarization, which is another reason why they do not enjoy widespread use. Cadmium telluride (CdTe) has been studied since the late 1960s as a candidate gamma-ray spectrometer. They have relatively good gamma-ray absorption efficiency, with Cd (Z = 48) and Te (Z = 52). The band gap of 1.52 eV allows CdTe to be operated at room temperature. Compared to HgI2 , the crystals are easier to grow and are not as fragile. Further, although still difficult to manufacture, detectors are easier to produce than HgI2 . There are commercial vendors of CdTe detectors, although the devices are relatively small, typically being only a few mm thick with area of only a few mm2 . CdTe detectors have been used for room temperatureoperated low-energy gamma-ray spectroscopy systems and also for electronic personal dosimeters. Over time, CdTe detectors also suffer from polarization. Cadmium zinc telluride (CdZnTe or CZT) has been studied as a gamma-ray spectrometer since 1990. By far, the most studied version of CZT has 10% Zn, 40% Cd, and 50% Te molar concentrations, which yields a band gap energy of approximately 1.6 eV. CZT detectors offer an excellent option for low-energy x ray spectroscopy where cooling is not possible. Although the detectors are quite small compared to HPGe and Si(Li) detectors, they are manufactured in sizes ranging from 0.1 to 2.5 cm3 , depending on the detector configuration. Still, due to their small size, they perform best at gamma-ray energies below 1.0 MeV. Various clever electrode designs have been incorporated into new CZT detectors to improve their energy resolution, and CZT has become the most used compound semiconductor for gamma-ray spectroscopy. Some detector cooling (near −30 ◦ C), usually performed with miniature electronic Peltier coolers, improves the resolution performance, although excellent performance can be achieved at room temperature. The average ionization energy is 5.0 eV per electron-hole pair, which is greater than Ge (2.98 eV) or Si (3.6 eV). Hence, the resolution of CZT detectors is not as good as HPGe or Si(Li) detectors, although much better than gas-filled and scintillation detectors (Fig. 20). When LN2 chilling is not an option, CZT detectors are a good choice for radiation measurement applications requiring good energy resolution. Typically, CZT detectors do not show polarization effects.

Factors Affecting Energy Resolution The energy resolution achievable from a semiconductor spectrometer is largely determined by the average ionization energy, leakage currents, electronic noise, mean free drift times, and the charge carrier mobilities. Energy resolution is quoted in terms of energy spread at the full width at half the maximum (FWHM) of a spectral full-energy peak, 

2 1/2 √ 2 FWHM = (FWHMnoise ) + 2.35 wF E ,

(67)

where w is the average energy to produce an electron-hole pair, E is the photon energy, and F is the Fano factor (typically 0.1). The Fano factor is a correction

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Fig. 20 Spectroscopic results from 137 Cs for several Frisch collar CdZnTe detectors, each having a 2:1 aspect ratio. The sizes and FWHM resolutions are (a) 0.9% for a 4.7 × 4.7 × 9.5 mm device, (b) 1.1% for a 6.5 × 6.5 × 13 mm device, (c) 1.2% for a 7.8 × 7.8 × 15.6 mm device, and (d) 2.4% for a 11 × 11 × 22 mm device. (After Kargar et al. 2009)

factor to account for typically higher-energy resolution than predicted from pure Gaussian statistics. For semiconductor detectors with short charge carrier mean free drift times τe,h and low charge carrier mobilities μe,h , the energy resolution will suffer from loss of charge carriers during the collection process. Consequently there is a variance in the current measured from monoenergetic gamma-ray events as a function of the interaction position and detector size. The total charge collected is usually affected by crystalline imperfections that serve as trapping sites, which are energy states that remove free charge carriers from the conduction and valence bands. Charge is induced while these charge carriers are in motion; hence, their removal diminishes the output voltage. Although the actual trapping process is complicated, it is typical to describe the relative charge collection efficiency as a simplified function of trapping. For planar-shaped detectors, the induced charge is given by Q = ξe (1 − e−x/(ξe Wd ) ) + ξh (1 − e(x−Wd )/(ξh Wd ) ), Q0

(68)

where Wd is the detector active region width, Q0 is the initial excited charge magnitude, and x is the event location in the detector, and

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 ξe,h =

τe,h ve,h Wd



 =

μe,h τe,h V , Wd2

(69)

where v is the charge carrier speed, V is the applied operating voltage, and the e and h subscripts denote properties for electrons and holes, respectively. Note that the relative charge collection is dependent upon the interaction location x, and for low values of ξe,h , the energy resolution is poor. Typically, good energy resolution is achieved if ξe,h > 50 for both electrons and holes, where Q/Q0 has little deviation over the detector width Wd . Otherwise, the energy resolution suffers for higher-energy γ rays (300 keV). The value of ξe,h can be increased by decreasing the detector width Wd , increasing carrier mean free drift times τe,h through material improvement, or increasing the applied voltage V . Due to practical voltage limitations and the fundamental difficulty with improving materials, most compound semiconductor detectors are manufactured with small active widths to improve detector energy resolution, and, hence, the devices are relatively small. The μτ values for electrons and holes are often quoted measures of quality for compound semiconductors used as γ -ray spectrometers.

Cryogenic Spectrometers (Microcalorimeters) Microcalorimeter detectors are energy dispersive spectrometers that measure the thermal change T in an absorber rather than the change in charge concentration Q. The detector consists of an absorber in contact with a type of low-temperature (mK range) thermometer. When absorbed, an x ray produces heat in the absorber material which can then be measured as T ≈ E/Ch , where Ch is the heat capacity of the absorber and E is the initial x ray energy. Hence, a measurement of the thermal rise in temperature can yield the photon energy. Early microcalorimeters used semiconductor thermistors as the thermometer. An x ray absorption causes the resistance in the thermistor to increase, hence producing a change in voltage for current-biased devices. These voltages can be measured as an indication of the T absorbed in the detector. Although effective, yielding energy resolutions below 8 eV for 5.9 keV gamma rays from 55 Fe, the resolution is limited by the heat capacity of the absorbers. The heat capacity is a function of the absorber volume and T 3 . In general, the change in FWHM can be approximated by  FWHM ≈ 2.35η kT 2 Ch ,

(70)

where k is Boltzmann’s constant, T is the absolute temperature, and η is an experimental constant dependent upon thermal conductance and heat capacity. From Eq. 70, it becomes clear that the energy resolution improves as the sample volume decreases, yet this resolution improvement comes at the expense of detection efficiency.

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Another form of the microcalorimeter utilizes superconducting transition-edge sensor (TES) thermometers. The device is chilled well below the transition edge and heated ohmically by applying a constant voltage bias to the absorber. The bias is adjusted such that the temperature of the device is maintained slightly below the transition edge. The absorption of an x ray causes the superconducting absorber to become normal conducting, thereby increasing the resistance and decreasing the current. The current is measured through induction with a superconducting quantum interference device (SQUID) current amplifier. Typically the choice of absorber depends greatly upon the photon energy of interest. Energy resolution below 2 eV has been achieved for 5.9 keV gamma rays from 55 Fe using Bi absorbers on Mo-Au TES thermometers. Higher-energy gamma rays, yet generally below 100 keV, have good results from superconducting Sn, producing energy resolution below 30 eV for 102 keV gamma rays. The response time is limited by the heat capacity, in which the reset time is dependent upon the time it takes to return the detector temperature to equilibrium, where the cooling time is represented by τ = Ch /G where G is the thermal conductance between the thermometer and the cryostat. Arrays of microcalorimeters can be used to maintain fast response time while increasing detection efficiency. Figure 21 shows comparison spectra for a typical HPGe semiconductor detector and a TES microcalorimeter array. 104 241

Counts / 10 eV bin

239

Pu

Am

241

Ge

238

Pu

241

Cal

103

Np K

2

UK

Am

1

Pu Pu K

1

240

Pu

Pu K 2 Sn escape x rays

102

Np K

101

96

98

1

102 100 Energy (keV)

104

Fig. 21 Pu spectrum from a microcalorimeter array using data from 11 of 13 active pixels. The combined array resolution is approximately 45 eV. At this resolution, the broad x ray peaks can be readily distinguished from gamma-ray peaks. The solid line curve is a spectrum taken with a conventional HPGe detector (c) [2009] IEEE. Reprinted, with permission, from Bacrania et al., IEEE Trans Nucl Sci, 56, 2299–2302, [2009]

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Crystal Diffractometers (Wavelength-Dispersive Spectroscopy) Ultrahigh resolution can be achieved for low-energy gamma rays and x rays with wavelength-dispersive spectroscopy (WDS), which can yield x ray peak resolution better than semiconductor or cryogenic detectors. The method utilizes Bragg scattering, in which the Bragg condition must be satisfied: nλ = 2d sin θ,

(71)

where n is an integer, d is the spacing between crystalline planes, λ is the wavelength of the photon under inspection, and θ is the angle at which radiation intersects the crystal from the parallel condition. It is difficult to make a portable system; hence, these instruments are generally attached to an electron microprobe or scanning electron microscope. Shown in Fig. 22 is a common arrangement for the tool, in which a sample under inspection is irradiated with an electron beam. thereby producing characteristic x rays from the sample. These x rays intersect a slightly bent diffraction crystal. Those x rays satisfying the Bragg condition will diffract into a detector and be recorded, whereas other x rays are absorbed, scatter randomly, or pass through the crystal. Because only the number of counts at a given diffraction angle need be recorded, the detector need not be a high-resolution spectrometer; hence, a gasfilled proportional counter is commonly used as the x ray detector. During operation, the crystal and detector are rotated through a Rowland circle, which allows for the

crystal crystal crystal electron beam

electron beam

detector

sample

R

detector 2R

Rowland circle

(a)

sample

R

Rowland circle

(b)

Fig. 22 A typical WDS diffraction arrangement is aligned on a Rowland circle. The sample location remains stationary. The diffraction crystal is bent with a radius twice that of the Rowland circle radius R, and it is typically ground with radius R. The Bragg condition is maintained for various values of λ by moving both the crystal and detector, with the sample remaining stationary, such that all points remain on the Rowland circle

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Fig. 23 Shown are (a) a comparison of EDS spectra from a Si(Li) detector and a microcalorimeter detector and (b) an additional comparison to a WDS detector. Reproduced from Wollman et al., J Microscopy, 188, 196–223, (1997) with the permission of Wiley Publishing

Bragg condition to be maintained as the arrangement rotates through a continuum of wavelengths. As a result, the x ray detector records the number of counts as a function of wavelength. The stringent requirement for the Bragg condition results in ultrahigh resolution, which can be plotted as a function of photon energy (see Fig. 23). The important advantage of WDS is the superior identification ability it provides to the user. Unfortunately, the system can be used only on photons of energy low enough to Bragg diffract. Several commercial systems have a rotating rack of different diffraction crystals that extend the sensitive range. WDS systems are laboratorybased and hence are not generally considered portable.

Summary Gamma-ray spectroscopy seeks to determine, first, the gamma-ray energies emitted by a sample or the nuclides (which emit gamma rays of certain energies) present within a sample. This goal can be called qualitative analysis. However, generally, one also seeks either the source strength of the particular gamma rays or the concentration of the nuclide emitting the gamma rays. This desired outcome is often referred to as quantitative analysis.

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One achieves the objectives of gamma-ray spectroscopy by analyzing spectra. In this chapter, pulse-height spectra in which number of counts are specified by discrete channel number are considered. This approach is used because channel number is directly proportional to pulse height and photon energy can then be obtained from pulse height whether or not the spectrometer is linear. Spectroscopic analysis techniques begin by attempting to determine the continuous channel number that corresponds to the centroids of the full-energy peaks in the spectrum that are of interest. The MCLLS approach focuses on the entire spectrum and seeks to determine the parameters of models that best fit all or major portions of the spectra. The symbolic Monte Carlo approach holds promise for spectroscopic applications in which the model is nonlinear in terms of the nuclide concentrations of samples. Depending upon the need, there are several devices that can be used for gammaray spectroscopy. Efficiency with adequate energy resolution can be provided with large volume scintillators, whereas high-energy resolution can be achieved with semiconductor detectors. Both scintillator and semiconductor detectors can be acquired as portable units with good detection efficiency for gamma rays. For ultrahigh-energy resolution, microcalorimeters or WDS diffractometers offer excellent performance. Yet, microcalorimeters and WDS spectrometers are generally restricted to laboratory-based instrumentation for low-energy gamma rays and x rays. Note that the spectrometers discussed in the present chapter represent only a select sample of variations commercially available. More information can be found in the book chapters dedicated to semiconductor and scintillation detectors.

Cross-References  Scintillators and Scintillation Detectors  Semiconductor Radiation Detectors

References Bacrania MK et al (2009) Large-area microcalorimeter detectors for ultra-high-resolution x ray and gamma-ray spectroscopy. IEEE Trans Nuc Sci 56(4):2299–2302 Barache D, Antoine J-P, Dereppe J-M (1997) The continuous wavelet transform, an analysis tool for NMR spectroscopy. J Magn Res 128:1–11 Bevington PR (1969) Data reduction and error analysis for the physical sciences. McGraw-Hill, New York Cline JE (1968) Studies of detection efficiencies and operating characteristics of Ge(Li) detectors. IEEE Trans Nucl Sci NS-15:198–213 Dunn WL (1981) Inverse Monte Carlo analysis. J Comput Phys 41(11):154–166 Dunn WL, Dunn TS (1982) An assymetric model for XPS analysis. Surf Interface Anal 4(3):77–88 Dunn WL, Shultis JK (2009) Monte Carlo analysis for design and analysis of radiation detectors. Radiat Phys Chem 78:852–858 Gardner RP, Sood A (2004) A Monte Carlo simulation approach for generating NaI detector response functions (DRF’s) that accounts for nonlinearity and variable flat continua. Nucl Instrum Methods B213:87–99

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Gardner RP, Xu L (2009) Status of the monte carlo library least-squares (MCLLS) approach for non-linear radiation analyzer problems. Radiat Phys Chem 78:843–851 Gentile NA (2001) Implicit monte carlo diffusion – an acceleration method for monte carlo timedependent radiative transfer simulations. J Comput Phys 172:543–571 Gilmore G (2008) Practical gamma-ray spectrometry, 2nd edn. Wiley, New York Haitz RH (1961) Model of the electrical behavior of a microplasma. J Appl Phys 35:1370–1376 Heath RL, Helmer RG, Schmittroth LA, Cazier GA (1967) Method for generating single gammaray shapes for analysis of spectra. Nucl Instrum Methods 47:281–304 IEEE/ANSI (1996) IEEE standard test procedures for germanium gamma-ray detectors, standard 325–1996 Kargar A, Brooks AC, Harrison MJ, Chen H, Awadalla S, Bindley G, McGregor DS (2009) Effect of crystal length on CdZnTe frisch collar device performance. In: IEEE Nucl Sci Symp Conf Rec, Orlando, 24 Oct–1 Nov, pp 2017–2022 Kis Z, Fazekas B, Östör J, Révay Z, Belgya T, Molnár GL, Koltay L (1998) Comparison of efficiency functions for Ge gamma-ray detectors in a wide energy range. Nucl Instrum Methods A418:374–386 Marshall III JH, Zumberge JF (1989) On-line measurements of bulk coal using prompt gamma neutron activation analysis. Nucl Geophys 3:445–459 McGregor DS (2016) Detection and measurement of radiation, Ch 8. In: Shultis JK, Faw RE (eds) Fundamentals of nuclear science and engineering, 3rd edn. CRC Press, New York McGregor DS (2018) Materials for gamma-ray spectrometers: inorganic scintillators. Ann Rev Mater Res 48:13.1–13.33 McGregor DS, Shultis JK (2020) Radiation detection: concepts, methods, and devices. CRC Press, Boca Raton McIntyre RJ (1961) Theory of microplasma instability of silicon. J Appl Phys 32:983–995 Mickael MW (1991) A complete inverse Monte Carlo model for energy-dispersive x ray fluorescence analysis. Nucl Instrum Methods A301:523–542 Molnar GL (2004) Handbook of prompt gamma activation analysis with neutron beams. Kluwer Academic Publishers, Boston Moré JJ, Garbow BS, Hillstrom KE (1980) User’s guide for MINPACK-1, Report ANL-80-74, Argonne National Laboratory Nafee SS (2011) A mathematical approach to determine escape peak efficiencies of high-purity germanium cylindrical detectors for prompt gamma neutron activation analysis. Nucl Tech 175:162–167 Press WH, Teukolsky SA, Vetterling WT, Flannery BP (1992) Numerical recipes in FORTRAN 77. The art of scientific computing, 2nd edn. Cambridge University Press, New York Renker D (2006) Geiger-mode avalanche photodiodes, history, properties and problems. Nucl Instrum Methods A567:48–56 Wollman DA, Irwin KD, Hilton GC, Dulcie LL, Newbury DE, Martinis JM (1997) High-resolution, energy-dispersive microcalorimeter spectrometer for x ray microanalysis. J Microscopy 188(3):196–223 Xu Y, Weaver JB, Healy DM Jr, Lu J (1994) Wavelet transform domain filters: a spatially selective noise filtration technique. IEEE Trans Image Proc 3(6):747–758 Yacout AM, Dunn WL (1987) Application of the inverse monte carlo method to energy-dispersive x ray fluorescence. Adv x ray Anal 30:113–120

Further Reading Birks JB (1964) The theory and practice of scintillation counting. Pergamon Press, Oxford Enss C (ed) (2005) Cryogenic particle detectors, vol 99, In: Topics in applied physics. Springer, New York

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Goldstein JI, Newbury DE, Echlin P, Joy DC, Fiori C, Lifshin E (1981) Scanning electron microscopy and x ray microanalysis. Plenum Press, New York Hornbeck RW (1975) Numerical methods with numerous examples and solved illustrative problems. Quantum Publishers, New York Knoll GF (2010) Radiation detection and measurement, 4th edn. Wiley, New York Owens A (2019) Semiconductor radiation detectors. CRC Press, Boca Raton Price WJ (1964) Nuclear radiation detection, 2nd edn. McGraw-Hill, New York Rodnyi PA (1997) Physical processes in inorganic scintillators. CRC Press, Boca Raton Schlesinger TE, James RB (1995) Semiconductors for room temperature nuclear detector applications. In: Semiconductors and semimetals, vol 43. Academic Press, San Diego Tsoulfanidis N, Landsberger S (2015) Measurement and detection of radiation, 4th edn. CRC Press, Boca Raton

Radiation Spectrometer Suppliers – – – – – – – – – – – – – – –

AmpTek-Ametek; www.amptek.com Baltic Scientific Instruments; bsi.lv/en/ Berkeley Nucleonics Corp.; www.berkeleynucleonics.com Dynasil; www.dynasil.com Eurorad; www.eurorad.com/detectors.php Itech Instruments; www.itech-instruments.com/ Kromek; www.kromek.com/ Ludlum Measurements, Inc.; ludlums.com Mirion Technologies; www.canberra.com/cbns/ Moxtek; www.moxtek.com/ Ortec-Ametek; www.ortec-online.com/ Radiation Monitoring Devices dynasil.com/rmd Redlen Technologies; www.redlen.com/ Saint Gobain; www.crystals.saint-gobain.com/ Scionix; scionix.nl

Cherenkov Radiation

19

Blair Ratcliff and Jochen Schwiening

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Basic Cherenkov Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cherenkov Counters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cherenkov Counter Components: Radiators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cherenkov Counter Components: Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Counter Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Threshold Counters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Imaging Counters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Examples of Cherenkov Counters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Accelerator-Based Particle Identification Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Astroparticle Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract When a charged particle passes through an optically transparent medium with a velocity greater than the phase velocity of light in that medium, it emits prompt photons, called Cherenkov radiation, at a characteristic polar angle that depends on the particle velocity. Cherenkov counters are particle detectors that make use of this radiation. Uses include prompt particle counting, the detection of fast

B. Ratcliff () SLAC National Accelerator Laboratory, Stanford, CA, USA e-mail: [email protected] J. Schwiening GSI Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt, Germany e-mail: [email protected] © This is a U.S. Government work and not under copyright protection in the U.S.; foreign copyright protection may apply 2021 I. Fleck et al. (eds.), Handbook of Particle Detection and Imaging, https://doi.org/10.1007/978-3-319-93785-4_18

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particles, the measurement of particle masses, and the tracking or localization of events in very large, natural radiators such as the atmosphere, or natural ice fields, like those at the South Pole in Antarctica. Cherenkov counters are used in a number of different fields, including high energy and nuclear physics detectors at particle accelerators, in nuclear reactors, cosmic ray detectors, particle astrophysics detectors, and neutrino astronomy, and in biomedicine for labeling certain biological molecules. This chapter begins with a brief history of the Cherenkov effect. It then describes some salient features of the radiation that leads to its unique value in particle detection. Several different classes of Cherenkov detectors will be described, along with the technology needed to build them. The chapter will conclude with a review of a number of different Cherenkov counters, including some historically important counters, more recent devices now in operations, and devices that remain under research and development that make use of innovative technologies.

Introduction More than 100 years ago, Marie and Pierre Curie enjoyed seeing beautiful, if slightly eerie, bluish-white luminescence from their concentrated radioactive solutions (Curie 2001), but their observations occurred long before the complex light emitting effects in these solutions were understood, or, indeed, before the health dangers of the ionizing radiation producing the effects were realized. Early investigations into the light emitting effects of particles moving with a velocity greater than the phase velocity of light through a medium, now called Cherenkov radiation, were deterred not only by competing effects, such as fluorescence, but by the very limited number of photons emitted, and by the lack of light detectors with sufficient sensitivity. Moreover, the observability of such phenomena seems not to have been widely anticipated, even though it had been predicted in 1889 by O. Heaviside (Heaviside 1889) directly from Maxwell’s Equations. Thorough, inventive experimental investigations to fully explore the phenomena were carried out with quite simple apparatus beginning in 1934 by P. Cherenkov (Cherenkov 1934). These detailed observations both agreed with and were fully explained theoretically by I. Frank and I. Tamm using classical electromagnetic theory in a landmark paper in 1937 (Frank and Tamm 1937), resulting in the award of the Nobel Prize to these three physicists in 1958.

Basic Cherenkov Theory Cherenkov light is an electromagnetic analog of the more familiar sonic boom produced by an aircraft moving faster than the speed of sound in air and is possible only because the phase velocity of light in transparent materials with refractive index n is slower than the speed of light (c) in a vacuum. The shock wave (sometimes

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called the Mach cone) can be observed as a very prompt pulse of light emitted uniformly in azimuth (φ c ) around the particle direction with the characteristic Cherenkov polar opening angle (θ c ), cos θc =

1 , n (λ) β

where β = υp /c, υp is the particle velocity, and n(λ) is the index of refraction of the material. Since the index of refraction, n, is a function of the photon wavelength, in normal optical materials there is an intrinsic Cherenkov angle resolution smearing that depends on the bandwidth of the detected photons. No Cherenkov light emission occurs below a particle threshold velocity β t = 1/n. Since γ t = 1/(1 − β t 2 )1/2 , β t γ t = pt /m = 1/(2η + η2 )1/2 , where pt is the threshold particle momentum for a particle with rest mass m, and η = n – 1. Cherenkov emission is a weak effect and, as such, causes no significant loss to the particle energy. The number of Cherenkov photons Nphotons produced by a charged particle of charge z, within the total Cherenkov bandwidth, is given by the Frank-Tamm equation (Frank and Tamm 1937). Nphotons.

α 2 z2 =L re me c 2

 sin2 θc (E)dE,

where L is the length of the particle through the radiator in cm, and E is the photon energy in eV. The integral is taken over the region where n(E) is greater than 1, and α 2 /(re me c2 ) = 370 cm−1 e V−1 . As first shown in a classical paper by Tamm in 1939 (Tamm 1939), the conical Cherenkov radiation shell is not quite perpendicular to the Cherenkov propagation angle in normal optical media, which are always dispersive. With angles defined in Fig. 1, the half-angle of the cone opening (ηc ) is given by, 

d cot ηc = (ω tan θc ) dω

 ω0

  dn 2 cot θc = tan θc + β ω n (ω) , dω ω0

where ω0 is the central value of the small frequency range under consideration. As Motz and Schiff pointed out in 1953 (Motz and Schiff 1953), the presence of the second term means that the Mach Cone half-angle (ηc ) is the complement of the Cherenkov angle (θ c ) only for a nondispersive medium where dn /dω = 0. Though subtle and unimportant in many Cherenkov applications, this can affect the performance of many modern devices that either are large or that have very fast photon timing. In principle, since three measurements (a space-point (x, y) and a propagation time (tp )) may be made at a fixed z location to measure the two Cherenkov angles (θ c ,φ c ) with respect to a known track, there is a nominal over-constraint, even for a single photoelectron. In practice, exploiting the time-dimension requires very fast

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Fig. 1 Schematic showing the Cherenkov cone and angles defined in the text

photon detectors and/or rather long propagation times, such as those that occur with the DIRC or large water detectors discussed later, so it is less frequently utilized. For pedagogical purposes, it is useful to recall specifically how the measured quantities are related to the Cherenkov angles. Consider a frame (q), as shown in Fig. 2a, where the particle moves along the (z) axis. The direction cosines of the Cherenkov photon emission in this frame (qx , qy , and qz ) are related to the Cherenkov angles by, qx = cos φc sin θc , qy = sin φc sin θc , qz = cos θc . Defining the emission point (ze ) and the detection point (zd ), the propagation time tp over a length Lp is given by tp =

Lp ng (ze − zd ) ng , = c cqz

where the photon group velocity (υgroup = c/ng ) must be used rather than the photon phase velocity (υphase = c/n) since, in a dispersive medium, energy propagates at the photon group velocity. This is another way to understand why the conical Cherenkov radiation shell is not quite perpendicular to the Cherenkov propagation angle in a dispersive medium. In a real counter, the photon measurements are made in a lab frame such as that defined in Fig. 2b, perhaps after further reflections and focusing (not shown). The photon emission coordinates are not necessarily well known, but, if the photons are focused, it may not be necessary to know all emission coordinates well, in order to derive Cherenkov angular information. In any case, measured

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Fig. 2 Schematic of typical Cherenkov cones and reference frames: (a) with respect to the particle path and (b) in the lab coordinate system

positions and times for photons must be transformed from the measurement frame such as Fig. 2b back to one like that of Fig. 2a typically using additional tracking and timing information, taken either from outside detectors, or from the correlations between the photons measured within the event itself. The relationship between group and phase velocities, as a function of photon wavelength (λ), is usually derived in a simple one-dimensional picture (Jackson 1962) and leads to the following relationship between the group and phase refractive indices: ng (λ) = n (λ) − λdn (λ) /dλ. ng (λ) is typically several percent larger than n(λ) for photons in the visible and UV energy range and, more importantly for the resolution performance of a counter that uses time focusing (as discussed below), the dispersion of ng (λ) is also substantially greater.

Cherenkov Counters Cherenkov counters are particle detection devices that utilize Cherenkov radiation. They are sometimes thought of as being useful mostly as particle identification (PID) detectors for accelerator physics experiments. PID detectors provide a measure of the mass of charged particles (and thus, determine their identity) by

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combining a measurement of the velocity of each charged particle made in the PID detector with a measurement of the particle’s momentum made in a tracking chamber system that tracks the trajectory of the particle in a magnetic field using, m=

p . γβc

However, in practice, the use of Cherenkov counters extends over a broad range of applications including, for example, (1) very fast particle counters for accelerator and detector instrumentation, (2) hadronic PID in high energy physics particle detectors, (3) tracking detectors performing complete event reconstruction in neutrino astronomy, and (4) quantitative radiation measurements in biology and medicine. Examples of applications from each category include (1) the BaBar luminosity detector (Ecklund et al. 2001) and the Quartic fast timing counter designed to measure small angle scatters at the LHC (Albrow et al. 2012); (2) the hadronic PID detectors at the B factory detectors – DIRC in BaBar (Adam et al. 2005), the aerogel threshold Cherenkov counter in Belle (Abashian et al. 2002), and the modern Imaging Aerogel and TOP counters at Belle II (Torassa et al. 2016); (3) large water Cherenkov counters such as Super-Kamiokande (Fukuda et al. 2003); and (4) quantitative measurements of beta particles in microfluidic chips (Cho et al. 2009). Cherenkov counters contain two main elements: (1) a radiator through which the charged particle passes and (2) a photodetector. As Cherenkov radiation is a weak source of photons, light collection and detection must be as efficient as possible. The refractive index n and the particle’s path length through the radiator L appear in the Cherenkov relations – allowing the tuning of these quantities for particular applications. Cherenkov detectors utilize one or more of the properties of Cherenkov radiation discussed in section “Basic Cherenkov Theory”: the prompt emission of a light pulse; the existence of a velocity threshold for radiation; and the dependence of the Cherenkov cone half-angle θ c and the number of emitted photons on the velocity of the particle and the refractive index of the medium. In practical detectors, Cherenkov radiation is nearly always observed using a sensitive photon detector that converts individual photons into photoelectrons. The number of photoelectrons observed by a typical detector for a particle of unit charge is  Npe. = 370L

(E)sin2 θc (E)dE,

where (E) is the energy dependence of the photon transducer, and the integral is taken over the detector bandwidth. The quantities  and θ c are functions of the photon energy E. As the typical energy dependent variation of the index of refraction is modest, a quantity called the Cherenkov detector quality factor N0 can be defined as

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N0 =

α 2 z2 re me c 2

  dE,

so that, taking z = 1 (the usual case in high-energy physics),   Np.e ≈ L N0 sin2 θc . This definition of the quality factor N0 is not universal, nor, indeed, very useful for those common situations where  factorizes as  = Coll det with the geometrical photon collection efficiency (Coll ) varying substantially for different tracks while the photon detector efficiency (det ) remains nearly track independent. In this case, it can be useful to explicitly remove (Coll ) from the definition of N0 . A typical value of N0 for a photomultiplier detection system working in the visible and near UV, and collecting most of the Cherenkov light, is about 100 cm−1 . Practical counters, utilizing a variety of different photodetectors, have values ranging between about 30 and 180 cm−1 . In theory, in a nondispersive medium, the shock cone wavefront is arbitrarily thin, so that the light pulse duration is a delta function. In practice, since all media are dispersive, light collection systems are not synchronous, and all photon detectors have finite time resolution, the observed pulse duration will be finite as will the pulse rise time. A short pulse with a very rapid rise time could lead to the development of very fast counting devices that would have many applications. Recent experiments have been able to demonstrate a time resolution of ∼8 × 10−12 s, which is dominated by the photon detector timing response of the microchannel plate photomultipliers (MCP-PMTs) that are used to detect the Cherenkov photons (Vavra et al. 2017). This remains a very active area for R&D.

Cherenkov Counter Components: Radiators There are many transparent radiators available, ranging from light gases to dense glasses, which allow counters to be designed to cover an extremely wide range of particle momenta. Table 1 compares the Cherenkov threshold gamma (γ t ) for a number of different radiator types with differing indices of refraction. In addition to refractive index, the choice requires consideration of factors such as material density, radiation length and radiation hardness, transmission bandwidth, absorption length, chromatic dispersion, optical workability (for solids), availability, and cost. Tables giving the properties of a variety of commonly used radiator materials can be found or are referenced in the Particle Data Group Reviews (Patrignani et al. 2016). When the momenta of particles to be identified is high, the refractive index must be set close to one, so that the photon yield per unit length is low and a long particle path in the radiator is required as shown in Table 3.1. The gap in refractive index that has traditionally existed between gases and liquid or solid materials has been

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Table 1 Threshold and radiator length (R.L.) required to obtain 10 photoelectrons for β = 1 particle for a number of different radiator materials assuming the typical photodetector described in the text with N0 = 100

He (gas) Ne (gas) N2 (gas) C5 F12 (gas) Aerogel (low density) Aerogel (high density) Argon (liquid) C6 F14 (liquid) H2 O (liquid) SiO2 (solid) LiF (solid) Diamond (solid)

Index of Refraction 1.000035 1.000067 1.00030 1.0017 1.007 1.13 1.23 1.28 1.34 1.47 1.50 2.417

γ tβt 119.75 86.4 40.8 17.1 8.4 1.90 1.39 1.25 1.12 0.93 0.89 0.45

R.L. (cm) 1429. 746. 167. 29.5 7.22 0.46 0.29 0.26 0.23 0.19 0.18 0.12

partially closed with transparent silica aerogels with indices that range between about 1.007 and 1.13.

Cherenkov Counter Components: Detectors Cherenkov counters became a practical technique for particle detection following the invention and development of the Photomultiplier tube (PMT) (Jelley 1958) over 70 years ago. Even today, photon detectors for Cherenkov counters are challenging as they must detect single photons with high efficiency and little noise. Very fast timing resolution is essential in time-imaging counters and is useful in any case to reject background. Good segmentation in space may be needed to obtain adequate angular resolution in ring imaging counters (RICH, see below) and is also useful to reject backgrounds. On the other hand, many costs scale with the number of pixels and must be strictly controlled. Detectors continue as an active arena for R&D (RICH 1994). There are several distinct types of photon detectors in use or proposed. Vacuum photon detectors include dynode based PMTs, microchannel plate PMTs, hybrid PMTs (HPMT), etc. All use a photocathode in vacuum but with different techniques for obtaining gain. A wide variety of photocathodes are available that are sensitive to wavelengths from the UV cutoff of the window material (LiF cuts off around 100 nm) to the near IR. They have an illustrious history in Cherenkov detectors, as most successful counters used PMTs until the 1980s. They are still very widely used, with many opportunities for further development. As a class, they are very sensitive, versatile, fast, high-gain, and low noise. Many are also quite robust in operation. Many types are commercially available, but all are

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difficult to produce and develop in a normal laboratory without a large infusion of capital and expertise. The usual types are quite sensitive to magnetic fields, but some will work in fields of over 1 T in the appropriate direction. Development continues and highly pixelated fast types have become available commercially recently. Gaseous detectors can provide inexpensive coverage of a large photon collection area with good point resolution. The single photoelectrons are typically read out with proportional chambers and/or time projection chambers. (Recently built instruments may use other devices like the gaseous electron multiplier (GEM).) Gaseous (tetrakis-dimethylaminoethylene (TMAE) or Triethyl-amine (TEA)) and solid (Csl) photocathodes have been employed. Their operational characteristics can be especially challenging. Since these photocathodes work near the UV window cutoff, the number of photoelectrons is modest, and there is substantial chromatic dispersion. Performance at high luminosities is limited depending in detail on the photocathode and readout. Devices with TMAE photocathodes are quite slow, but TEA and Csl devices can be moderately fast. They can be used in a magnetic field but are not an option for a time imaging RICH. Solid state photon detectors, such as Geiger-mode APDs (MPPCs, SiPMs), are an intriguing possibility for certain future applications. They are very compact, highly segmented, fast, efficient and have been used successfully in imaging air Cherenkov telescopes (Anderhub et al. 2013). However, major challenges, such as noise performance, radiation resistance, and cost, have so far prevented the widespread application in accelerator-based experiments (RICH 1994).

Counter Types Cherenkov counters may be classified as either imaging or threshold types, depending on whether they do or do not make use of Cherenkov angle (θ c ) information. Imaging counters may be used to track particles as well as identify them. The use of very fast photodetectors such as microchannel plate PMTs (MCP-PMT) also potentially allows very fast Cherenkov based time of flight (TOF) detectors of either class (RICH 1994).

Threshold Counters Threshold Cherenkov detectors (Litt and Meunier 1973), in their simplest form, make a yes/no decision based on whether the particle is above or below the Cherenkov threshold velocity β t = 1/n. A straightforward enhancement of such detectors uses the number of observed photoelectrons (or a calibrated pulse height) to discriminate between species or to set probabilities for each particle species (Bartlett et al. 1987). This strategy can increase the momentum range of particle separation by a modest amount (to a momentum some 20% above the threshold momentum of the heavier particle in a typical case).

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Careful  designs give coll   90%. For a photomultiplier with a typical bialkali cathode, det dE ≈ 0, 27 eV, so that   Np.e. /L ≈ 90 cm−1 sin2 θc i.e., N0 = 90 cm−1 . Suppose, for example, that n is chosen so that the threshold for species a is pt ; that is, at this momentum species a has velocity β a = 1/n. A second, lighter, species b with the same momentum has velocity β b , so cos θ c = β a /β b , and Np.e. /L ≈ 90 cm−1

m2a − m2b pt2 + m2a

.

For K/π separation at p = pt = 1 GeV/c, Np e ./L ≈ 16 cm−1 and at p = pt = 5 GeV/c, Np .e ./L ≈ 0.8 cm−1 for π’s while, by design, Np .e . = 0 for K’s. For limited path lengths, Np.e . will usually be small. The overall efficiency of the device is controlled by Poisson fluctuations, which can be especially critical for separation of species where one particle type is dominant. Moreover, the effective number of photoelectrons is often less than the average number calculated above due to additional equivalent noise (ENF) from amplification statistics in the photodetector (Patrignani et al. 2016). It is common to design for at least 10 photoelectrons for the high velocity particle in order to obtain a robust counter. As rejection of the particle that is below threshold depends on not seeing a signal, electronic and other background noise can be important. Physics sources of light production for the below threshold particle, such as decay to an above threshold particle or the production of delta rays in the radiator, often limit the separation attainable and need to be carefully considered.

Imaging Counters Imaging counters make the most powerful use of the information available by measuring the ring-correlated angles of emission of the individual Cherenkov photons. Since low-energy photon detectors can measure only the position (and, perhaps, a precise detection time) of the individual Cherenkov photons (not the angles directly), the photons must be “imaged” onto a detector so that their angles can be derived (Ratcliff 2003). It is helpful to consider two quite distinct imaging device types. The first device type, the correlated Cherenkov Tracking Calorimeter, uses Cherenkov imaging as a relatively inexpensive technique to instrument a very large volume of material for particle detection as is necessary to search for or study very rare processes such as neutron decay or neutrino interactions. These are complete experimental detectors with the capability to track particles, vertex events, identify charged particles, measure energies via calorimetry, reject backgrounds, and

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self-trigger (Patrignani et al. 2016). The photodetectors are distributed either on the surface or throughout the volume of a very large radiator of a kiloton of more. The radiator might be either an optically transparent natural material (such as glacial ice, or deep sea or lake water) or large tanks of purified material such as mineral oil or water. The photodetectors are usually large PMTs. The reconstruction makes use of all available (space, time) information for each measured photon (xm , ym , zm , tm ) as shown in Fig. 2 above. Since, in this instance, there is no tracking information available from outside detectors, and the photon emission points are unknown at the outset, the number and locations of tracks must be iteratively derived by combining the measured information from the photons with the constraint that Cherenkov photons emerge from source tracks, acting as line sources for the Cherenkov radiation, at a constant polar angle θ c . The reconstruction methodology is quite complex, not only because events can contain many tracks, with different lengths and vertices, but also because, in practice, even a single particle can shower and produce many overlapping rings (RICH 1994). However, once reconstructed, these showers provide useful separation between particle species, since nonshowering particles such as muons, pions, and protons produce sharp rings, while showering particles such as electrons and photons produce diffuse rings. The number of photons observed provides a measure of the particle energy. The energy for showering particles is essentially linear with the observed photon number, but the relationship for more massive particles is complex. Careful energy calibration is essential. Examples of this detector type are described more extensively in section “Examples of Cherenkov Counters.” The second device type, generically referred to as a RICH counter, contains separable radiator and photon detector regions (Séquinot and Ypsilantis 1977). The detector and its optics constitute a “camera.” Typically the camera optics map the Cherenkov cone onto (a portion of) a distorted “circle” at the photodetector. Though the imaging process is generally analogous to familiar imaging techniques used in telescopes and other optical instruments, there is a somewhat bewildering variety of methods used in a wide variety of counter types with different names. General discussions of imaging methods in Cherenkov counters can be found elsewhere (Ratcliff 2003). Some of the general imaging methods used include (1) focusing by a lens or mirror, (2) proximity focusing (i.e., focusing by limiting the emission region of the radiation), and (3) focusing through an aperture (a pinhole). In addition, the prompt Cherenkov emission coupled with the speed of modern photon detectors allows the use of (4) time imaging, a method which is little used in conventional imaging technology. Several of these general imaging techniques are often combined within the same counter, and clever extensions of the basic concepts continue to be developed. Figure 3 illustrates the application of different RICH imaging methods in some recent high-energy physics experiments. The SLD CRID (Va’vra et al. 1999) performed imaging with a combination of proximity focusing, for the photons produced in the liquid (C6 F14 ) radiator, and mirror focusing, for the photons emitted in the gaseous (C5 F12 ) radiator. The BaBar DIRC (Adam et al. 2005) utilized

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Fig. 3 Schematic representation of the imaging principles used by recent RICH counters: SLD CRID (Va’vra et al. 1999) (proximity and mirror focusing), BaBar DIRC (Adam et al. 2005) (pinhole focusing), and PANDA Barrel DIRC (Schwiening et al. 2018) (lens focusing and time imaging)

pinhole focusing – incorporating the pinhole formed by the relatively small crosssection size of the fused silica radiator bars and the long photon path length in the camera provided by the water-filled expansion volume. The PANDA Barrel DIRC (Schwiening et al. 2018) will focus photons with a compound spherical lens and measure the arrival time of the photons with a timing precision of 100 ps to perform time imaging. It should be noted that there are additional Cherenkov imaging device types that partially bridge the gap between these types of imaging counters, but that are not always called RICH detectors. As a particular example, the imaging atmospheric Cherenkov telescopes use the atmosphere as a very large radiator to convert high energy gamma rays into electromagnetic showers. The Cherenkov light produced by the relativistic shower particles are observed by a ground level Cherenkov telescope, which measures the position and energy of the shower origin, and provides some information about the type of particle initiating the shower (RICH 1994). Typical RICH detectors are usually components of a larger detector in an accelerator physics experiment. In a simple model of such a RICH, the fractional error on the particle velocity (δ β ) is given by

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δβ =

σβ = tan θc σ (θc ), β

where σ (θi ) σ (θc ) =

⊕ C, Np.e. and σ (θ i ) is the average single photoelectron resolution, as defined by the optics, detector resolution, and the intrinsic chromaticity spread of the radiator index of refraction averaged over the photon detection bandwidth. C combines a number of other contributions to resolution including, (1) correlated terms such as tracking, alignment, and multiple scattering, (2) hit ambiguities, (3) background hits from random sources, and (4) hits coming from other tracks. The actual separation performance is also limited by physics effects such as decays in flight and particle interactions in the material of the detector. In many practical cases, the performance is limited by these effects. For a β ≈ 1 particle of momentum (p) well above threshold entering a radiator with index of refraction (n), the number of σ separation (Nσ ) between particles of mass m1 and m2 is approximately   2 m − m 2  1 2 Nσ ≈ . √ 2p2 σ (θc ) n2 − 1 In practical counters, the angular resolution term σ (θ c ) varies between about 0.1 and 5 mrad depending on the size, radiator, and photodetector type of the particular counter. The range of momenta over which a particular counter can separate particle species extends from the point at which the number of photons emitted becomes sufficient for the counter to operate efficiently as a threshold device (∼20% above the threshold for the lighter species) to the value in the imaging region given by the equation above. For example, for σ (θ c ) = 2 mrad, a fused silica radiator (n = 1.47), or a fluorocarbon gas radiator (C5 F12 , n = 1.0017), would separate π /K’s from the threshold region starting around 0.15 (3) GeV/c through the imaging region up to about 4.2 (18) GeV/c at better than 3 σ . Many different imaging counters have been built during the last several decades (RICH 1994). Among the earliest examples of this class of counters are the very limited acceptance Differential Cherenkov detectors, designed for particle selection in high momentum beam lines. These devices use optical focusing and/or geometrical masking to select particles having velocities in a specified region. With careful design, a velocity resolution of σ β /β ≈ 10−4 − 10−5 can be obtained (Litt and Meunier 1973). Practical multitrack RICH counters in accelerator particle physics detectors are a more recent development, which have had substantial impact as PID detectors in particle physics during the last three decades. RICH counters have used a variety

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of different radiators, imaging arrangements, and photon detectors that will be described in more detail below.

Examples of Cherenkov Counters Cherenkov counters play an important role in many modern experiments in particle physics, nuclear physics, and particle astrophysics. This section presents a brief review of Cherenkov detectors used in current or past experiments as well as those planned in the near future. Rather than attempting a comprehensive review, a few select detectors will be described which can be considered as representative of a class of Cherenkov counter, with a focus on counters which may be either historically significant or state-of-the-art.

Accelerator-Based Particle Identification Detectors The typical use of Cherenkov counters in detectors at accelerators is to identify and thus to separate hadronic particle types. A closely related use is to separate electrons from hadrons in a hadron rich environment such as a heavy ion collider like RHIC (Tserruya 2006) or FAIR (Adamczewski-Musch et al. 2017).

Threshold Cherenkov Counters Among the earliest applications of Cherenkov counters for hadronic PID were threshold counters. The Aerogel Cherenkov Counter (ACC) of the Belle experiment (Sumiyoshi et al. 1999) was one of the most complex threshold counters to date. The Belle detector at the asymmetric KEKB e+ e−− collider studied the decays of particles produced on or near the ϒ(4S) resonance. For the primary physics goal of Belle, the measurement of CP violation, excellent pion/kaon separation in hadronic decays of B mesons was crucial. The radiator for the Belle ACC was silica aerogel. Fine mesh PMTs were used for photon detection in the 1.5 T magnetic field of the Belle solenoid. Due to the asymmetric beam energies, and the resulting correlation between particle momentum and polar angle of the decay products from B mesons, the Cherenkov thresholds for different particle species varied as a function of the polar angle. Therefore, the best separation was obtained by carefully selecting the refractive indices in each kinematic region so that most pions produced Cherenkov radiation while most kaons were below Cherenkov threshold. The resulting optimized refractive indices of the aerogel went from n = 1.028 in the backward part of the barrel up to n = 1.01 in the forward region of the barrel ACC, and n = 1.03 in the endcap ACC. During more than 10 years of successful operation, the Belle ACC achieved a kaon identification efficiency of up to 90% with a pion misidentification probability as low as 6% (Iijima et al. 2000).

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Imaging Cherenkov Counters: RICH Imaging RICH counters are sometimes classified by “generations” that differ based on historical timing, performance, design, and photodetection techniques. Prototypical examples of first generation RICH counters are those used in the DELPHI and SLD detectors at the LEP and SLC Z factory e+ e− colliders (RICH 1994). In both cases the RICH was designed to efficiently identify charged particles with momenta from about 0.25 to 20 GeV/c. This large momentum range required the use of two types of radiators, liquid (C6 F14 , n = 1.276) and gas (C5 F12 , n = 1.0017), the former being proximity imaged with the latter using mirrors. The phototransducers are a TPC/wire-chamber combination. They are made sensitive to photons by doping the TPC gas (usually, ethane/methane) with ∼0.05% TMAE (tetrakis(dimethylamino)ethylene). Great attention to detail is required, (1) to avoid absorbing the UV photons to which TMAE is sensitive, (2) to avoid absorbing the single photoelectrons as they drift in the long TPC, and (3) to keep the chemically active TMAE vapor from interacting with materials in the system. In spite of their unforgiving operational characteristics, these counters attained good e/π /K/p separation over the wide momentum ranges during several years of operation at LEP and SLC (Va’vra et al. 1999; Albrecht et al. 1999). Related but smaller acceptance devices include the OMEGA RICH at the CERN SPS, and the RICH in the balloonborne CAPRICE detector (RICH 1994). Later generation counters generally operate at much higher rates, with more detection channels, than the first generation detectors just described. They also utilize faster, more forgiving photon detectors, covering different photon detection bandwidths. Radiator choices have broadened to include materials such as lithium fluoride, fused silica, and aerogel. Vacuum based photodetection systems (e.g., single or multianode PMTs, MCP-PMTs, or hybrid photodiodes (HPD)) have become increasingly common. They handle high rates and can be used with a wide choice of radiators. Examples include (1) the SELEX RICH at Fermilab, which mirror-focused the Cherenkov photons from a neon radiator onto a camera array made of ∼2000 PMTs to separate hadrons over a wide momentum range (to well above 200 GeV/c for heavy hadrons) (Engelfried et al. 2003); (2) the HERMES RICH at HERA, which mirror-focused photons from C4 F10 (n = 1.00137) and aerogel (n = 1.0304) radiators within the same volume onto a PMT camera array to separate hadrons in the momentum range from 2 to 15 GeV/c (De Leo 2008); (3) the NA62 RICH at CERN, which uses a 17 m long tank filled with neon gas as radiator and spherical mirrors to focus the photons on two arrays of 2000 PMTs to separate pions from muons for momenta between 15 and 35 GeV/c (Anzivino et al. 2017); (4) the CBM RICH at FAIR where the Cherenkov photons, produced in about 30 m3 of CO2 radiator gas, are mirror-focused on arrays of multi-anode PMTs (MaPMTs) with a total of about 55,000 pixels, to identify electrons with momenta up to 10 GeV/c (Adamczewski-Musch et al. 2017); and (5) the LHCb detector at the LHC (Papanestis et al. 2014). It uses two separate counters. One volume, like HERMES, contains two radiators (aerogel and C4 F10 ) while the second volume contains CF4 . Photons are mirror-focused onto detector arrays of HPDs to cover a π /K separation momentum range between 1 and 150 GeV/c. The LHCb RICH

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counters exceeded design specifications and are being upgraded to deal with the increases in luminosity. The aerogel was removed prior to the start of Run II in 2015. Both LHCb RICH counters are scheduled for a major upgrade during the upcoming 2019–2020 LHC shutdown. The readout electronics will be updated and the HPDs will be replaced by MaPMTs to prepare for the expected higher event occupancy (Easo et al. 2017). Recent technological advances in the production of aerogel with improved transparency in the UV range and finely tuned refractive indices enabled several new RICH designs. The CLAS12 RICH (Mirazita et al. 2017) uses aerogel tiles with a refractive index n = 1.05 in an innovative hybrid geometry. Cherenkov light from tracks with smaller polar angles and higher momenta will be produced in aerogel tiles with 2 cm thickness and detected via proximity focusing on an array of flat panel MaPMTs placed near the beamline. For tracks with larger polar angles and smaller momenta, the Cherenkov light from 6 cm thick aerogel tiles will be focused by spherical mirrors on the same MaPMT array after two passes through the thinner aerogel and a reflection from a flat mirror. This complex photon path, which is only possible due to the improved scattering length of the aerogel, minimizes the material inside of the detector acceptance and the cost of the photon sensor array. Beam tests have demonstrated that the CLAS12 RICH will be able to provide clean π /K separation up to 8 GeV/c. In the so-called focusing aerogel approach (Iijima et al. 2005), radiators are created by combining several (typically 2–4) layers of aerogel with different refractive indices into single tiles. This makes it possible to increase the photon yield by using thicker aerogel tiles while maintaining the good angular resolution of a single proximity-focused layer. The Aerogel RICH (ARICH) (Pestotnik et al. 2017) for the Belle II upgrade at KEKB was developed to provide clean separation of pions and kaons in the forward endcap region of the detector with 4 standard deviations or more up to 3.5 GeV/c momentum. The radiator is a dual-layer aerogel, with a thickness of 20 mm for each layer and increasing refractive indices of n = 1.045 and n = 1.055 along the particle path. The Cherenkov ring images from the two layers overlap on the array of Hybrid Avalanche Photo Detectors (HAPDs), which provide efficient single photon detection in the 1.5 T magnetic field. The Belle II ARICH was installed in 2017 and first physics data is expected in 2019. Other fast detection systems that use solid cesium iodide (CsI) photocathodes or TEA doping in proportional chambers are useful with certain radiator types and geometries. Examples include (1) the CLEO-III RICH at CESR that used a LiF radiator with TEA doped proportional chambers (Sia 2005); (2) the ALICE detector at the LHC that uses proximity-focused liquid (C6 F14 radiators and solid CsI photocathodes (De Cataldo et al. 2014) (similar photodetectors have been used for several years by the HADES and COMPASS detectors), and the hadron blind detector (HBD) in the PHENIX detector at RHIC that couples a low index CF4 radiator to a photodetector based on electron multiplier (GEM) chambers with reflective CsI photocathodes (Tserruya 2006). A DIRC (Detection [of] Internally Reflected Cherenkov [light]) is a distinctive, compact RICH subtype first used in the BaBar detector (Adam et al. 2005). A DIRC

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“inverts” the usual RICH principle for use of light from the radiator by collecting and imaging the total internally reflected light rather than the transmitted light. It utilizes the optical material of the radiator in two ways, simultaneously: as a Cherenkov radiator and as a light pipe. The magnitudes of the photon angles are preserved during transport by the flat, rectangular cross section radiators, allowing the photons to be efficiently transported to a detector outside the path of the particle where they may be imaged in up to three independent dimensions (the usual two in space and, due to the long photon paths lengths, one in time). Because the index of refraction in the radiator is large (n ∼ 1.47 for fused silica), the momentum range with good π /K separation goes up to 4–5 GeV/c. It is plausible, but difficult, to extend it up to about 10 GeV/c with an improved design. The BaBar experiment at the asymmetric PEP-II e+ e− collider studied CP violation in ϒ(4S) decays. Excellent pion/kaon separation for particle momenta up to 4 GeV/c was required. The BaBar DIRC used 4.9 m long, rectangular bars made from synthetic fused silica as radiator and light guide. The photons were imaged via a “pin-hole” through an expansion region filled with 6000 liters of purified water onto an array of 10,752 densely packed photomultiplier tubes placed at a distance of about 1.2 m from the bar end. During more than 8 years of operation, the BaBar DIRC achieved π /K separation of 2.5 standard deviations or more up the 4 GeV/c momentum. For a pion identification rate around 85%, the DIRC provided a kaon misidentification rate well below 1% up to 3 GeV/c (Adam et al. 2005). New DIRC detectors are being developed that take advantage of the new, very fast, pixelated photodetectors becoming available, such as MaPMTs and MCPPMTs. They typically utilize either time imaging or lens/mirror-focused optics, or both, leading not only to a precision measurement of the Cherenkov angle, but in some cases, to a precise measurement of the particle time of flight, and/or to correction of the chromatic dispersion in the radiator. The Belle II Time of Propagation (TOP) counter emphasizes precision timing for both Cherenkov imaging and TOF (Fast et al. 2014) to perform π /K separation of at least 3 standard deviations up to 4 GeV/c. The counter consists of 16 optically isolated radiator and readout modules, covering the barrel region of the experiment. Each module comprises a 2.5 m long and 45 cm wide fused silica plate as radiator and light guide and a spherical mirror, attached to the forward end of the plate, to focus the light on an array of 32 MCP-PMTs, coupled to a compact fused silica prism with 10 cm depth, which serves as expansion volume, at the other end of the plate. All modules were successfully installed in the Belle II detector in 2016 in preparation for the first Belle II physics run scheduled for 2018. The FDIRC (Roberts et al. 2014) was developed for the SuperB detector at the Italian SuperB collider as an upgrade of the BaBar DIRC counter. By replacing the large BaBar DIRC water tank with compact fused silica blocks, the pinhole focusing approach with a cylindrical mirror, and the conventional PMTs with MaPMTs, the FDIRC was designed to provide similar PID performance as the BaBar DIRC at a two orders of magnitude higher luminosity in a much more compact space. Detailed FDIRC prototype tests in particle beams demonstrated that the large number of smaller pixels and better timing precision of the MaPMTs can be used not only for improving the angle reconstruction and

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TOP measurement, but also to correct the chromatic dispersion. The Barrel DIRC for the PANDA detector at FAIR will be the first DIRC counter to use lens focusing and is expected to provide more than 3 standard deviations π /K separation up to 3.5 GeV/c (Schwiening et al. 2018). The Cherenkov light produced in the 2.4 m long fused silica radiator bars will be focused by a 3-layer spherical lens on the back of a 30 cm deep fused silica expansion volume and detected with a timing precision of about 100 ps by an array of MCP-PMTs. Inside the spherical triplet lens transitions between the high-refractive index material lanthanum crown glass (NLaK33, refractive index n = 1.786) and synthetic fused silica (n = 1.473) create focusing and defocusing elements to achieve a flat image on the MCP-PMT array without the large photon loss that would otherwise occur in a lens system containing an air gap. This lens-focusing concept, in combination with even smaller pixels and better timing precision, is expected allow the proposed high-performance DIRC for the electron-ion collider detector (Kalicy et al. 2018) to extend the useful π /K separation range of DIRC counters up to momenta of 6–7 GeV/c. In addition to the barrel DIRC devices, described above, several experiments plan to use DIRC counters as part of the detector endcap. The DIRC upgrade of the GlueX experiment at Jefferson Lab will place four decommissioned BaBar DIRC modules perpendicular to the beamline in the forward part of the detector (Barbosa et al. 2017). The large BaBar DIRC water tank will be replaced by two optical boxes where the cylindrical focusing of the FDIRC design is approximated by multiple flat mirrors to image the photons on an array of MaPMTs. The GlueX DIRC will be installed in the fall of 2018 and is expected to provide PID performance slightly better than the BaBar DIRC and significantly extend the physics reach of the experiment. The Endcap Disc DIRC for the PANDA experiment will provide π /K separation with at least 3 standard deviations up to 4 GeV/c (Föhl et al. 2018). The radiator will be made of four optically isolated fused silica disk quadrants, forming a dodecagon with a diameter of about 1.5 m. Light guides will be attached to the outer rim of each quadrant and connect to compact focusing elements which include cylindrical mirrors to image the photons on MCP-PMTs with very small pixels. The proposed TORCH counter for the LHCb upgrade at CERN will use a similar focusing light guide design to perform high-precision time-of-flight measurements in the momentum region of 2–10 GeV/c in a very compact space (Harnew et al. 2017).

Astroparticle Physics A diverse range of Cherenkov counters is found in astroparticle physics experiments that study neutrinos, proton decays, γ -rays, and charged cosmic rays. From neutrino detectors located deep underground to antimatter searches at the International Space Station, the range includes (1) large volume tracking calorimetric devices used in the study of nucleon decays or neutrino interactions both from accelerators and from extraterrestrial sources; (2) massive imaging detectors made of strings of photon detectors submersed in the sea, deep lakes, or the polar ice cap; and (3) the detection

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of very high energy air showers either using large arrays of threshold Cherenkov detectors, or stereoscopic air shower Cherenkov telescopes.

Underground Neutrino Detectors The study of neutrinos requires large detector volumes to improve the likelihood of observing a neutrino interaction inside the active volume. Purified water (and even heavy water) is often used as an inexpensive Cherenkov radiator with large hemispherical PMTs as the photon detectors. The radiator has to be shielded from muons produced in the atmosphere by high energy cosmic radiation, which can be realized by placing the detector deep underground. The first massive Cherenkov imaging detector of this type was the ∼10 kiloton IMB (Becker-Szendy et al. 1993), which began operations in an Ohio, USA, salt mine in 1982, motivated both by the search for neutrino oscillations and proton decay. The even larger Super-Kamiokande (Super-K) experiment (Fukuda et al. 2003) is placed in the Kamioka Mozumi mine in Japan at 1000 m depth. The active volume is 50,000 tons of pure water in a cylindrical stainless steel tank, 39 m in diameter and 41 m in height. The detector is sensitive to decay products from nucleon decay; neutrinos from the sun, the atmosphere, and extra-terrestrial sources; as well as cosmic rays. To distinguish these contributions the Super-K detector is divided into an inner fiducial volume of 22,000 tons, viewed with some 11,000 large 51 cm PMTs and a 28,000 ton outer zone, viewed by some 1900 20 cm PMTs. A neutrino can interact with the electrons in the water target and transfer enough energy that the electrons will produce Cherenkov radiation. The number of photons produced provides a measure of the energy of the Cherenkov emitting particles. Differences in the responses of the inner and outer detector as well as the sharpness of the ring image and track lengths are used to separate electrons from muons and thus, for instance, events caused by neutrinos produced in the earth beneath the detector from muons produced by cosmic rays in the atmosphere. The Super-Kamiokande experiment has been in operation since 1996 and has made many fundamental measurements, including a detailed exploration of neutrino oscillations from the sun and stringent limits to the proton lifetime (Abe et al. 2016). The detector has been upgraded several times and, since 2009, is also being used for detecting man-made neutrinos as part of the T2K experiment to study long baseline neutrino oscillations (Abe et al. 2011). Its proposed successor detector, called Hyper-Kamiokande, would continue the broad program of its predecessor. It comprises a megaton scale water tank observed by high efficiency photon detectors, and has recently been included in the MEXT roadmap for large scale projects in Japan (Abe et al. 2014). Another recent detector of this generic type is the SNO detector located at a depth of 2000 m in the Creighton mine near Sudbury, Canada (Boger et al. 2000). SNO uses an acrylic spherical fiducial vessel filled with 1000 tons of heavy water, situated within a 30 m barrel shaped cavity filled with normal water and the photon detectors. The SNO device is unique in that the heavy water radiator makes it sensitive to all three neutrino types – thereby providing precise measurements of the rates and flavors of solar neutrinos that reach earth (Aharmim et al. 2013).

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Neutrino Detectors in Natural Water or Ice When instrumented with sensitive photon detectors, naturally occurring water in the sea, lakes, or ice allows the creation of neutrino experiments with active volumes several orders of magnitude larger than those of the underground water Cherenkov detectors described above. Strings of photon detectors suspended within the active volume form a three-dimensional matrix of space and time coordinates used to reconstruct the Cherenkov image and reject backgrounds. The DUMAND detector proposed for the deep ocean near Hawaii was the earliest of these detector concepts (Roberts 1992), and though significant prototyping occurred, a complete detector was never built. ANTARES (Astronomy with a Neutrino Telescope and Abyss environmental RESearch) is the first neutrino telescope constructed in the deep sea (Bertin et al. 2009) and is the most sensitive cosmic neutrino telescope in the northern hemisphere. It is located in the Mediterranean Sea 40 km off the coast of Southern France at a depth of 2400 m. Twelve lines of photon detectors are anchored to the sea floor, each comprising 75 large (25 cm diameter) PMTs, looking downward at an angle of 45◦ to be sensitive to Cherenkov light from upward going muon tracks produced in interactions of extraterrestrial neutrinos after traversing the Earth. The PMTs are contained in optical modules, 43 cm diameter glass pressure spheres, where they are shielded from the Earth’s magnetic field by a mu-metal cage. At a pitch of 60–70 m, the lines cover an area of 0.1 km2 with the PMTs suspended between 100 m and 450 m above the sea floor. The spacing between the optical modules is driven by the transparency of the water at 2400 m depth (Aguilar et al., 2005). Installation of the lines was completed in 2008, with data taking operations thereafter. Recent results from 9 years of operations complement those of IceCube (see below) and are consistent with the significant observations of an excess of very high energy cosmic rays observed there (Albert et al. 2018). ANTARES is a first step toward the construction of three large Cherenkov detectors with active volumes of one to several cubic kilometers in the Mediterranean Sea as part of the KM3NeT Collaboration (Adrin-Martnez et al. 2016). Three suitable deep sea sites have been selected that will be instrumented with similar “building blocks” comprising three dimensional arrays of photodetectors over a large water volume. Two building blocks will be sparsely configured (with similar volumes, but perhaps using different technologies with different field of view) to fully explore and study high energy astrophysical neutrino sources, such as those observed by Icecube (see below). One building block will be densely configured to precisely measure atmospheric neutrino oscillations. The data obtained by ANTARES and by a future KM3NeT (situated in the Northern Hemisphere) should complement and extend the results obtained by the IceCube (Halzen and Gaisser 2014) experiment, located at the South Pole. AMANDA (Antarctic Muon and Neutrino Detector Array) (Andres et al. 2000) was an early attempt to demonstrate the concept for using the polar ice cap for very high energy neutrino astronomy, using optical modules embedded within the clear ice cap underneath the Amundsen-Scott South Pole Station. It became the first part of the IceCube Neutrino Observatory in 2005. IceCube is presently the largest

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neutrino telescope in the world and was completed in 2010. It is a cubic kilometer scale device comprised of 5160 optical photon sensors deployed at depths between 1450 to 2450 m into holes melted in the ice using a hot water drill. IceCube is designed to look for point sources of neutrinos well into the TeV range to explore the highest-energy astrophysical processes and identify their sources, as well as perform studies of cosmic rays, dark matter, and neutrino physics. IceCube has recently reported the observation of 28 very high-energy candidate neutrino with observed energies between 30 and 1140 TeV. The number of events exceeds expected cosmic backgrounds by more the 4a and therefore constitutes the first solid evidence for astrophysical neutrinos coming from outside the solar system, pointing towards the beginnings of a new type of astronomy using neutrinos (Aartsen et al. 2013).

High Energy Cosmic Ray Shower Detection with Cherenkov Light In order to study very high energy cosmic rays whose energies can extend well above 1018 eV, the atmosphere can be used as a large optically transparent target to initiate the large air showers induced by both hadrons and gammas which then need to be efficiently and inexpensively detected. There are two different basic detector concepts that have been employed: the first is to use a telescope to detect the Cherenkov photons directly produced by the shower in the atmosphere (a technique that can be used for showers that die out before reaching the ground); the second is to build a large array on the ground to sample the particles in the very extended air shower (EAS) that reaches the ground. These very highest energy air showers are quite rare, with an estimated rate of about 1/km2 /century. Though the EAS detectors need to see charged shower particles directly, they have often featured Cherenkov detectors as an inexpensive method for this fast charged particle detection. The largest of these EAS devices (called the Pierre Auger Observatory (Aab et al. 2015)) covers a surface detection area of about 3000 km2 in the high western Argentinian Pampas near the Andes. Data taking began in 2005. Construction was completed in 2008, and data taking continues at present. In September 2017, data from 12 years of observations with this detector was published that supports an extragalactic source for the origin of extremely high energy cosmic rays (Aab et al. 2017). The Auger detector is a “hybrid” device, utilizing two complementary methodologies. The primary, large surface area device employs 1660 surface detection stations each separated by 1.5 km. Each station is a 12 kton threshold Cherenkov detector comprising a pure water radiator viewed by 3 PMTs. Excellent relative timing precision between the modules allows the track direction of the originating particles to be determined, while the observed energy provides a sampling measure of the total energy, although the shower size and spread can limit the precision. The other technique tracks the development of air showers by observing ultraviolet florescence light in a 24 telescope array. Though this can provide complementary and more precise measurements for some showers, these telescopes can only operate on clear, moonless nights. Another detector type, called an Imaging Air Cherenkov Telescope (IACT), directly images the Cherenkov photons from the shower. A y-ray interacting in the atmosphere will produce an air shower of secondary particles at an elevation of

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10–15 km. The shower particles produce Cherenkov light and the resulting light cone will cover a disk with a radius of 100–120 m at the ground level with an intensity of 10–100 photons/m2 . A ground-based telescope looking up at the night sky will be able to detect the Cherenkov light and measure the intensity, orientation, and shape of the air shower which are related to the primary energy and direction of the γ -ray. Such IACTs can be sensitive to an energy range from a few GeV to well above 100 TeV. Among the pioneering detectors of this type was the 10 m Whipple telescope located at over 2000 m in elevation in Arizona, USA (Weekes 1983). An important early physics result was the observation of gamma ray emission from the Crab nebula (Weekes et al. 1998), which along with several subsequent results, convincingly demonstrated the power of the IACT approach. It soon became clear that substantially improved performance could be obtained with IACT systems made of several larger telescopes with improved photon detectors that provide multiple high resolution views of the same air shower. This eventually led to a number of large third-generation IACT stereoscopic systems including VERITAS (Holder et al. 2006), HESS (Bernlöhr et al. 2003), MAGIC (Cortina et al. 2009), and CAN- GAROO (Kubo et al. 2004). The best of this class have received further upgrades and remain in operation. As an example, the High Energy Stereoscopic System (HESS) experiment is an array of five individual telescopes; four with 12 m diameter mirrors arranged in a square with 120 m sides, and a large telescope with a 28 m segmented mirror located at the center. HESS is located in the Khomas Highland in Namibia at an altitude of 1800 m above sea level. It has been in operation since 2003 and augmented (now called HESS II) with the large mirror telescope in 2012. Each of the smaller telescopes consists of 382 round mirror facets of 60 cm diameter, made of aluminumized glass with a quartz coating, focusing the light on a focal plane equipped with 960 PMTs. The cameras for these 4 telescopes were upgraded to state of the art electronics in 2016. The larger mirror telescope uses 875 hexagonal facets of 90 cm (flat to flat) size to form a mirror with 614 m2 total area. The photodetectors for all telescopes are large arrays of PMTs covering between 3.2 and 5 degrees on the sky. The combination of the images recorded by the five telescopes allows stereoscopic viewing of the air shower. This improves the sensitivity, the angular and energy resolution of the experiment and provides better background rejection and dead time. HESS has been performing many studies of the very high energy gamma sky for around 15 years, including surveys of the galactic center and plane, discovering many new sources of very-high-energy (E > 1 TeV) γ -rays. Many results from this full time period have been recently complied and published in 14 articles in the same journal (Abdallah et al. 2018). In one particularly intriguing observation, from 2016, HESS reported gamma ray observations which appear to show the presence of petaelectronvolt protons originating from the supermassive black hole at the center of the Milky Way (Abramowski et al. 2016). The next step in the evolution of ground based gamma ray detectors is the Cherenkov Telescope Array (CTA). It is designed to detect gamma rays over an energy range extending from 20 GeV to 300 TeV with a wide range of views incorporating more than 100 telescopes located in both hemispheres. The sensitivity

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is at least 10 times better than present detectors, with excellent angular resolution. The physics program of CTA goes beyond high energy astrophysics into cosmology and fundamental physics. The multinational project itself is proceeding well and is central to national and international strategies in the field, as reflected in the European Astroparticle Physics Strategy of the Astroparticle Physics European Consortium (Astroparticle Physics European Consortium Collaboration (APPEC) 2018). It is expected to begin full operation in 2023.

Conclusions Cherenkov light was first observed, although not immediately understood, more than 100 years ago, and fully explicated experimentally and understood theoretically within classical electromagnetic theory some three to four decades later. Today, more than 60 years after the first Cherenkov counters became operational, new detectors that exploit the special characteristics of Cherenkov radiation continue to be developed. Important properties of the radiation that are utilized in varying ways by these devices include the rapid emission of a sharp light pulse; the existence of a velocity threshold for radiation; the direct dependence between the track length and the number of photons emitted; and the dependence of the Cherenkov cone half-angle θ c and the number of emitted photons on the velocity of the particle and the refractive index of the medium. Moreover, useful numbers of photons are emitted in the visible and UV photon range where optical materials and large natural radiators, such as water, ice, and the atmosphere, are transparent, and where highly efficient photodetectors have been developed. Cherenkov detectors have benefited substantially from numerous technological advances over the last half-century. The first photomultiplier tubes, which allowed efficient photon counting, were especially crucial to the early adoption of Cherenkov devices and continue to be developed. Modern PMTs are much more efficient, have better single photon counting characteristics, come in many different sizes and shapes, and include a number of very fast, pixelated types. Some also tolerate substantial magnetic fields. Additional photodetection options include gas detectors and solid state devices such as Geiger-mode APDs. Radiator options have expanded due to the development of modern materials, and industrial applications, often for high-technology purposes. These include very transparent fused silica, fluorocarbons, aerogels with a refractive index that can be tuned to a wide range of applications, and the ability to clean large volumes of water inexpensively. Cherenkov detectors are now found in a wide variety of unique applications throughout physics, astrophysics, and biomedicine, with more powerful, and/or larger devices continuing to be developed and implemented. Particular examples include the many detectors at particle accelerators that rely on powerful imaging detectors for hadronic particle identification, the large water Cherenkov detectors used for neutrino detection both for astrophysics and accelerator studies, and the imaging air Cherenkov telescopes used to study very-high-energy γ -rays in cosmic

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radiation. The scientific impact of this broad class of devices is truly remarkable, having been crucial to three Noble Prize awards in physics since the turn of the century (2002, 2008, and 2015) (https://www.nobelprize.org/prizes/physics/).

Cross-References  Interactions of Particles and Radiation with Matter  Particle Identification  Photon Detectors Acknowledgements Work supported in part by the U.S. Department of Energy under contract number DE-AC02-76SF00515.

References Aab A, The Pierre Auger Collaboration et al (2015) Nucl Instrum Methods Phys Res Sect A798:172 Aab A, The Pierre Auger Collaboration et al (2017) Science 357(6357):1266 Aartsen MG, IceCube Collaboration et al (2013) Science 342(6161):947 Abashian A et al (2002) Nucl Instrum Methods Phys Res Sect A479:117 Abdallah H, HESS Collaboration et al (2018) Astron Astrophys 612:A1–A14 Abe K, Hyper-Kamiokande Working Group et al (2014) A long baseline neutrino oscillation experiment using J-PARC neutrino beam and Hyper-Kamiokande. arXiv:1412.4673 Abe K, T2K Collaboration et al (2011) Nucl Instrum Methods Phys Res Sect A659:106; Abe K, T2K Collaboration, et al (2017) Phys Rev Lett 118:151801 Abe K et al (2016) Phys Rev D 94:052010; Abe K et al. (2014) Phys Rev D 90:072005 Abramowski A, HESS Collaboration et al (2016) Acceleration of petaelectronvolt protons in the galactic centre. Nature 531:476479 Adam I, BaBar DIRC Collaboration et al (2005) Nucl Instrum Methods Phys Res Sect A538:281 Adamczewski-Musch J et al (2017) Nucl Instrum Methods Phys Res Sect A876:160 Adrin-Martnez S, KM3NeT Collaboration et al (2016) J Phys G Nucl Part Phys 43:084001 Aguilar JA et al (2005) Astropart Phys 23:131 Aharmim B, The SNO Collaboration et al (2013) Phys Rev C 88:025501 Albert V et al (2018) Astrophys J Lett 853:1 Albrecht E et al (1999) Nucl Instrum Methods Phys Res Sect A433:47 Albrow MG et al (2012) J Instrum 7:P10027 Anderhub H et al (2013) J Instrum 8:P06008 Andres E et al (2000) Astropart Phys 13:1 Anzivino G et al (2017) Nucl Instrum Methods Phys Res Sect A876:84 Astroparticle Physics European Consortium Collaboration (APPEC) (2018) European astroparticle physics strategy 2017–2026. http://www.appec.org/wp-content/uploads/Documents/Currentdocs/APPEC-Strategy-Book-Proof-19-Feb-2018.pdf Barbosa F, GlueX Collaboration et al (2017) Nucl Instrum Methods Phys Res Sect A876:69 Bartlett D et al (1987) Nucl Instrum Methods Phys Res Sect A260:55 Becker-Szendy R et al (1993) Nucl Instrum Methods Phys Res Sect 363:A324 Bernlöhr K, Carrol O, Cornils R et al (2003) Astropart Phys 20:111; Funk S, Hermann G, Hinton J et al (2004) Astropart Phys 22:285 Bertin V et al (2009) Nucl Instrum Methods Phys Res Sect A604:136 Boger J et al (2000) Nucl Instrum Methods Phys Res Sect 172:A449

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Cherenkov P (1934) Dokl Akad Nauk SSSR 2:451. See, for example, the earliest in a series of papers Cho JS et al (2009) Phys Med Biol 54:6757 Cortina J et al (2009) Technical performance of the MAGIC telescopes. In: Proceedings of the 31st international cosmic ray conference, Lodz, arXiv:0907.1211v1 [astro-ph.IM]. http://magic. mppmu.mpg.de/ Curie E (2001) Madame Curie. Da Capo Press, New York, 444 p De Cataldo G, ALICE Collaboration et al (2014) Nucl Instrum Methods Phys Res Sect A766:14 De Leo R (2008) Nucl Instrum Methods Phys Res Sect A595:19 Easo S, LHCb RICH Collaboration et al (2017) Nucl Instrum Methods Phys Res Sect A876:160 Ecklund S et al (2001) Nucl Instrum Methods Phys Res Sect A463:68 Engelfried J et al (2003) Nucl Instrum Methods Phys Res Sect A502:285 Fast J, Belle II Barrel Particle Identification Group et al (2014) Nucl Instrum Methods Phys Res Sect A766:145 Föhl K, PANDA Cherenkov Group et al (2018) J Instrum 13:C02002 Frank I, Tamm I (1937) Dokl Akad Nauk 14:109 Fukuda Y, Super-Kamiokande Collaboration et al (2003) Nucl Instrum Methods Phys Res Sect A501:418 Halzen F, Gaisser TK (2014) Annu Rev Nucl Part Sci 64:101 Harnew N et al (2017) J Instrum 12:C11026 Heaviside O (1889) Philos Mag 27(167):324 Holder J et al (2006) Astropart Phys 25:391 Iijima T et al (2000) Nucl Instrum Methods Phys Res Sect A453:321; Nakano E (2002) Nucl Instrum Methods Res Sect A494:402 Iijima T, Korpar S et al (2005) Nucl Instrum Methods Phys Res Sect 383:A548 Jackson JD (1962) Classical Electrodynamics, 1st edn. Wiley, New York Jelley JV (1958) Cherenkov radiation. Pergamon Press, New York Kalicy G, eRD14 Collaboration et al (2018) J Instrum 13:C04018 Kubo H et al (2004) New Astron Rev 48:323 Litt J, Meunier R (1973) Annu Rev Nucl Sci 23:1 Mirazita M et al (2017) Nucl Instrum Methods Phys Res Sect A876:54 Motz H, Schiff LI (1953) Am J Phys 21:258 Papanestis A, LHCb RICH Collaboration et al (2014) Nucl Instrum Methods Phys Res Sect A766:14 Patrignani C, Particle Data Group et al (2016) Chin Phys C 40:100001 Pestotnik R et al (2017) Nucl Instrum Methods Phys Res Sect A876:265 Ratcliff B (2003) Nucl Instrum Methods Phys Res Sect A502:211 RICH Workshop series (1994) Nucl Instrum Methods Phys Res Sect A343:1; Nucl Instrum Methods Phys Res Sect A371:1 (1996); Nucl Instrum Methods Phys Res Sect A433:1 (1999); Nucl Instrum Methods Phys Res Sect A502:1 (2003); Nucl Instrum Methods Phys Res Sect A553:1 (2005); Nucl Instrum Methods Phys Res Sect A595:1 (2008); Nucl Instrum Methods Phys Res Sect A639:1 (2011); Nucl Instrum Methods Phys Res Sect A766:1 (2014); Nucl Instrum Methods Phys Res Sect A876:1 (2017) Roberts A (1992) Rev Mod Phys 64:259 Roberts DA et al (2014) Nucl Instrum Methods Phys Res Sect A766:114 Schwiening J, PANDA Cherenkov Group et al (2018) J Instrum 13:C03004 Séquinot J, Ypsilantis T (1977) Nucl Instrum Methods Phys Res Sect A142:377 Sia R (2005) Nucl Instrum Methods Phys Res Sect A553:323 Sumiyoshi T et al (1999) Nucl Instrum Methods Phys Res Sect A433:385 Tamm I (1939) J Phys USSR 1:439 Torassa E et al (2016) Nucl Instrum Methods Phys Res Sect A824:152 Tserruya I (2006) Nucl Instrum Methods Phys Res Sect A563:333 Va’vra J, CRID Collaboration et al (1999) Nucl Instrum Methods Phys Res Sect A433:59 Va’vra J et al (2017) Nucl Instrum Methods Phys Res Sect A876:185

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Weekes TC (1983) Proceedings of the 17th international cosmic ray conference, Paris, vol 8. p 34 Weekes TC, Whipple Collaboration et al (1998) Astropart Phys 8:213

Further Reading Buckley J et al (2008) The status and future of ground-based TeV gamma-ray astronomy: a white paper prepared for the Division of Astrophysics of the American Physical Society. arXiv:0810.0444v1 [astro-ph] Cherenkova EP (2008) The discovery of the Cherenkov radiation. Nucl Instrum Methods Phys Res Sect A595:8 Inami K (2017) Cherenkov light imaging in particle and nuclear physics experiments. Nucl Instrum Methods Phys Res Sect A876:278 Križan P (2009) Advances in particle-identification concepts. J Instrum 4:P11017 Mirzoyan R (2014) Cherenkov light imaging in astro-particle physics. Nucl Instrum Methods Phys Res Sect A766:39 Patrignani C, Particle Data Group et al (2016) Review of particle properties. Chin Phys C 40:100001 Ratcliff B (2008) Advantages and limitations of the RICH technique for particle identification. Nucl Instrum Methods Phys Res Sect A595:1 RICH Workshop series (1994) Nucl Instrum Methods Phys Res Sect A343:1; Nucl Instrum Methods Phys Res Sect A371:1 (1996); Nucl Instrum Methods Phys Res Sect A433:1 (1999); Nucl Instrum Methods Phys Res Sect A502:1 (2003); Nucl Instrum Methods Phys Res Sect A553:1 (2005); Nucl Instrum Methods Phys Res Sect A595:1 (2008); Nucl Instrum Methods Phys Res Sect A639:1 (2011); Nucl Instrum Methods Phys Res Sect A766:1 (2014); Nucl Instrum Methods Phys Res Sect A876:1 (2017)

Muon Spectrometers

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Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . General Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Magnetic Spectrometers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Magnets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tracking Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Muon Detectors at Accelerator-Based Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Drift-Tube Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Resistive-Plate Chambers (RPC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Multi-Wire Chambers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Muon Spectrometers for Cosmic Ray Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Atmospheric Muon Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Air Shower Detector Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Muon Radiography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract The detection of muons and the measurement of their momenta is an important task both in astroparticle physics and in elementary particle physics. In cosmic ray physics, the need for muon detectors is obvious since atmospheric showers consist mainly of muons when reaching the surface of the earth. In acceleratorbased experiments, the muon plays a special role as a long-lived particle with only electromagnetic interactions; it can easily be identified, and muons provide in many theoretical models a characteristic signature for new physics. A muon

T. Hebbeker () · K. Hoepfner Department of Physics, RWTH Aachen University, Aachen, Germany e-mail: [email protected]; [email protected] © Springer Nature Switzerland AG 2021 I. Fleck et al. (eds.), Handbook of Particle Detection and Imaging, https://doi.org/10.1007/978-3-319-93785-4_19

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spectrometer consists of a position-sensitive detector that records tracks of charged particles, and a magnetic field so that charge and momentum can be deduced from the track curvature. The identification of muons often relies on the large amount of absorber material in front of the muon detector, which allows only muons (and neutrinos) to pass. We first describe the general detector layout and discuss the related uncertainties. Then we present several examples of muon spectrometers that were or are successfully operated in accelerator physics or in cosmic ray physics. We include also muon detectors without a magnetic field. Finally, we report on the application of muon detectors outside particle and astroparticle physics.

Introduction Muon spectrometers play a central role in particle and cosmic ray physics. Pioneering experiments used muon spectrometers for the measurement and identification of elementary particles. Almost all modern general-purpose detectors at electron– positron or proton colliders use muon spectrometers of multifunctional design with various magnetic field configurations.

General Considerations Muons can be detected via their electromagnetic interactions in matter (see  Chap. 1, “Interactions of Particles and Radiation with Matter”): • In modern detectors, often the ionization of gas molecules (Blum et al. 2008) or the creation of electron–hole pairs in semiconductors (Spieler 2005) is exploited to recognize the passage of a muon and to measure at the same time space points along the trajectory. A resolution of 10 μm to some 100 μm can be achieved, while the detection efficiency is near 100%. Gaseous detectors have been used for particle detection in many variations, from Geiger–Müller counters to spark chambers and multi-channel drift chambers. In earlier experiments the ionization of fluids along a particle’s trajectory was made visible in Wilson and bubble chambers. • Also chemical processes can be exploited, notably in nuclear emulsions; this technique is still used today (OPERA Coll 2010), since it provides a threedimensional spatial resolution of the order of a μm. • Scintillators yield light through excitation and de-excitation of molecules, see  Chap. 15, “Scintillators and Scintillation Detectors.” In some applications like veto counters, only a very crude position measurement is provided, while modern scintillating fiber detectors allow for resolutions of better than 100 μm. • Cherenkov and transition radiation are also suitable to detect relativistic muons, see  Chap. 19, “Cherenkov Radiation.” Examples are water tanks of air shower observatories like Auger (Pierre Auger Coll 2004) or the transition radiation tracker (ATLAS Coll 2008) in the ATLAS detector.

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Since we focus here on spectrometers which need a precise tracking of muons, mainly gaseous and semiconductor detectors are considered in the following. We concentrate on relativistic muons and on detectors specializing on muon measurements. See  Chaps. 11, “Gaseous Detectors,” and  12, “Tracking Detectors,” for more details on these detection methods. Relativistic muons can be identified in different ways. The most suitable property distinguishing muons from other long-lived charged particles is their relatively small energy loss in matter. The reach of electrons and hadrons is limited by the corresponding shower lengths of ∼10 X0 and ∼20; for water, this translates into 4 and 17 m. Muons on the other hand lose in water only about GeV dE ∼ 0.2 dx m

(1)

through ionization and can penetrate several km for momenta in the TeV regime. In accelerator experiments, the electromagnetic and hadronic calorimeters, and additional absorber material like iron of the magnet yoke, stop nearly all charged particles before reaching the outer muon chambers. Cosmic ray experiments are often carried out in underground caverns, thus the overburden provides the required shielding. The momentum and simultaneous charge measurement of muons require the combination of a magnetic field and a tracking detector. We will discuss the resolution achievable with these muon spectrometers in section “Magnetic Spectrometers.” The energy of a high-energy muon (but not its charge) can also be determined from the amount of multiple scattering when passing a material of thickness l with radiation length X0 (Particle Data Group et al. 2008):  θ rms

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(2)

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Ec ≈

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(3)

(for solids) bremsstrahlung becomes the dominant energy-loss mechanism for muons.

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Magnetic Spectrometers Inside a homogeneous magnetic field, a particle with unit charge follows a circular path with radius R=

p⊥ p⊥ / (GeV/c) = 3.3 m · , eB B/T

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where p⊥ is the momentum component perpendicular to the B field. The direction of the bending depends on the sign of the charge. Since momentum components parallel to the B field are not affected, the trajectory will be a helix in general. Equation 4 is the basis for all magnetic spectrometers. In the following, we consider only the movement of the particle – muon or antimuon – in the plane perpendicular to the B field. A high-energy muon cannot be “trapped” in the magnetic field; it will enter the field region, follow a short arc of a circle with a large bending radius R, and leave the field in a slightly different direction, see Fig. 1. Often the sagitta s as defined in the figure is measured. To determine p⊥ we need • A strong and large magnet with a well-known field strength • Several precise measurements of the particle’s position along its trajectory inside and/or outside the magnetic field with (nondestructive) tracking detectors And we have to keep the principal “adversary” under control:

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Magnets Dipoles, solenoids, and toroids are common geometries. For example, at the LHC, the ATLAS experiment uses a large air-core toroid (plus a smaller solenoid) and CMS a solenoid, see Fig. 2. LHCb with its fixed-target-like detector geometry relies on a dipole magnet. Often superconducting coils are used, with B fields up to 4 T. The length of the field region can reach several meters and the stored energy up to 2.5 GJ (CMS Coll 2008). Magnetized iron is sometimes used to increase the B field inside a conventional coil or to guide the field lines outside a solenoid (return yoke), see Fig. 2 (CMS and ATLAS (via hadron calorimeter)).

Tracking Detectors Space points along the muon’s path can be measured precisely with silicon pixel or silicon strip trackers reaching a resolution of σx ∼ 20 μm or drift chambers achieving typically σx ∼ 200 μm. The number of points N measured varies between 10 and 100 for most detectors. In addition, other constraints can be exploited, in particular the collision vertex, see Fig. 2. In section “Muon Detectors at Accelerator-Based Experiments,” some tracking detectors are described in detail. A nice summary of momentum measurements for different spectrometer geometries can be found in Grupen and Shwartz (2008). Here we discuss only the configuration as shown in Fig. 1, and assume that the N points were all measured in

Fig. 2 Top: Bending in CMS solenoid, bottom: ATLAS toroid and solenoid (C. Mai 2010, private communication)

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the magnetic volume of length L, with equidistant spacing and equal spatial resolution σx . The resulting momentum resolution σ( p⊥ )tracking was already calculated by R.L. Gluckstern about 50 years ago (Gluckstern 1963). For N  1: σ (p⊥ )tracking σx /μm p⊥ = 89 · 10−6 · · . √ p⊥ B/T · L2 /m2 · N + 4 GeV/c

(5)

Example: In the CMS inner detector (CMS Coll 2008) (4 T solenoid plus silicon tracker of 1.2 m radius), a resolution of σ (p⊥ )tracking p⊥ = 1.5 · 10−4 · p⊥ GeV/c

(6)

can been reached. In addition, multiple scattering (MS) has to be included, see Eq. 2, so that the total momentum resolution, assuming the particle is moving perpendicular to the B field, is given by σ (p)tracking σ (p)MS σ (p) = ⊕ , p p p

(7)

σ (p)MS 0.055 = . √ √ p B/T · L/m · X0 /m

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Here X0 is the effective radiation length in the magnetic volume of length L. The relative importance of the two terms in Eq. 7 is illustrated schematically in Fig. 1. For very high momenta, the resolution is further degraded by bremsstrahlung, see Eq. 3. Example: The muon spectrometer of the ATLAS experiment (ATLAS Coll 2008) consists of an air-core toroid, thus minimizing the MS term, and Monitored Drift Tube chambers (MDT) with a spatial resolution of better than 100 μm. The resulting momentum resolution for centrally produced muons can be parametrized as σ (p) p = 1.0 · 10−4 ⊕ 0.02. p GeV/c

(9)

Including also the inner tracking systems inside the solenoid magnet the resolution is further improved, in particular at low momenta. In cosmic ray physics, often the maximum detectable momentum pmdm is used to characterize the momentum resolution (Grupen and Shwartz 2008); it is defined as the momentum value for which the resolution equals its value: σ(pmdm )/pmdm = 1.

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Muon Detectors at Accelerator-Based Experiments Muon spectrometers play a key role in accelerator-based experiments, since muons in the final state often constitute the “golden channel” in the search for new particles. Besides their main task of muon identification, precise muon momentum and charge measurements are required in order to allow for the reconstruction of invariant mass(es) and kinematics of the primary physics reaction. A popular example is the search for the Higgs boson decaying into four leptons via H → ZZ(∗ ) → + − + − (with  = μ, e), as seen in Fig. 3. Such events are reconstructed via the invariant mass of both Z bosons based on the measured lepton momenta, which are subsequently combined to reconstruct the Higgs invariant mass. Other potential new phenomena or particles, ranging from supersymmetry to extra dimensions to heavy vector bosons, are also searched for with muons in the final state. To select interesting physics events, a muon level-1 trigger relies on muon identification and momentum determination. To provide the information within O(μs), detector response and readout have to be sufficiently fast. Rate capability and aging are a lesser problem than for inner detectors due to the lower occupancy as only muons should arrive. However, calorimeter leakage and punch through may occur (especially around pseudorapidity η = 0 where the particle’s track length through the calorimeter is minimal), thus increasing the rates from O(1 Hz/cm2 ) to O(10 Hz/cm2 ). In muon spectrometers with iron, only the first station is affected as the iron acts as additional absorber. For reactions such as the Higgs boson decaying into four muons, hermeticity and acceptance are key parameters as the efficiency goes with ε4 . In order not to align insensitive areas along a particle’s path, stations are staggered as can be seen in the event display of Fig. 3. An unavoidable exception is often the interface region between barrel and endcaps, resulting in a slightly reduced trigger efficiency for these pseudorapidities.

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In this section, technology implementations for muon systems are discussed with the intent to illustrate their diversity on selected examples. Detectors at accelerators may be arranged in fixed-target geometry (layered structure perpendicular to the incident beam) or in cylindrical layers around a central collision point. The latter geometry is far more common at modern accelerators. Examples are: the Tevatron experiments CDF (CDF Coll 1996) and D0 (D0 Coll 2006), at CERN’s LHC the ATLAS (ATLAS Coll 2008), ALICE (ALICE Coll 2008), and CMS (CMS Coll 2008) experiments, or the BELLE (BELLE Coll 2002) and BaBar (BaBar Coll 2002) detectors at the B-factories. The cylindrical layers around the interaction point (often referred to as “barrel” detectors) cover pseudorapidities up to O(|η| ≤ 1), and these are complemented by disks of “forward” detectors (also referred to as “endcap”) extending the reach in pseudorapidity up to O(| η| ≤2.5)O(|η| ≤ 2.5), see Fig. 11 for a typical example. Due to the lower center-of-mass energy, fixedtarget experiments are rarely being built anymore, with the notable exception of neutrino experiments, OPERA (OPERA Coll 2010) in the CERN-to-Gran Sasso neutrino beam, and MINOS (MINOS Coll 2009) at the end of the long-baseline neutrino beam from Fermilab. Many earlier experiments around 1960–1980 were of fixed-target type, with the exception of e+ e− machines, until the era of UA1 and UA2 at the CERN proton–antiproton collider. Although it is a colliding-beam experiment, LHCb (LHCb Coll 2008) is constructed in fixed-target geometry, since the strongly boosted B mesons, the subject of LHCb’s research, fly mainly in the forward/backward direction with one of the hemispheres being instrumented. Figure 4 shows the LHCb muon spectrometer in such a fixed-target arrangement, while Fig. 5 displays the ATLAS muon spectrometer at the LHC in collidingbeam geometry. In LHCb, the active muon stations are interleaved with iron (also found in many other experiments such as D0, CMS, BaBar, Belle, and OPERA), an arrangement often implemented as it is convenient to insert the muon chambers in the return yoke of the magnet. In addition to the absorber function, the iron causes multiple scattering of the muons, thus limiting the overall resolution (as discussed in section “Magnetic Spectrometers”). This is not the case for the ATLAS muon system with its air-core toroid, where the chamber resolution is actually the limiting parameter and, hence, has been maximized to yield the presently best stand-alone momentum resolution of a muon system. Common to all detectors is the position of the muon system as the outermost subsystem, given that muons are the only charged particles passing several interaction lengths of material with little energy loss. Consequently, identification of muons based on their reach is the main task of the muon system. Before the start of the LHC era, a signal based on 1, 2, or 3 hits in muon detectors was sufficient for many experiments. Momentum measurement and tracking were provided by the inner tracker. Such an example is shown in Fig. 6 in form of the D0 muon system (D0 Coll et al. 1997; D0 Coll 2006) using layers of 1/2 thick scintillator planes with PMT readout along with layers of drift-tube chambers, either mini drift tubes or proportional drift tubes. Like in many systems, a muon from the interaction point can pass up to three stations. Below the detector, regions of poor coverage are present around the feet. Modern muon systems at the LHC are independent

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tracking detectors providing stand-alone track segments with up to O(50) muon hits, an example of which is shown in Fig. 3, of O(200) μm point resolution along with charge and momentum determination independently of the tracker. As a consequence of their location at large radii, muon systems have to cover large areas of the order 10–100 m2 , limiting the technology choice to scintillators

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Barrel toroid Resistive-plate chambers (RPC) ATLAS

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Fig. 5 The ATLAS detector with its muon system (ATLAS Coll 2008) exploiting several detection technologies based on gaseous detectors

or gaseous detectors. Scintillator is sufficient if the identification of a muon as such is the only task of the muon system and has been used for the Tevatron detectors. To observe a track segment based on many hits and to make a precise momentum measurement, gaseous detectors have a large advantage as their cost per channel is moderate while being able to provide a track resolution better than 100 μm. Therefore, this has been the choice of all LHC experiments. As the oldest particle detection technology, a large variety of gaseous detectors have been developed, notably for applications in muon systems. The key types are discussed in the following sections. The history of searches for new physics often required new detectors and increasing resolution to cope with the tiny cross sections. Detectors at the LHC with their muon systems being essentially stand-alone trackers are a good example of this development.

Drift-Tube Detectors Drift tubes with either round, hexagonal, or rectangular cross section and a central anode wire operating in avalanche or drift mode are very common. In muon spectrometers, tubes of O(cm) diameter are typically arranged in layers of

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O(1 – 5)m2 area. Examples are depicted in Fig. 7. They are usually operated with a standard drift gas, often an Ar/CO2 mixture (ATLAS, CMS), or CH4 -based mixtures (D0). Even relatively slow gas mixtures can be used given the very low occupancy in muon systems. For example, the mixture of 85% Ar with 15% CO2 exhibits a drift velocity of ∼ 55 μm/ns at nominal pressure and electric field of O(E = 2 kV/cm), yielding a maximal drift time for the CMS drift chambers of 380 ns (max. drift distance = 2 cm), thus integrating over 16 bunch crossings at the LHC. All modern applications measure the drift time for electrons in the gas with respect to the time when the muon passed (time given by the accelerator clock or external trigger counters), a method pioneered by drift chambers, yielding a resolution which is about 50 times better than a pure “digital” readout where only the signal wire is identified. Such a resolution can be improved considerably when operating at overpressure, e.g., the point-resolution of the ATLAS drift tubes at 3 bar is about 80 μm (ATLAS Coll 2008) to be compared to 250 μm at nominal pressure. The ATLAS tubes are assembled and tested individually before being glued together to form either rectangular or even trapezoidal chambers (by varying the length of the individual drift tubes). Each drift-tube station measures the two-dimensional rφ projection of the muon track in the magnetic field of the air-core toroid of 0.9 T with a momentum resolution given by Eq. 9. The third dimension is determined by resistive-plate chambers, coupled to the drift chamber.

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Fig. 7 Implementations of drift tubes in muon systems. From the top: D0 mini drift tubes (D0 Coll et al. 1997); ATLAS monitored drift tubes (MDT) (ATLAS Coll 2008) combine two groups of three layers measuring the transverse projection (here shown opened up). CMS barrel drift-tube chambers (DT) (CMS Coll 2008) combine three superlayers of four individual layers and measure both projections

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A similar tube geometry is implemented in the OPERA muon systems, where 3-cm drift tubes are used as well, although of 8-m length arranged in three large stations of parallel layers. Also OPERA measures the muon momentum through bending of the muon track with dipole magnets. Being a neutrino experiment, the occupancy is very low and multiple hits along the drift tube are practically absent. In general, multiple hits can be resolved with a resolution of O(cm) by determining the travel time of electrons along the anode wire or by using a multi-hit time-to-digital converter (TDC). CMS uses 4 × 1 cm2 drift cells with a 50-μm gold-plated steel wire, operated at ambient pressure. These cells are not pre-fabricated as individual tubes but by gluing together large aluminum plates with a set of spacers forming these rectangular cells. This so-called MIT design was first used for UA1 with cell sizes of 10 × 3 cm2 , almost one order of magnitude larger than the CMS cells, reflecting the increasing resolution requirement for muon systems. The CMS drift chambers are located in the iron return yoke for the inner solenoid magnet. The iron is magnetized (B ∼ 1.9 T), but the field is largely contained in the iron and the intermediate gaps hosting the chambers are essentially field-free, except for the large-η regions. The muon track is bent when passing through the iron with its bending direction inverted in the middle of the track, see Fig. 2. Per cell a resolution of about 250 μm is achieved. Three of the four CMS muon barrel stations are arranged as three superlayers of four individual layers each. While two such superlayers (separated by 30 cm) measure the rφ projection, the rz projection is measured by a third superlayer which is rotated by 90◦ with respect to the other two (see Fig. 7). This yields an arrangement of hits as shown in Fig. 3. This way, every muon station allows to reconstruct a 3D track segment and the resistive-plate chambers provide a complementary, redundant measurement. Drift tubes have to be constructed with a precision of O(100) μm, and especially the wire position in the center has to be precise. Wires are strung with a tension to avoid sagging. This force has to be held either by the tube wall (which should not flex) or by a dedicated support. The drift of electrons to the anode wire is influenced by the magnetic field which exhibits a Lorentz force. The resulting deviations from the straight drift path change the drift time. In a magnetic environment, one should preferentially operate insensitive detectors such as RPCs or detectors with very short drift distances to minimize the impact of magnetic effects.

Resistive-Plate Chambers (RPC) Resistive-plate chambers were developed as spark chambers which provide a large signal amplitude while being relatively simple in their construction. It is one of the few implementations of gaseous detectors without anode wires. A thin (2 mm) gas gap is enclosed between highly resistive plates (either Bakelite with ρ ≈ 109 − 1011  cm or glass with ρ ≈ 1013  cm) covered with a conductive graphite coating on the outside. The movement of the charge in the gas-filled

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gap induces a signal outside the plates, which is subsequently picked up by external readout strips (or pads), usually crossing each other and thus providing a 2-dimensional readout. Together with the small thickness, a 3-dimensional space point is provided by an RPC station. Figure 8 shows a double-gap RPC with a common readout strip enclosed between both chambers. Due to the very short distance, the response time is short, of the order 4 ns, thus making RPCs a good choice for triggering chambers at high interaction rates, as is done for all four LHC experiments. The chamber design allows one to produce thin, large-area detector panels to cover hundreds of m2 area and may even fit in thin gaps, as for example in the dipole magnets of the OPERA experiment (OPERA Coll 2010) or the instrumented flux return of BaBar (BaBar Coll 2002), as shown in Fig. 9, and Belle (BELLE Coll 2002). The achievable spatial resolution (O(cm–mm)) depends on the resistivity of the plates, which prevents the charge from spreading out, and the granularity of the readout strips. Depending on the operating voltage (usually of the order of 10 kV), the amplification varies between O(105 ) in avalanche or proportional mode, for example, in ATLAS, CMS, STAR, and ALICE TOF, and O(107 ) in streamer mode, for example, in BaBar, Belle, and ALICE. The high electric field strengths related to sparks may potentially damage the inner Bakelite coating, followed by a small but constant reduction of the efficiency, as seen by BaBar (Anulli et al. 2002, 2003, 2005). It appears that, besides the amplification, other quality parameters of the gaps also play a role, such as the surface coating and variations of the gap thickness. Given that the BaBar interaction rate is much lower than that at LHC, where all four experiments exploit RPCs, an intensive R&D program was initiated. As a source for such damage, roughness of the inner

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surface has been identified. Little bumps on the surface receive higher charges due to the smaller gap which may yield damage with time. To some extent, the surface roughness can be minimized by applying a thin film of oil. Another aspect is the amount of charge generated for the signal. By lowering the voltage, the efficiency drops slightly but also the damage potential is reduced. Therefore, the RPC chambers of the CMS muon system are operated at only 9.5 kV. The lower efficiency is compensated by combining two chambers as shown in Fig. 8. ATLAS and CMS instrumented 3,650 and 8,000 m2 , respectively, in the muon barrel and the forward systems. Both RPC systems are operating in avalanche mode. While the CMS chambers provide redundant information to the high-resolution muon drift and cathode strip chambers, the ATLAS RPCs provide the necessary third projection complementing the 2D information of the precision drift tubes.

Multi-Wire Chambers Under the label of multi-wire proportional chambers, we want to summarize all implementations of gaseous detectors where several wires arranged as a plane share a gas volume. The important aspect here is the plane, to be distinct from drift chambers, where many (102 –103 ) wires are arranged concentrically inside a gas-filled cylinder of O(m) diameter. Such drift chambers are used as central tracking chambers, but not for the outside muon systems. Also, the planar, multiwire chambers have been used as inner trackers (e.g., HERA-B) but also find implementation in muon systems, for example, in LHCb (see Fig. 4) and the CMS forward muon system (see Fig. 11).

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The conceptual design of multi-wire chambers is shown in Fig. 10. The anode wires are arranged in planar layers spaced by d = 1–2 mm. The minimal distance is limited by electrostatic forces, just as in drift chambers. If wires are read out individually, their separation distance determines the spatial resolution, but cost constraints may force the user to match several wires onto one readout channel. The layer of wires is enclosed between two cathodes and the gap is filled with an appropriate gas mixture for generating primary electrons and amplifying the signal near the anode wires, just like with drift tubes. The anode signal is fast, determined by the drift velocity, but the positively charged ions drift about a factor of 1,000 times slower to the cathode. While the previously described detectors do not use the cathode signal, multi-wire chambers with a segmented cathode do, and this principle is sketched in Fig. 10. The charge spreads over several strips, and √ charge interpolation provides a resolution better than the strip width divided by 12. This way a high-resolution 2D space point can be extracted while keeping the number of readout channels at a reasonable level. Combining the information of the cathode strips and anode wires provides a 3D space point. Such cathode strip chambers are the precision detector component of the CMS muon endcaps (Fig. 11) and instrument the regions of high pseudorapidity of the ATLAS muon endcaps (see region indicated in Fig. 5). Their main advantages in these forward regions are their capability to handle larger occupancies than

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drift tubes and to be rather insensitive to the magnetic field due to their short drift distances. Most of the ATLAS endcap region is instrumented with thin-gap chambers (TGC), multi-wire proportional chambers with a signal based on anode wires.

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Several multipurpose detectors, built for accelerator-based particle physics, have also been used to measure cosmic muons, see  Chap. 26, “Indirect Detection of Cosmic Rays.” Their large effective surfaces and/or their excellent spectrometers based on a huge magnetic volume allow for precise measurements of the flux as a function of momentum, charge, and direction. Recent examples are the extended LEP detectors Cosmo-Aleph (Grupen et al. 2008), Delphi (Travnicek and Ridky 2003), and L3+C (L3 Coll 2002), the underground neutrino detectors MINOS (MINOS Coll 2009) and OPERA (OPERA Coll 2010), and the CMS experiment (CMS Coll 2010) at the LHC collider. Figure 12 shows a multi-muon event recorded in the L3+C detector. The deep underground detectors (at depths of a few km of water equivalent) combine the measurement of momentum and charge inside the detector with the angle-dependent energy loss in the overburden, thus allowing a charge and momentum measurement even for multi-TeV muons. Figure 12 shows the recently measured ratio of the fluxes of positive to negative cosmic muons, as a function of the vertical momentum component, together with model fits (CMS Coll 2010). Dedicated cosmic spectrometers are operating at the top of the atmosphere (balloons) or above (satellites) to measure the primary cosmic particles, nuclei, and

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electrons. Atmospheric muons produced as secondary particles in air showers can be detected at earth’s surface or underground. Detectors are built to measure either individual muons or to reconstruct the whole air shower – by sampling the secondary particles on the ground, muons, and also electrons and hadrons, depending on shower energy, altitude, and zenith angle. In addition, cosmic neutrino experiments like ANTARES (ANTARES Coll 2010) or IceCube (IceCube Coll 2006) detect the muons created in charged-current neutrino interaction in liquid or frozen water. In the following, we first present three examples for cosmic muon spectrometers and then we discuss briefly the measurement of the muon component of air showers.

Atmospheric Muon Detectors The Okayama muon telescope (Yamashita et al. 1996) is shown in Fig. 13. It was set up in the year 1992 at the Okayama University in Japan at sea level. Its alt-azimuthal mount can – like an optical telescope – move the apparatus in all directions, in particular zenith angles from 0◦ to 80◦ can be accessed. The magnet consists of an iron cube with dimension 32 cm and a conventional coil. The magnetic field has a strength of 1.8 T. The geometrical acceptance is rather small, 75 cm2 sr. Drift chambers (wall-less multi-wire proportional chambers, PC1, PC2, PC3 in the figure) measure the trajectory (both coordinates) with a resolution of 0.28 mm per point. Scintillators are used for triggering. The maximum detectable momentum pmdm is 270 GeV/c. The Okayama telescope has been used to measure the flux of cosmic muons in the momentum range 1.5 − 250 GeV/c for a variety of zenith angles, and also the charge ratio (Tsuji et al. 1998). In addition, the azimuthal angular dependence was investigated, clearly showing the east–west effect for lowenergy muons, caused by the geomagnetic field. Searches for point sources were unsuccessful. The MACRO detector (Monopole, Astrophysics, Cosmic Ray Observatory) was installed in the Gran Sasso underground laboratory, at an average depth of 3.7 km (water equivalent) (MACRO Coll 2002). Data were taken from 1989 till end of 2000. The multipurpose detector consisted of six supermodules of dimensions 12.6 m (length) × 12 m (width) × 9.3 m (height). Figure 14 shows a cross section. A muon traversing the detector from the top passes through three scintillator planes (top, middle, bottom), streamer tubes (at the top and in lower hemisphere), and track-etch detectors. This detector design was optimized for searches for magnetic monopoles, slow and strongly ionizing particles. MACRO analyzed – among other topics – the flux of downgoing atmospheric muons, and measured also upgoing muons from neutrino interactions in the earth. The direction of muons passing through the detector could be measured with a resolution of about 0.2◦ . The MACRO detector included neither an active magnet nor magnetized iron components. Nevertheless, the local momentum (but not the charge) of muons could be determined. For this purpose, transition radiation detectors (TRD), foam radiators plus proportional counters, were installed in the empty

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upper hemisphere of the MACRO detector. The TRDs measure γ = Eμ /(mμ c2 ) so that MACRO was able to determine the local muon energy from 0.1 to 1 TeV. As an alternative method, the determination of the amount of multiple scattering in the rock absorber layers inside the detector had been proposed – it allows for momentum measurements up to 40 GeV. The local muon measurement can be combined with the calculable muon energy loss in the overburden to determine the momentum spectrum at the surface. Even without any momentum measurement inside the MACRO detector the near vertical muon energy spectrum at the earth’s surface could be determined, exploiting the complex topography of the surface, resulting in a variation of the depth from 3 to 7 km (water equivalent), depending on the muon direction: The underground muon intensity was measured for different angles, corresponding to different rock thicknesses, and with the help of a simple model for the energy dependence of the flux (power law  ∼ E−γ ), the surface muon spectrum could be fitted, in the range 0.5 – 20 TeV, see Fig. 14. Normally, the BESS detector (Balloon-borne Experiment with a Superconducting Spectrometer) is airborne – several balloon flights were undertaken in the Antarctica from 1993 to 2008. In addition, measurements of atmospheric muons were performed at various heights, and also at ground level. The “BESS-TeV” spectrometer (Haino et al. 2004) is depicted in Fig. 15. The following components are relevant for precise muon momentum and charge measurements: • The uniform magnetic field is provided by the superconducting solenoid of 1 m diameter and 1 m length, with a field strength of 1 T.

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Three kinds of tracking devices measure the muon trajectory, over a distance of up to 1.7 m: • The jet-type central drift chamber (JET) • Inner drift chambers (IDC), inside the coil • The outer drift chamber (ODC) In total about 60 measurements are made, the typical spatial accuracy is 150 μm per point. The small scintillating fiber system (SciFi) was used for calibrating the ODC. The maximum detectable momentum pmdm is 1.4 TeV/c. The measured atmospheric muon spectra (Haino et al. 2004) are shown in Fig. 15, for zenith angles smaller than 26◦ . They are complementary to the MACRO results in the TeV regime, see Fig. 14.

Air Shower Detector Arrays The first air showers were measured by P. Auger et al. in the Swiss Alps using Geiger tubes at distances of up to 300 m (Auger et al. 1939). Some of the larger air shower detectors built later were equipped also with muon track detectors, covering a small fraction of the total array. An example is the KASCADE detector (KASCADE Coll 2003) with its underground setup of limited streamer tubes to measure the direction of muons, but not their momenta. The biggest air shower detector today, the 3,000 km2 large Auger observatory (Pierre Auger Coll 2004), uses water tanks in which charged particles generate Cherenkov light, which is detected by photomultipliers. For inclined showers (zenith angle >60◦ ), the muons are the dominant component at the earth’s surface.

Muon Radiography Muon detectors can also be used to localize absorbing material through the resulting reduction in the flux of cosmic muons or via multiple scattering of muons – we speak of “muon radiography.” The possible applications reach from archaeology (Alvarez et al. 1970) and geology (Macedonio and Martini 2009) to the detection of smuggled nuclear weapons (Szeptycka and Szymanski 2009), see also  Chaps. 30, “Accelerator Mass Spectrometry and Its Applications in Archaeology, Geology, and Environmental Research,”  “Particle Detectors Used in Isotope Ratio Mass Spectrometry, with Applications in Geology, Environmental Science, and Nuclear Forensics,” and  28, “Technology for Border Security.” As a first example, we present the search for cavities in pyramids. This idea, illustrated in Fig. 16, was put forward by L. Alvarez who searched in the 1960s – unsuccessfully – for hidden chambers in the Chephren Pyramid in Egypt (Alvarez et al. 1970). He used a stack of 2 m2 large spark chambers placed in a void beneath the pyramid and measured the counting rate as a function of direction. The typical

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Fig. 16 Principle of muon radiography of pyramids

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counting rate in a 3◦ × 3◦ bin was of the order of 1/h. No significant local maximum, as expected for reduced absorption, was found. Recently, the Pyramid of the Sun in Mexico has been selected for similar measurements using multi-wire proportional chambers (Alfaro et al. 2008). Another application of muon detectors is the use of the 7 m2 large drift-tube (DT) chambers designed for the CMS experiment to inspect transport containers from the outside (Benettoni et al. 2007; Pesente et al. 2009). Figure 17 shows the principle: The size of the Coulomb scattering angle θ of a downward going cosmic muon is a measure of the amount of material. As can be seen from Eq. 2, the scattering angle depends on the size l of the object, its mass density ρ, and atomic number Z:

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√ lρZ . θ∝ p

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A typical projected scattering angle for iron and l = 10 cm, p = 1 GeV is 30 mrad, to be compared with the angular resolution of about 1 mrad. The momentum is not measured, but since the cosmic momentum spectrum is known, a statistical analysis can reveal the enclosed material. Figure 17 shows the result obtained for a test setup with a lead and a bigger iron block placed in between the chambers, obtained in 1 h of data taking. The color scale is a measure of the scattering angle. Also the moon has been seen via particle radiography – this is again an astroparticle application of muon detectors. The absorption of primary cosmic particles causes a reduction of the atmospheric muon flux in the direction of the moon – after correcting for geomagnetic effects. In the last couple of years, for example, L3+C (L3 Coll et al. 2005), ARGO-YBJ (ARGO-YBJ Coll et al. 2008), IceCube (Boersma et al. 2009), ANTARES (Distefano 2009), and MACRO (MACRO Coll 2002) have observed the moon shadow. These measurements can be translated into limits on the cosmic antiproton flux (reversed bending in the earth’s magnetic field), and they allow to determine the detector’s angular resolution, since the moon’s diameter is only 0.5◦ .

Conclusions Muon spectrometers have played a central role in particle and cosmic ray physics since the discovery of atmospheric muons in form of charged-particle tracks bending in the magnetic field of a cloud chamber in the year 1936. Today it is a “must” for all big particle detectors at lepton or hadron colliders to include sophisticated muon detectors embedded in strong magnetic fields. Muons are on the one hand easy to detect, on the other hand they provide clear signatures for many processes involving new physics. Due to their long range in matter, muons have also become interesting tools for various radiography applications, measuring the thickness of materials not directly accessible. By now we have seen an enormous variety of muon spectrometer types, combining different detection methods with various magnetic field configurations.

References Alfaro R et al (2008) Searching for possible hidden chambers in the pyramid of the sun. Proceedings of the 30th international cosmic ray conference, Mexico City ALICE Coll (2008) The ALICE experiement at the CERN LHC. J Instrum 3:S08001 Alvarez L et al (1970) Search for hidden chambers in the pyramids. Science 167:832 ANTARES Coll (2010) Measurement of the atmospheric muon flux with a 4 GeV threshold in the ANTARES neutrino telescope. Astropart Phys 33:86 Anulli F et al (2002) The BaBar instrumented flux return performance: lessons learned. Nucl Instrum Methods A 494:455

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Anulli F et al (2003) Mechanisms affecting performance of the BaBar resistive plate chambers and searches for remediation. Nucl Inst Methods A508:128 Anulli F et al (2005) Performance of second generation BaBar flux resistive plate chamber. Nucl Instrum Methods A 552:276 ARGO-YBJ Coll, Wang Y et al (2008) Preliminary results of the Moon shadow using ARGO-YBJ detector. Nucl Phys Proc Suppl 175:551 ATLAS Coll (2008) The ATLAS Experiment at the CERN LHC. J Instrum 3:S08003 Auger P et al (1939) Extensive cosmic-ray showers. Rev Mod Phys 11:288 BaBar Coll (2002) The BaBar detector. Nucl Inst Methods A479:1 BELLE Coll (2002) The Belle detector. Nucl Inst Methods A479:117–232 Benettoni M et al (2007) Muon radiography with the CMS muon barrel chambers. Proceedings of the 2007 IEEE nuclear science symposium, Honolulu, Hawaii Blum W, Riegler W, Rolandi L (2008) Particle detection with drift chambers. Springer, Berlin Boersma DJ et al for the Icecube Collaboration (2009) Moon shadow observation by ice-cube. Proceedings of the 31st international cosmic ray conference, Lodz, Poland CDF Coll (1996) The CDF II technical design report. Fermilab-Pub-96-390-E, November 1996 CMS Coll (2008) The CMS experiment at the CERN LHC. J Instrum 3:S08004 CMS Coll (2010) Measurement of the charge asymmetry of atmospheric muons with the CMS detector. Physics Analysis Summary CMS-PAS-MUO-10-001 D0 Coll (2006) The upgraded D0 detector. Nucl Inst Methods A565:463–537 D0 Coll, Baldin B et al (1997) Technical design of the central muon system. D0 Note 3365, 29 March 1997 Distefano C for the Antqres Coll (2009) Detection of the moon shadow with the ANTARES neutrino telescope. International workshop on very large volume neutrinotelescopes, Athens, Greece Gluckstern RL (1963) Uncertainties in track momentum and direction due to multiple scattering and measurement errors. Nucl Inst Methods 24:381 Grupen C, Shwartz B (2008) Particle detectors. Cambridge University Press, Cambridge/New York Grupen C et al (2008) Cosmic ray results from the CosmoALEPH experiment. Nucl Phys B 175–176:286 Haino S et al (2004) Measurements of primary and atmospheric cosmic-ray spectra with the BESSTeV spectrometer. Phys Lett B 594:35 IceCube Coll (2006) First year performance of the IceCube neutrino telescope. Astropart Phys 26:155 KASCADE Coll (2003) The cosmic-ray experiment KASCADE. Nucl Instrum Methods A 513:490 L3 Coll (2002) The L3 + C detector, a unique tool-set to study cosmic rays. Nucl Instrum Methods A 488:209 L3 Coll, Achard P et al (2005) Measurement of the shadowing of high-energy cosmic rays by the Moon: a search for TeV-energy antiprotons. Astropart Phys 23:411 LHCb Coll (2008) The LHCb detector at the LHC. J Instrum 3:S08005 Macedonio G, Martini M (2009) Motivations for muon radiography of active volcanoes. Earth Planets Space 61:1 and references therein MACRO Coll (1995) Vertical muon intensity measured with MACRO at the Gran Sasso Laboratory. Phys Rev D 52:3793 MACRO Coll (2002) The MACRO detector at Gran Sasso. Nucl Instrum Methods A 486:663 MINOS Coll (2009) Measurement of the atmospheric muon charge ratio at TeV energies with the MINOS detector. Phys Rev D 76:052003 OPERA Collaboration (2010) Measurement of the atmospheric muon charge ratio with the OPERA detector. High Energy Physics - Experiment. https://arxiv.org/abs/1003.1907 Particle Data Group, Amsler C et al (2008) Review of particle physics. Phys Lett B 667:1, and references therein Pesente S et al (2009) First results on material identification and imaging with a large-volume muon tomography prototype. Nucl Instrum Methods A 604:738

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Pierre Auger Coll (2004) Properties and performance of the prototype instrument for the Pierre Auger Observatory. Nucl Instrum Methods Phys Res A 523:50 Spieler H (2005) Semiconductor systems. Oxford University Press, New York Szeptycka M, Szymanski P (2009) Remarks on myon radiography. In: Begun V, Jenkovszky LL, Polanski A (eds) Progress in high energy physics and nuclear safety. Springer, Dordrecht, pp 353–362 Travnicek P, Ridky J (2003) Cosmic multi-muon bundles measured at DELPHI. Nucl Phys B 122:285 Tsuji S et al (1998) Measurements of muon at sea level. J Phys G Nucl Part Phys 24:1805 Tsuji S et al (2001) Atmospheric muon measurements II: zenith angular dependence. In: Proceedings of the 27th international cosmic ray conference, Hamburg, Germany Yamashita Y et al (1996) An altazimuthal counter telescope with a magnet spectrometer tracing Cygnus X-3. Nucl Instrum Methods A 374:245

Calorimeters

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Felix Sefkow and Frank Simon

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Basic Principles of Particle Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Interaction of e± , μ± , and Photons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Interaction of Hadrons with Matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Particle Showers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Calorimetric Measurements: Response, Resolution, and Additional Capabilities . . . . . . . . . . Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Energy Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Additional Capabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Calorimeter Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Calorimeter Concepts and Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Electromagnetic Calorimeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hadronic Calorimeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Role of Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conceptual Refinements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dual Readout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . High Granularity and Particle Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Selected Other Calorimeter Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Concluding Remark . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract In nuclear and particle physics, calorimeters are used to measure the energy and other properties of charged and in particular also neutral particles. They have a central role in accelerator-based and other experiments. A rich variety of different detector designs are used to cover a wide range of energies, from the eV range to TeV and beyond. Modern calorimeter systems are highly complex instruments that push the technological boundaries in terms of sensor capabilities, data readout, and system integration. In this chapter we review the key features and performance criteria and discuss technologies and design choices for selected detector systems.

Introduction In particle and nuclear physics, calorimeters are detectors that are used to measure the energy of particles. In contrast to momentum measurements of charged particles via tracking in a magnetic field, the energy measurement in a calorimeter is a destructive process, where the particle is absorbed and its full energy is deposited in the material of the detector. Depending on the application, and on the type of particles to be detected and their energy range, different design and signal generation principles are used to convert the deposited energy into a measurable signal. This results in a wide variety of calorimeter techniques in use today. Here, we focus on calorimeter applications for high-energy physics experiments, in particular those at particle colliders. Selected examples of other applications will also be discussed at the end of this chapter. Calorimeters are central components of modern high-energy physics experiments. This is due to the ability of calorimeters to measure the energy of not only charged particles (with the exception of muons, which leave the signal of a minimum ionizing particle in the detector) but also of photons and neutral hadrons. They are thus indispensable for the measurement of particle jets created in high-energy collisions, which consist of charged and neutral particles including photons. Calorimeters also enable the detection of the presence of “invisible” particles such as neutrinos and hypothetical particles such as dark matter candidates via the measurement of missing energy (or missing transverse energy in hadron colliders), using the total momentum balance of collision events. The importance of calorimeters tends to increase with increasing collision and particle energies due to two central performance features of this type of detectors, namely, the improvement of the energy resolution with increasing energy and an only logarithmic growth of the required detector size with increasing particle energy. Ideally, a calorimeter would convert the full energy deposited by an incoming particle into a measurable signal. In practice, this is rarely the case; only a fraction of the deposited energy is ultimately detected. This has an important influence on the energy resolution of the device. Here, signal generation mechanisms in the materials

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used for particle detection in calorimeters and the overall design of the detector play a crucial role. In the following we discuss the basic principles of particle interaction in material as relevant for calorimeters, the key aspects of calorimetric energy measurements, and the different types of calorimeters used in high-energy physics experiments as well as additional conceptual refinements and selected other calorimeter types. A much more extensive discussion of calorimetry in particle physics can be found in Wigmans (2017).

Basic Principles of Particle Interaction A prerequisite for the understanding of the function of calorimeters is the interaction of particles in the calorimeter material and the mechanisms for the creation and development of particle showers, which depend strongly on the particle type. It is via these showers that particles are fully absorbed in the calorimeter material, depositing all their energy. In order to measure this deposited energy, a medium is needed which allows a signal to be extracted that ideally is proportional to the energy deposited. This so-called active medium measures directly only the energy loss of charged particles by charge collection from ionization processes or by detecting light from scintillation or Cherenkov radiation. Neutral particles do not generate a direct signal. In the following, we discuss the interaction of electrons, muons, and photons, as well as hadrons, followed by electromagnetic and hadronic particle showers. Further details can be found in  Chap. 1, “Interactions of Particles and Radiation with Matter.”

Interaction of e± , μ± , and Photons A highly energetic electron or positron, e± , which passes through a medium will lose its energy mainly due to bremsstrahlung and ionization. Bremsstrahlung , which originates from the deceleration of the particle in the electric field of the atoms, is dominant for energies above the critical energy Ec , at which both processes yield the same energy loss. The value of Ec depends on the charge number Z of the material and can be parametrized for solids and liquids by Ec = 610 MeV/(Z + 1.24) (Zyla et al. 2020). The energy loss due to bremsstrahlung is proportional to the energy of the e± , E dE =− , dx X0

(1)

where X0 denotes the so-called radiation length, which denotes the mean path length of an e± until its energy is reduced to E/e by bremsstrahlung processes. X0 depends on 1/Z 2 of the material and on the particle mass squared m2 . Bremsstrahlung produces photons with an 1/E energy spectrum.

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Since all material dependence is parametrized in terms of the radiation length X0 , it is a good scale to describe the energy loss of high-energetic e± and photons as function of the depth of the calorimeter. A rule-of-thumb formula for the radiation length (2.5% precision for Z > 2) is Zyla et al. (2020) X0 =

 g  . √ Z(Z + 1) ln(287/ Z) cm2 716.4 A

(2)

The ionization of atoms in the absorber material is due to the interaction of the incoming charged particle with the electrons in the atomic shell. The energy loss depends on the square of the speed of the particle, β 2 , on the square of the particle’s charge and on the square of the atomic number of the material. The mean energy loss is given by the Bethe–Bloch formula (Zyla et al. 2020). The typical energy loss in a gas is 1–3 keV/cm, while it is much higher in liquids or solids, for example, 3.9 MeV/cm in silicon. For highly energetic photons the conversion into e+ e− pairs is the dominant process. The path length until such a process occurs can be related to the radiation length X0 : the mean free path length until a pair-production process occurs is 9/7 of a radiation length. For energies below the threshold of 1 MeV, the photon can only be scattered off or ultimately absorbed by electrons in the atomic shell (Compton scattering and photoelectric effect). For muons, due to the approx. 200 times larger mass than the electron, and the 1/m2 dependence of the cross section, bremsstrahlung is heavily suppressed. Hence, the μ± loses energy mainly due to ionization. This leads to the effect that the muons travel long distances as minimally ionizing particles (MIP) even in dense media, so calorimeters are very often parts of the muon filter of a detector system.

Interaction of Hadrons with Matter Charged hadrons also continuously lose energy due to ionization processes, as described in the previous section. Due to the high particle masses, bremsstrahlung is of no importance. However, the main energy loss for highly energetic charged and neutral hadrons originates from inelastic strong interactions with atomic nuclei. In so-called spallation processes, the collision of the incoming hadron with one nucleon leads to subsequent collisions of the struck nucleon with other nucleons within the nucleus (intra-nuclear cascade). In these interactions pions (π 0 , π ± ) and other hadrons can be produced which escape the nucleus if their energy is high enough. In addition nucleons can be emitted. The residual nucleus will very likely be in an excited state and undergo a de-excitation process, possibly through nuclear fission, which involves an evaporation step, i.e., the emission of low-energetic nucleons, photons, and heavy particles (e.g., α particles or deuterons). As a result, part of the deposited energy is converted into nuclear binding energy which is not observable. The same is true for nuclear recoil absorbed by the surrounding medium.

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The mean free path length of protons, before undergoing an inelastic interaction, is the so-called nuclearinteraction length, λI , which can be parametrized by λI = 20 · A0.4 + 32 g/cm2 (±1% for A > 7). It should be noted that the interaction length for pions is larger. For high A materials, as used for the efficient absorption in a compact detector, the hadronic interaction length is much larger than the radiation length X0 . In Pb, for example, X0 = 5.6 mm, but λI = 18 cm. This leads to the effect that, compared to electromagnetic interactions, the hadronic interactions happen on a substantially larger scale; hence, a greater material depth is required for hadronic than for electromagnetic calorimeters. The π 0 mesons produced in a spallation process will immediately decay into pairs of photons which subsequently undergo electromagnetic interactions. Some of the produced particles are short-lived and decay before undergoing a subsequent inelastic interaction. Part of the resulting decay products (muons and neutrinos) can escape the volume of the calorimeter, with their energy share undetected. A special case is the neutron which can travel long distances within the calorimeter, undergoing elastic scattering or inelastic interactions. It may escape, or, once slowed down sufficiently, its cross section for capture processes becomes large in some materials (e.g., hydrogen, cadmium). Most capture processes will lead to the emission of photons. In the elastic scattering processes on hydrogen, the proton will take up a large recoil and subsequently lose its energy by ionization. For heavy materials such as uranium, neutron-induced fission plays a role, with subsequent neutron emission. In consequence the yield of secondary neutrons and low-energetic photons is high even for relatively low-energetic neutrons (below 1 MeV, while all other hadrons will no longer produce secondaries in this energy regime.

Particle Showers High-energetic particles entering a block of material will, after undergoing a primary interaction, initiate a so-called particle cascade or shower and create a multitude of secondary particles. Depending on the nature of the primary particle, they are classified into electromagnetic and hadronic cascades. Figure 1 shows showers of a 100 GeV electron (top) and a 100 GeV negative pion (bottom) in a solid block of iron, simulated with the GEANT4 program (Agostinelli et al. 2003). As apparent from the figure, the two classes of showers exhibit a very different spatial structure, driven by the underlying interactions of the shower particles in matter. In the following the features of electromagnetic and hadronic showers are described in more detail.

Electromagnetic Cascades When electrons or photons enter a dense material, the combination of bremsstrahlung and pair production gives rise to a chain reaction in which a cascade of secondary particles is created: the radiated photons convert, and the conversion pairs radiate. In a simple model, the particle multiplicity doubles, and the average energy per

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particle is halved within one radiation length. Multiplication stops at the critical energy, when ionization takes over. For an initial energy E0 , N ≈ E0 /Ec particles are being produced, most of them being electrons and photons, while positrons are produced only above a threshold of 1 MeV; they carry about 25% of the energy. Showers initiated by electrons and positrons start immediately on their entrance into the material, while for photons the onset follows an exponential absorption law and occurs after 9/7 X0 on average. If expressed in terms of radiation lengths, the shapes of electromagnetic showers are roughly material-independent, and in the longitudinal direction they scale logarithmically with energy. Thanks to this moderate dependence, a calorimeter of fixed size can cover a large range of energies. The longitudinal profile can be parametrized as dE f (t) = = at ω · exp(−bt) (3) dt (t in units of X0 ), and the maximum of the multiplicity and energy deposition occurs at tmax = ln(E0 /Ec ) − 0.5. Since the critical energy Ec decreases with Z, ranging from 22 MeV for iron to 7 MeV for uranium, showers in heavy absorbers reach their maximum later and decay more slowly. Another effect of the lower Ec is that the number of soft photons becomes very large, which can introduce a dependence of the energy response on the step in the cascade. For an accurate energy measurement, it is critical that the calorimeter is deep enough to (almost) fully contain the shower. In copper, for example, for 99%

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containment one needs 16 X0 at 1 GeV and 27 X0 at 1 TeV. The numbers are smaller for lighter absorbers and higher for dense materials. The transverse extension of electromagnetic showers is characterized by the Molière radius, ρM , which corresponds to a cylinder containing 90% of the energy. It scales with X0 , ρM = 21.2 MeV · X0 /Ec ,

(4)

but is energy-independent. Therefore, showers become increasingly elongated with higher incident energy. A simulated shower initiated by an electron with 100 GeV energy is shown in Fig. 1. It is important to note that the shower shape and composition fluctuate from event to event, mostly due to statistical variations in the early shower stage. Therefore, it is not sufficient to probe the energy deposition at one position, e.g., in the maximum. Instead, one has to integrate the whole energy or sample it at sufficiently many representative positions. Fluctuations in longitudinal leakage, for example, are considerably larger than the mean value of the leakage itself.

Hadronic Cascades Compared with electromagnetic showers, hadron showers are much more complex and diverse, due to the large variety of the underlying physics processes. The multiplicity in a single interaction is larger, but the number of “generations” in the cascade and the total number of particles are much smaller, such that the inevitable fluctuations have a stronger impact. The pion production threshold of about 300 MeV plays the role of a cut-off, to be compared to the considerably smaller critical energy in the electromagnetic case. Typically, depending on the material, there is around one charged pion per GeV and ten times as many (softer) nucleons. At each nuclear interaction, charged and neutral hadrons are being produced, together with π 0 and η mesons which immediately decay into photons and give rise to electromagnetic showers near the production point. Soft short-range hadrons also deposit energy locally, while the harder fragments travel further until they initiate another nuclear interaction. The shower topology is thus described by two scales: the overall evolution is governed by the nuclear interaction length, λI , while the substructure is characterized by the radiation length, X0 . This is illustrated in the simulated cascades shown in Fig. 1, where the electromagnetic sub-showers within the hadronic shower are clearly visible. The transfer of energy into these electromagnetic sub-showers is a “one-way street,” since π 0 mesons are likely to be produced at each new nuclear interaction, whereas no hadrons emerge from π 0 decays and subsequent electromagnetic interactions. Therefore, the fraction of electromagnetic energy, fem , increases with the number of steps in the cascade and therefore on average with the energy of the incident particle, but with large event-to-event fluctuations. Ultra-high-energy cosmic hadrons asymptotically produce purely electromagnetic showers. fem also depends on the incident particle type; protons, for example, produce less π 0 mesons due to baryon conservation.

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Around two thirds of the energy of the non-electromagnetic part is deposited via ionization by charged hadrons, and 5–10% is released as kinetic energy of evaporation neutrons. The remainder is “invisible”: nuclear binding energy and target recoil do not contribute to the detector signal. The particle composition of the shower depends on the development stage (shower depth or “age”) and on the radial distance from the line of impact. For a charged primary hadron, there is a core enriched with electromagnetic sub-showers, surrounded by a more hadron-rich halo. Thermal neutrons are found in all directions at distances of several meters (“neutron gas”). The longitudinal shower profile reaches its maximum about 1 λI after the position of the first nuclear interaction, which itself is exponentially distributed. So the length of an individual shower is considerably shorter than the energy profile averaged over many events may suggest. Variations in the onset are the biggest single source of fluctuations in longitudinal energy distribution and leakage (energy leaving the calorimeter volume). In iron, about 8 λI are required to contain the energy of a 100 GeV pion shower. Transversely, roughly 90% of the energy are contained in a cylinder with radius λI , although this fraction is energy-dependent. Figure 2 summarizes λI and X0 for all heavier elements in units of cm. To achieve compact detectors, minima in this distribution are preferred. For hadronic calorimeters, also the ratio of λI and X0 , which ranges approximately from 10 to 30, plays a role, as it influences the sampling of electromagnetic sub-showers relative to the length scale of the evolution of the hadronic cascade in the detector. The elements in the region of Ru and Pd are excluded due to their high cost. This makes 50

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lead and tungsten typical choices for electromagnetic calorimeters and steel, copper, and brass for hadronic calorimeters, with tungsten, lead, and uranium also used for specific hadron calorimeter applications.

Calorimetric Measurements: Response, Resolution, and Additional Capabilities The central task of calorimeters in particle physics experiments is the measurement of energy; thus, they are often characterized by their energy reconstruction and energy resolution. However, also additional capabilities, such as spatial and time resolution and particle identification, are relevant performance criteria.

Response The determination of the energy deposited by an electromagnetic or hadronic shower within the calorimeter volume is done by collecting signals from the generated charged particles in the active medium. This medium is either identical with the absorber (homogeneous calorimeter) or interleaved with the absorber material (sampling calorimeter). Any medium which allows to measure the energy loss of charged particles can be utilized (e.g., scintillators, liquid noble gases, crystals, silicon, or gas amplification structures). More details are given in section “Calorimeter Types.” The number of charged particles in a shower is, to first order, proportional to the total deposited energy. The number of charged particles producing a signal in the active material is proportional to the total number, and therefore the signal is proportional to the energy E0 of the primary particle. For sampling calorimeters, this is only approximately true; in particular in heavy absorber materials, a significant energy fraction is deposited by short-range particles, or in hydrogenous active media neutrons transfer more energy than in denser media. In the previously mentioned simple model of an electromagnetic shower, the sum of the track lengths of all particles is given by T [X0 ] = F · E0 /Ec . Due to the proportionality between T and E0 , the former quantity is a good estimator for the energy of the particle. The factor F accounts for a lower cut-off energy for a track to be measured. The fluctuation of the total track length T limits the energy resolution. An additional contribution to the measured resolution is the actual statistical fluctuation of the ionization, scintillation, or Cherenkov light process (charge production and photon statistics).

Energy Resolution The number of generated charged particles, N, varies statistically√from shower to shower. The intrinsic resolution, σ , is therefore proportional to√ N. Since N is proportional to E0 , the resolution can be parametrized by σ = A E0 . The relative

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√ resolution σ/E therefore improves with A/ E0 . The parameter A denotes the so-called stochastic term of the resolution, which is determined by the statistical fluctuation of the measured signal. The readout system of the active medium will contribute noise to the resolution, σN = B, which is not energy-dependent, but depends on the number of involved electronic channels and the details of the readout electronics. Imperfections of the calorimeter, such as mechanical and density variations, instabilities, imperfections of the readout, or incorrect calibration of channels, will further worsen the resolution. The corresponding contribution σI = C · E scales with the total deposited energy and thus constitutes a constant term in the relative energy resolution. Adding up all contributions in quadrature yields the standard parameterization of the energy resolution of a calorimeter: A B σ = √ ⊕ ⊕ C. E E E

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Figure 3 illustrates the interplay of the different components of the energy resolution for one homogeneous and one sampling electromagnetic calorimeter at the Large Hadron Collider. For the homogeneous calorimeter with a small stochastic term, the constant term becomes dominating from 40 GeV on, while the resolution of the sampling calorimeter is driven by the stochastic term up to high energies. In specific hadron calorimeters, additional terms in the resolution function may appear, which exhibit a different scaling with energy, for example, contributions from leakage or from the fluctuations of the electromagnetic fraction in the shower. Typically, primarily the stochastic term – which is determined by the calorimeter design in terms of material and geometry – is considered in order to describe the properties of a calorimeter. In practice, the energy resolution of a calorimeter at high

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energies is limited by the constant term C, which mainly reflects the precision and stability of the mechanical construction, electronic readout system, and calibration. For sampling calorimeters, the stochastic term depends on the sampling fraction, i.e., the ratio of active to passive material, and is given by the fraction of the total energy deposited by a fully penetrating MIP in the calorimeter that is deposited in the active layers. Also the sampling frequency enters, which is determined by the number of different sampling elements present in the regionin which the shower develops. The stochastic term A scales approximately with d/fsamp , where d is the thickness of the active layers and fsamp is the sampling fraction, showing that a high sampling fraction, and frequent sampling by thin active layers, results in better energy resolution.

Additional Capabilities Beyond energy reconstruction and resolution, additional parameters that characterize the performance of calorimeters can be the spatial, directional and time resolution, as well as particle identification capabilities. These typically require specific solutions for the detector design to provide the desired capabilities. Good spatial resolution requires lateral segmentation of the calorimeter below the characteristic shower size, given by ρM for electromagnetic showers, λI for hadronic showers. This allows the application of center-of-gravity methods using the energy sharing between neighboring √ cells. The resolution scales roughly with square root of the cell size and with 1/ E. For electrons and photons, a resolution of the order of 1 mm is achievable. Due to their strong fluctuations, the resolution for hadronic showers is substantially worse. Longitudinal segmentation in addition opens up the possibility for directional reconstruction, which becomes relevant in experiments where the point of origin of the particles is not defined. Examples for this are electromagnetic calorimeters in near detector systems in neutrino beam experiments, as used in T2K and planned for DUNE. Good time resolution requires appropriate active materials that provide a fast signal rise time and capable electronics. As other resolution parameters, also the √ time resolution has a strong stochastic component, scaling with 1/ E. Electromagnetic calorimeters optimized for timing achieve time resolutions well below 100 ps, with future scintillator and silicon-based calorimeters targeting 20 ps for highenergy showers. Such performance will enable the suppression of pile-up occurring from multiple collisions within one bunch crossing in colliders such as the LHC, by allowing to associate photons to identified vertices based on time. Using the longitudinal and transverse energy profiles or the time distribution of the signals, calorimeter system can also provide particle identification. While electromagnetic showers originating from electrons, positrons, and photons are characterized by an early start and a well-defined profile, hadron-induced showers start deeper in the detector and have significantly higher fluctuations along the shower. All energy deposits in electromagnetic showers are prompt, distinguishing them from hadronic showers which have considerable delayed components

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connected to neutron activity. Muons lead to a prompt MIP-like energy deposit over the full depth of the calorimeter.

Calorimeter Types Calorimeters exist in a wide variety of different concrete implementations and can be classified according to their geometrical properties, the medium used for signal generation, the approach to the readout, or the primary use case of the calorimeters. This section begins with a few more general considerations on calorimeter concepts, before examining some of the calorimeter classes in more detail with selected concrete examples.

Calorimeter Concepts and Design A key challenge for calorimeters is to carry the signals created by energy depositions inside of the detector volume to the outside, which drives the overall design, the choices of the readout geometry and of the active materials. The requirements in detector depth in units of X0 or λI , often competing with space constraints, result in a preference for higher-density materials. Goals for the energy resolution and other performance parameters influence the choice of the active medium and, in the case of sampling calorimeters, also the choice of the passive absorber material and the geometrical structure. Possible requirements of hermeticity, meaning a maximum coverage of the solid angle around the interaction point, define options for the readout geometry and signal routing. In the case of homogeneous calorimeters, where the active medium is also the absorber material in which the shower develops, all readout aspects are constrained to be outside of the actual detector volume. Thus an optical transmission of the signal information in a transparent medium is the solution of choice. Typical active materials are scintillating crystals or glasses making use of the Cherenkov effect for signal generation. The light yield, meaning the number of photons per unit energy deposited, of scintillating crystals varies considerably for different materials, with the high-density crystal PbWO4 producing about three orders of magnitude less light than the common material NaI(Ti). More details are given in  Chap. 15, “Scintillators and Scintillation Detectors.” The yield of Cherenkov photons is lower by approximately another order of magnitude, making this a key limiting factor for the energy resolution in Cherenkov-based calorimeters. In addition to crystal- and glass-based detectors, also the deep UV scintillation of cryogenic liquids such as liquid xenon and liquid krypton, as well as Cherenkov light emission in water, is used for calorimetric measurements. Due to the properties of hadronic showers, homogeneous calorimeters are typically only well suited for the detection of electromagnetic showers, in terms of both required overall detector depth and achievable energy resolution.

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Since sampling calorimeters decouple the signal generation from the shower evolution, they open up a wide range of possibilities of active media while at the same time being able to satisfy geometrical constraints with appropriately chosen high-density absorber materials. They are usually also significantly lower in cost per instrumented volume than homogeneous calorimeters, with details depending on the choice of active and passive materials and other detector parameters, such as readout granularity. A wide range of active detectors are used in sampling calorimeters, with plastic scintillators as plates, tiles, strips, or fibers as the most common solution. Liquid argon and silicon pad detectors are higher-density, very radiation hard options, and silicon pixel sensors and large-area gas detectors are used in digital or semi-digital electromagnetic and hadronic calorimeters, respectively. Across homogeneous and sampling calorimeters, optical readout of scintillation photons represents the most common technology in high-energy physics calorimetry. In these systems, different photodetectors are used, from the traditional photomultiplier tubes to vacuum photo triodes, avalanche photo diodes, and to the increasingly common silicon photomultipliers. More details on photon detection are given in  Chaps. 13, “Photon Detectors,” and  17, “Silicon Photomultipliers.” Figure 4 illustrates different geometrical concepts for calorimeters with optical readout. Conceptually, the considerations presented here also apply, with suitable modifications, to other methods of readout, for example, for the case of the direct charge collection, e.g., in liquid noble gases. The typical design of a homogeneous crystal calorimeter, as used for highresolution electromagnetic calorimetry in many different experiments, is shown in Fig. 4a. Here, the scintillation light is collected at the back of the crystals. Sampling calorimeters consisting of matrices of plastic scintillating fibers embedded in absorber structures, as shown in Fig. 4b, have similar features. They offer additional possibilities for hadronic calorimeters, as discussed in section “Dual Readout.” The classic sampling calorimeter design, with a sandwich structure of absorber plates and active medium, is shown in Fig. 4c. Here, each scintillator layer is read out individually with a photon sensor, which renders achieving a hermetic coverage in applications in collider detectors difficult. This issue is addressed by tower-like readout solutions, with one example shown in Fig. 4d. Here, the light from the scintillating layers is collected by wavelength shifters, which shift the light to longer wavelengths and then guide it to the photodetector, either via plates as shown in the figure or via fibers penetrating the scintillator and the absorber layers (“shashlik calorimeter”). In such schemes, the signals from multiple readout layers are combined, removing or at least reducing the possibility for longitudinal information. A variant of such detectors is “tile calorimeters”, where wavelengthshifting fibers, embedded in scintillator plates, are used to guide the light of one or more plates to the photon detectors, where the light of multiple fibers is combined. Highly granular calorimeters, illustrated in Fig. 4e, represent a relatively new class of detectors with high lateral and longitudinal segmentation achieved by individual readout of small active cells, providing increased flexibility in geometrical

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choices. Such detectors require photodetectors, front-end electronics, and possibly even high-density data concentrators embedded inside of the active volume and to bring out already digitized signals. More details are given in section “High Granularity and Particle Flow.”

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Electromagnetic Calorimeters Electromagnetic calorimeters are primarily targeting electrons and photons but normally will also produce signals for other types of particles. Hadrons often begin to shower in the electromagnetic calorimeter, with showers typically extending significantly beyond it into a downstream hadron calorimeter; the electromagnetic calorimeter inevitably also represents the front section of the calorimeter system for hadrons. While this dual role must be taken into account in the design, the properties of electromagnetic showers discussed in section “Particle Showers” define the main parameters for the design of electromagnetic calorimeters. The required depth is given by the radiation length X0 of the detector material and the energy of the particles, while the shower width, and with that the possibility for two-shower separation, is determined by the Molière radius of the material composition. For calorimeters at high-energy colliders, this drives the detector design to high-density, high-Z materials. Homogeneous electromagnetic calorimeters are used in particular when excellent energy resolution is required, which is here in principle only limited by the fluctuations of the measurable signal, since the full particle energy is deposited in the active medium. These can be photon statistics in the case of light detection (scintillation or Cherenkov light) or fluctuations of the liberated charge in liquid noble gas-based calorimeters with charge collection readout. The use of scintillating crystals is the most common technique for homogeneous calorimeters, with a prominent example being the electromagnetic crystal calorimeter of the CMS experiment at the Large Hadron Collider (LHC) (Chatrchyan et al. 2008). To achieve the necessary compactness that allows sufficient detector depth in units of X0 for the high energies, high-density crystals are required, which also fulfill the stringent radiation hardness requirements imposed by the LHC environment. CMS uses PbWO4 , which has a density of 8.3 g/cm2 , an X0 of 8.9 mm, and a ρM of 22 mm, and provides a very fast scintillation response. A particular challenge is the relatively low light yield of the material, with approximately 80 photons per MeV of deposited energy, which requires very low-noise readout and limits the use of this crystal to high-energy applications. The CMS electromagnetic calorimeter consists of 61 200 crystals with a size of 22 × 23 × 230 mm3 in the barrel section, and 14 648 crystals with a size of 30 × 30 × 220 mm3 in the endcap region, with the length corresponding to 26 X0 . Figure 5 shows one PbWO4 crystal (left) and one half of an endcap with the crystal ends√ visible. The detector achieved an energy resolution with a stochastic term of 3%/ E and a spatial resolution of 1 mm at an energy of 100 GeV. One example for a homogeneous calorimeter with liquid xenon as active medium is the photon detector of the MEG experiment. This device, which is based on the collection of the scintillation light via 846 photomultipliers enclosing an active volume of 800 liters of liquid xenon, achieved an energy resolution of 1.6% for 54.9 MeV photons (Adam et al. 2013). An upgraded detector, where

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Fig. 5 The homogeneous electromagnetic calorimeter of the CMS experiment, showing one PbWO4 crystal of the barrel calorimeter (left), and the full crystal matrix of one half endcap (Dee) during assembly, with the crystal ends visible (right). (Images © CERN 2020)

one part of the PMTs is replaced with 4092 large-area silicon photomultipliers, has recently been completed and is expected to achieve even better energy resolution. Sampling electromagnetic calorimeters typically do not reach the same level of energy resolution but become competitive at high energies where the importance of the stochastic term diminishes. Their main advantage lies in a higher flexibility in terms of geometry and materials and, in most cases, lower cost. Just as for homogeneous calorimeters, the same arguments about high-density high-Z absorbers also apply for electromagnetic sampling calorimeters. For the active elements, plastic scintillators are the most common choice, but higher-density materials such as liquid argon provide the potential for large sampling fractions in compact detectors. A prominent example for such a system is the liquid argon electromagnetic calorimeter of ATLAS (Aad et al. 2008), which uses 1.53 -mm-thick Pb absorbers with 0.2 mm stainless steel cladding on each side and a 2.1 mm liquid argon gap as active medium. In addition to the increased sampling fraction due to the higher density of liquid argon compared to plastic scintillator, liquid argon also provides excellent radiation hardness required in the LHC environment. The detector readout collects the ionization from the LAr on pickup electrodes via high voltage applied between absorbers. The absorbers are arranged in an accordion pattern, as shown in Fig. 6, to enable tower readout on the outer radius of the detector while keeping the sampling structure constant with radius and avoiding inactive gaps in the detector. The overall depth of the barrel detector, including a 4.3 X0 pre-shower segment, is 22.3 X0 . In total, the calorimeter system has 173 312 readout channels. With a sampling fraction √ of 17%, the calorimeter achieves an electromagnetic energy resolution of 10%/ E with a constant term of 0.4% (Table 1).

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Fig. 6 Detail of the sampling structure of the ATLAS liquid argon electromagnetic calorimeter, showing the accordion-shaped lead absorber sheets, spacers for the argon gaps, and the pick-up electrodes. (Image © CERN 2020)

Table 1 Energy resolution of selected electromagnetic calorimeters in past and present experiments. Energy E given in GeV Experiment Belle CMS KLOE H1 ZEUS ATLAS

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Depth Homogeneous calorimeters CsI(Ti) 16 X0 PbWO4 26 X0 Sampling calorimeters Pb/scintillating fibres 15 X0 Pb/LAr 20 – 30 X0 depleted U / plastic scintillator 20–30 X0 Pb/LAr 25 X0

e.m. energy resolution 1.7% for Eγ > 3.5 GeV √ 3.0%/ E ⊕ 0.5% ⊕ 0.2/E √ 5.7%/ E ⊕ 0.1/E √ 12.0%/ E ⊕ 1.0% √ 18%/ E √ 10.0%/ E ⊕ 0.4% ⊕ 0.3/E

Hadronic Calorimeters Hadronic calorimeters measure charged and neutral hadrons via the formation of hadronic showers. Since neutral hadrons are not observed in other detector systems, these detectors have a crucial role in the measurement of the overall energy and the momentum balance of collision events, and they are central for the reconstruction of particle jets originating from the hadronization of quarks and gluons. The larger spatial extent of hadronic showers compared to electromagnetic showers, given by the significantly larger λI compared to X0 in most materials, means that hadronic calorimeters are always downstream of the electromagnetic calorimeter in a detector system. Since the typical depth of an electromagnetic calorimeter is around 1 λI , a

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significant fraction of hadrons will start showering already in the electromagnetic calorimeter, resulting in additional complications for the reconstruction of hadronic energy in realistic experimental settings, which have to be considered in the design of complete detector systems. The complexity of hadronic showers, with a mixture of charged and neutral hadrons, including neutrons, photons, electrons, and invisible energy, leads to a response which strongly depends on material, geometry, and energy as well as on the integration time of the detector electronics. The different processes contributing to the signal generation in hadronic calorimeters are illustrated in Fig. 7 and are presented in more detail in the following. As discussed in section “Particle Showers,” there are two distinctly different shower components, the electromagnetic and the purely hadronic (or non-electromagnetic) component. The latter contains a fraction that does not contribute to visible signals finv , which may be as large as 40% and does fluctuate significantly from event to event, thereby fundamentally limiting the precision of hadron calorimeters. This invisible energy typically results in a lower detector response to the purely hadronic part than to the electromagnetic component, expressed via the h/e ratio. This has profound consequences for the performance and the design of hadronic calorimeters. The response of the detector to a primary hadron, e.g., a pion, is typi-

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cally lower than that to an electron of the same energy, π/e = fem + (1 − fem )h/e, which is smaller than 1, if h/e < 1. Thus, the fluctuations of the electromagnetic fraction fem within the hadron shower deteriorate the energy resolution, and the energy dependence of the average electromagnetic fraction, which is around 30% at 10 GeV and rises to approximately 55% at 100 GeV, may lead to a non-linearity in the detector response. Homogeneous calorimeters, in particular those based on scintillating crystals or Cherenkov light readout, have h/e ratios substantially smaller than 1, and so suffer strongly from the fluctuations between the shower components; they normally do not constitute viable solutions for hadronic calorimetry, even if sufficient depth could be achieved. For the same reason, calorimeter systems with a homogeneous crystal-based front electromagnetic section typically exhibit a worse energy resolution for hadrons than the hadronic section alone, a tribute paid to the superior electromagnetic performance. Another key factor in the response of hadronic calorimeters is neutrons, which are created in spallation reactions. The amount of neutrons in the shower can be quite substantial, is correlated with the non-electromagnetic fraction of the shower, and increases strongly with heavier absorber nuclei. The sensitivity to neutrons depends on the active medium, with hydrogenous materials such as plastic scintillator more sensitive than others due to elastic scattering of neutrons on protons in the plastic compounds, which then results in an ionization signal. The scattering leads to a moderation of the neutrons, which, once they reach sub-eV energies, are captured by nuclei, leading to the emission of photons which can convert and be detected in the active medium. Due to the long time scales involved in the moderation processes which extend beyond many 100s of nanoseconds, the integration time of the front-end electronics has a significant influence on the sensitivity to this part of the hadronic cascade. Equalizing the response to electrons and hadrons has the potential to improve the calorimeter performance, since it removes the fluctuation of the signal amplitude with fluctuations in the electromagnetic fraction and the non-linearity with energy. So-called compensation can be achieved by reducing the response to electrons, which can be obtained with a reduced sampling fraction, at the expense of the electromagnetic resolution, or by increasing the response to the purely hadronic part of the cascade, which is possible by enhancing the response to neutrons. This is done by combining absorbers which emit a large number of neutrons, such as uranium or lead, with plastic scintillator with finely tuned sampling fractions and frequencies and an appropriate integration time. While h/e = 1 only removes the effect of fem fluctuations, the neutron signal in addition shows some correlation with the invisible nuclear excitation energy. An example for this approach is the ZEUS uranium-scintillator calorimeter, which showed the best hadronic energy resolution in a collider experiment to date, achieving a stochastic term of 35% for single pions in beam tests (Behrens et al. 1990). In longitudinally and laterally segmented calorimeters, electromagnetic sub-showers can be identified based on energy density. With an energy

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Table 2 Energy resolution of selected hadronic calorimeters in combination with the respective electromagnetic calorimeters upstream in past and present experiments, with results taken from beam tests of prototypes. Energy E given in GeV Experiment H1 ZEUS ATLAS CMS

Technology (ECAL, HCAL) Pb/LAr, Steel / LAr Depleted U / plastic scintillator Pb/LAr, Steel/plastic scintillator PbWO4 , brass/plastic scintillator

Combined hadronic energy resolution √ 46%/ E ⊕ 2.6% ⊕ 0.73/E √ 35%/ E √ 52%/ E ⊕ 3.0% ⊕ 1.6/E √ 84.7%/ E ⊕ 7.4%

density-dependent weighting function of the signals in each calorimeter segment, the h/e ratio can be equalized in software. This method has been pioneered by the CDHS collaboration (Abramowicz et al. 1981), further improved by the H1 (Andrieu et al. 1993) and ATLAS (Cojocaru et al. 2004) experiments for their liquid-argon calorimeters, and extensively studied in highly granular calorimeters, as discussed in section “High Granularity and Particle Flow.” In practice, the combined performance of the electromagnetic and hadronic calorimeter for hadrons is the relevant criterion. Table 2 summarizes the energy resolution of selected hadronic calorimeters together with the respective electromagnetic calorimeter. The comparison with the electromagnetic performance given in Table 1 shows the conflict between electromagnetic and hadronic performance, given by the properties of hadronic showers. Optimal electromagnetic performance as provided by homogeneous calorimeters results in a reduced hadronic performance, while optimizing the hadronic resolution requires compromises in the electromagnetic resolution. Typically, the hadronic energy resolution of combined sampling calorimeter systems is comparable to the respective stand-alone resolution achieved with the hadron calorimeter alone, while the combination with a homogeneous crystal electromagnetic calorimeter results in a significant deterioration of the resolution on the order of 25%. This is particularly apparent in the combined hadronic performance of the CMS barrel calorimeter system (Abdullin et al. 2009). It should also be noted that generally the performance for jets is subject to additional degrading effects. ZEUS quotes a hadronic Z mass core resolution of 6 GeV (Abramowicz et al. 2013), which is considerably worse than one might naively expect on the basis of the single-hadron resolution. So in summary it depends strongly on the design and chosen materials of a hadron calorimeter what the dominant contributions to the performance are: fluctuations in the electromagnetic shower fraction, in the fraction of invisible energy, or sampling fluctuations, which are also enhanced by the larger event-toevent fluctuations of hadronic relative to electromagnetic showers. The optimization of a calorimeter system for a given set of physics goals is thus a complex task. Thanks to improvements in the last 10–15 years, shower simulation programs (see section “The Role of Simulations”) are nowadays a reliable tool for this, in contrast to the situation when the first calorimeters for jet physics at Tevatron and at HERA had been developed.

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The Role of Simulations With increasing complexity of the detector systems and reconstruction techniques, simulations have become indispensable for the design of detectors, the optimization of their performance, and the development of reconstruction algorithms. Simulations are also central in the process to better understand the physics of particle showers. For these tasks, the analytical parameterization of average properties of particle showers is insufficient. Since event-to-event fluctuations drive calorimeter performance, Monte Carlo techniques that accurately model the evolution of particle cascades in material are required. The by far most common computer code in use today is the Geant4 toolkit (Agostinelli et al. 2003), which provides a step-based simulation of the passage of particles through matter allowing the implementation of complex geometries and arbitrary materials. The quality of the simulations depends on the accuracy of the description of the elementary interactions of particles in the detector material. In Geant4, the description of the underlying interaction models is included as so-called physics lists, which are chosen depending on the concrete application. Thanks to the relative simplicity of electromagnetic cascades, and the wellunderstood electromagnetic interactions, simulations of electromagnetic showers are typically highly accurate. Nevertheless, subtleties in the details, such as energy cut-offs that are needed to avoid infrared divergences, need to be considered when performing the simulations. The effects of these settings depend on the material, in particular also on the density, and may require specific choices of physics lists in some cases, for example, when simulating calorimeters with gaseous readout. The modelling of hadronic showers is significantly more complex and suffers from larger uncertainties. The description of the physics is split into different energy regimes, with models for the high-energy interactions of relativistic particles combined with complex nuclear physics models to form physics lists that are valid over the full energy range. Significant improvement has been achieved in this area since the early 2000s, moving from simpler parametrized models to physicsdriven interaction models. The data from calorimeter beam tests in the R&D and construction phase of the LHC detectors, and more recently from highly granular calorimeters developed by the CALICE collaboration, have helped to improve the models considerably. The precise modelling of low-energy neutrons, provided by specific high-precision physics lists, has been recognized to be of particular importance for the simulation of calorimeters with heavy absorber materials such as tungsten and lead and for the description of the extended time structure of hadronic showers. For scintillator-based active elements, the inclusion of scintillator saturation according to Birks’ law or alternative parameterizations in the modelling of the response of the active elements is crucial. The saturation constants depend on the exact type of scintillator, but their effect is also correlated with the values for cut-offs used in the simulation, requiring care when setting the constants. Figure 8 shows the longitudinal profile of pion showers in the CALICE analog hadron calorimeter, a highly granular steel-scintillator calorimeter discussed in more

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detail in section “High Granularity and Particle Flow,” compared to simulations as one example for a comparison of data with hadronic shower simulations. While there is in general good qualitative agreement, present-day hadronic shower models do not yet reproduce observations with a precision approaching that achieved for electromagnetic showers. The figure also shows the contributions of different shower particles to the energy loss in the simulations. It should be noted that the e+ e− distribution also includes delta electrons in addition to pairs in electromagnetic sub-showers. When comparing Fig. 1 with Fig. 14, it is however apparent that the general features of the substructure of hadronic showers, characterized by dense shower activity and sparser MIP-like track segments, are well reproduced by modern simulation codes.

Conceptual Refinements Typical calorimeter systems of recently or currently running collider detectors provide a jet energy resolution with a stochastic term attaining values of 50 − −100%, while the constant term is a few percent. The limitation of the present systems stems from the fact that most of the jet energy (∼70%) is carried by hadrons and the jet measurement thus inherits the intrinsically poor performance of traditional hadronic calorimetry, if no tracking information is used. On the other hand, the precision physics program at a future Higgs factory requires the identification of W and Z bosons by means of the invariant mass of their 2-jet final states, which in turn demands a jet energy resolution of 3–4% in a wide energy range from 50 to several 100 GeV. This goal has motivated developments which tackle the jet energy challenge with novel approaches. One direction of research explores dual readout techniques (Akchurin et al. 2005; Lee et al. 2018) which can in principle minimize the effect of fluctuations in the electromagnetic fraction in hadron showers by measuring this fraction independently event by event.

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Another direction, the particle flow (Pflow) approach (Brient and Videau 2001; Morgunov 2001), starts from the observation that most particles in a jet – charged particles and photons – can in principle be measured with much better precision than generally provided for hadrons and thus aims at disentangling the energy depositions of individual particles in the calorimeter.

Dual Readout In non-compensating hadron calorimeters with h/e significantly smaller (or larger) than 1, fluctuations in the electromagnetic energy fraction, fem , represent the biggest single contribution to the hadron energy resolution. The dual readout method measures fem event by event in parallel to the total deposited energy. It uses the fact that most of the relativistic particles in the shower originate from the electromagnetic part, and that only those produce Cherenkov light, while the signal of the hadronic part is mostly due to non-relativistic protons. In practice either two different active media, scintillator and quartz, are used to register scintillation and Cherenkov light, respectively, or the optical signals from the two processes occurring in heavy crystals are disentangled, using their different spectral, directional, or timing properties. The Cherenkov and scintillation signals, normalized to the response for electrons, are given by C = [fem + (h/e)C (1 − fem )]E,

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where ξ = [1 − (h/e)C ]/[1 − (h/e)S ]. This is illustrated in Fig. 9, which shows their correlation for a set of simulated events. It was noted that the method demands a steep slope ξ , which implies that the scintillator readout should be as compensating as possible, which however reduces the room for improvement by adding Cherenkov information. The method was tested with the DREAM module, a 1 ton copper matrix with embedded quartz and scintillating fibers. The value of ξ was about 0.3 in this detector. A resolution of about 5% was obtained for 200 GeV “jets” produced on a target. Due to the small size of the module, this presumably includes contributions from transverse leakage and thus underestimates the potential of the method. A further limitation was due to the small light yield of the Cherenkov signal, 8 photoelectrons per GeV. This was improved in the more recent RD52 prototype based on√ SiPM readout, which also had a larger sampling fraction. Here a resolution of 70%/ E(GeV) was obtained for single hadrons.

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The separate Cherenkov readout evidently provides excellent pion electron separation for particle identification. In the RDs52 prototype, each fiber is read out individually by SiPMs, giving also a superior transverse granularity. A fiberbased calorimeter with full solid-angle coverage requires a pointing geometry due to the limited or missing longitudinal segmentation. The resulting challenges for a mechanical design are studied in the framework of the IDEA detector concept.

High Granularity and Particle Flow Particle Flow Approach The PFlow method optimizes the jet energy resolution by reconstructing each particle individually and by using the best available measurement for each. Charged particles are best measured with tracking detectors, which offer relative resolutions of about 10−4 E(GeV), and photon energies can be measured with relative precision √ of about 15%/ E(GeV) or better in electromagnetic calorimeters. In a typical jet, 60% of the energy is carried by charged particles, 30% by photons, and only 10% by long-lived neutral hadrons (KL0 and n), for which hadronic calorimetry is unavoidable. With the above resolutions for tracks and photons, and assuming √ 55%/ E(GeV) for hadrons, then, √ in the ideal case, where each particle is resolved, a jet energy resolution of 19%/ E(GeV) could be obtained. Here the dominant part

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√ (17%/ E(GeV)) is still due to the calorimeter resolution for the neutral hadrons. The jet composition fluctuates from event to event; so for jets with a smaller neutral hadron fraction, the precision is higher and vice versa. Particle flow-like techniques were first applied in the ALEPH √detector (Buskulic et al. 1995), which achieved a jet energy resolution of 60%/ E or 6.2 GeV for hadronic Z decays. More recently, particle flow techniques are successfully used in the CMS experiment (Sirunyan et al. 2017). The net performance in CMS is comparable to that of the ATLAS detector using calorimetric methods (Aad et al. 2013), illustrating the power of particle flow for an optimal combination of the capabilities of different detectors, compensating for the relatively poor single-hadron resolution of CMS compared to ATLAS (see section “Hadronic Calorimeters”). However, both do not yet match the goals formulated for the experiments at a future Higgs factory. The particle flow method relies on the ability to properly assign the calorimetric energy depositions to individual particles, which places high demands on the imaging capabilities of the calorimeters, and on the pattern recognition performance of the reconstruction algorithms. The principle is illustrated in Fig. 10. Only those deposits not associated with charged particles and not identified as photons will be interpreted as neutral hadrons. In practice, this cannot always be done unambiguously, and mis-assignments give rise to an additional measurement uncertainty, which is called confusion. For example, a neutral particle shower developing close to that of a charged one could be mis-interpreted as part of the charged hadron shower, which is replaced by the track measurement; so the neutral energy would be lost. On the other hand, a detached fragment of a charged particle shower could be mis-identified as a separate neutral hadron, and the fragment energy could be double-counted. The Pandora particle flow algorithm (PFA) (Thomson 2009) is the most developed and best performing today in the context of future lepton colliders. Recently developed alternatives deliver an independent validation of the particle flow concept. The algorithms make use of topological information, including the substructure of

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showers, as well as the compatibility of calorimetric and track-based measurements. In this way, it is ensured that at higher energies, as jets get more collimated and particles become harder to separate, a smooth transition is made to a classic energy flow like reconstruction, in which neutral particles are identified as excess in energy above the track-based expectation. In this way the purely calorimetric performance for the jet is either retained or improved. In the framework of studies for CLIC (Linssen et al. 2012), it was shown that the required jet energy resolution can be achieved with the PFlow technique for jet energies up to 1500 GeV. For the use of energy momentum match in the assignment of energy depositions, and for energy flow treatment of dense jets, particle flow calorimeters with their emphasis on imaging must still feature a good energy resolution. Furthermore, the neutral hadron energy uncertainty is the dominant contribution to the jet resolution for low-energy jets, where particles are well separated, while at higher energies the confusion effects take over. For the particle-flow-driven detectors envisioned for the Higgs factories, the transition is around 100 GeV, yet an improvement is expected even for jet energies as high as 500 GeV. This is illustrated in Fig. 11, where the contributions to the jet energy resolution are shown separately as a function of energy.

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High Granularity A detector fully optimized for this approach must have a highly efficient tracking system, an ultra-compact electromagnetic calorimeter with minimized Molière radius and fine three-dimensional segmentation in both electromagnetic and hadronic calorimeter, which are both placed inside the magnetic coil. The detector concepts developed for future Higgs factories foresee cell dimensions of typically 5 mm in the electromagnetic calorimeter and typically 3 cm in the hadronic section. This leads to approximately 108 and 107 channels for the electromagnetic and hadronic systems, respectively. High granularity brings additional advantages; for example, it offers ideal conditions for the application of software compensation methods, which improves the intrinsic resolution and also reduces “confusion” (Tran et al. 2017). A particular strength is the possibility to use topological information such as the reconstructed starting point of the shower for the estimation of leakage. Moreover, the combination of fine-grained topological reconstruction and cluster-wise timing cuts allows for powerful pile-up rejection. This extends the application range of particle flow methods toward collider environments with less benign background conditions, like multi-TeV e+ e− collisions, and it is an asset on its own for high-intensity hadron colliders, even if particle flow methods are difficult to apply. Last, but not least, reading each cell individually enormously enhances the transparency and redundancy of the response, the calibration, and the corrections. In contrast to a situation, where signals from several geometrical cells are merged optically or electronically into a single readout channel, no assumptions on shower shapes or particle densities are needed to infer the signal from an individual cell. Most detector concepts proposed for future Higgs factories are based on the particle flow concept. The principle has been experimentally tested (Sefkow et al. 2016) by the CALICE collaboration with test beam prototypes using a variety of absorber materials and readout techniques. The most commonly proposed technologies are silicon diodes for the electromagnetic section and scintillating tiles individually read out by silicon photomultipliers (SiPMs) for the hadronic part. Scintillator ECAL and gaseous HCAL technologies have been explored, too. In all cases, the high channel density requires the integration of the front-end electronics into the active layers, such that the digitized and zero-suppressed data are read out via a small number of lines. As an example, Fig. 12 shows the design of an integrated readout element for the silicon-tungsten ECAL of the proposed ILD detector. The detector slabs, which can be as long as 2 m, are built around an H-shaped supporting structure incorporating a layer of tungsten absorber. The active layer consists of printed circuit boards, the silicon sensors, the front-end electronics, and electrical infrastructure. A hadron calorimeter prototype with 21888 SiPM-on-tile channels (Sefkow and Simon 2019), recently constructed by the CALICE collaboration, is shown in Fig. 13. A hadronic shower recorded with this prototype in a test beam at CERN is displayed in Fig. 14 and exhibits a rich substructure which is well resolved.

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Fig. 12 Active layer stack-up of the silicon tungsten ECAL in the ILD design. The figure shows the supporting structure including a tungsten absorber element, sensors, and embedded front-end electronics as well as an external interface card (Brient et al. 2018). (Reproduced with permission from J.-C. Brient, July 20, 2020)

Fig. 13 The highly granular scintillator tile/steel hadronic calorimeter technological prototype of the CALICE collaboration, showing one active layer with the scintillator tiles mounted on circuit boards housing the very front-end electronics and the photon sensors (left) and the absorber structure with the readout interfaces for the active elements (right)

The first calorimeter to use these technologies at a collider will be the upgraded endcap calorimeter of the CMS detector for the high-luminosity phase of the LHC, to begin in 2027. A cross section through the conical structure is shown in Fig. 15. The electromagnetic section is instrumented with hexagonal silicon sensors, bonded to the readout electronics; an element is also displayed in Fig. 15. In the hadronic section, scintillator tiles are used wherever radiation levels permit the operation of SiPMs, otherwise the same silicon elements are used as in the electromagnetic section. The total silicon area amounts to about 600 m2 , and about 240’000 SiPMs are foreseen.

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Fig. 14 Display of a hadronic shower of a 60 GeV π − recorded in the CALICE hadron calorimeter prototype, illustrating the capability of highly granular calorimeters to resolve the substructure of particle showers in the calorimeter volume. The colors indicate the signal amplitude of the cells, with red being the highest and green the lowest

Fig. 15 Left: Cross section through the upgraded CMS endcap calorimeter. Green, silicon section; blue, scintillator section. Right: Active element of the silicon part with (bottom to top) WCu base plate, Kapton layer, silicon sensor, and hexagonal readout board. (Images © CERN, on behalf of the CMS Collaboration)

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Selected Other Calorimeter Types There are a wide variety of applications of calorimeters in research beyond those at high-energy accelerators in nuclear and particle physics discussed in depth in this chapter. Here, we give a few selected examples. The best energy resolution for MeV photons, occurring, for example, in nuclear spectroscopy, is achieved with large semiconductor crystals (see  Chap. 16, “Semiconductor Radiation Detectors” for more details), in particular with high-purity germanium detectors. These achieve permille-level energy resolution in the relevant energy range, far superior to other calorimeter types. To limit thermal noise, they are operated at cryogenic temperatures, often cooled by liquid nitrogen. High-purity crystals enriched with the isotope 76 Ge are used in the search for neutrinoless double beta decay, which would manifest itself by a mono-energetic line at the endpoint of the β spectrum at the Q value of the decay at 2.039 MeV on top of the much higher background of regular double beta decays. An excellent energy resolution is thus crucial for the potential to observe a signal. This technique has already been used for several generations of experiments with increasing detector mass and improving sensitivity, most recently in the GERDA and MAJORANA experiments. The LEGEND experiment, which will initially use 200 kg of germanium detectors, is currently under development, with the final goal of reaching a detector mass of one ton. Figure 16 illustrates the energy resolution achieved with germanium detectors used in GERDA (Agostini et al. 2019), demonstrating permille-level resolution for photons in the MeV range.

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A special class of calorimeters are cryogenic calorimeters, operated at temperatures close to absolute zero, in mK to 1 K range. These devices are used, for example, in the search for WIMP dark matter and to exploit the properties and behavior of matter at these low temperatures. Most notably, the heat capacity of dielectric crystals scales with T3 , such that also very small energy deposits by particle scatters result in a measurable temperature change. An example for such a detector is the CRESST experiment, which operates CaWO4 crystals at temperatures around 7 mK, coupled to superconducting transition-edge thermometers. The generation of phonons and scintillation photons by particle interactions results in a temperature increase by a fraction of a mK, which in turn leads to a sizeable change of the resistivity of the superconducting thermometer, making very small energy depositions measurable. These devices are calorimeters in the true sense of the word, as they actually measure temperature increases induced by particle interactions. Very low background levels in such detectors are typically achieved by measuring two types of signals in coincidence, in the case of CRESST the temperature increase by phonons together with the scintillation light from the crystals. A similar dual-mode readout is used in large liquid noble gas time projection chambers. One such example is the XENON experiment. This detector aims at the direct detection of dark matter particles via scintillation and charge signals extracted from a multi-ton volume of liquid xenon. Similarly, liquid argon-based neutrino detectors reconstruct the energy deposited in neutrino interactions via charge and scintillation light signals, as discussed in more detail in  Chap. 14, “Neutrino Detectors.” In general, neutrino detectors are the largest homogeneous calorimeters in operation, with large liquid scintillator and water Cherenkov detectors used in underground installations. Detectors targeting high-energy cosmic neutrinos are natural calorimeters, using cubic kilometer volumes of ice or deep sea water instrumented with photon detectors to measure the energy deposited by neutrino interactions. Finally, in cosmic ray Cherenkov detectors, the Earth’s atmosphere acts as a homogeneous calorimeter. More details are given in  Chap. 26, “Indirect Detection of Cosmic Rays.”

Concluding Remark The main goal of calorimeters is the measurement of energy. In modern particle physics experiments, they are essential components, with their unique role of also detecting neutral particles, both via the direct measurement of their energy and, for non-interacting particles such as neutrinos, indirectly via the measurement of the total energy balance of collision events. Modern calorimeters make use of state-of-the-art sensor technologies and of the highest electronics integration levels, which push the boundaries of complexity, system integration, and data rates. Thanks to these advances in the last decades, calorimeters have evolved from coarse instruments to detectors with well-understood principles, capable of precision measurements. They assume a role that extends beyond the simple measurement

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of energy to central contributions to the overall reconstruction of event properties and topologies, including the discrimination against background. With increasing demands for energy, space and time resolution, radiation tolerance in collider experiments, and ultimate sensitivity and background reduction in astroparticle physics, calorimetry will continue to be a driver of technological advances and an enabler for future discoveries.

Cross-References  Indirect Detection of Cosmic Rays  Interactions of Particles and Radiation with Matter  Neutrino Detectors  Photon Detectors  Scintillators and Scintillation Detectors  Semiconductor Radiation Detectors  Silicon Photomultipliers Acknowledgments One of the authors has benefited strongly from the cooperation with C. Zeitnitz on a similar project on this topic (Sefkow and Zeitnitz 2011); the enlightening discussions are gratefully acknowledged.

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Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Radiation Environment at Contemporary Hadron Accelerators . . . . . . . . . . . . . . . . . . . . . . . . Artificial Diamond as a Sensor Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chemical Vapor Deposition (CVD) Diamond . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Diamonds as Solid State Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Charge Collection in Polycrystalline CVD Diamonds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Radiation Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cadmium Telluride and Cadmium Zinc Telluride as Sensor Materials . . . . . . . . . . . . . . . . . . New Passive Thermoluminescence Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

669 670 671 671 673 673 675 680 681 683 683 684

Introduction Contemporary particle accelerators for fundamental research in particle physics, especially CERN’s Large Hadron Collider (LHC), provide researchers with higher and higher luminosities. This sets the pace for the need for radiation-hard detector materials for both beamline instrumentation and the physics experiments themselves. Silicon pixel and silicon microstrip detectors are well-developed devices for tracking applications in these high-energy physics experiments. However, these detectors are expected to reach the end of their lifetime within a few years due to their exposure to harsh radiation, of which the yearly level amounts to up to several

C. J. Ilgner () WUBS, Magdeburg-Stendal University of Applied Sciences, Magdeburg, Germany e-mail: [email protected]; [email protected] © Springer Nature Switzerland AG 2021 I. Fleck et al. (eds.), Handbook of Particle Detection and Imaging, https://doi.org/10.1007/978-3-319-93785-4_21

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1014 hadrons/cm2 during the foreseen 10 years of operation of LHC experiments. With the LHC upgrade, the radiation exposure of the new LHCb vertex detector, for instance, is expected to sum up to 9·1015 1 MeV neq at an integrated luminosity of 50 fb−1 over its lifetime. The high-luminosity LHC even aims at achieving an integrated luminosity of 250 fb−1 per year. In order to protect sensitive experimental devices from adverse beam conditions, chemical vapor deposition (CVD) diamond, an artificially generated diamond material, is more and more being used in systems called Beam Conditions Monitors (BCM). The radiation level these sensors are exposed to is even higher than in the case of position-sensitive tracking detectors. An example is the CVD diamond sensors of the BCM of the LHCb experiment at CERN, which have proven to withstand even 1015 hadrons/cm2 during 10 years. Preparation of CVD diamond sensors for BCM applications is discussed in detail, together with the properties of this new material as a candidate for position-sensitive devices in high-energy physics experiments, addressing also operational questions like the appearance of erratic dark currents in polycrystalline diamond bulks. Other new materials for position-sensitive devices such as CdZnTe and CdTe are discussed as well and compared to the well-established silicon, together with a compilation of their properties relevant to particle detection. Recent advances in the field of passive radiation monitors, where thermoluminescent sensors made from lithium fluoride now cover a dynamic range from several μGy up to 105 Gy, are also discussed briefly.

Radiation Environment at Contemporary Hadron Accelerators Particle physics experiments installed at high-luminosity hadron accelerators such as the Large Hadron collider (LHC) at CERN, the European Organization for Nuclear Research, need to cope with possible adverse conditions of the hadron beams they are using, resulting in exposure of their sensitive detection equipment to high levels of ionizing radiation. In the case of the LHC, these are particularly hadronic showers from misaligned beams hitting structure material, or failures of components upon particle injection into the LHC from its preaccelerator chain. In such a case, beam particles would interact with matter, causing a significant buildup in ionizing-radiation dose which potentially destroys sensitive detector components. A prominent example is the Vertex Locator of the LHCb experiment installed at the LHC (Bates et al. 2006). This detector is one out of two movable devices along the LHC ring; it consists of 42 silicon detector modules which are being moved close to the LHC beams during operation in order to do B tagging, that is, the identification of b- and c-hadron decays, on which the physics analysis of the LHCb experiment will focus. That is why a system called Beam Conditions Monitor (BCM) has been installed, consisting of sensors around the beam pipe, which is meant to trigger a beam abort from the LHC in case of adverse beam conditions. At the location of the innermost

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sensors of this BCM, which have a surface of 10 mm × 10 mm out of which 8 mm × 8 mm are active, already under normal operation of the LHC, the particle flux sums up to be 1particle/(collision · cm2 ) ≈ 5 · 1015 particles/(10 years · cm2 ).

Artificial Diamond as a Sensor Material In order to cope with this flux in a way that the lifetime of the BCM extends at least over 10 years, polycrystalline CVD diamond has been used as the sensor material for this application. Diamond as a sensor material features the following properties: • Low atomic number (Z = 6) can be considered a tissue-equivalent sensor material, thus low absorption of radiation • Relative radiation hardness as compared to other sensor materials • Wide band gap of 5.47 eV, so virtually no thermally generated noise • High mobility of both electrons and holes • Low capacitance • Low leakage currents • High thermal conductivity • Operation at ambient or even higher temperatures, no need for cooling

Chemical Vapor Deposition (CVD) Diamond Chemical vapor deposition (CVD) diamond detectors are more and more becoming considerable alternatives to silicon detectors due to their high radiation hardness. Nevertheless, their operation differs in various respects from that of the wellestablished silicon devices.

Production of Artificial Diamond The production principle of CVD diamond in a plasma-enhanced process with hydrogen and methane as the reactants is as follows: The substrate surface in the CVD process is hydrogen-saturated while the surrounding gas contains methane (CH4 ). The highly active hydrogen atoms are able to break the C–H bonds of the methane and create H–H bonds. The resulting free space is then filled by carbon atoms. Until 1962, it was expected that graphite is formed (Eversole 1962), but in fact, a diamond structure builds up instead. During the chemical vapor deposition process, the diamond grows from a substrate of Pt(111) (Shintani 1996) or silicon oxide at a rate of several micro-meters per hour. The CVD process is shown in Fig. 1, from which it can be concluded that the presence of hydrogen is essential. During the carbon deposition process, grains of different sizes are formed: Fig. 2 shows a side view of a polycrystalline diamond as it grows in the chemical vapor deposition process. The grains are smaller at the bottom, close to the substrate, and

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Fig. 1 The typical processes during chemical vapor deposition of carbon: The surface (Pt(111), for instance) is saturated with hydrogen, but reacts with hydrogen radicals from the gas phase (left). Carbon atoms are added at spots where no hydrogen is present anymore (center). The process continues, forming a carbon bulk in the form of the diamond lattice (right) (Sauerbrey 2009) Fig. 2 A polycrystalline CVD diamond seen from the side. The structure originating from the growing process from bottom to top is clearly visible (Meier 1999)

larger toward the top. The different grain sizes are considered to be due to impurities interfering with the growing process close to the substrate. With respect to this, for applications in particle detection, single-crystal diamond is of course best suited. Grown on a diamond substrate, it is available already in surface sizes of about 3 cm × 3 cm, at significantly higher costs. The material commonly being used for beam monitors at particle accelerators is called polycrystalline. Here, the effective grain size is enlarged by mechanical removal of material from the substrate side. Typically, the grain size is then on the order of 1 micrometers or larger. The grain size is crucial for the use of diamonds as particle detectors, since the detection principle is based on ionization of lattice atoms along the trajectory of a crossing particle. In the band model, electrons are shifted from the valence band into the conduction band. Then, diamond, which by definition is an insulator due to its large band gap, can therefore be considered a semiconductor where it is possible to supply electrons to the conduction band through the interaction with ionizing particles.

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Diamonds as Solid State Detectors The basic working principle of particle detection with solid state detectors is the creation of electron-hole pairs in a sensitive volume with an external electric field applied, which is followed by an amplification stage. The intrinsic chargecarrier density inside the sensitive volume is low. If semiconductors like silicon or germanium are used as detectors, the sensitive volume is the depleted zone in an asymmetrically doped, reversely biased diode. Also in the case of (CVD or natural) diamond, the intrinsic charge-carrier density inside the sensitive volume is low. The energy loss of charged particles passing through the detector is given by the Bethe-Bloch formula, based on which a restricted energy loss can be calculated, which takes energy loss by escaping secondary particles into account and represents the energy deposited in the bulk. This restricted energy loss generates free charge by producing electron-hole pairs, which then move to the contact electrodes. The collected charge is proportional to the energy deposition by ionization in the detector volume. Due to the larger band gap (5.47 eV as compared to 1.11 eV for silicon and 0.67 eV for germanium, all measured at a temperature of 300 K), diamond is an insulator at room temperature, so it is depleted by itself; thus, the detector noise is low and dark currents are negligible. As a result of phononic excitation, the electron–hole pair production energy is larger than the band gap, namely 13 eV, three to four times higher than for silicon. The average ionization density for a minimum-ionizing particle is 36 electron–hole pairs per micro-meters only, so sensitive frontend electronics needs to be used for readout. Instead, both an electron mobility of 2200 cm2 /(V s) and a hole mobility of 1700 cm2 /(V s) (as compared to 1450 cm2 /Vs and 450 cm2 /(V s) for silicon) make diamond detectors good candidates for fast detectors with response times on the order of a few nanoseconds. When it comes to the question of radiation hardness, the high lattice displacement energy of 37–47 eV (Koike et al. 1992) as compared to 11 to 22 eV for silicon is expected to be an advantage of diamond over silicon and germanium.

Charge Collection in Polycrystalline CVD Diamonds The lifetime of charge carriers in silicon or monocrystalline CVD detectors is theoretically unlimited. But any defect in the lattice of diamond helps electrons and holes to recombine or simply traps charge, limiting the lifetime of charge carriers and thus the charge collection efficiency of the sensor. The corresponding parameter is called charge collection distance, often referred to as CCD. This is somehow unfortunate, since the acronym CCD also stands for charge-coupled device and may thus be a source of confusion. Here, the symbol δq is being used, since the charge collection distance can be understood as the thickness of an ideal diamond, in which no charge is being trapped or recombination of electrons and holes takes

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place. δq is thus smaller or equal to the physical thickness d of the diamond. Both parameters are measured parallel to the lines of the electric field the sensor is biased with. For contemporary polycrystalline CVD diamond sensors, δq used to have a value between 200 and 300 μm. The minimum energy necessary to produce one electron–hole pair is on the order of 13 eV (Meier 1999). Oh describes the effect of charge-carrier lifetime by the following ansatz (Oh 1999) (also citing from (Schleich 2008)): An ionization process creates a free electron. After Ramo’s theorem, its movement in the electrical field induces a current, which is I = ev/d with the electron charge e, the drift velocity v, and the distance between the metalization electrodes d. Accounting for the carrier lifetime τ , the total charge Qm seen outside the detector is: Qm =

e d



τ

v dt =

0

e vτ, d

(2)

where the schubweg δ:= vτ = μEτ can be expressed in terms of the chargecarrier mobility μ and the electric field strength E. In the following calculations, the statistical nature of electron capture and local variations of the schubweg have to be taken into account, and finally the following approximation can be made: δ Qm ≈ Qi , d

(3)

d where Qi is the total charge created by ionization and δ = d1 0 δ(z) dz. z is counted along the axis parallel to the electric field. Accounting for both, electrons and holes, one obtains the expression (Oh 1999): Qm = Q i

δq d

(4)

with a parameter called the charge collection distance: δq = δe + δh = E (μe τe + μh τh ) .

(5)

It can be interpreted as an average separation distance of electron–hole pairs before they recombine. It is important to notice that the charge-carrier mobility depends on the electric field E and that dδq /dE ∝ E1 with the electric field strength approaching saturation. Measurements (Fernandez-Hernando et al. 2005) with diamond samples similar to the ones used in LHCb have shown that δq = 140 μm at 250 V. Applying a voltage four times as high increases δq only by 43%. In addition, the signal-to-noise ratio decreases considerably above 300 V bias voltage (Müller

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2011). Due to the saturation of the charge collection distance above 250 V and erratic dark currents occurring especially at higher field strengths, a bias voltage value below that value was chosen for the Beam Conditions Monitor of the LHCb experiment.

Radiation Effects Radiation causes damage to the diamond bulk, resulting in a decrease of the chargecarrier lifetime, which reduces the charge collection distance. Exposure to protons of 24 GeV has shown that the charge collection distance remains constant up to a fluence of 3 · 1015 /cm2 (Adam et al. 2000). However, protons of 25 MeV only, instead, degraded the charge collection properties of polycrystalline CVD diamond significantly after exposure to fluences on the order of 1016 /cm2 . The effect of several types of radiation on artificial diamond is summarized in Table 1. Schleich (2008) explains the reversible effect of ionizing particles as being linked to the ionization density: This is nonuniform for hadrons, which leads to polarization effects diminishing the electric field and the charge collection distance of the detector. In contrast, electron and gamma radiation excite a constant ionization density leading to filling of traps. This effect increases the charge collection distance. This is called pumping. Most polycrystalline CVD diamond detectors can only be used after having received a certain radiation dose to fill up the charge traps in their electronic band structure. An adverse effect of radiation is the occurrence of erratic dark currents. These are current spikes lasting several hundred milliseconds, well exceeding nominal signals by several orders of magnitudes. As they only occur in polycrystalline CVD diamonds, grain boundaries seem to play a role in their generation. These erratic dark currents can be suppressed by a magnetic field of the order of 0.1–0.6 T, which is oriented perpendicularly to the grain boundaries or by lowering the bias voltage to 0.2 V per micro-meters of sensor thickness (Edwards et al. 2005).

Table 1 Performance of diamond sensors after irradiation Radiation Protons Protons Neutrons Pions Alpha particles Photons Photons

Energy 24 GeV 25 MeV 1 MeV 300 MeV 5 MeV 100 keV 1 MeV

Fluence or dose 3 · 1015 cm−2 5.7 · 1016 cm−2 2 · 1015 cm−2 1.7 · 1015 cm−2 2 · 1015 cm−2 6.8 MGy 10 MGy

Effect on charge collection distance No degradation 50% of initial value 70% of initial value 70% of initial value 70% no degradation No degradation No degradation

Reference Adam et al. (2000) Domke et al. (2008) Adam et al. (2000) Adam et al. (2000) Dulinski et al. (1994) Dulinski et al. (1994) Dulinski et al. (1994)

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The radiation hardness of chemical vapor deposition (CVD) diamond has exhaustively been investigated by the RD42 collaboration at CERN (http://rd42. web.cern.ch/rd42) up to fluences of 3 · 1015 protons per cm2 (Kagan 2005).

The Beam Conditions Monitor of the LHCb Experiment: An Application Example For the Beam Conditions Monitor of the LHCb experiment (The LHCb Collaboration 2008), polycrystalline CVD diamond sensors are being used. These sensors are arranged in the LHCb experimental cavern around the beam pipe of the Large Hadron Collider in a way that the sensitive area of the innermost sensor starts at a radial distance of 37.0 mm from the beam axis. From the mechanical dimensions and the relative permittivity of 5.7 for diamond, the capacitance of one sensor can be calculated to be 6.5 pF (Schleich 2008). The charge collection distances of the LHCb BCM diamonds range from 192 to 240 micro-meters with the exception of one diamond showing a charge collection distance of 132 micro-meters (Schleich 2008). In order to estimate the particle flux through the sensors at LHCb, simulation results for a detector in close proximity are used (Lieng 2008): During 10 years of LHCb operation, 8 · 1012 neutrons and 9.6 · 1013 charged hadrons per cm2 are expected, so no significant reduction of the charge collection distance is expected to take place. The simulated minimum bias signal of the BCM detectors (Lieng 2008) under normal running conditions according to the simulated radiation field will then be between 5 and 20 nA. Diamond sensors show a linear relationship between the flux of particles and the current signal over up to nine orders of magnitude, as shown in Fig. 3. This is essential for applications in beamline instrumentation at particle accelerators, where diamonds are more and more being used to protect other detectors sensitive to excess radiation. Here it is essential that the diamond sensor yields a measurable current signal under normal operating conditions and a much higher signal when it comes to a malfunction of the accelerator. This sounds trivial at a first glance, but saturation effects upon excessive exposure to radiation that prevent the sensor from yielding sufficiently high a current onto which a beam abort trigger is based must be excluded. The linearity could be demonstrated by shining protons of 24 GeV onto a polycrystalline diamond sensor of the Beam Conditions Monitor of the CMS experiment at CERN (Chong et al. 2007). In order to validate the durability of metal contacts under irradiation, two different contact systems (titanium-silver and titanium-gold with a glued-on copper strip) were exposed to 1015 protons/mm2 at an energy of 25 MeV over a period of 18 h. Although the diamond bulk suffered from radiation damage, it could be demonstrated that both contact systems maintained their ohmic properties and will thus depass the lifetime of the diamond sensor itself. The CVD diamond sample used in the irradiation test was a prototype sensor for the Beam Conditions Monitor of CERN’s LHCb experiment (The LHCb Collaboration 2008), as described above and shown in Fig. 4. A metalized area of 8 mm × 8 mm covered the central part on both sides of the sensor. Upstream, with respect to the beam direction, the contact was made of a 50-nm gold layer with

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109

Particle fluence, measured by diamond sensors (cm−2)

108 107 106 105 104 Single particle counting 103

TLD measurement (ALNOR reader)

102

TLD measurement (Harshaw reader)

101

Scintillator particle counting Na-22 dosimetry

100 100

102

104

106

108

1010

Particle fluence (cm−2) Fig. 3 Diamond sensor response to the fluence of 24 GeV protons, as measured by a scintillator hodoscope of 5 mm × 5 mm cross section, by Na-22 dosimetry in aluminum, LiF thermoluminescence dosimetry, and by particle counting with scintillators (Chong et al. 2007)

Fig. 4 A single polycrystalline CVD sensor of the Beam Conditions Monitor of the LHCb experiment

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Detector current (µA)

50 nm of titanium as the undermetal. For the downstream contact, the gold layer was replaced by a silver layer of 50 nm, respectively. In this design, the electrical contact is established with a glued-on coppercladded HFS1 strip, using Epotecny E205 silver-doped conductive glue (see list of equipment providers at the end of this chapter). The advantage of this design is the large surface of the contact, in case readout at high frequencies is intended. A disadvantage is the danger of silver atoms diffusing into the diamond bulk. In order to prevent this from happening, the layer of the undermetal titanium was chosen to be significant (50 nm), that is, equal to the thickness of the gold contact itself. Of course, bonding techniques are also an option. Initially, the resistivity of this glued contact system was measured to be below 1 . After an exposure to 1015 protons/mm2 at an energy of 25 MeV shined on a surface of 4 mm2 , both contacts have maintained their ohmic properties. Despite the fact that the metallic contact was still operational after exposure, showing no measurable degradation, the current signal from the diamond had completely vanished. Over 34 min, this effect was further studied at a previously unexposed spot of the diamond sensor. The current decrease is shown in Fig. 5. The conclusion that can be drawn is that an electrical contact as described above shows, in terms of radiation damage, a lifetime well depassing that of the artificial diamond material itself. Sauerbrey (2009) applied a number of analysis methods to the irradiated sensor. After removal of the metalization as shown in Fig. 6, he could confirm that no new crystalline structures inside the diamond had formed. By scanning electron microscopy, it was shown that also no change in grain size or other visible damage had taken place. Also, by energy-dispersive X-ray microanalysis (EDX), it could be shown that no gold or silver had diffused into the diamond sensor.

160 120 80 40 0 0

2

4

6

8

Sensor exposure

10

12

14

·1016 protons

Fig. 5 Decrease of the sensor current during exposure to protons of 25 MeV over a surface of 2 mm2 over 34 min

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Fig. 6 Irradiation damage in polycrystalline CVD diamond

Fig. 7 Healing of a radiation-damaged diamond sensor by heating

By absorption spectroscopy, the presence of nitrogen in the bulk could be determined, which had formed green color centers. These damages have spoilt the charge collection capacity of the sensor. For completeness, in Fig. 7, the vanishing of the damage is shown under heating. Curing radiation-damaged sensors in real applications is certainly not an option, as the metalization would suffer from the heat, at least diffusion of atoms from the metalization into the diamond bulk would take place, deteriorating its charge collection properties. In Table 1, the influence of radiation of various types on diamond sensors is given.

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An alternative way of metalizing diamond sensors using a diamond-like carbon (DLC) layer has been proposed. This way of applying a metallic contact to the diamond sensors promises to transfer higher current densities. First tests with this new metalization are very promising (Galbiati et al. 2009). In an X-ray dosimetric application, a diamond-like carbon/Pt/Au metalization has led to a dark resistivity of (5.6 ± 0.1) × 1014  · cm with apparently no presence of deep traps in the bandgap of a single-crystal diamond film. Apparently, applying this contact technique had led to a very low defect density in the diamond films (Trucchi et al. 2012). Single-crystal CVD diamonds were also successfully used in Tokamak experiments for the detection of 14.2 MeV neutrons. The decreasing sensitivity due to polarization could be coped with by applying a reverse bias voltage up to a total energy deposition of 2 × 1021 eV/cm3 in the bulk in an experiment performed by Sato et al. (2015).

Cadmium Telluride and Cadmium Zinc Telluride as Sensor Materials Cadmium telluride (CdTe), a cadmium and tellurium compound material, is widely used as a solar cell material in photovoltaics. For this application, a pn junction is created between CdTe and layers of CdS (cadmium sulfide). With the highest (linear) electro-optic coefficient among all known II-VI compound materials (r41 r52 r63 ), CdTe is also used as an electro-optical modulator. For detector applications, CdTe is used in the form of various alloys, such as HgCdTe, which is sensitive to infrared radiation. Doped with chlorine, CdTe is in use as a radiation detector also sensitive to electrons and alpha particles. But of particular importance for radiation measurements is its alloy with zinc. Cadmium zinc telluride (CdZnTe or CZT) is an alloy of cadmium telluride and zinc telluride. It is a room-temperature direct-bandgap semiconductor directly sensitive to X-rays and gamma rays. CZT is the outcome of intensive research with the goal of finding a sensor material with better detection properties than silicon and germanium: CZT can be operated at room temperature and saturates only beyond a photon flux of 106 /(mm2 ·s). Also, the energy resolution of CZT, important for spectroscopic applications, is better than that of scintillation detectors. Combining good energy resolution and high count-rate capability in a detector operating at room temperature makes CZT an interesting material for applications in fundamental research, medicine, industry, and homeland security. The properties of most of the discussed sensor materials including diamond are summarized in Table 2.

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Table 2 Properties of detector materials. Zincblende (ZnS) has a cubic crystal system, its lattice type is face centered. The diamond structure is fairly similar, but obviously consists of carbon atoms only. (Based on data published by Sze (1981), Dulinski et al. (1994), Schieber et al. (1996), Lindner (1997), Nuclear Institute of Standards and Technology (1999), collected by KlaiberLodewigs (1999)) Material Lattice structure Bandgap type Atomic number – Z Atomic mass – A [atomic mass units] Density – ρ [g/cm3 ] Ionization potential Vi [eV] Bandgap width Egap [eV] Medium electron–hole production energy – Eeh [eV] Electron mobility μe [cm2 /(V s)] Hole mobility μh [cm2 /(V s)] Specific resistance Rs [ cm] Differential energy loss for minimum-ionizing particles [eV/μm] Energy-dependent intrinsic energy resolution E/E [(eV/E)1/2 ]

Si Diamond Indirect 14 28.09

Ge Diamond Indirect 32 72.61

GaAs Zincblende Direct 32 72.32

CdTe (CdZnTe) Zincblende Direct 50 120.0

Diamond (C) Diamond Indirect 6 12.01

2.33 173.0

5.32 350.0

5.31 384.9

6.20 539.3

3.50 ≈ 78

1.12

0.66

1.42

1.56

5.47

3.6

2.9

4.2

4.7

≈ 13

1500

3900

8500

1050

1800

450

1900

400

100

1200

2.3·105

47

107 –108

109 –1011

>1011

358.0

667.8

661.7

698.5

585.5

1.55

1.39

1.67

1.77

2.94

New Passive Thermoluminescence Detectors Also in the field of passive radiation sensors, new developments have taken place. Here, the term “passive radiation sensor” is used to describe a system that changes certain properties under the influence of ionizing radiation. After exposure, these properties are measured. This way, the passive sensor is read out and the integrated value of the energy dose the sensor was exposed to can be determined. Especially for thermoluminescence detectors, advancements could be achieved.

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Thermoluminescence is a form of luminescence shown by certain crystalline materials, such as lithium fluoride. Energy previously absorbed from exposure of the crystal to electromagnetic radiation or other ionizing radiation is re-emitted as light when the material is heated up to several 100 ◦ C. The way light is emitted during this heating process is described by the glow curve of the material. Radiation creates excited electronic states in crystalline materials. In some materials, these states are trapped by lattice defects. Although stable in time, energetically, these states are not stable. Heating the material enables the trapped states to interact with lattice vibrations (phonons), rapidly decaying into lowerenergy states. This process leads to the emission of photons. Thermoluminescent (TL) dosimeters made from lithium fluoride are routinely used to monitor absorbed doses in many kinds of radiation fields which contain photons, electrons, and neutrons. Lithium-fluoride detectors doped with manganese, copper, and phosphorus (LiF:Mg,Cu,P), usually referred to as MCP detectors, show a very high sensitivity and a simple signal-to-dose relation. They can be considered a de facto standard in modern environmental thermoluminescence dosimetry According to Obryk et al. (2011), these sensors are capable of measuring doses at pGy levels and even below. The shape of the glow curve resulting from doses ranging from a pGy to a kGy is practically identical (Obryk et al. 2011). The glow curve represents the light emission of the sensor when it is heated up at a given rate. However, significant changes of their glow-curve shape at high and very high doses have been discovered (Bilski 2002; Olko et al. 2010). High-temperature peaks start to grow at doses above 1 kGy and continue to grow up to doses of about 50 kGy when a completely new peak appears in the MCP’s glow curve beyond 400 ◦ C. Using these properties, one single sensor covers a dynamic range of nine orders of magnitude. A dynamic range covering five orders of magnitude can be seen in Fig. 8. This feature opens up applications of thermoluminescence dosimeters also in

TL signal, arb. units

3 107

0–250°C 250–350°C 350–550°C

2 107

1 107

0 0,01

0,1

1

10

100

Dose kGy

Fig. 8 Dynamic range of MCP TLD (LiF:Mg,Cu,P) (Obryk et al. 2011)

1,000

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the field of dosimetry at contemporary particle accelerators in fundamental research, where the expected dose cannot easily be determined beforehand. Another application uses the radiophotoluminescence of F2 and F3 + color centers in LiF: The material has also successfully been exploited for imaging tracks of energetic heavy charged particles. LiF crystals were irradiated with helium, carbon, neon, silicon, and iron ions. The tracks could then be visualized with a wide-field fluorescent microscope under blue-light excitation. The original method of fluorescent imaging of charged-particle tracks was developed by Akselrod et al. and used C and Mg-doped aluminum oxide crystals (Bilski et al. 2019 – reference to the original work therein).

Conclusions Coping with the radiation environment at modern high-luminosity particle accelerators, such as the Large Hadron Collider at CERN or Tevatron at Fermilab, represents a major challenge. Accelerators need to be equipped with radiation-hard sensors to provide input to their control systems. Chemical vapor deposition diamond can already be considered an established sensor material for these applications. Activities are going on to develop this material further, in order to use it also for position-sensitive devices in high-energy physics experiments, the way the less radiation-hard silicon is used today. When energy resolution at relatively high particle fluxes is needed, cadmium zinc telluride can be used for sensors which can be operated at room temperature. Also in the field of passive sensors for longer-term radiation monitoring, for instance, in experimental caverns, developments have taken place. New thermoluminescence detectors made from lithium fluoride doped with manganese, copper, and phosphorus (LiF:Mg,Cu,P) are very sensitive offer a simple signal-to-dose relation, but nevertheless cover a dynamic range of nine orders of magnitude.

Cross-References  Interactions of Particles and Radiation with Matter  Radiation Damage Effects  Semiconductor Radiation Detectors  Tracking Detectors Acknowledgments I would like to thank Harris Kagan, Dirk Meier, Alexander Oh, Shaun Roe, and Peter Weil-hammer for valuable discussions on the subject of diamond detectors. In the same way, I owe thanks to Pawel Bilski, Maciej Budzanowski, Barbara Obryk, and Pawel Olko, when it comes to the discussion of thermoluminescence detectors. Jan Sauerbrey was so kind to provide material that originates from the work he carried out for his diploma thesis. The detector design referred to in this chapter as an example is based on concepts developed when the author was with Technische Universität Dortmund, Experimentelle Physik 5, 44221 Dortmund, Germany.

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C. J. Ilgner

Suppliers of Equipment CVD diamond sensors, also metalized ones: Diamond Detectors Ltd., United Kingdom, www.diamonddetectors.com Conductive glue: Epotecny, France, www.epotecny.com/uk/;www.bicron.com/ Thermoluminescence detectors: Thermo Scientific, Germany, http://www.thermo scientific.com/ ; Institut Fizyki Jadrowej, Poland, www.ifj.edu.pl/ Metalized polymers as sensor contacts: ISTechnologie, Germany, www.istechnologie.de/; MiCryon Technik, Germany, www.micryon.de/

References Adam W et al (2000) Pulse height distribution and radiation tolerance of CVD diamond detectors. Nucl Instrum Methods Phys Res A 447:244–250 Bates AG, Borel J, Buytaert J, Collins P, Eckstein D, Eklund L (2006) IEEE Trans Nucl Sc 53(Part 3):3 Bilski P (2002) Lithium fluoride: from LiF:Mg,Ti to LiF:Mg,Cu,P. Radiat Prot Dosim 100(1– 4):199–206 Bilski P, Marczewska B, Gieszczyk W, Kłosowski M, Naruszewicz M, Sankowska M, Kodaira S (2019) Fluorescent imaging of heavy charged particle tracks with LiF single crystals. J Lumin 213:82–87 Brüning and Rossi, Nat Rev Phys 1:241–243, 2019 Chong D, Fernandez-Hernando L, Gray R, Ilgner CJ, Macpherson AL, Oh A, Pritchard TW, Stone R, Worm S (2007) Validation of synthetic diamond for a beam condition monitor for the compact muon solenoid experiment. IEEE Trans Nucl Sci 54(1):182–185 Domke M, Gernhäuser R, Ilgner C, Schwertel S, Warda K (2008) Validation of titanium-gold and titanium-silver and copper contacts on CVD diamond sensors for beam conditions monitors and tracking detectors for heavy ions under proton irradiation. Maier-Leibnitz-Laboratorium der Universität München und der Technischen Universität München Dulinski W et al (1994) Diamond detectors for future particle physics experiments. In: 27th international conference on high-energy physics, Glasgow, CERN-PPE-94-222 Edwards AJ, Bruinsma M, Burchat P, Kagan H, Kass R, Kirkby D et al (2005) Radiation monitoring with CVD diamonds in BABAR. Nucl Instrum Methods Phys Res A 552:176–182 Eversole WG (1962) Synthesis of diamond, US Patent, o. 3,030,187 Fernandez-Hernando L, Chong D, Gray R, Ilgner C, Macpherson A, Oh A, Pritchard T, Stone R, Worm S (2005) Development of a CVD diamond beam condition monitor for CMS at the Large Hadron Collider. Nucl Instrum Methods Phys Res A 552:183–188 Galbiati A, Lynn S, Oliver K, Schirru F, Nowak T, Marczewska B et al (2009) Performance of monocrystalline diamond radiation detectors fabricated using TiW, Cr/Au and a novel Ohmic DLC/Pt/Au electrical contact. IEEE Trans Nucl Sci 56(4):1863–1874 Kagan H (2005) Recent advances in diamond detector development. Nucl Instrum Methods Phys Res A 722–122:145 Klaiber-Lodewigs JM (1999) Eigenschaften und Einsatz von CdTe/CdZnTeMikrostreifendetektoren, diploma thesis, Bonn University 1999, BONN-IB- 99-08 Koike J, Parkin DM, Mitchell TE (1992) Displacement threshold energy for type IIa diamond. Appl Phys Lett 60(12):1450–1452 Lieng M (2008) Summary of simulations for the beam conditions monitor at the LHCb. Technical report LHCb-2008–027, Technische Universität Dortmund Lindner M (1997) Einsatz von GaAs-Mikrostreifendetektoren im Bioscope-System. Diploma thesis, Bonn University, BONN-IB-97-22 Meier D (1999) CVD diamond sensors for particle detection and tracking. PhD thesis, RuprechtKarls-Universität Heidelberg Müller S (2011) The beam condition monitor 2 and the radiation environment of the CMS detector at the LHC. PhD thesis, Karlsruhe Institute of Technology Nuclear Institute of Standards and Technology, USA, 1999

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Obryk B, Bilski P, Olko P (2011) Method of thermoluminescent measurement of radiation doses from micrograys up to a megagray with a single LiF:Mg,Cu,P detector. Radiat Prot Dosim 144(1–4):543–547. https://doi.org/10.1093/rpd/ncq339 Oh A (1999) Particle detection with CVD diamond. PhD thesis, University of Hamburg Olko P, Bilski P, El-Faramawy NA, Göksu HY, Kim JL, Kopec R, Waligórski MPR (2010) On the relationship between dose-, energy- and LET-response of thermoluminescent detectors. Radiat Prot Dosim 119:15–22 Sato Y et al (2015) Radiation hardness of a single crystal CVD diamond detector for MeV energy protons. NIM A 784:147–150 Sauerbrey J (2009) Upgrade evaluation of the LHCb beam conditions monitor and pCVD diamond sensor irradiation analysis. Diploma thesis, Technical University of Dortmund Schieber M et al (1996) Material properties and room-temperature nuclear detector response of wide bandgap semiconductors. NIM A 377:492–495 Schleich S (2008) FPGA based data acquisition and beam dump decision system for the LHCb beam conditions monitor. Diploma thesis, Technical University of Dortmund Shintani Y (1996) J Mater Res 11:29–55 Sze SM (1981) Physics of semiconductor devices, 2nd edn. Wiley, New York The LHCb Collaboration (2008) JINST S08005, 3. https://doi.org/10.1088/1748-0221/3/08/S08005 The LHCb VELO upgrade. PoS(Vertex 2012)039 The web site of the RD42 collaboration at CERN is http://rd42.web.cern.ch/rd42. Accessed 4 Mar 2011 Trucchi DM, Allegrini P, Calvani P, Galbiati A, Oliver K, Conte G (2012) Very fast and primingless single-crystal-diamond X-ray dosimeters. IEEE Electron Device Lett 33(4):615–617

Radiation Damage Effects

23

Ren-Yuan Zhu

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Scintillation Mechanism Damage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Radiation-Induced Phosphorescence and Energy Equivalent Readout Noise . . . . . . . . . . . . . Radiation-Induced Absorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Recovery of Radiation-Induced Absorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Radiation-Induced Color Centers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dose Rate Dependence and Color Center Kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Light Output Degradation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ionization Dose–Induced Radiation Damage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Proton-Induced Radiation Damage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Neutron-Induced Radiation Damage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Light Response Uniformity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Damage Mechanism in Alkali Halide Crystals and CsI:Tl Development . . . . . . . . . . . . . . . . Damage Mechanism in Oxide Crystals and PWO Development . . . . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

688 690 691 692 694 695 698 699 699 701 701 703 704 705 708 708 709 710

Abstract Radiation damage is an important issue for particle detectors operated in a hostile environment where radiations from ionization dose, protons, and neutrons are expected. This is particularly important for future high energy physics detectors designed for the energy and intensity frontiers. This chapter describes the radia-

R.-Y. Zhu () High Energy Physics Group, Physics, Mathematics and Astronomy Division, California Institute of Technology, Pasadena, CA, USA e-mail: [email protected] © Springer Nature Switzerland AG 2021 I. Fleck et al. (eds.), Handbook of Particle Detection and Imaging, https://doi.org/10.1007/978-3-319-93785-4_22

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tion damage effects in inorganic scintillators, including scintillation mechanism damage, radiation-induced phosphorescence, radiation-induced absorption, and radiation-induced light output degradation. While radiation damage in halides is attributed to the oxygen/hydroxyl contamination, it is the structure defects, such as the oxygen vacancies, which cause damage in oxides. Various material analysis methods used in investigations of the radiation damage effects as well as the improvement of crystal quality through systematic R&D are also discussed.

Introduction Total absorption shower counters made of inorganic crystal scintillators have been known for decades for their superb energy resolutions and detection efficiencies (Gratta et al. 1994) ( Chaps. 15, “Scintillators and Scintillation Detectors,” and  21, “Calorimeters”). In high energy and nuclear physics experiments, large arrays of scintillating crystals of up to more than ten cubic meters have been assembled for precision measurements of photons and electrons. These crystals are working in a radiation environment, where various particles, such as γ-rays, charged hadrons, and neutrons, are expected. Table 1 (Mao et al. 2008) lists basic properties of heavy crystal scintillators commonly used in high energy physics (HEP) detectors. They are thallium-doped sodium iodide (NaI(Tl) or NaI:Tl), thallium-doped cesium iodide (CsI(Tl) or CsI:Tl), undoped CsI, barium fluoride (BaF2 ), bismuth germanate (Bi4 Ge3 O12 or BGO), lead tungstate (PbWO4 or PWO), and ceriumdoped lutetium oxyorthosilicate (Lu2 (SiO4 )O:Ce or LSO) (Melcher and Schweitzer 1992) and cerium-doped lutetium yttrium oxyorthosilicate (Lu2(1−x) Y2x SiO5 :Ce, LYSO) (Cooke et al. 2000; Kimble et al. 2002). All crystals have either been used in, or actively pursued for, high energy and nuclear physics experiments. Some of them, such as NaI:Tl, CsI:Tl, BGO, LSO, and LYSO are also widely used in the medical industry. All known crystal scintillators suffer from radiation damage (Zhu 1998). There are three possible radiation damage effects in crystal scintillators: (1) scintillation mechanism damage, (2) radiation-induced phosphorescence (afterglow), and (3) radiation-induced absorption (color centers). A damaged scintillation mechanism would reduce crystal’s scintillation light yield and cause a degradation of crystal’s light output. It may also change crystal’s light response uniformity for large size crystals used to construct total absorption calorimeters since radiation dose profile is usually not uniform along the crystal length. Radiation-induced phosphorescence, commonly called afterglow, causes an increased dark current in photo-detectors, and thus an increased readout noise. Radiation-induced absorption reduces crystal’s light attenuation length (Ma and Zhu 1993a), and thus crystal’s light output and possibly also crystal’s light response uniformity. Table 2 summarizes radiation damage effect for various crystal scintillators. There is no experimental data supporting scintillation mechanism damage. All crystal scintillators studies so far, however, suffer from radiation-induced phosphorescence and radiation-induced absorption.

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Table 1 Properties of heavy crystal scintillators Crystal Density(g/cm2 ) Melting point (◦ C) Radiation length (cm) Moliere radius (cm) Interaction length (cm) Refractive indexa Hygroscopicity Luminescenceb (nm) (at Peak) Decay timeb (ns)

NaI:Tl 3.67 651

CsI:Tl 4.51 621

CsI 4.51 621

BaF2 4.89 1280

BGO 7.13 1050

PWO 8.3 1123

LSO/LYSO 7.40 2050

2.59

1.86

1.86

2.03

1.12

0.89

1.14

4.13

3.57

3.57

3.10

2.23

2.00

2.07

42.9

39.3

39.3

30.7

22.7

20.7

20.9

1.85 Yes 410

1.79 Slight 560

Light yieldb,c

100

165

d(LY)/dTb,d (%/o C) Experiment

−0.2

0.4

2.20 No 425 420 30 10 0.30 0.077 −2.5

1.82 No 420

1220

Crystal Bball

CLEO BaBar BELLE BES III

1.50 No 300 220 650 0.9 36 4.1 −1.9 0.1 TAPS Mu2e-II

2.15 No 480

245

1.95 Slight 420 310 30 6 3.6 1.1 −1.4

CMS ALICE PrimEx Panda

COMET HERD CMS

KTeV Mu2e-I

300 21 −0.9 L3 BELLE

40 85 −0.2

a At

the wavelength of the emission maximum line: slow component, bottom line: fast component c Relative light yield of samples of 1.5 X and with the PMT QE taken out 0 d At room temperature b Top

Table 2 Radiation damage in crystal scintillators Item Scintillation mechanism Phosphorescence (afterglow) Absorption (color centers) Recover at room temperature Dose rate dependence Thermally annealing Optical bleaching

CsI:Tl No Yes Yes Slow No No No

CsI No Yes Yes Slow No No No

BaF2 No Yes Yes No No Yes Yes

BGO No Yes Yes Yes Yes Yes Yes

PWO No Yes Yes Yes Yes Yes Yes

LSO/LYSO No Yes Yes No No Yes Yes

Radiation-induced absorption is caused by a process called color center formation, which may recover spontaneously under the application temperature through a process called color center annihilation. If so, the damage would be dose rate dependent (Ma and Zhu 1993b; Zhu 1997). If radiation-induced absorption does not recover, or the recovery speed is very slow, however, the color center density would increase continuously under irradiations until all defect traps are fully filled. In this

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case the corresponding radiation damage effect does not depend on the dose rate applied. Color centers may also be annihilated thermally by heating the crystal to a high temperature through a process called thermal annealing, or optically by injecting light of various wavelength through a process called optical bleaching (Ma and Zhu 1993b). The recovery process, either spontaneous or applied through thermal annealing or optical bleaching, reduces the color center density, or the radiationinduced absorption. The recovery process, however, also introduces an instability in crystal’s transparency, so is crystal’s light output. In this case, a precision monitoring system is mandatory to follow variations of crystal’s transparency, and provide corrections for crystal’s light output calibration. Radiation damage caused by charged hadrons and neutrons may differ from that caused by ionization dose or γ-rays. Studies (Huhtinen et al. 2005) on protoninduced radiation damages in PWO crystals, for example, show a very slow (or no) recovery under room temperature, which seems contrary to the radiation damage caused by γ-rays. This leads to a cumulative proton-induced damage in PWO with no dose rate dependence. Radiation damage level may also be different at different temperature for crystals with dose rate dependent damage since the spontaneous recovery speed is temperature dependent. PWO crystals used at low temperature, for example, suffer more damage than that at high temperature (Semenov et al. 2007). Commercially available mass produced crystals may not meet the quality required for high energy physics detectors. The quality of mass produced crystals thus need to be improved by removing harmful impurities and/or defects in the crystal. The rest of this chapter discusses radiation-induced damage phenomena in inorganic scintillators, the origin of the radiation damage in halides and oxides as well as the improvement of the quality of commercially available crystals. All data presented in this chapter, except that specified, are measured for full size crystals adequate for total absorption calorimeters, which are typically 18 to 25 X0 long. Since both the radiation-induced phosphorescence and absorption are of the bulk effect, it is important that full size crystals are used in radiation damage studies.

Scintillation Mechanism Damage Experimental data show that crystal’s scintillation mechanism is not damaged by radiation. This is observed for irradiations of γ-rays, neutrons as well as charged hadrons (Huhtinen et al. 2005; Batarin et al. 2003). A common approach is to compare the shape of the emission spectra measured before and after irradiations. It is well known that the measured intensity of emission suffers from a large systematic uncertainty caused by sample position and orientation, sample surface quality, and internal absorption. Care thus should be taken in such measurements to maintain a well-controlled location of the sample and excitation source, and avoid emission light going through crystal bulk so that the measured emission spectrum is not affected by the radiation-induced absorption.

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Fig. 1 Normalized photo-luminescence spectra measured before (blue) and after (red) γ-ray irradiation and corresponding difference (green) are shown as a function of wavelength for a PWO sample (left) and an LYSO sample (right)

The top plots of Fig. 1 show the photo-luminescence spectra measured before (blue) and after (red) γ-ray irradiations for a PWO sample (left) and an LYSO sample (right). These spectra are normalized to an integration around the emission peaks as shown in the figures. The relative difference between these normalized spectra (green) is shown in the bottom. Also shown in the bottom plots are the average of the absolute values of the relative difference, which are 0.7% and 0.6%, respectively, for PWO and LYSO. Such differences are much lower than the 1% systematic uncertainty of the measurements, showing that no statistically significant difference is observed between the photo-luminescence spectra taken before and after irradiations for both PWO and LYSO, indicating no damage to the scintillation mechanism. Similar investigations show that there is no scintillation mechanism damage observed for BGO (Zhu et al. 1991), BaF2 (Zhu 1994), and CsI:Tl (Zhu et al. 1996a) as well. This conclusion is also supported by more complicated measurements of the light response uniformity before and after irradiations with a nonuniform dose profile (Batarin et al. 2003).

Radiation-Induced Phosphorescence and Energy Equivalent Readout Noise Radiation-induced phosphorescence is observed by measuring photo-current during and after radiation is turned off. The left plot of Fig. 2 shows the γ-ray-induced photo-current after radiation, normalized to that during the irradiation, as a function of time during and after γ-ray irradiations for several crystal samples: PWO, BGO, and LSO/LYSO. All samples are of full size adequate for calorimeter applications. The amplitude of the normalized phosphorescence is at a level of 10−5 for BGO

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Fig. 2 Left: Normalized anode current is shown as a function of time during and after γ-ray irradiations for BGO, PWO, LSO, and LYSO samples. Right: γ-ray-induced anode photo-current is shown as a function of the dose rate applied to LSO and LYSO samples

and PWO, 3 × 10−4 for LYSO, and 2 × 10−3 for LSO, showing that LYSO has a smaller phosphorescence, or afterglow, than LSO. The right plot of Fig. 2 shows γ-ray-induced anode photo-currents as a function of the γ-ray dose rate applied to several LSO and LYSO samples. Consistent slopes are observed for all samples because of the similar light yield of these samples. These slopes may be used to extract the readout noise in electron numbers for the crystal and photo-detector combination in a particular integration gate, which can then be converted to the energy equivalent readout noise by normalizing to the crystal’s light output (Mao et al. 2009a, b). Because of its high light yield (200 times PWO and 5 times BGO) and short decay time (40 ns), the energy equivalent readout noise in LSO and LYSO is an order of magnitude lower than that in PWO for both γ-ray and neutron irradiations.

Radiation-Induced Absorption The main consequence of radiation damage in scintillation crystals is radiationinduced absorption, or color center formation. Depending on the type of the defects in the crystals, color centers may be electrons located in anion vacancies (F center), holes located in cation vacancies (V center), and interstitial anion atoms (H center) or ions (I center), etc. Radiation-induced absorption is measured by comparing the longitudinal optical transmittance spectra measured after and before irradiation. A spectrophotometer of good quality provides systematic uncertainties as low as 0.2%. Figure 3 shows longitudinal transmittance spectra as a function of wavelength measured before and after several steps of irradiations for halide crystals: CsI(Tl)

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Fig. 3 The longitudinal transmittance spectra measured before and after several steps of the irradiation are shown as a function of wavelength for several CsI(Tl) (top left), a BaF2 (top right), a PWO (bottom left), and an LYSO (bottom right) crystal samples

(top left) and BaF2 (top right), and oxide crystals: PWO (bottom left) and LYSO (bottom right). While the color center width appears narrow in CsI(Tl), it is relatively wide in other crystals. It is interesting to note that the CsI(Tl) sample SIC-5 suffers much less radiation damage than other two CsI(Tl) samples since it was grown with a scavenger in the melt to remove the oxygen contamination, which is an effective approach to improve radiation hardness for halide crystals as discussed later in section “Damage Mechanism in Alkali Halide Crystals and CsI:Tl Development.” For the BaF2 sample we also notice that the damage levels of the longitudinal transmittance spectra are identical for the same integrated dose, while the fast dose rate (top) is up to a factor of 30 of the slow rate (bottom). Such a dose rate independence is expected since no recovery at the room temperature was

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Fig. 4 Degradation on EWLT for a PWO sample (left) and an LYSO sample (right)

observed for BaF2 as discussed later in section “Dose Rate Dependence and Color Center Kinetics.” It is also interesting to note that the radiation-induced absorption is much smaller in LSO and LYSO than that in other crystals. Figure 4 shows an expanded view of the longitudinal transmittance spectra measured before and after several steps of γ-ray irradiations for a PWO (left) and an LYSO (right) sample. Also shown in the figures is the corresponding photo-luminescence spectra (blue) and the numerical values of the emission weighted longitudinal transmittance (EWLT), which is defined as:  LT (λ) Em (λ) dλ  EW LT = (1) Em (λ) dλ The EWLT value represents crystal’s transparency more accurate than the transmittance at the emission peak, so is widely used in radiation damage studies. This is particularly true for LSO and LYSO, which have a nonnegligible selfabsorption since a part of their emission spectra is not within the transparent region of the crystal (Chen et al. 2005).

Recovery of Radiation-Induced Absorption Depending on color-center depth, the radiation-induced absorption may recover spontaneously at the application temperature. Figure 5 shows typical recovery behavior of the longitudinal optical transmittance at 440 nm and 420 nm, respectively, measured up to 4,000 and 500 h after γ-ray irradiations for two PWO (left) and four LSO and LYSO (right) samples. Three recovery time constants were determined by an exponential fit for PWO samples. While the short time constant

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Fig. 5 Recovery of γ-ray-induced transmittance damage is shown as a function of time after irradiation for two PWO samples (left) and four LSO/LYSO samples (right)

is of a few tens of hours, the medium time constant is at a few thousands hours, and the third time constant is much longer, which may be considered as no recovery for the time scale of these measurements. It is also interesting to note that the LSO and LYSO samples show very slow recovery speed, consisting with no recovery. Similarly, the radiation-induced absorption in BaF2 (Zhu 1994) and CsI:Tl (Zhu et al. 1996a) does not recover as well at room temperature. The radiation damage in LYSO, BaF2 , and CsI crystals thus is not dose rate dependent. On the other hand, the radiation damage in BGO and PWO are dose rate dependent. In addition to the spontaneous recovery at the application temperature, the radiation damage level may also be reduced by heating crystals to a high temperature (thermal annealing) or injecting light of various wavelength to the crystal (optical bleaching). It is known that γ-ray-induced damage can be completely removed by thermal annealing at 200 ◦ C for BaF2 (Zhu 1994), BGO (Zhu et al. 1991), and PWO (Zhu et al. 1996b), or 300 ◦ C for LSO and LYSO (Chen et al. 2005). Optical bleaching was also found effective for BaF2 (Zhu 1994), BGO (Zhu et al. 1991), and PWO (Zhu et al. 1996b). On the other hand, the γ-ray-induced absorption in CsI:Tl can neither be annealed thermally or bleached optically (Zhu et al. 1996a). Optical bleaching may be used to reduce color center density in crystals in situ. Such an approach has been extensively studied for BaF2 (Ma and Zhu 1993b) and PWO (Zhu et al. 1996b; Yin et al. 1997).

Radiation-Induced Color Centers Crystal’s longitudinal transmittance data can be used to calculate crystal’s light attenuation length as a function of wavelength (Ma and Zhu 1993a):

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LAL (λ) =

l

      2 2 4 2 2 2 ln T (λ) (1 − Ts (λ)) / 4Ts (λ) + T (λ) 1 − Ts (λ) − 2Ts (λ) (2)

where T(λ) is the longitudinal transmittance measured along crystal length l, and Ts (λ) is the theoretical transmittance assuming multiple bouncings between two crystal ends and without internal absorption: Ts (λ) = (1 − R (λ))2 + R 2 (λ) (1 − R (λ))2 + · · · = (1 − R (λ)) / (1 + R (λ)) (3) and  2 ncrystal (λ) − nair (λ) R (λ) =  2 ncrystal (λ) + nair (λ)

(4)

where ncrystal (λ) and nair (λ) are the refractive indices for crystal and air, respectively. Radiation-induced absorption coefficient RIAC (λ), or color center density D (λ),and the emission weighted radiation-induced absorption coefficient (EWRIAC) can be calculated as (Ma and Zhu 1993b): RI AC (λ) or D (λ) = 1/LALafter (λ) − 1/LALbefore (λ)  EW RI AC =

RI AC (λ) Em (λ) dλ  Em (λ) dλ

(5)

(6)

where LALafter (λ) and LALbefore (λ) are the light attenuation length after and before irradiation, respectively, and Em(λ) is the emission spectrum. The above equations are accurate presentations for crystal’s transparency and radiation-induced absorption coefficient. They are light path length independent, so can be used to represent radiation damage level. A simplified representation for RIAC(λ) is: RI AC (λ) =

1 T0 (λ) ln l T (λ)

(7)

where T0(λ) is the transmittance along crystal length l measured before irradiation and T(λ) is the transmittance measured after irradiation. This equation does not

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take into account multiple bounces between two end surfaces of the crystal, so is an approximation of the eq. 5 above (Ma and Zhu 1993a). Spectrum of radiation-induced absorption coefficient can also be presented as a function of the photon energy, and be further decomposed to a sum of several color centers with Gaussian energy distributions (Zhu et al. 1991):

RI AC (λ) =

n

Ai e

−

(E(λ)−Ei )2 2σi2

(8)

i=1

where Ei , σ i , and Di denote the energy, width, and amplitude of the color center i, respectively, and E(λ) is the photon energy. Figure 6 shows the radiation-induced absorption coefficient as a function of the photon energy for four BGO samples doped with Ca, Mn, Pb, and Cr (left) and two PWO samples in the equilibrium under γ-ray irradiation with dose rates of 100 rad/h and 9,000 rad/h (right). It is interesting to note that although the overall shapes of radiation-induced absorption coefficients are different, the color centers are located at the same energy and with the same width for both crystals. While there are three color centers peaked at 2.3 eV, 3.0 eV, and 3.8 eV for the BGO samples, the PWO samples show two color centers peaked at 2.3 eV and 3.1 eV. This observation hints that the color centers in these oxide crystals are caused by crystal structure–related defects, such as oxygen vacancies, not particular impurities. Readers are referred to the corresponding references (Zhu et al. 1991, 1996b) for more discussions about the color centers in these crystals.

Fig. 6 Radiation-induced absorption coefficient spectra (data points with error bars) are shown as a function of the photon energy for four doped BGO samples (Left) and two PWO samples (Right)

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Dose Rate Dependence and Color Center Kinetics Because of the balance between two dynamic processes: a color center creation process (irradiation) and a color center annihilation process (room temperature recovery), radiation damage in inorganic scintillators is usually dose rate dependent. Assuming that the annihilation speed of the color center i is proportional to a constant ai and its creation speed is proportional to a constant bi and the dose rate (R), the differential change of color center density when both processes coexist can be expressed as (Ma and Zhu 1993b): dD (λ) =

n

   −ai Di (λ) dt + Diall (λ) − Di (λ) bi Rdt

(9)

i=1

where Di (λ) is the density of the color center i in the crystal, and the summation goes through all the centers. The solution of Eq. 9 is   n  bi RDiall (λ)  −(ai +bi R)t 0 −(ai +bi R)t D (λ) = 1−e + Di (λ) e ai + bi R

(10)

i=1

where Diall (λ) is the total density of the trap related to the color center i and the Di0 (λ) is its initial value. The color center density in the equilibrium Deq (λ) depends on the dose rate R: Deq (λ) =

n bi RD all (λ) i

i=1

ai + bi R

(11)

Following these equations, crystal’s optical transmittance, and thus crystal’s light output, decreases when the crystal is exposed to a radiation under a dose rate R, and would reach an equilibrium. At the equilibrium, the speed of the color center formation (damage) equals to the speed of the color center annihilation (recovery), so that the color center density, or radiation-induced absorption, does not change unless the dose rate (R) or temperature (ai ) changes. Applying a bleaching light introduces an additional color center annihilation process (ai ), thus changes the color center density at the equilibrium as well. More detailed discussions on the behavior of the color center densities with a bleaching light applied can befound in (Ma and Zhu 1993b). Equation 11 also indicates that the radiation damage level does not depend on the dose rate if the recovery speed (ai ) is small, which is the characteristics of the radiation damage caused by deep color centers. For crystals with no dose rate dependence, an accelerated irradiation with a high dose rate would lead to the same effect as a slow irradiation with a low dose rate provided that the total integrated dose is the same. This is clearly shown in the transmittance data of a BaF2 crystal in the top right plot of Fig. 3.

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Light Output Degradation Crystal’s light output is a convolution of crystal’s emission, light propagation inside the crystal, and the quantum efficiency (QE) of the photo-detector. All these are wavelength-dependent. Since crystal emission and photo-detector QE are usually not affected by radiation, the degradation of crystal’s light output is correlated to the degradations of crystal’s transparency, i.e., the radiation-induced absorption. A light monitoring system, which measures variations of crystal’s transparency, thus provides necessary information for calibration of crystal’s light output in situ under radiation. It is also clear that degradation of crystal’s light output is light path length dependent. Crystals of small size thus suffer less radiation damage than crystals of large size. In HEP experiments, radiation in situ is expected from ionization dose, charged hadrons, and neutrons. During the LHC Run-I, significant light output losses were observed by the CMS light monitoring system for PWO crystals (T. Dimova on behalf of the CMS Collaboration 2017). With a 5 × 1034 cm−2 s−1 luminosity and a 3,000 fb−1 integrated luminosity ( Chap. 6, “Particle Identification”), the HL-LHC will present a radiation environment, where up to 130 Mrad ionization dose, 3 × 1014 charged hadrons/cm2 , and 5 × 1015 fast neutron/cm2 are expected (Bilki 2015). In this section, light output degradation induced by ionization dose, protons, and neutrons with an integrated dose up to 340 Mrad, a proton fluence up to 3.0 × 1015 p/cm2 , and a fast neutron fluence up to 3.0 × 1015 n/cm2 , respectively, is presented for various crystals, thus putting an emphasis on LYSO, BaF2 , and PWO crystals.

Ionization Dose–Induced Radiation Damage Ionization dose–induced radiation damage was investigated at the Total Ionization Dose (TID) facility of Jet Propulsion Laboratory. Figure 7 shows normalized EWLT (top) and light output (LO, bottom) as a function of the integrated dose for six LYSO/LSO/LFS crystals (left) and three BaF2 crystals from different vendors, where the fast scintillation component peaked at 220 nm with sub-ns decay time is shown for BaF2 . The losses of EWLT and light output are at a level about 40– 60% for both LYSO and BaF2 crystals after 100 Mrad, showing excellent radiation hardness of these crystals. It is also interesting to note that while the light output of BaF2 degrades below 10 krad, it is more or less stabilized after that, which is consistent with the transmittance data shown in Fig. 3 (Zhu 1994). Figure 8 shows the RIAC values at the emission peak (left) and the normalized light output (right) as a function of the integrated dose for various crystal samples of large size (Yang et al. 2016a). We note that beyond 1 Mrad LYSO, BaF2 and BGO crystals show significantly better radiation hardness than CeF3 , CsI, and PWO. In terms of light output loss, LYSO is the best among all crystal scintillators. The best sample of this type maintains 75% and 60% light output, respectively, after 120 and

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Fig. 7 Normalized EWLT (top) and light output(bottom) are shown as a function of the ionization dose up to 340 and 120 Mrad, respectively, for six LYSO/LSO/LFS crystals (left) and three BaF2 crystals (right) from different vendors

Fig. 8 The RIAC values at the emission peak (Left) and the normalized light output (Right) are shown as a function of integrated dose for various crystal scintillators

340 Mrad. On the other hand, BaF2 and BGO crystals also maintain 45% and 35% light output, respectively, after 120 and 200 Mrad, so may be considered as costeffective alternatives for future HEP experiments in a severe radiation environment. Undoped CsI shows good radiation hardness below 100 krad, so is a cost-effective choice for future HEP experiments in a modest radiation environment ( Chap. 18, “Gamma-Ray Spectroscopy”).

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Fig. 9 The EWRIAC values (left) and the normalized light output (right) are shown as a function of the integrated 800 MeV proton fluence for LYSO, BaF2 , and PWO crystal plates

Proton-Induced Radiation Damage Following early studies (Huhtinen et al. 2005; Dissertori et al. 2010, 2014; Yang et al. 2016b; Auffray et al. 2012, 2013; Dormenev et al. 2014; Lecomte et al. 2006), proton-induced radiation damage was investigated at the Weapons Neutron Research facility of Los Alamos Neutron Science Center (WNR of LANSCE) (Hu et al. 2018a). A total of 21 samples (six each for BaF2 and PWO of 25 × 25 × 5 mm3 and nine LYSO of 10 × 10 × 3 mm3 ) were irradiated by 800 MeV protons in three batches to reach 2.7 × 1013 , 1.6 × 1014 and 9.7 × 1014 p/cm2 . Samples were measured 183 days after irradiation. Figure 9 shows their EWRIAC values (left) and the normalized light output (right) as a function of the proton fluence. The EWRIAC values are 7, 18, and 71 m−1 , respectively, for LYSO, BaF2 , and PWO after a proton fluence of 9.7 × 1014 p/cm2 . The light output losses are 10% and 13%, respectively, for the LYSO and BaF2 , indicating excellent radiation hardness of LYSO and BaF2 crystals against charged hadrons. The light output of PWO samples after proton fluence of 9.7 × 1014 p/cm2 is too low to be experimentally determined.

Neutron-Induced Radiation Damage Early works did not find clean evidence on neutron-induced damage in scintillating crystals (Chipaux et al. 2005; Zhang et al. 2009). While the investigation presented in (Zhang et al. 2009) was carried out for a fast neutron fluence up to 6 × 108 n/cm2 , that in (Chipaux et al. 2005) was carried out for PWO crystals up to a fast neutron fluence of 1019 n/cm2 . Following these studies, neutron-induced radiation damage was investigated at WNR of LANSCE by using a combination of particles,

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Fig. 10 The RIAC values at the emission peak (left) and the normalized light output (right) are shown as a function of the integrated fast neutron fluence for LYSO, BaF2 , and PWO crystal plates

including neutrons, protons, and γ-rays with a fast neutron (>1 MeV) fluence up to 3.6 × 1015 n/cm2 , a proton fluence up to 1 × 1013 p/cm2 , and 5 Mrad of ionization dose (Hu et al. 2018b). A total of 36 samples, 12 each for BaF2 , LYSO, and PWO of 10 × 10 × 5 mm3 , were irradiated in three batches for 21.2, 46.3, and 120 days to reach fast neutron fluences of 7.4 × 1014 , 1.6 × 1015 , and 3.6 × 1015 n/cm2 , respectively. In this experiment a half of the samples were shielded with 5 mm lead to reduce the ionization dose background. Samples were measured 189, 164, and 90 days after the irradiation. Figure 10 shows their RIAC values at the emission peak (left) and the normalized light output (right) as a function of the fast neutron (>1 MeV) fluence. While the average RIAC values of two samples each after a fast neutron fluence of 3.6 × 1015 n/cm2 are 14.1, 49.8, and 97.1 m−1 , respectively, for LYSO, BaF2 , and PWO without 5 mm Pb shielding, the corresponding values are 7.3, 44.2, and 110.5 m−1 with Pb shielding. The corresponding light output losses after 3.6 × 1015 n/cm2 are 23% and 24%, respectively, for LYSO and BaF2 crystals without Pb shielding, and 20% and 20% with Pb shielding. In both cases, the light output of PWO samples after a fast neutron fluence of 3.6 × 1015 n/cm2 is too low to be experimentally determined. The data point for the PWO crystals in the group 3 thus indicates an upper limit. It is clear that LYSO and crystals are more radiation hard than PWO under neutron irradiations. It is interesting to note that the damage observed here is more than a factor of ten larger than the damage expected by the 5 Mrad ionization dose along with 1 × 1013 p/cm2 proton fluence. These data thus show a clear evidence of neutroninduced radiation damage in these scintillating crystals. Additional investigation with an effective Pb shielding for ionization dose background would be useful to clarify the nature of neutron-induced damage, compared to ionization dose and/or charged hadrons–induced damages.

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Light Response Uniformity An adequate light response uniformity along crystal length is a key for maintaining excellent energy resolution promised by a total absorption crystal calorimeter. Light output along a long crystal LO (x) may be parameterized as a linear function

LO(x) = 1 + δ (x/xmid − 1) LOmid

(12)

where LOmid represents the light output measured at the middle point of the crystal, δ represents the deviation from a flat response, and x is the distance from one end of the crystal. An alternative measure of light response uniformity is the rms values of the light out values measured along the crystal length. Commercially available crystals of a rectangular shape have a flat light response uniformity, but may also be the photo-detector coupling end dependent. A common practice is to choose the coupling end which provides a better light response uniformity. Figure 11 shows the light response uniformity for a PWO sample (left) and an LYSO sample (right) after several steps of γ-ray irradiation. The γ-ray irradiation was carried out step by step under a fixed dose rate to reach an integrated dose in each step. It is clear that the δ values were not changed for both crystals, indicating that the energy resolution would not be compromised after the γ-ray irradiation. This is due to the fact that the degraded light attenuation length is long enough to maintain the light response uniformity as predicted by ray-tracing simulations (Zhu 1998).

Fig. 11 Light output is shown as a function of the distance to the end coupled to PMT for a PWO samples (left) and an LYSO sample (right) after several steps of γ-ray irradiations

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Damage Mechanism in Alkali Halide Crystals and CsI:Tl Development Material analysis is important for investigations on the radiation damage mechanism. Glow Discharge Mass Spectroscopy (GDMS) analysis was used to identify trace impurities harmful to radiation hardness for a batch of CsI:Tl crystals. Samples were taken 3–5 mm below the surface of the crystal to avoid surface contamination. A survey of 76 elements, including all of the lanthanides, indicates that there are no obvious correlations between the detected trace impurities and the crystal’s susceptibility to the radiation damage. This hints an important role of the oxygen contamination which cannot be determined by GDMS analysis. Oxygen contamination is known to cause radiation damage in the alkali halide scintillators. In BaF2 (Zhu 1994), for example, hydroxyl (OH− ) may be introduced into crystal through a hydrolysis process, and later decomposed to interstitial and substitutional centers by radiation through a radiolysis process. Equation 13 shows a scenario of this process: OH − → Hi0 + Os− or Hs− + Oi0

(13)

where the subscript i and s refer to the interstitial and substitutional centers, respectively. Both the Os− center and the U center (Hs− ) were identified (Zhu 1994). Following the BaF2 experience, significant improvement of the radiation hardness was achieved for CsI(Tl) crystals by using a scavenger to remove oxygen contamination (Zhu et al. 1996a). Figure 12 (left) shows normalized light output as a function of the integrated dose for a group of CsI(Tl) samples, and compared to the BaBar radiation hardness specification (solid lines) (Zhu 1998). While the late samples SIC-5, 6, 7, and 8 satisfy the BaBar specification, early samples SIC-2 and 4 do not. This improvement of CsI(Tl) quality was achieved following an understanding that the radiation damage in the halide crystals is caused by the oxygen orhydroxyl contamination. Various material analysis was carried out to quantitatively identify the oxygen contamination in the CsI(Tl) samples. Gas fusion (LECO), for example, was found not sensitive enough to identify the oxygen contamination. The identification of oxygen contamination was finally achieved by using the secondary ionization mass spectroscopy (SIMS) analysis. A Csion beam of 6 keV and 50 nA was used to bombard the CsI(Tl) samples. All samples were freshly cleaved prior being loaded into the UHV chamber. An area of 0.15 × 0.15 mm2 on the cleaved surface was analyzed. To further avoid the surface contamination, the starting point of the analysis is at about 10 μm deep inside the fresh cleaved surface. Figure 12 (right) shows the depth profile of the oxygen contamination for two radiation soft samples (SIC-T1 and SIC-2) and two radiation hard samples (SIC-T3 and Khar’kov). Crystals with poor radiation resistance have oxygen contamination of 1018 atoms/cm3 or 5.7 PPMW, which is 5 times higher than the background count (2 × 1017 atoms/cm3 , or 1.4 PPMW).

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Fig. 12 Left: The progress of the CsI(Tl) radiation hardness is shown for CsI(Tl) samples from SIC together with the BaBar radiation-hardness specification. Right: The depth profile of the oxygen contamination is shown for two rad-soft CsI(Tl) samples (SIC-T1 and SIC-2) and two rad-hard samples (SIC-T3 and Khar’kov)

Damage Mechanism in Oxide Crystals and PWO Development Similarly, GDMS analysis was used for BGO and PWO crystals, and was found no particular correlation with crystal’s radiation hardness. This hints an important role of the structure-related defects in the crystal, which cannot be determined by the GDMS analysis. Crystal structure defects, such as oxygen vacancies, are known to cause radiation damage in oxide scintillators. In BGO, for example, three common radiation-induced absorption bands at 2.3 eV, 3.0 eV, and 3.8 eV were found in a series of 24 doped samples (Zhu et al. 1991) as shown in the left plot of Fig. 6. Observations in the PWO crystals are similar with two color centers peaked at 2.3 eV and 3.1 eV as shown in the right plot of Fig. 6. Following these observations, effort was made to reduce oxygen vacancies in PWO crystals. An oxygen compensation approach, which was carried out by a postgrowth thermal annealing in an oxygen-rich atmosphere, was found effective in improving PWO’s radiation hardness for samples up to 10 cm long (Zhu et al. 1996b). This approach, however, is less effective for longer (25 cm) crystals because of the variation of the oxygen vacancies along the crystal. In practice, yttrium doping, which provides a local charge balance for oxygen vacancies to prevent the color center formation, was found effective for PWO (Zhu et al. 1996b). Figure 13 shows the normalized light output as a function of time for three PWO samples under the γ-ray irradiations with a dose rate of 15 rad/h. PWO samples produced after 2002 with yttrium doping is much more radiation hard than the early samples.

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Fig. 13 The progress of PWO radiation hardness is shown for PWO samples from SIC

This improvement of PWO quality was achieved following an assumption that the radiation damage in the oxide crystals is caused by the oxygen vacancies. Various material analysis was carried to quantitatively identify the stoichiometry deviation and the oxygen vacancies in the PWO samples. Particle-induced X-ray emission (PIXE) and quantitative wavelength dispersive electron micro-probe analysis (EMPA) were tried. PWO crystals with poor radiation hardness were found as having a nonstoichiometric W/Pb ratio. Both PIXE and EMPA, however, do not provide quantitative oxygen analysis. X-ray photoelectron spectroscopy (XPS) was found to be very difficult because of the systematic uncertainty in oxygen analysis. Electron paramagnetic resonance (ESR) and electron-nuclear double resonance (ENDOR) were tried to find unpaired electrons, but were also found to be difficult to reach a quantitative conclusion. The final identification of the oxygen vacancies is achieved by using the transmission electron microscopy (TEM) coupled to energy dispersion spectrometry (EDS) with a localized stoichiometry analysis. A TOPCON-002B scope was first used at 200 kV and 10 μA. The PWO samples were made to powders of an average grain size of a few μm, and then placed on a sustaining membrane. With a spatial resolution of 2 Å, the lattice structure of the PWO samples was clearly visible.

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Figure 14 shows TEM pictures taken for a sample with poor (left) and good (right) radiation hardness. Black spots of a diameter of 5–10 nm were clearly observed in the sample with poor radiation hardness, but not in the sample with good radiation hardness. A TEM/EDS stoichiometry analysis was carried out by using a JEOL JEM-2010 scope and a Link ISISEDS. The fine spatial resolution of this system allows a localized stoichiometry analysis in an area down to 0.5 nm diameter. Table 3 lists result atomic fractions (%) in for areas inside and surrounding the black spots as well as far away from the black spots (Matrix) (Yin et al. 1997). The systematic uncertainty of this analysis is about 15%. A clear deviation from the atomic stoichiometry of O:W:Pb = 66:17:17 was observed for samples taken inside these black spots, revealing a severe oxygen deficit. In the peripheral area, the oxygen deficit was less, but still significant. There was no oxygen deficit observed in the area far away from the black spots.

Fig. 14 TEM pictures of a PWO crystal of poor radiation hardness (left), showing clearly the black spots of φ5–10 nm related to oxygen vacancies, as compared to that of a good one (right) Table 3 Atomic fraction (%) of O, W, and Pb in PWO samples measured by TEM/EDS (Yin et al. 1997)

As grown sample Element Black spot Peripheral Matrix1 O 1.5 15.8 60.8 W 50.8 44.3 19.6 Pb 47.7 39.9 19.6 The same sample after oxygen compensation Element Point1 Point2 Point3 O 59.0 66.4 57.4 W 21.0 16.5 21.3 Pb 20.0 17.1 21.3

Matrix2 63.2 18.4 18.4 Point4 66.7 16.8 16.5

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As a comparison, the same sample after a thermal annealing in an oxygen-rich atmosphere was re-analyzed. No black spot was found. The result of the analysis is also listed in Table 3. In all randomly selected points, no stoichiometry deviation was observed. This analysis thus clearly identified oxygen vacancies in PWO samples of poor radiation hardness .

Conclusion Inorganic scintillators suffer from radiation damage with the following possible consequences: (1) scintillation mechanism damage, (2) radiation-induced phosphorescence, and (3) radiation-induced absorption. No experimental evidence has been observed for scintillation mechanism damage in any crystals studied so far. All crystals show radiation-induced phosphorescence and absorption. Radiationinduced phosphorescence increases dark current in photo-detector, and thus the readout noise. This leads to energy equivalent noise, which is low for crystals with high light yield. The predominant radiation damage effect in the crystal scintillators is the radiation-induced absorption, or color center formation. Radiation-induced absorption may recover spontaneously at the application temperature, and leads to a dose rate dependence. Thermal annealing and optical bleaching are effective for shallow color centers, but may not for deep color centers. While radiation damage induced by ionization dose is well understood, hadronspecific radiation damage in inorganic scintillators is under investigation, which is very important for future high energy physics experiments at the energy frontier. Recent data obtained at LANSCE show that LYSO and BaF2 crystals are more radiation hard than PWO under proton and fast neutron fluences up to a few × 1015 /cm2 . Additional investigation is needed to fully understand hadron-specific radiation damage. Radiation damage in alkali halide crystals is understood to be caused by the oxygen and/or hydroxyl contamination as demonstrated by a SIMS analysis. Radiation hardness of the mass produced CsI(Tl) crystals is improved by using a scavenger to remove oxygen contamination. Radiation damage in oxide crystals is found to be caused by stoichiometry-related defects, e.g., oxygen vacancies, as demonstrated by a localized stoichiometry analysis with TEM/EDS. Yttrium doping improves radiation hardness of the mass produced PWO crystals.

Cross-References  Calorimeters  Gamma-Ray Spectroscopy  Particle Identification  Scintillators and Scintillation Detectors

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Acknowledgments Measurements at Caltech were carried out by Drs. J.M. Chen, Q. Deng, C. Hu, H. Wu, D.A. Ma, R.H. Mao, X.D. Qu, F. Yang, and L.Y. Zhang. This work is supported by the US Department of Energy, Office of High Energy Physics program under Award Number DE-SC0011925.

References Auffray E, Korjik M, Singovski A (2012) Experimental study of lead tungstate scintillator protoninduced damage and recovery. IEEE Trans Nucl Sci 59:2219–2223 Auffray E, Barysevich A, Fedorov A, Korjik M, Koschan M, Lucchini M, Mechinski V, Melcher CL, Voitovich A (2013) Radiation damage of LSO crystals under γ -and 24 GeV protons irradiation. Nucl Instrum Meth A721:76–82 Batarin VA, Butkler J, Chen TY, Davidenko AM, Derevschikov AA, Goncharenko YM et al (2003) Study of radiation damage in lead tungstate crystals using intense high-energy beams. Nucl Instrum Meth A512:488–505, 530:286–292 (2004) and 540:131–139 (2005) Bilki B (2015) CMS forward calorimeters phase II upgrade. J Phys Conf Ser 587:012014 Chen JM, Mao RH, Zhang LY, Zhu R-Y (2005) Large size LYSO crystals for future high energy physics experiments. IEEE Trans Nucl Sci 52:2133–2140. and IEEE Trans Nucl Sci 54:718–724 (2007) Chipaux R, Korzhik MV, Borisevich A, Lecoq P, Dujardin C (2005) Behaviour of PWO scintillators after high fluence neutron irradiation. In: Getkin A, Grinyoveds B (eds) Proceedings of the 8th international conference on inorganic scintillators, SCINT2005, Alushta, Crimea, 19–23 September 2005, pp 369–371 Cooke DW, McClellan KJ, Bennett BL, Roper JM, Whittaker MT, Muenchausen RE (2000) Crystal growth and optical characterization of cerium-doped Lu1.8 Y0.2 SiO5 . J Appl Phys 88:7360– 7362 Dissertori G, Lecomte P, Luckey D, Nessi-Tedaldi F, Pauss F, Otto T, Roesler S, Urscheler C (2010) A study of high-energy proton induced damage in cerium fluoride in comparison with measurements in lead tungstate calorimeter crystals. Nucl Instrum Meth A622:41–48 Dissertori G, Luckey D, Nessi-Tedaldi F, Pauss F, Quittnat M, Wallny R, Glaser M (2014) Results on damage induced by high-energy protons in LYSO calorimeter crystals. Nucl Instrum Meth A745:1–6 Dormenev V, Korjik M, Kuske T, Mechinski V, Novotny RW (2014) Comparison of radiation damage effects in PWO crystals under 150 MeV and 24 GeV high fluence proton irradiation. IEEE Trans Nucl Sci 61:501–506 Gratta G, Newman H, Zhu R-Y (1994) Crystal calorimeters in particle physics. Annu Rev Nucl Part Sci 44:453–500 Hu C, Yang F, Zhang L, Zhu R-Y, Kapustinsky J, Nelson R, Wang Z (2018a) Proton-induced radiation damage in BaF2 , LYSO and PWO crystal scintillators. IEEE Trans Nucl Sci 65:1018– 1024 Hu C, Yang F, Zhang L, Zhu R-Y, Kapustinsky J, Mocko M, Nelson R, Wang Z (2018b) Neutroninduced radiation damage in BaF2 , LYSO/LFS and PWO crystals. Presented at Calor2018 conference, will appear in Journal of Physics: Conference Series, Oregon. IEEE Trans Nucl Sci 67:1086–1092 Huhtinen M, Lecomte R, Lucky D, Nessi-Redaldi F, Pauss F (2005) High-energy Proton Induced Damage in PbWO4 calorimeter crystals. Nucl Instrum Meth A545:63, 564 (2006) 164 and 587 (2008) 266 Kimble T, Chou M, Chai BHT (2002) Scintillation properties of LYSO crystals. In: IEEE NSS conference record, Norfolk, pp 1434–1437 Lecomte P, Luckey D, Nessi-Tedaldi F, Pauss F (2006) Highenergy proton induced damage study of scintillation light output from PbWO4 calorimeter crystals. Nucl Instrum Meth A564: 164–168

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Ma DA, Zhu R-Y (1993a) Light attenuation length of barium fluoride crystals. Nucl Instrum Meth A333:422–424 Ma DA, Zhu R-Y (1993b) On optical bleaching of barium fluoride crystals. Nucl Instrum Meth A332:113–120. and Nucl Instrum Meth A356:309–318 (1995) Mao RH, Zhang LY, Zhu R-Y (2008) Optical and scintillation properties of inorganic scintillators in high energy physics. IEEE Trans Nucl Sci NS-55:2425–2431 Mao RH, Zhang LY, Zhu R-Y (2009a) Gamma ray induced radiation damage in PWO and LSO/LYSO crystals. Paper N32-5 in IEEE NSS 2009 conference record, Orlando Mao RH, Zhang LY, Zhu R-Y (2009b) Effect of neutron irradiations in various crystal samples of large size for future crystal calorimeter. Paper N32-4 in IEEE NSS 2009 conference record, Orlando Melcher C, Schweitzer J (1992) Cerium-doped lutetium oxyorthosilicate: a fast efficient new scintillator. IEEE Trans Nucl Sci NS-39:502–505 Semenov PA, Uzunia AV, Davidenko AM, Derevschikov AA, Goncharenko YM, Kachanov VA et al (2007) First Study of Radiation Hardness of Lead Tungstate Crystals at Low Temperature. Nucl Instrum Meth A562:575–580, IEEE Trans Nucl Sci NS-55:1283–1288 (2008) and Paper N32-2 in IEEE NSS 2009 Conference Record (2009) T. Dimova on behalf of the CMS Collaboration. Monitoring and correcting for response changes in the CMS lead-tungstate electromagnetic calorimeter in LHC run2. Presented at the Instrumentation for Colliding Beam Physics, Novosibirsk, Feb/Mar 2017 Yang F, Zhang L, Zhu R-Y (2016a) Gamma-ray induced radiation damage up to 340 Mrad in various scintillation crystals. IEEE Trans Nucl Sci 63:612–619 Yang F, Zhang L, Zhu R-Y, Kapustinsky J, Nelson R, Wang Z (2016b) Proton induced radiation damage in fast crystal scintillators. Nucl Instrum Meth A824:726–728 Yin ZW, Li PJ, Feng JW (1997) TEM study on lead tungstate crystals. In: Yin Z et al (ed) Proceedings of SCINT97 international conference edition, CAS, Shanghai Branch Press, pp 191–194 Zhang L, Mao R, Zhu R-Y (2009) Effects of neutron irradiations in various crystal samples of large size for future crystal calorimeter. In: 2009 IEEE nuclear science symposium conference record (NSS/MIC), Orlando, pp 2041–2044 Zhu RY (1994) On quality requirements to the barium fluoride crystals. Nucl Instrum Meth A340:442–457 Zhu RY (1997) Precision crystal calorimetry in future high energy colliders. In: IEEE NSS1996 Conference Record, published in IEEE Trans Nucl Sci, Anaheim, NS-44:468–476 Zhu R-Y (1998) Radiation damage in scintillating crystals. Nucl Instrum Meth A413:297–311. And references therein Zhu RY, Stone H, Newman H, Zhou TQ, Tan HR, He CF (1991) a study on radiation damage in doped BGO crystals. Nucl Instrum Meth A302:69–75 Zhu RY, Ma DA, Wu H (1996a) CsI(Tl) radiation damage and quality improvement. In: Antonelli A et al (ed) Proceedings of the 6th international conference on calorimetry in high energy physics. Frascati Physics Series, Frascati, pp 589–598 Zhu RY, Ma DA, Newman HB, Woody CL, Kierstead JA, Stoll SP, Levy PW (1996b) A study on the properties of lead tungstate crystals. Nucl Instrum Meth A376:319–334, IEEE Trans Nucl Sci 45:688–691 (1998), Nucl Instrum Meth A438:415–420 (1999), Nucl Instrum Meth A480:470–487 (2002) and IEEE Trans Nucl Sci 51:1777–1783 (2004)

Further Reading Claeys C, Simoen E (2002) Radiation effects in advanced semiconductor materials and devices. Springer Claude L, Pier-Giorgio R (2016) Principles of radiation interaction in matter and detection. 4th edition, World Scietific

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Grupen C, Shwartz B (2008) Particle detectors. Cambridge University Press Holmes-Siedle A, Adams L (2002) Handbook of radiation effects. Oxford University Press Iniewski K (2010) Radiation effects in semiconductors. CRC Press Knoll G (2000) Radiation detection and measurement, 3rd edn. Wiley Lecoq P, Annekov A, Gektin A, Korzhik M, Pedrini C (2005) Inorganic scintillators for detector systems. Springer

Complementary Metal-OxideSemiconductor (CMOS) Pixel Sensors

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Marc Winter and Michael Deveaux

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Technology of CPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A Brief Introduction into the CMOS Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Sensing Element of CMOS Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Signal Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Noise and Noise Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Readout Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sensor Performances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Response to Photons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Response to Charged Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Performances of CPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Device Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Radiation Tolerance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ionizing Radiation Damage in CPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Non-ionizing Radiation Damage in CPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Random Telegraph Signal and Hot Pixels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Vertex Detectors Based on CPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Role of Vertex Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Technology and Integration of Vertex Detectors Based on CPS . . . . . . . . . . . . . . . . . . . . . . Summary and Perspectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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M. Winter () Department of Subatomic Physics, Institut Pluridisciplinaire Hubert Curien (IPHC), Strasbourg Cedex 2, France e-mail: [email protected] M. Deveaux Helmholtzzentrum für Schwerionenforschung GmbH (GSI), Darmstadt, Germany e-mail: [email protected] © Springer Nature Switzerland AG 2021 I. Fleck et al. (eds.), Handbook of Particle Detection and Imaging, https://doi.org/10.1007/978-3-319-93785-4_55

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Abstract CMOS pixel sensors (called CPS hereafter) have become a prominent technological option for vertex and tracking detectors composing elementary particle and heavy ion physics experiments. They also received attention for electromagnetic calorimetry. This emergence in the field finds its origin in the evolution of ASIC industry in the last decades and in the pioneering use of CPS for light imaging in the 1990s. The technology is particularly attractive as it allows for very fine-grained and thin pixelated sensors incorporating most, if not all, of the signal processing microcircuit chain. It became therefore a favorite candidate for vertex detectors and, since more recently, for larger area tracking devices. CMOS industry is not supposed to fabricate ASICs suited for charged particle detection, in particular because the latter requires a detection volume featuring low doping and a thickness exceeding typically 10 μm. However, its evolution has found a market driven by light imaging applications, which requires manufacturing parameters often adapted to charged particle detection. This chapter is intended to provide basic understanding of the technical aspects of CPS as well as the performances achieved with existing devices equipping instruments used in subatomic physics. These aspects are complemented with an overview of the trend followed by present R&D and the prospect of the technology associated with the progress of industrial ASIC fabrication. CPS are developed for a variety of experimental conditions. These may allow privileging the physics-driven performances (spatial resolution, material budget) which exploit the most prominent assets of CPS. In some other cases, priority has to be given to particularly demanding running conditions at the expense of physics-driven requirements. The first case provides the common thread of this chapter, which concentrates on applications where the CPS approach has provided a breakthrough in experimental sensitivity when compared to its alternatives such as hybrid pixel sensors and silicon strips.

Acronyms ADC ASIC CDS CMOS CPS DAC ENC FET MAPS M.I.P. MOSFET N-MOS transistor P-MOS transistor RTS

Analog-to-digital converter Application-specific integrated circuit Correlated double sampling Complementary metal-oxide semiconductor CMOS monolithic active pixel sensor Digital-to-analog converter Equivalent noise charge Field-effect transistor CMOS monolithic active pixel sensor Minimum ionizing particle Metal-oxide semiconductor field-effect transistor N-channel metal-oxide semiconductor field-effect transistor P-channel metal-oxide semiconductor field-effect transistor Random telegraph signal

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Introduction Experience with semiconducting detectors over several decades has shown that they are high-performance position-sensitive devices adapted to particularly demanding requirements. They have become unique in subatomic physics experiments when short-lived particles are to be reconstructed from their decay products. CMOS monolithic active pixel sensors (also known as MAPS, CMOS sensors, or CPS) occur as second- or third-generation semiconducting devices, on the tracks of silicon strip and hybrid pixel detectors. They surpass the performances of these established technologies with their high granularity and very low material budget, combined with the intrinsic property of integrating their readout circuitry. Unlike other semiconducting pixel sensors, CPS integrate photodiodes and data processing electronics into one compact system-on-chip (SoC). They are ASICs produced at low cost in standard CMOS factories addressing an extensive commercial market of CMOS image sensors exceeding US$ 15 billion annual revenue, which is presently dominated by the production of smartphone cameras (Clarke 2019). Photodiodes composing CPS being sensitive to light, they were identified as potential cost-effective and highly integrated alternatives to charge coupled devices (CCD) already in the early 1990s (Fossum 1993; Dierikx et al. 1997). The capability for CPS to sense charges generated by ionizing particles was also suspected, but the industrial technologies available at that time featured several properties limiting the detection efficiency and spatial resolution. First trials to realize sensors allowing to detect impacts of fast charged particles, such as protons, electrons, and pions, started in the late 1990s (Turchetta et al. 2001). With the subsequent evolution of CMOS industry, the feasibility of position-sensitive detectors for charged particles based on CPS was finally established. Customizing CPS for charged particle detection benefits from the availability of commercial standard design and production tools. A variety of complicated technological issues can be addressed with cost-efficient industrial standard solutions. On the other hand, CMOS technology is primarily intended for analog and digital electronics such as computers, portable MP3 players, vision-guided robotics, logistics, and automated guided vehicles. Building pixel detectors calls for changing the purpose of some functional units of the technology and excludes some valuable design options. Fortunately, the commercial success of digital cameras motivates industry to improve continuously its technologies, thereby adapting indirectly the fabrication parameters of CPS to charged particle detection. CPS are particularly well suited to high-precision charged particle tracking. This type of application calls for sensors with small pixels, which allow to determine the impact position of a particle trajectory with excellent precision. Moreover, the devices are supposed to be very thin in order to minimize multiple scattering of particles in the detector material. CPS are now routinely used, which feature pixel dimensions of typically 20 × 20 μm2 in combination with a thickness of ∼50 μm. Such performances are out of reach of conventional hybrid pixel sensors by factors. Because of this asset, which combines with a low power consumption and a steadily

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increasing rate capability, the technology was chosen for vertex detectors of several large experiments in heavy ion and particle physics. It was also retained to equip high-precision beam telescopes adapted to sub-GeV electron beams. Besides their use for charged particle tracking, CPS are getting used in numerous other places beyond usual light imaging. For instance, they are exploited for X-ray imaging, where they may be preferred to hybrid pixel sensors, being more sensitive to low-energy X-rays. Moreover, by sampling the flow of X-rays delivered by a source, stacked thin CPS offer the perspective of precise X-ray energy determination. CPS may also provide an excellent spatial resolution at places where traditional photographic films would provide too limited image sharpness. Because of their sensitivity to charged particles, CPS are also advantageous for detecting low-energy β-rays, even if poorly penetrating. They become therefore relevant for applications using 3 H as radiotracer and in electron microscopes.

Technology of CPS A typical CPS may be seen as composed of four major building blocks, which tend to be integrated in one single silicon chip. The first building block of the signal formation chain is the sensing element itself, which is formed from a PN-junction similar to a photodiode. The weak signal of the diode is picked up by a preamplifier, which is located inside the pixel. Next, the signal gets processed by analog circuits aiming at distinguishing the signal from electronic noise and extracting information about the signal’s properties. In case the signal exceeds a threshold, a hit is spotted. The digital information is picked up and compressed by dedicated digital circuits. Hereafter, the data is sent to the outside world by means of a digital network protocol. In state-of-the-art CPS, most of the chip is covered with pixels and thus sensitive to particles. However, some limited surface is needed to host building blocks providing the chip steering, its slow control, and the signal formatting and transfer. These functionalities encompass the data compression computer, the numerous DACs required for steering the in-pixel circuitry and matrix readout, and the clocks and drivers needed for steering and transfer purposes. As shown in the photograph presented in Fig. 1, those structures are typically integrated in a band located aside the pixel matrix. This band is not sensitive to particles and introduces therefore blind zones in the geometrical acceptance as well as extra material on the particle path. Minimizing the dimensions of this band is thus among the prominent goals of the design of a CPS, with potential impacts on its overall architecture. Ultimately, to obtain a detector system with full geometrical acceptance, one has to take care of covering the insensitive bands with the active pixel matrix of a neighboring sensor. The size of a CPS is typically restricted by the so-called reticle size of the production process. The reticle size is set by the maximum extension of the lithography masks and ranges typically from about 20 × 20 mm2 to 25 × 30 mm2 . Although larger sensors are regularly produced with dedicated industrial techniques (called stitching) (Hafiz et al. 2010), subatomic physics experiments did not yet

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Fig. 1 A MIMOSA-26 CPS (Hu-Guo et al. 2010) for charged particle tracking on a vacuum chuck. The 50 μm thin sensor is slightly bent because of inner tensions. The pixel matrix and the (left) side band hosting the supporting electronics are visible. This sensor was developed to equip a beam telescope adapted to low-energy electron beams (Rubunskiy 2012). See Table 2 for technical data. (© M. Koziel, reproduced with permission)

exploit the possibility to realize sensors exceeding the limits imposed by reticle dimensions. This may change in the near future. Some basic knowledge of the CMOS technology allows for deeper understanding of the features and limitations of CPS entering their application in subatomic physics. A brief introduction is provided in the following subsection, followed by an introduction to the properties of the sensors themselves.

A Brief Introduction into the CMOS Technology A cross section of a CMOS chip similar to a CPS is shown in Fig. 2. The processing of this chip starts from the substrate, a 4), the pixel is under recharge, and the output after CDS reads as follows: g Qs ΔU (ti , ti+1 ) = C



    th − ti+1 t h − ti exp − − exp − τ (Il ) τ (Il )

(8)

One observes that for such post-signal cases, ΔU happens to be negative. This situation occurs as a signal charge is removed by the clearing process and as the integrated removed charge is indicated. For τ  tint , the equations may be approximated as g × Qs C ΔU (ti , ti+1 ) ≈ 0

ΔU (ti , ti+1 ) ≈

If ti < th < ti+1 If ti > th

(9) (10)

Therefore, the signal charge is spotted in case a particle hit occurred between ti and ti + 1, while no signal is spotted otherwise. The condition τ  tint is typically met by well-designed, non-irradiated pixels operating at room temperature. The clearing time constant τ is given by the expression:

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τ≈

n kB T C e Il

(11)

Here, Il stands for the leakage current of the photodiode, 1 < n < 2 represents the emissivity of the biasing diode, e is the elementary electric charge, kB is the Boltzmann constant, T expresses the temperature and C the capacity of the diode. Typical values for τ exceed 100 ms, but this value may drop by orders of magnitude in case Il increases due to high temperature or radiation damage. For SB-pixels, the condition τ  tint is mandatory during the full sensor operation. Otherwise, the signal charge gets partially cleared before the pixel is actually read out, leading to a situation often misinterpreted as problems in the charge collection process. In case τ is reduced, the good operation conditions may be restored by cooling the pixel, reducing the leakage current and thus increasing τ . Alternatively, tint may be reduced by accelerating the readout. Note that there is virtually no risk to obtain a too long τ as this value is dynamically shortened in case the pixel capacity is drained by high hit rates.

Noise and Noise Optimization The magnitude of the noise in CPS is measured in units of volts but often expressed in units of electron equivalent noise charge (ENC). The unit ENC denotes the signal charge which would be required to generate a voltage signal equivalent to the measured noise amplitude. The conversion is done based on the conversion factor g/C in analogy with Eq. 3. It is particularly suited to compare the signal with the noise and to compute straightforwardly the signal-to-noise ratio (SNR) of the pixel. It is important to distinguish the noise in units of volts from the noise in ENC units as some noise reduction strategies aim at increasing the signal in voltage units created by a certain number of signal electrons, while keeping the noise in units of volts constant. If successful, one obtains the ambitioned reduction of the noise in ENC units (noise as compared to the stronger signal) although the noise amplitude measured with a voltmeter or an ADC remains constant. The noise found in CPS may roughly be subdivided into two categories, according to its associated frequency. A frequency is considered as high in this context, if it exceeds the sampling frequency 1/tint of the CPS substantially. A historically important high-frequency noise is the so-called kTC-noise. In the context of CPS with 3T-pixels, this term stands originally for the limited accuracy of the pixel reset, which turns into variations in the charge of the pixel capacitance at the start of the integration time. This fluctuation generates a dominant noise reaching typically ∼50 e ENC, which is eliminated reliably by CDS processing nowadays. The high-frequency thermal noise forms the dominant source of noise for welldesigned, non-irradiated pixels. The term reflects strictly speaking the thermal movement of charge carriers in the electronic components of the device, but it is best understood as a built-in baseline noise of the preamplifier of a CPS. In √ theory, its amplitude scales with T , where T is the absolute temperature of the

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device. Therefore, one might consider reducing this noise by means of cooling. However, this approach is rather academic as the cooling necessary to achieve the required noise suppression is often excessive. Instead, the thermal noise is minimized by reducing the capacity C of the pixel. By doing so, the signal is further amplified, while the noise in ENC units gets suppressed. Reducing C may be done by squeezing the surface of the photodiode and by diminishing the input capacitance of the preamplifier. The first of both approaches is limited by the risk of making the photodiodes too small to achieve an efficient signal charge collection. The second approach is limited to the risk of making the preamplifier input transistors too small, thereby exposing their gates to random telegraph signal (RTS see below), which may become the dominant source of noise. Still, not minimizing C turns rapidly into a high increase of the thermal noise. The detector performance is indeed degraded when employing sizable charge collection diodes in order to improve the depletion and the radiation tolerance of the sensing element (e.g., classical HV-MAPS). The shot noise is caused by the leakage current of the photodiode. To understand it, one has to keep in mind that this current is formed from individual traveling electrons and that it describes the mean value of the number of electrons (Ne ) traversing the diode within a certain interval of time. The shot noise is the statistical fluctuation of this value, and it may be described with the following expression: ΔQ = ΔNe × e = =

 

e Il (T ) tint

(3T-pixels)

(12)

2e Il (T ) tint

(SB-pixels)

(13)

Here, e denotes the elementary electric charge. The 3T-pixel and the SB-pixel behave differently as the biasing current of the SB-pixel does also contribute. As for the thermal noise, the shot noise is mostly Gaussian. Thanks to the small leakage currents of the photodiodes, which is Il  1 fA for non-irradiated diodes at room temperature, the shot noise is typically small as compared to the thermal noise. This does not hold for irradiated pixels, which may exhibit values of Il increased by orders of magnitude. As the magnitude of this current increases exponentially with temperature, modest cooling as well as a faster readout may reduce the shot noise quite efficiently. A first source of typically low-frequency noise is the so-called common mode noise. It is usually not generated within the CPS but injected from outside sources into it. It occurs, for example, if some noise is coupled to the biasing lines of the device. Common mode noise may be identified by representing graphically the pixel output signal after CDS in a 2D plot just as one would do in case of a digital photograph. In the presence of common mode noise, the photos will show patterns of multiple pixels, which exhibit a different dark level than other groups. Unlike fixed pattern noise (see below), the position of those features may change from frame to frame. Such a common mode noise can be reduced by adding decoupling capacitors at the lines through which it is injected. In case the sensor is equipped with an analog readout, one may also try to fit and subtract the patterns before doing the signal discrimination.

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As compared to the common mode noise, the fixed pattern noise (FPN) does strictly speaking not represent a noise of the CPS. Instead, it reflects a pixelto-pixel dispersion. It concretely refers to the fact that the dark output signal tends to be stable for individual pixels, while it varies from pixel to pixel. Those differences reflect the manufacturing tolerances governing the production of CMOS components. Fixed pattern noise is uniquely of concern if those constant offsets in the dark signal cannot be corrected. This applies in particular if multiple pixels deliver their signals to a common hardware discriminator, which is frequently done to comply with space constraints. The threshold setting of such discriminators is then determined by the small fraction of the connected pixel assembly featuring the highest dark signal and is thus not optimal for a majority of all pixels. FPN is of concern in most of the modern CPS designs as their compact design and high degree of integration cannot be reached without sharing discriminators or at least the DACs generating the underlying steering voltages. Therefore, FPN often represents the dominating source of noise in modern CPS. It is alleviated by subtle analog circuit design aiming to compensate the consequences of the manufacturing tolerances of the components. Summarizing, the dominant impact of CPS noise on their detection performances comes from the thermal noise, the shot noise, and potentially the common mode noise, which are injected upstream of the amplification stage. The noise from those sources is therefore amplified together with the signal and increasing the gain of the pixel does not benefit to the pixel SNR. In contrast, this remark does not hold for the fixed pattern noise and for the noise related to downstream functionalities such as the charge encoding with an integrated ADC or the signal compression.

Readout Approaches The readout of CPS exploits the assets of ASIC technology by integrating the full signal processing circuitry in the sensor. Compromises have to be made which make the readout design depart from the ideal situation where each pixel would be connected to its own readout chain. The general trend remains to select and encode the signal as upstream as possible, which turns into integrating inside each pixel a maximum of filtering and processing functionalities. The optimization of this strategy has to adapt to the pixel dimensions imposed by the required spatial resolution and to the CMOS process feature size and number of metal layers. Among others, it has simultaneously to achieve the required readout speed and power saving as well as to adapt to the specific data flow generated by each individual application. A difficulty specific to CPS follows from their thin sensitive volume, which imposes a particularly low noise front-end electronics. The readout architectures used up to now belong essentially to two categories described hereafter. The “rolling-shutter readout” is an approach privileged in earlier times when the characteristics of the available CMOS processes restricted dramatically the in-pixel circuitry, imposing to achieve the signal processing essentially on the edge of the pixel array. The evolution of CMOS industry has

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opened up the possibility to integrate sophisticated circuitry inside the pixel array, leading to the “asynchronous readout,” which can be significantly faster and less power consuming than the rolling-shutter readout. The latter preserves however the advantage of offering the smallest pixel dimensions as it incorporates an in-pixel circuitry with modest footprint.

The Rolling-Shutter Readout Scheme In traditional silicon detectors, e.g., silicon strips, each sensor cell is connected to an individual amplifier, shaper, and discriminator chain, which allows for reaching a precise timing of 10 ns. In CPS, this approach is rarely considered since placing a metal line for each pixel, if possible at all, comes with substantial drawbacks. The traditional workaround consists in connecting the output of a group of pixels, one after the other, to shared readout blocks placed at the end of a common metal line. This multiplexing allows to share those blocks, e.g., discriminators or ADCs, and thus reduces dramatically the complexity and power consumption of the device at the expense, however, of a longer readout time. The steering concept of a traditional CPS as used for imagers is shown in Fig. 5. All pixels of a column share a common readout bus and are connected to it by a switch (the select transistor M3 in Fig. 3). The state of the switch is set by the line select shift register located at the side of the pixel matrix. This register contains precisely one logical true, which closes the switch and which is shifted in the register. The state of the register is broadcasted to the pixels of a line via a shared bus. The second column selection shift register sets the state of the switches located at the end of the readout buses. As only one specific line and one specific column is selected by the registers, one specific pixel out of the several 105 pixels of a matrix is activated for readout. The disconnected pixels keep measuring and hold potential signal charge in their capacitance until they are connected to the readout bus. Due to the multiplexing, the start and end of the integration time of the pixels is delayed in accordance with the order of the readout. The delay ts of the start of a pixel integration time with respect to the start of the readout at t = t0 is given with ts = t0 +

j f

(14)

Here, j is the number of the pixel in the order of readout, and f  10 MPixel/s denotes the readout frequency. The time required for the readout is sometimes referred to as readout speed and equal to the integration time tint of the sensor, which is given with tint =

Np f

(15)

Here, NP stands for the number of pixels sharing a common readout block. For the typically NP  105 pixels of a full size sensor, one obtains a readout and integration time of tint  10 ms.

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Fig. 5 Diagram of a CPS with sequential rolling-shutter readout

The sequential readout of the pixel is referred to as rolling shutter. It may create striking artifacts once rotating objects are filmed with CPS-based video cameras. More importantly, it distributes the hit information of particles impinging the sensor simultaneously over two consecutive frames, which has to be accounted for while analyzing particle physics data. The measured hit time is determined by the start and end of the integration time of the individual pixel, and the associated resolution is equal to tint . This tint is typically by multiple orders of magnitude slower than the charge collection time of the photodiodes. The time resolution of CPS is thus determined by the readout structures.

Column Parallel Rolling Shutter The classical rolling-shutter readout is efficient but too slow to satisfy the requirements of most modern particle physics experiments. It can be accelerated by using multiple readout blocks in parallel. This reduces Np for the individual channel and thus creates a speedup factor, which scales in first order with the number of parallel readout blocks. However, the data rate expands accordingly and faces rapidly the

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limit of data transfer capacity out of the chip with a reasonable number of links. To overcome this, the data has to be compressed on the chip. The data compression is done by implementing functionalities performing CDS and hit discrimination on the chip itself. Once the data is discriminated, only information on pixels with a charge above a tuned discrimination threshold is communicated. The readout time still scales with Np , but the data rate scales now with the number of hits instead of Np . This is of strong added value as only a small fraction of pixels is hit in a CPS in most operation scenarios. A first solution for doing massive parallel readout relies on the so-called clamping pixels. Clamping pixels can be implemented in N-MOS logic in the pixel area and are thus compatible with ordinary planar standard CMOS processes. Prominent sensors of this kind are known as MIMOSA-26 and ULTIMATE in literature (Hu-Guo et al. 2010; Deveaux et al. 2011; Valin et al. 2012). The pixels of those sensors integrate analog circuits for performing pedestal correction and CDS. Their analog, CDS processed, output signal is multiplexed to a column parallel readout bus and discriminated by a unique discriminator block integrated in each column. The discriminator array is located at the end of the columns outside of the pixel matrix. Therefore, also P-MOS transistors may be used for building it without interfering with the sensing elements. The readout frequency of the individual column composing these CPS is restricted to f = 5 MHz, but operating ∼1000 processing blocks with a value of Np reduced to ∼103 allowed to reach tint  100 μs. The high data rate of ∼5 Gbps, which is delivered by the discriminators, is scanned for groups of up to four active pixels in a line. Information on such groups is packed to compact data words holding the information on the location of the active pixels. The information on dark pixels is discarded at this stage, which is also referred to as zero suppression. This zero suppression reduces the data stream by slightly less than two orders of magnitude.

Asynchronous Readout A remaining weak point of the column parallel readout consists in the fact that all pixels have to be addressed and scanned for signal charge. A natural approach to reach a further speedup consists in skipping the dark pixels and addressing only the active pixels. Doing so requires to discriminate the signal at the pixel level in order to connect to the readout system exclusively the pixels indicating a hit. Introducing a discriminator in the pixel triggers the use of P-MOS transistors. Isolating them from the sensitive medium calls for an optimized, so-called quadruple well process. These processes feature deep p-wells and are meanwhile provided by a number of commercial vendors. A prominent sensor featuring an asynchronous readout is the ALPIDE sensor (Suljic et al. 2016; Kim et al. 2016). The sensor features a full amplifier, shaper, and discriminator unit into the pixel itself. Once a global shutter signal is sent, this state of the discriminator is stored to an output buffer, and the pixel resumes measuring. The data is collected in parallel by one priority encoder per column pair. In other words, a priority encoder provides the address of an active input (e.g., pixel with hit)

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with highest priority (e.g., pixel number). The output is a list of addresses of pixels, which indicated a hit. After readout, the pixel output buffer is reset. The global shutter signal of ALPIDE may be sent by a trigger (with undetermined tint as requested by the trigger) or by internal pulsing (with tint ≈ 10 μs). The time resolution is limited by the  10 μs time-over-threshold of the in-pixel amplification chain, the ∼20 MHz (active pixels/s) readout frequency of the priority encoder, and the external communication bandwidth. In the pulsed mode, the precision of the time measurement of the pixels and the readout time are decoupled. Optimal performance for each specfic application follows from a well suited trade-off between both parameters accounting for the sensor occupancy.

Sensor Performances Response to Photons Photons with an energy above 1 keV, which are absorbed in the epitaxial layer, are reliably detected by CPS. This is as a radiation energy of 3.6 eV is required to form an e/h-pair and as a signal charge of a few 100 electrons is well enough for a reliable detection. The detection efficiency of the sensors depends on the attenuation of the X-rays in the entrance window and in the epitaxial layer. In the absence of dedicated post-processing (see below), the radiation should cross the 10μm thick sensor top layer comprising the readout circuitry before reaching the >10 μm thick epitaxial layer. For small X-ray energies, most photons are absorbed already in the entrance window. For energies 50 keV, the photons penetrate the entrance window but exhibit also a poor interaction probability with the epitaxial layer. Overall, CPS are reasonably sensitive to X-rays of at least a few keV but nearly blind to γ-rays. This γ-blindness may be exploited in specific circumstances, such as when one intends to observe weak β-radiation on top of a γ-background. Otherwise, the quantum efficiency for γ-rays may be improved – to some limited extent though – by increasing the thickness of the active volume. On the low-energy side, the detection efficiency may be improved by reducing the thickness of the entrance window to  100 nm, after removal of the substrate layer, and performing the so-called backside illumination. Such CPS are referred to as “back-thinned” CPS. The response of CPS to X-rays reflects the fact that they release their energy in a very small volume of roughly 1 μm diameter in a typically rather complex sensor topology. One may then essentially distinguish three scenarios: 1. In case the photon hits the depleted zone of the photodiode, nearly 100% of the charge carriers are collected in this diode. Moreover, in case the sensor is illuminated with monochromatic X-rays, e.g., emitted by an 55 Fe-source, the total number of electrons is known, and the corresponding signal peak in the amplitude spectrum is used to calibrate the sensor charge-to-voltage gain g/C. The peak is thus often referred to as “calibration peak.”

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2. In case, the non-depleted part of the epitaxial layer is hit, the charge is collected by diffusion and thus shared among several diodes. Therefore, the central diode of the pixel cluster receives only a fraction of the full charge. In conventional pixels, this is reflected by a sizable peak located at roughly 30% of the full amplitude. Note that nearly 100% of all electrons are collected overall, which becomes visible in case the signal of all pixels in a cluster is summed up (not shown). 3. In the third case, the hit occurs in the highly doped silicon structures nearby the epitaxial layer. In this case, a fraction of the charge recombines already in the nearby silicon, and only the remaining charge is collected. Amplitude spectra representing the response of a CPS with classical highly doped epitaxial layer and of a CPS with a (likely) fully depleted epitaxial layer are shown in Figs. 6 and 7, respectively. The spectra were recorded with X-rays emitted by a 55 Fe source, which emits dominantly 5.9 keV and some 6.4 keV photons. The peaks and features reflecting the different interaction scenarios are indicated in the spectrum in Fig. 6. By comparing the different spectra, one notes that their shape changes substantially depending on the sensor technology and the depletion voltage applied. This reflects the dramatic impact on the shape of the spectra of the share between depleted and non-depleted zones in the epitaxial layer. The energy resolution of CPS may be improved by selecting clusters which show no charge outside of the central (i.e., seed) pixel. This eliminates the uncertainty on

Fig. 6 Response of a standard CPS with a highly doped epitaxial layer to X-rays emitted by an 55 Fe source. See text. (After Deveaux 2008)

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Fig. 7 Response of a CPS with lowly doped epitaxial layer as a function of the depletion voltage of the sensing diode. As the voltage increases, the size of the depleted volume increases, which is reflected by the growing number of entries in the 55 Fe-peaks. Moreover, the diode capacity diminishes, which turns into a higher gain

the signal charge generated by charge sharing. By doing so, a remarkably good energy resolution (not FWHM) of σ  122 eV for a 8 keV Cu Kα can be reached (Doering et al. 2016).

Response to Charged Particles In thin silicon layers, charged particles (namely, M.I.P.) generate in average about 80 e/h-pairs per μm along their trajectory. This average signal is subject to the so-called Landau fluctuations. A related seed pixel amplitude spectrum of a CPS sensing ∼120 GeV/c pions is shown in Fig. 8. It was recorded with a CPS based on a 14 μm thick low-resistivity epitaxial layer and 30 μm × 30μm large pixels. The most probable value (MPV) of the charge found in this central pixel of cluster amounts to 250 e in this example. This corresponds to 25% of the summed charge found in all pixels (not shown). The seed pixel spectrum recorded appears like a Landau distribution which, strictly speaking, is folded with a nontrivial response function describing the charge sharing between the pixels. The average signal charge scales in first order with the thickness of the active volume. However, while increasing the layer thickness enhances the signal charge, it also extends the charge sharing up to a turning point where the charge collected by the seed pixel diminishes to the point where it starts to be difficult to identify. The turning point is not restrictively depending on the thickness; it is also influenced by the doping profile. The latter may, for instance, have a minimum in the middle of the layer, which gets more pronounced as the layer gets thicker. As expressed by Eq. 2, this doping minimum generates a potential minimum for signal electrons, which traps an increasing fraction of the signal as the layer thickness is increased. Another parameter influencing the effectiveness of the epitaxial layer concerns the interface between the epitaxial layer and the outer layers, in particular with the substrate. The

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24 Complementary Metal-Oxide-Semiconductor (CMOS) Pixel Sensors 1400

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15101 400.6 7447 ± 2.8 250.7 ± 0.0 63.94 ± 0.03

600 400 200 0

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Fig. 8 Signal amplitude of the seed pixel of a CPS sensing ∼120 GeV/c pions. The data was taken with a CPS featuring a 14μm thick low-resistivity epitaxial layer and 30 μm × 30μm large pixels. (From (Dritsa 2011). ©Dr. Christina Deveaux, reproduced with permission. All rights reserved)

variation of the doping in those regions impacts their reflection power (see Eq. 2). If this variation is smooth, signal electrons may be only weakly reflected, resulting in a growing fraction of charges not reaching the sensing diode as one increases the layer thickness. Summarizing, a thick epitaxial layer may have negative consequences in terms of cluster separation and single point resolution beyond a certain thickness. An optimum may thus be desirable for each application. The ratio between the pixel pitch and the layer thickness has shown to be relevant for this purpose. For instance, a thickness of about 15 μm was observed as well adapted to pixel pitches in the range 20–30μm for conventional CPS (Deveaux 2008). Thicker layers may be of advantage if the depleted volume of the sensing diodes is extendable by applying an effective depletion voltage (a few volts). The cases discussed up to now assume in general that the radiation impinging the sensor is more or less orthogonal to its detection plane. In case of inclined particle trajectories, the total signal charge generated increases due to the longer path of the particle in the sensitive volume. This increase may be estimated reliably from geometrical arguments. Charge sharing is an important input to spatial resolution. Data on charge sharing between the pixels is displayed in Fig. 9, which shows the most probable charge of the seed pixel and the neighboring pixels in a cluster. The experimental distribution may be fitted empirically with a Lorentz distribution. The width of this distribution scales in first order with the pixel pitch and remains thus constant if expressed in multiples of this pitch. This is remarkable as a random walk of the signal electrons in a non-depleted active volume should create a charge cloud with constant width in units of μm. The origin between the expected and the observed behavior of the charge cloud is not clarified. One may consider that the photodiodes modify

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Fig. 9 Response of a CPS to ∼120 GeV/c pions. The data was taken with a CPS featuring a 14 μm thick low-resistivity epitaxial layer and 30 μm × 30μm large pixels. (©Dr. Christina Deveaux, reproduced with permission. All rights reserved)

the electron density gradients by collecting charge carriers, which might cause the observed modification of the diffusion process. In case the depleted volume of the pixel is increased by using high-resistivity epitaxial layers and/or applying significant depletion voltages, the width of the signal distribution decreases. This comes with a beneficial enhancement of the signal in the central pixel, possibly at the expense of the single point resolution consecutive to a reduction of the cluster size. Here again, an optimum should be found, which depends on requirements specific to each application. CPS show in general an excellent detection efficiency for relativistic charged particles. Multiple measurements carried out, e.g., with 120 GeV/c pions and 3– 4 GeV/c electrons demonstrated that a detection efficiency amounting to 99.9% is rather easily obtained. Simultaneously, the sensors show a very low dark occupancy, which may range from 10−4 for first-generation sensors down to very low values of ∼10−8 for optimized devices fabricated with contemporary CMOS technology. The latter value is reached neglecting a tiny number of faulty pixels which may be disabled by slow control. The mean number of fired pixels in a cluster, the cluster size, amounts generally to a couple of pixels for relativistic elementary particles. At least a small fraction of clusters shows a multiplicity of one. Choosing exclusively clusters formed from more than one firing pixel comes with a great rejection power for false hit indications but also causes an efficiency drop of several percents, which is not acceptable for particle tracking. The precise values of the cluster multiplicities depend on numerous parameters, including the pixel pitch, the fraction of depleted to nondepleted active volume, and the discrimination threshold chosen. Non-depleted

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sensors with small pitch show the most pronounced charge sharing, while fully depleted sensors concentrate the signal almost exclusively on the central pixel. Measurements done with the vertex detector of the NA61/SHINE experiment (NA61/SHINE 2016) show that relativistic heavy ions generate huge clusters with a size of ∼200 fired pixels in the case of lead ions. This reflects the fact that the number of signal electrons excited by ions scales with the square of their atomic number Z, which helps to identify nuclear fragments (Spiriti et al. 2017). Note that CPS are not suited to measure the velocity of particles with Z = ±1 by means of dE/dx-measurements. This is because their particularly thin active volume generates large Landau fluctuations. The spatial resolution of standard CPS for measuring the track position is roughly found to amount σ ≈ p/10 for pixels with a pitch scaling from p = 10 − 40μm and 12 bit analog readout and σ ≈ p/5 for pixels with√one-bit digital readout. In both cases, the resolution outperforms the σ = p/ 12 resolution expected for a single square pixel with digital readout. This is as the center of gravity of a pixel cluster may be used to improve the position information. The improved resolution is also reached for the subset of clusters with multiplicity one. This happens because this kind of clusters occurs only when a particle hits the sensor in the immediate neighborhood of a sensing diode. Hits which are more distant from any sensing diode originate inevitably a higher cluster multiplicity. Note that the abovementioned values hold for pixels with partially depleted epitaxial layer. The fully depleted pixels show a substantially smaller pixel multiplicity, and their spatial resolution remains to be studied. As mentioned earlier, CPS are sensitive to β-rays. As soft β-rays are subject to an intense scattering in the sensors, they tend to create relatively large, “spaghetti”shaped clusters. Thanks to their extremely thin entrance window, back-thinned CPS were observed to be sensitive to few keV energy electrons, including beta rays emitted by tritium (Deptuch et al. 2005).

Performances of CPS CPS are extremely light and granular silicon pixel detectors, which allow for outstanding precision on particle trajectories. The particular advantage of the CPS technology consists in combining this excellent sensitivity with a high rate capability, time resolution and radiation tolerance, and a low power consumption. Alternative position-sensitive silicon detectors may outperform CPS in some of those aspects (e.g., hybrid pixel detectors show a dramatically better time resolution). However, this superiority arises with relaxed performances on the other parameters, such as the spatial resolution, material budget, and power consumption. The sensor technology may be customized within a rather wide parameter space, which allows to adapt it to a variety of measurement challenges. However, the parameters are correlated, and concentrating the optimization on one of them is likely to degrade the performances achievable with some other parameters. This section will introduce the parameter space and its correlations. For illustrative

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purposes, detection performances of some existing sensors used in heavy ion and particle physics experiments will be presented. A representative overview of the parameter range within reach with today’s CPS technology is given in Table 1. The first part covers the global sensor properties: CPS are built on initially several 100 μm thick wafers, which may be thinned down to 50 μm once the lithography is completed. Being more than 100 μm thick, sensors remain self-supporting, while thinner sensors are somewhat flexible and need external mechanical support. An entrance window as thin as 100 nm may be created by removing the substrate fully and depositing a passivation layer on the etched surface. This step creates a sensitivity for soft X-rays and low-energy β-rays but requires to fix the sensor on a thick handling wafer. Epitaxial layers of various thicknesses were tested in the past. Best M.I.P. detection performances were obtained with thicknesses of 15–25 μm. A thicker epitaxial layer may be considered, if depleted, which requires high-resistivity silicon or an access to dedicated high-voltage CMOS processes. X-rays with an energy of 300 keV will be detected reliably in case they interact in the epitaxial layer. However, a fraction of the low-energy X-rays may be absorbed in the entrance window, and a sizable fraction of high-energy photons will penetrate the thin

Table 1 Recommended parameter range of CPS as known in the year 2018 and remarks on correlations with other parameters Sensor, thickness Epi, thickness Epi, resistivity Surface Pixel size Power dissipation Operation temp. Spatial resolution Time resolution Det. eff. (M.I.P) Dark occupancy Entrance windows X-ray sensitivity Det. eff. (photons) Max. occupancy Particle rate Ionizinig rad. tol. Non. Io. rad. tol.

Min. 50 μm 4 μm 10  · cm few mm2 10 × 10μm2 40 mW/cm2

Max. 700μm > 40 μm > 10 kΩ · cm 3 × 2 cm2 80 × 80μm2 250 mW/cm2

Remark/correlation Mind material of infrastructure Best results at 15 − 25 μm High resistivity, better performance Wafer size demonstrated; see text Multiple correlations, see text. For system-on-a-chip

−60 ◦ C 1 μm < 10 μs > 99% 10−8 ∼100 nm

40 ◦ C ∼10 μm 10 ms – 10−4 Few 10 μm

Tested range Typical: ∼4 μm in both directions Determined by readout concept Typically > 99.9%. Increases with rad. damage Thin window requires post-processing

∼0.3 keV Poor

Few 10 keV > 10%

For single photon counting Determined by interaction probability

– 10 Hz/cm2 0.1 MRad < 1012 neq /cm2

1% > 1 MHz/cm2 10 MRad ∼1015 neq /cm2

For single particle detection ∼10 MHz/cm2 under design Cooling required if > 0.1 MRad Cooling required if > 1013 neq /cm2

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active medium without interacting. Both aspects restrict the detection efficiency for photons and makes it strongly energy dependent. The dimensions of individual sensors are by default limited by the so-called reticle size, which is defined by the maximum extension of the lithography masks used in a CMOS process. These limits vary from one manufacturer to another and may exceed 3 × 2 cm2 in presently available processes. Larger sensors can be fabricated with the so-called stitching technology. This approach consists in subdividing the final sensor design into elementary building blocks, each being significantly smaller than a reticle. The complete sensor layout results from the assembly of these blocks on a wafer and their electrical interconnection. Such large sensors, sometimes reaching the wafer scale, are used in light imaging devices. The extension of the concept to subatomic physics, which may be more complicated, is presently in an early exploration phase. The spatial resolution of CPS is determined by the pixel pitch p, the epitaxial layer properties, and the readout concept. In the absence of strong depletion, one obtains typically values slightly better than p/5 for sensors with binary readout and about p/10 for sensors with 12-bit analog readout. In both cases, computing the center of gravity of the signal clusters is used to improve the resolution. Studies were realized with values of p varied from 10 to 80 μm. It comes out that all those values should provide a reasonable detection efficiency if wafers with high-resistivity epitaxial layer are used. However, the signal over noise ratio (SNR) of the device, and thus the robustness of the system, diminishes with increasing pitch. For pixels smaller than 40 μm × 40μm, which are not exposed to particularly high radiation loads, a standard epitaxial layer with a resistivity of 10 Ω · cm is sufficient for a panel of applications. If needed, still better performances can be obtained with 1 kΩ · cm. To illustrate the progress achieved, one may observe that more than 10 years ago, a pitch exceeding 18 μm was required to design relatively simple digital clamping pixels (hosting O(10) in-pixel transistors) delivering a time resolution of ∼100 μs. Presently, a pitch smaller than 30 μm allows to integrate a complex priority encoding circuitry providing a time resolution of 10 μs, based on some 200 in-pixel transistors. Reducing p to improve the spatial resolution tends to increase the power consumption of the sensor because of the increased number of pixels it hosts. Power scales approximately linearly with the number of readout blocks operating in parallel and thus with 1/p, provided that only one readout block per pixel column is employed. At the same time, the number of pixels per column increases with decreasing pixel pitch. For pixels with column parallel rolling-shutter readout, this turns into a linear loss of time resolution because of the sequential row wise readout of all pixels. On the contrary, for sensors relying on a priority encoder, this dependency is diluted. However, the higher number of hits recorded by longer columns, possibly combined with an extension of the cluster size, may challenge the bandwidth of the priority encoder. Sensors with rolling-shutter readout show ab initio a small power consumption per pixel in comparison with hybrid pixels. This consumption is further reduced

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if pixels with priority encoder are employed. This is mostly as those pixels are combined with a particularly power efficient, non-clocked preamplifier. The power consumption of the sensors is of particular concern as the dissipated power has to be cooled away, resulting into specific material and complexity composing the cooling system. In general, CPS are well suited for room temperature operation, but cooling is usually required to stabilize large detector systems at this temperature. A cooling well below 0 ◦ C should be considered in case the sensors are intended to operate properly after being exposed to radiation doses above ∼100 kRad and/or few 1012 neq /cm2 . Warming up the sensors to temperatures above 60 ◦ C for about 10 hours reduces/anneals permanently a fraction of the ionizing radiation damage (Doering et al. 2011). No reliable particle measurement will be possible during this annealing phase. By reducing the pixel pitch for the sake of spatial resolution, one may also improve the tolerance to nonionizing radiation, possibly with a striking benefit (see section “Non-ionizing Radiation Damage in CPS”). The tolerance may be further improved by relying on wafers with a high-resistivity epitaxial layer. It may still gain an additional order of magnitude in tolerated fluence by depleting the epitaxial layer fully. The performances of some existing CPS, fabricated over a 20 years long period of time, are shown in Table 2. The list includes the first full size CPS designed for charged particle detection (MIMOSA-5) and the three fully developed sensors, which were, or will be, used in heavy ion or particle physics experiments. MIMOSA-5 was fabricated in a 600 nm planar process. It was subdivided into four independent blocks of 512 × 512 pixels each. The readout was performed via four analog data links, which were read with one external ADC each. This concept turned into a modest time resolution of 6.5 ms. The 12-bit resolution of the ADCs allowed for obtaining a spatial resolution of a few micrometers. MIMOSA-5 was back-thinned after its return from foundry and was successfully used to detect the soft β-rays emitted by tritium. No particular efforts were made to obtain a good radiation tolerance. The sensors of the next generation, namely, MIMOSA-26 and ULTIMATE, were manufactured in a 350 nm process. They were the first CPS used in large experiments, namely, addressing heavy ion physics. The sensors used a column parallel readout and a clamping pixel, which performs on-chip CDS and pedestal correction. Moreover, the sensors were equipped with digital circuits on the edge of the pixel array for zero suppression. The tolerance to nonionizing radiation was improved by the use of a high-resistivity epitaxial layer, while few specific measures were foreseen to harden the devices to ionizing radiation. Thanks to its limited power consumption, ULTIMATE could be operated with forced air cooling. The latest generation sensor ALPIDE relies on a so-called quadruple-well CMOS process with 180 nm feature size and a high-resistivity epitaxial layer. As this process provides for the first time the necessary features, ALPIDE integrates the discriminating block into the pixel and performs the readout with a priority encoder. This improves the time resolution substantially while reducing nevertheless the

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Table 2 Performances of existing CPS used in the vertex detector of large experiments at the RHIC and the CERN-SPS and -LHC as compared to the first full size technology demonstrator (MIMOSA-5) used for beam monitoring in hadrontherapy (SUCIMA EU project) and various imaging applications. The power consumptions indicated correspond to specific sensor’s applications. They may vary according to the sensor application targeted Provider Year Technology Epitaxial layer User Pixel Pixel size Spatial resolution Time resolution Discriminator Readout Power dissipation Max. data rate Ionizinig rad. tol. Non. Io. rad. tol. a b

MIMOSA-5 IPHC 2001 AMS 0.6μm Low res. SUCIMA

Ultimate IPHC 2011 AMS 0.35μm High res. STAR

ALPIDE CERN 2017 Tower 0.18 μm High res. ALICE

1024 × 1024 17 × 17μm2 2μm 6.5 ms External ADC RSa N/A

MIMOSA-26 IPHC 2008 AMS 0.35 μm High res. EUDET NA61/SHINE 1152 × 576 18.4 × 18.4μm2 3.1 μm 115.2 μs End of column RS col. parallel 250 mW/cm2

960 × 928 20.7 × 20.7μm2 3.8 μm 185.6 μs End of column RS col. parallel 160 mW/cm2

1024 × 512 29.2 × 26.9μm2 ∼5 μm 10 μs In pixel Priority encoding 35 mW/cm2

4 × 40 MHzb ∼100 kRad < 1012 neq /cm2

160 Mbps 150 kRad > 1013 neq /cm2

320 Mbps 150 kRad > 1013 neq /cm2

1 Gbps > 500 kRad > 1013 neq /cm2

Rolling shutter Analog readout

power consumption. ALPIDE may be operated autonomously but is also equipped to react to an external trigger. Its tolerance to nonionizing radiation is ensured by combining a high-resistivity epitaxial layer with a few volt depletion voltage. As expected from its relatively short readout time, its tolerance to ionizing irradiation came out to improve by one order of magnitude the tolerance observed with previous sensors.

Device Modeling Each application of CPS calls for an optimization of their design accounting for specific, often conflicting, requirements while optimizing simultaneously the design of the detector on which the sensors will be assembled. Software tools have been developed for this purpose, which simulate most aspects of the functioning of CPS and may be incorporated in the global simulation program of an experimental setup. The latter relies on the technological standard for computing the propagation of particles through detectors, i.e., the so-called GEANT software package.

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The GEANT package includes the necessary databases on the (decay-) properties of elementary particles produced in collisions and on their interaction with matter. It is complemented with a dedicated software simulating the sensor response, which embraces a sequence of functional steps, ranging from the generation of signal charges to the distribution of hits occurring in the sensor array within a readout cycle. The simulation of the sensor response starts from the information on the particle impact in the sensitive volume of the CPS impinged. This software is often referred to as digitizer. Its simplest approach consists in doing a Gaussian smearing of the hit position delivered by the GEANT software. This is obtained by shifting the original impact position of the particle in the sensitive volume according to random numbers taken from a Gaussian random generator. The advantage of the concept consists in its simplicity; however, effects like dark hits, limited detection efficiency, the merging of hit clusters, and radiation damage are not accounted for. This may be improved with simulation models which try to reproduce the effective field map followed by the signal electrons inside the epitaxial layer toward the sensing nodes. While this approach is well adapted to sensors featuring a fully depleted sensitive volume (as explained later in this section), cases where the epitaxial layer is only partially depleted cannot be reproduced. On the other hand, the alternative approach consisting in simulating individual paths of signal electrons with first principles (Bichsel 1988) through parts of the epitaxial layer free of depletion gets too time-consuming to be considered, facing moreover the lack of knowledge of the epitaxial layer detailed characteristics. A compromise was adopted, which consists in first parametrizing the response of real sensors featuring various pixel pitch values and epitaxial layer properties, exposed to charged particles. This parametrization is next used to simulate the response of any given sensor according to its pitch and epitaxial layer (Dritsa 2011). Such a model may incorporate a parametrization of the Landau distributed signal amplitude spectrum as obtained from the summed amplitude of all pixels in a cluster. Random numbers from this distribution are used to estimate the energy deposit in the detector material in units of excited signal electrons. This approach is preferable with respect to using the energy deposit information provided by GEANT as the latter refer to the passage of the particle through the thickness of the full silicon volume, while only the thickness of the epitaxial layer has to be considered. Naive scaling turns into a correct mean value of the signal but underestimates the fluctuation. The signal of inclined tracks may be approximated by scaling the random number with the modified length of the trajectory in the epitaxial layer, which tends to overestimate (moderately in most cases) the Landau fluctuations for large angles. The charge is distributed among the pixels in a cluster based on the measured width of the clusters distribution as displayed in Fig. 9. To do so, the particle trajectory in the epitaxial layer is subdivided into a series of segments, and the charge is distributed uniformly among them. The charge and location of the segment define the amplitude and center of the cluster distribution function, while the charge arriving at the pixel is obtained from reading the function at the pixel diode center

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position. The charge obtained in the pixels from the individual segments is next added up. Fine-tuning of the cluster distribution function starting from the measured values is sometimes needed to obtain satisfactory results. The pixel signal obtained is modified by a Gaussian noise in a last step. This parametrization of the sensor response provides reasonably good results in a reasonably short computing time. However, it imposes to have access to measured sensor responses. Recently, an approach has emerged (Spannagel et al. 2021), which combines electrostatic field simulations with Monte Carlo methods in a sequential process. First, the field inside the sensor is generated with a dedicated finite element software (TCAD). Next, the signal charge creation and the movement of the individual signal electrons are simulated by a software accounting for their random walk and the micro-drift fields. Unlike the approaches mentioned earlier, this model turns out to be sufficiently precise to even simulate the complex response of CPS to X-rays. However, it comes with substantial overhead in terms of computing time. The latter is nevertheless still much faster than a simulation model sticking to first principles only, which would require to simulate the movement of individual signal electrons in the nontrivial electrical potential of the epitaxial layer.

Radiation Tolerance As a direct consequence of their exposure to particles, CPS undergo radiation damage during their operation. The capability to withstand this undesired effect is a decisive feature of the detectors and does typically limit both their lifetime and their rate capability. The radiation tolerance of CPS was initially modest as compared to other silicon counters, which gave the impression that the technology may be intrinsically radiation soft. This image stands somewhat in contrast to the fast progresses in the field, which are driven by the increasing availability of optimized CMOS processes and are summarized in (Deveaux 2019). Radiation damage in CMOS devices can be subdivided into two major categories, which are denoted as ionizing and non-ionizing. Both terms are also used in the context of radiation protection and life science with different meaning. The definition in the context of nuclear instrumentation is as follows: Ionizing radiation damage follows from a displacement of electrons from the electron shell of their atoms. This generates the wanted free signal electrons and is mostly reversible inside silicon. However, it also creates so-called surface damage at the interfaces between the silicon and the frequently used SiO2 structures. Most ionizing damage is caused by photons and charged particles with an energy above roughly 10 eV. The energy deposit of ionizing radiation is measured in the SI-unit Gray (1 Gy = 1 J/kg) or the outdated unit 1 Rad = 0.01 Gy. Surface damage consists in the generation of defect states in the band gap of silicon nearby the interface. Those tend to ease the thermal generation of free charge carriers, which may inject, possibly sizable, leakage currents toward the photodiodes. Moreover, permanent charges are built up at the interfaces (Schwank et al.

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2008). These, typically positive, charges generate electric fields, which superimpose to the steering fields of FET and modify their characteristic response. This effect is referred to as threshold shift and has the potential to disable electronics. The surface charge may however be reduced by thermal annealing. In few nm thick silicon structures, the charge is neutralized by opposite charge carriers tunneling into the isolator (Saks et al. 1986). As their gate oxide is that thin, sizable transistors such as those manufactured in 0.35 μm CMOS processes are considered as reasonably radiation hard. Non-ionizing radiation damage is by definition created by interactions between the radiation and the nuclear core of atoms. In case of an energy transfer of 25 eV, silicon atoms are displaced from their position in the crystal lattice (Lutz 1999). The related crystal defects are referred to as bulk damage. A substantial momentum transfer is required to transfer the energy. Therefore, non-ionizing radiation damage is created preferably by heavy particles like heavy ions and hadrons and to a smaller degree by fast electrons. Photons, namely, soft X-rays, create only marginal bulk damage. The precise damage generated by a particle depends on its nature and energy. Within the non-ionizing energy loss (NIEL) model (Vasilescu et al. 1997), the damage is normalized to the damage caused by a 1 MeV neutron. The related unit is 1 neq /cm2 . Energy-dependent normalization factors are available in literature and plotted in Fig. 10.

Fig. 10 NIEL per particle for different particle species (Data from (Vasilescu and Lindstroem 2000))

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Bulk damage eases the thermal generation of minority charge carriers and thus increases the leakage current (Lindstroem et al. 2003). Moreover, the defaults created in the irradiated silicon crystal may trap signal electrons before they reach the sensing diode, which is expressed as a decrease of their average lifetime (Kramberger et al. 2002). Finally, bulk damage may absorb both the initial p- and n-dopants found in moderately doped silicon and build up in parallel defect states, which act as effective p-doping (Mandic et al. 2017). Within the NIEL model, it is assumed that all radiation damage scales with the radiation dose. This assumption is seemingly not fulfilled for thermal neutrons impinging p-doped CPS. This is likely as the fission reaction n +10 B →7 Li + α + Ekin cannot be neglected (Linnik et al. 2017).

Ionizing Radiation Damage in CPS Ionizing radiation damage in the sensing element of CPS manifests itself typically as an increase of the leakage current of the sensing diode. This expansion may reach three orders of magnitude, e.g., going from ∼1 fA to ∼1 pA per diode after a dose of 1 MRad (Deveaux et al. 2005). Simultaneously, the pixel-to-pixel fluctuations of the leakage current increase. As the leakage currents are thermal, both effects can be alleviated by moderate cooling. High leakage currents may fully discharge the pixel capacity of 3T-pixels prior to the readout and thus saturate the pixel. Moreover, the dark signal of the pixel gets shifted, which may conflict with the range of the amplification stages. More importantly, the shot noise of the photodiode increases. Knowing that the leakage current is formed from N electrons passing the photodiode within a √ certain time interval, this noise can be considered as the Poisson fluctuation ΔN ≈ N of this electron flow. This fluctuation adds to the high-frequency noise of the pixel and may relatively rapidly reach a worrying magnitude. As N scales with the integration time, shortening the latter as well as reducing the leakage current by cooling may reduce the shot noise. SB-pixels do not saturate as the leakage current increase is compensated by a corresponding recharge current growth. However, the dark signal of the pixel is shifted and shot noise is added. Moreover, the clearing time constant τ of the pixel (see Eq. 11 in section “Signal Encoding”) is reduced in proportion of the current increase. This effect tends to constitute the most limiting factor for the radiation tolerance of SB-pixels and related advanced pixels. Already after a dose of a few 100 kRad, τ may come close to the integration time of the pixel, and a significant fraction of the charge may be cleared prior to the pixel readout. Again, accelerating the readout and reducing the leakage current by means of cooling alleviates the effect. Intrinsically, the radiation tolerance of CPS is reasonably good. This holds in particular if guard rings are employed to reduce the radiation-induced leakage current increase (Deveaux 2008). However, enclosed transistors may be ten times

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larger than non-enclosed ones, which can impact the pixel dimensions at a degree conflicting with the required spatial resolution. Simple imagers featuring a typical integration time of O(1) ms exposed to an integrated dose of 10 MRad were observed to still exhibit S/N values at room temperature which complied with charged particle detection requirements (Doering et al. 2014). More sophisticated and faster sensors, which incorporate data processing circuitry, like on-chip discrimination, show so far a tolerance to a few MRad at room temperature. It is worth noting that such a level of tolerance does not require enclosing any transistor, thereby avoiding undesired impacts on the pixel size.

Non-ionizing Radiation Damage in CPS Elder CPS, based on highly doped epitaxial layers, collect their signal charge slowly (typically ∼100 ns) by means of thermal diffusion. This makes the devices vulnerable to the radiation-induced reduction of the minority charge carrier lifetime. Starting from a dose of few 1011 neq /cm2 and above, the lifetime of the signal electrons shortens such that the electrons recombine before being collected by the photo diode. Consequently, the collected signal charge decreases (Deveaux et al. 2007). Once the S/N diminishes below ∼10, the detection efficiency for charged particles starts to drop rapidly. The spatial resolution tends to degrade as well, though relatively mildly, as a consequence of the cluster size reduction. The radiation-induced signal loss is found to be essentially independent of the temperature in practical terms. It may be alleviated significantly by shrinking the pixel pitch, as it shortens the distance between the position where a minority charge carrier is created and the charge collection diodes, thereby also accelerating the charge collection. As shown in Fig. 11, CPS manufactured in a 350 nm CMOS technology are tolerant to a few 1011 neq /cm2 up to ∼1013 neq /cm2 , depending on the pixel pitch. The charge collection time may be further shortened by depleting the epitaxial layer, at least partially. Reducing the doping of the epitaxial layer as done in HR-MAPS increases the depleted depth of the diode to a few μm, which accelerates the charge collection dramatically and increases the radiation tolerance by one order of magnitude (Dorokhov et al. 2010). Pixels with a pitch of up to 80 μm realized with this technology have been operated successfully. Adding a high voltage as done with HV-MAPS and depleted MAPS allows to reach a full depletion, and the charge collection becomes sufficiently fast to tolerate non-ionizing doses of ∼1015 neq /cm2 (Doering et al. 2015; Benoit et al. 2017; Pernegger et al. 2017). The leakage currents of CPS are increased by bulk damage and scale according to the expression: ΔI = α(T ) · Φ · V

(16)

Here, Φ represents the NIEL in units of neq /cm2 , and the scaling factor α(T ) depends exponentially on the temperature. It is usually given for T = 20◦ C and amounts to α(20◦ C) = 4.0 × 10−17 A/neq /cm and is subject to thermal annealing

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Fig. 11 Tolerance of MIMOSA-series CPS to non-ionizing radiation doses as a function of√the effective pixel pitch and of the epitaxial layer properties. The effective pitch is defined peff = A with A the pixel surface. The measurements were made with partially depleted imaging sensors featuring an integration time of 100 μs. Sensors were considered as radiation tolerant if a S/N >15 for β-rays was observed and if moreover no significant losses in the relative counting rate were observed. The sensors were cooled to appropriate temperatures of down to −60 ◦ C to suppress shot noise. Shaded areas reflect the measurement’s uncertainties, which are given by the irradiation steps and dosimetry uncertainty. Pipper-2 is the only fully depleted sensor used for the measurements. Arrows state that the sensor resisted to the highest dose applied or failed at the lowest one. See Deveaux (2019) and references therein for further details. (From Deveaux 2019. ©IOP Publishing Ltd and Sissa Medialab. Reproduced by permission of IOP Publishing. All rights reserved)

(Lindstroem et al. 2003). V stands for the depleted volume of the photodiode. It is worth mentioning that the non-depleted active volume of the diode of partially depleted CPS pixels does not contribute. As for ionizing radiation, the increase of the leakage current adds shot noise and accelerates the clearing of SB-pixels. The effect may be alleviated by cooling and fast readout, but it is worsened by increasing the depleted volume of the pixel. Besides the leakage current, a radiation-induced increase of the effective p-doping of the epitaxial layer, which complicates the depletion of the sensor, appears as another limiting factor.

Random Telegraph Signal and Hot Pixels A particular source of pixel noise is the so-called random telegraph signal (RTS). RTS manifests itself as a fluctuation between two steady states in the dark signal of

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the pixel. By plotting the dark signal over time, one observes a rectangular signal with fixed amplitude but random period length, which appears indeed like a random digital (telegraphic) signal transmission. The period of the signal may be very long and reach several minutes. RTS has been attributed to the presence of a local crystal defect, which may change its charge state by accepting or emitting a single electron. Being located at a crucial (likely high field) position in a diode or transistor, the field may modulate an external current source. As long as the properties of this source remains unchanged, the modulation generates discrete states, which would reflect the quantum charge states of the crystal defect. In CPS, the sensing diode of the pixel and the transistor composing the first stage of the in-pixel amplifier are found particularly vulnerable to RTS (Virmontois et al. 2011). RTS in diodes acts on the leakage currents of the diodes. It is known to be caused by bulk damage or, to a smaller extend, by surface damage. The amplitude and the frequency of the modulation increases with temperature. Once the RTS signal switches to the high state in 3T-pixels, the affected pixel collects more charge within its integration time tint . If this charge exceeds the discrimination threshold, a fake hit is generated. This process is repeated until the RTS signal switches to the low state, which may require a significant time. Consequently, affected pixels indicate a typical excessive number of consecutive fake hits with similar signal amplitude. The number of fake hit indications may be suppressed by reducing the RTS amplitude by means of cooling or of shortening tint . Both measures reduce the integrated charge and may push it again below the threshold. Note that after irradiation, most pixels show RTS, but few are affected to an extent, which is sufficient to generate fake hits. Therefore, one may consider masking these without any significant loss of detection efficiency. The diodes of SB-pixels are as well affected by RTS, but their internal leakage current compensation follows and attenuates the RTS modulation to a large extent. Fake hit indications are to be expected at the edges of the rectangular RTS signal. Here too, one may rely on cooling to deem the RTS frequency and therefore to reduce the number of fake hits. RTS in the input transistor of the preamplifier generates as well two levels in the current traversing the transistor. However, once CDS has been applied, one observes three voltage levels representing the steady state (no matter if high or low) and the two edges of the signal. This RTS is a known short channel effect of transistors and occurs predominantly if the surface of the transistor gate is designed too small. As of today, transistors are being designed carefully to minimize risks of RTS with fully satisfactory results.

Vertex Detectors Based on CPS CPS are particularly relevant for those components of an experiment which govern the reconstruction of charged particle trajectories. This task has four interconnected objectives: the reconstruction of the track origin, the selection and interconnection

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of the hits belonging to a track, and the determination of the particle momentum and electric charge. Most experimental setups dispatch these functionalities between trackers and a vertex detector. The performances of vertex detectors have notably improved with the emergence of CPS, while their impact in characterizing collision final states has grown in importance.

Role of Vertex Detectors Vertex detectors are most essential for finding the origin of tracks and determining the momentum of the softest ones. They are placed as close as possible to the beam interaction point (IP) in order to maximize their track extrapolation capacity toward the IP. It follows that they are particularly exposed to beam-related background and face a very high hit density. These conditions make granularity and material budget their driving design parameters. In this context, CPS appear as a particularly attractive technological option for the charged particle-sensitive components of subatomic physics experiments. Vertex detectors are prominently used to reconstruct trajectories of secondary particles originating from the decay of short-lived mother particles decaying nearby the IP before reaching the detector. A typical example is the so-called open heavy flavor production. This term denotes particles which are typically composed from a light quark and one s-, c-, or b- quark. Those particles decay after a short flight which may not exceed a few hundred micrometers. Reconstructing their production from their daughter particles appears as a unique way to identify them and determine their properties. Once identified, the kinematics of the daughter particles originating from a common decay vertex are determined, and their mass, energy, electric charge, and momentum are combined to derive the properties of the mother particle. A central kinematic parameter used to identify the mother particle is its rest mass, derived from the four-momenta of the decay products. In practice, the data analysis requires first reconstructing the trajectory (socalled track) and momentum of all charged particles produced in each collision. Next, tracks are extrapolated back to the beam line, and their origin is searched for. A large majority of the tracks intersects at a common intersection point. The latter is identified with the primary vertex, and the corresponding tracks may be discarded from the analysis. Intersection points of individual tracks which are located significantly away from the primary vertex are identified as originating from a decay vertex of an invisible mother particle of interest, decaying before reaching the vertex detector. This is illustrated by the decay topology of the open-charm particle sketched in Fig. 12. The related tracks are identified as daughter particles and retained in the analysis. To separate the primary and secondary vertices reliably, the trajectories of all particles have to be measured with utmost precision. Vertex detectors are central for this task. Their precision is primarily limited by the finite precision of the measurement of the particle impact position in the detector and by the so-called multiple Coulomb scattering of the particles in the detector material which disturbs

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Fig. 12 Reconstruction concept for short-lived particles for a detector in a fixed-target topology. A primary beam of high energy particles impinges a target and creates particles. A decay D 0 → K − + π + is shown in front of a background made of a primary K − and π + in the example. The real number of primary K − and π + may reach several 10 to 100 in heavy ion collisions

their trajectories. The effect of the latter increases with the distance to the IP of the first measured hit in the detector. Consequently, vertex detectors are supposed to feature three mandatory outstanding properties: • Excellent resolution on the particle impact point • Minimum material intercepting the particle trajectories • Minimum distance to the IP With respect to more conventional silicon detector technologies, CPS show exceptionally good performances in this field. This follows from their modest thickness (50 μm instead of few 100 μm), which minimizes multiple Coulomb scattering, and from their tiny pixels (∼10 μm instead of ∼100 μm for other devices), which allow for a very accurate position measurement. Simultaneously, the radiation tolerance and rate capability of CPS improved continuously up to now, which allows to place them near the interaction point even in high-rate experiments. As a consequence of those assets, CPS have been identified as the prominent technology for achieving open charm measurements in heavy ion physics as well as heavy flavor-related studies in the future lepton-collider experiments such as at a Higgs factory.

Technology and Integration of Vertex Detectors Based on CPS Detectors in particle and heavy ion physics are typically larger systems, which are composed of multiple sensors. Integrating the individual sensors into a running system forms a science on its own. The basic requirement for a successful integration is to hold the sensor mechanically, to bias it, and to evacuate the data. Moreover, the power dissipated by the sensor has to be cooled away. Dedicated instances for slow and fast control of

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Fig. 13 Five out of ten sectors of the STAR pixel detector (so-called half-barrel). Each sector is made from a carbon fiber structure, which also serves to guide cool air. Groups of 10 CPS are glued and bonded each on a flex print cable used for readout. Three overlapping groups per sector are mounted at the outer radius of each sector. One additional group is placed at the inner radius (not visible here). One readout and biasing card per group is visible in the background (right side). The detector is held on one side only (right side) by a mobile support, which allows a fast replacement of the detector. One bolt per sector at the front side serves as guiding pin ultimately locking the detector in fixing holes, thereby ensuring the necessary mechanical stability of the detector. (© 2010 The Regents of the University of California, through the Lawrence Berkeley National Laboratory)

the sensors have to be foreseen. Finally, the sensors have to be synchronized with each other and with the detector system. The solution found has to fulfill physicsdriven requirements on spatial resolution and material budget while complying with running condition-related requirements on radiation tolerance and rate capability. CPS are self-supporting down to a thickness of 100 μm. When thinned to 50 μm, they become flexible and tend to bend due to inner stress. 50 μm thin sensors should not be transported with the popular Gel-Paks® as they cannot be released from those packs. Despite such thinned sensors tend to crack, they may be placed and glued reliably on flat surfaces by means of appropriate vacuum holding tools. This can be done with a ∼20 μm precision using specific manual tools and even more accurately with dedicated placement machines. 50 μm thin sensors may be spanned above a cutout in the support in order to suppress the material budget of the detector plane locally to that of the sensor, a practice allowing to use CPS in beam telescopes installed on low-energy electron beams. The material budget of CPS is remarkably small when compared to the budget of their entire infrastructure. To obtain the lightest possible system, the contributions

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Table 3 Selected properties of carbon materials used for the integration of vertex detectors based on CPS. Note that the numbers for carbon fiber and in particular of carbon foam may vary depending on the precise composition/density Density (g/cm3 ) Rad. length X0 (cm) Heat cond. (W/m/K) Cost Shaping Conductive grainsd Surfaces size Thin layers Mech. robustness

Carbon fiber 1.5 25.0 17/12a o ob No ++ + ++

Carbon foam 0.38 113.0 70 + + Yes + −− −−

TPG 2.26 19.0 1500/20a + + Yes + – o

CVD diamond 3.52 12.2 2000 −− −−c No 4" Wafer ++ ++

a

Along/perpendicular to plane or fiber direction Specialized know-how and tooling required c Cannot be cut with conventional tools. Shaping by manufacturer possible d Material may break into conductive grains Legend: ++ Best suited, − − Most problematic b

from holding structures, cooling, and cabling have to be minimized. Existing solutions for building light holding structures rely on carbon materials, which are both stiff and light and may feature a heat conductivity comparable to copper, possibly better. The properties of some relevant materials are listed in Table 3. Various solutions to integrate CPS into light holding and biasing structures are shown in Fig. 14. They rely on supporting structures (called ladders or staves) which are made from carbon fiber in the case of air or water cooling. The sensors are assembled on the supports, which also guide the coolant flow. To avoid dead zones in the geometrical acceptance of the detector, the positioning of the ladders in a detector layer should ensure that the insensitive peripheral area of each sensor overlaps with the pixel array of a sensor hosted by a neighboring ladder. The sensors are wire bonded to flex print cables, which provide the necessary electrical connections. Care should be taken when arranging the sensors and the cables to minimize the distance between the sensors and the coolant, thereby maximizing the cooling efficiency. A specific solution is needed if the sensors are to be operated in vacuum since no air cooling may be envisaged and as low mass micro-pipes for liquid cooling may be too fragile. Alternatively, the sensors may be mounted on a support made from highly heat conductive material (TPG, CVD-diamond). This support evacuates the heat toward a liquid cooled heat sink located outside the acceptance of the experiment. The necessary overlap between the sensors is ensured by placing sensors on both sides of the cooling support (see right hand side of Fig. 14). This concept is particularly well suited to fixed target experiments. Despite being based on double-sided detector layers, it exhibits a material budget of 0.3% X0 per layer, i.e., substantially less than anything

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Fig. 14 Different concepts of integrating CPS in a ladder structure. A system relying on air cooling (left; see also picture in Fig. 13) places the sensors on the cable in order to maximize the heat transfer from sensors to air. The holding structure is made from carbon fiber and guides the air flow. In case of water cooling (center), the heat is distributed by the carbon fiber support. In the vacuum compatible system (right), the heat is evacuated from the sensors by a highly heat conductive support (CVD-diamond or TPG) and conducted toward a robust, liquid cooled heat sink located outside the acceptance of the detector

achievable with conventional detectors. The low power consumption of CPS is a key feature for this achievement. Besides the occasional use of decoupling capacitors, no components are required on the cable itself: The sensors process their data on-chip and drive the digital data obtained directly to receivers outside the acceptance. However, the ohmic losses of the power and mass lines have to be considered with care. This holds in particular in case the sensors change their power consumption with time, e.g., as a reaction to data load. The sensors are steered by means of FPGA-boards, which are located outside of the detector fiducial volume. While most sensors are pushing their data out, the boards must feature a sufficient processing power to handle the incoming data stream without delay. Moreover, they have to handle potential failures or overload of the more downstream data processing instances by rejecting data in a controlled way. Operation experience shows that CPS are moderately vulnerable to latch-up. This reversible short circuit occurs, once parasitic thyristors found in the chips are switched to their conductive state by the charge of a heavily ionizing particle like a slow heavy ion. Thin sensors are found more vulnerable to this type of events than thick ones. Persisting latch-ups were observed to provoke a thermal destruction of the sensor. A latch-up can be stopped by an early detection of the induced current excess, followed by an immediate power cut, before restarting the sensor. Microcircuits performing this task should be integrated into the biasing system of the sensor. In fact, the sensor design layout can be optimized to deem latch-up risks. The strategy consists in avoiding too short distances between circuit elements. Advanced simulation tools associated with the CMOS process used to fabricate a sensor come out to be very helpful for finding out those parts of the circuitry which may be vulnerable to latch-up.

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Summary and Perspectives This chapter provides an overview of the monolithic CMOS pixel sensor technology, showing its advantages in terms of spatial resolution, material budget, and power consumption. The chapter concentrates on those applications where these assets are most essential, would it be at the expense of time resolution and radiation tolerance. CPS are particularly well adapted to vertex and tracking detectors of large experiments intended for heavy ion or particle physics. Those detectors are essential for identifying short-lived particles decaying before reaching the detector, as they allow for a highly accurate reconstruction of their daughter particles generated in the decays. The role of CPS has therefore increased with the rising importance of flavor tagging in an enlarged spectrum of experimental programs. For these applications, CPS constitute a state of the art for the silicon pixel detector technology. They are well suited for charged particle detection but also attractive for their sensitivity to soft X-rays. As a consequence of their small pixel size and minute thickness, a spatial resolution of a few μm and a material budget of 0.05% X0 are easily achieved. The radiation tolerance of the sensors faces the smallness of the signal generated by impinging particles in the thin sensitive epitaxial layer; it has nevertheless improved significantly with the emergence of high-resistivity epitaxial layers. As of today, values as high as several 1014 neq /cm2 and 1 MRad are reachable at room temperature without compromising the spatial resolution and material budget performances. The sensors’ time resolution is restricted by the readout concept and the priority given to power saving, thereby privileging the material budget suppression. Values 10 μs are reachable with established sensors, which comply with demanding spatial resolution and material budget requirements, and provide a hit rate capability exceeding 10 MHz/cm2 . Besides the dominating trend of designing CPS privileging spatial resolution and material budget, CPS may alternatively be designed for applications which are most demanding in terms of readout speed and radiation hardness, at the expense of spatial resolution and power saving. Such developments are underway but did not yet reach a degree of maturity allowing to use them in an experiment. There is every prospect that CPS will continue evolving toward higher particle detection performances, mainly as a consequence of industrial progress. Besides the latter, accessing a wider panel of existing commercial CMOS processes and establishing a contact with foundries ready to customize their process in some extent (e.g., optimal epitaxial layer doping profile) would already allow going significantly beyond present detection performances. Despite these access limitations, the general trend is that the situation improves continuously. There are thus serious reasons to expect significant performance progress, would it be because of the steady decrease of the feature size or from microtechniques allowing to stack several chips in a single multitier unit, etc.

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An emblematic source of spin-offs from industrial evolution lies in ASIC production, which drives a constant push for miniaturization of integrated circuits. CMOS foundries also extend steadily the possibilities of stitching, which allows for wafer-scale sensors. Once thinned to a few tens of microns, such large sensors may be curved according to a cylindrical surface, with a sizeable gain in stiffness. A few sensors only are then required to equip a complete detector layer, with a drastic suppression of mechanical support material consecutive to the disappearance of overlaps between neighboring detector modules. This concept is already getting shaped by the ALICE collaboration, which targets a vertex detector upgrade (Mager et al. 2019). Maximum benefit is expected for the innermost detector layer, where the beam pipe may act as a mechanical support. Stitching is already available in the 180 nm process used to fabricate current sensors (e.g., ALPIDE). It is also accessible in a forthcoming 65 nm imaging process investigated for the purpose of future charged particle detectors equipping heavy ion and particle physics experiments. The process is expected to allow improved spatial resolution resulting from reduced pixel dimensions. It is also appealing for very brief charge collection and signal processing times, offering perspectives of time resolutions well below 1 ns. Power reduction is also awaited from the lower, 1.2 V supply voltage, as compared to the 1.8 V used in a 180 nm process. Overall, the evolution toward 65 nm CMOS processes is particularly promising and should open up new performance standards for a variety of tracking devices. Another promising R&D direction addresses the realization of two-tier chips interconnected at the pixel level through industrial high-density micro-bonding techniques, with marginal increase of the sensor material budget. This type of chip architecture allows to distribute the analog front-end and the digital circuitry of a pixel among two different chips being ultimately tightly interconnected at the pixel level with minor extra material introduced by the bonding. The two chips may actually be manufactured in two different processes. This evolution serves the reduction of the pixel size and thus improves the spatial resolution. It may also enhance the data compression capability through increased sophistication of the circuitry and therefore suppress the data flow delivered by the sensor to the outside world. Finally, one may also mention more futuristic technical goals, such as wireless communication or micro-channel cooling, which already exist per se but were never integrated in CPS. The first of both technological advances would benefit to material budget suppression by alleviating the impact of the flex cable used to steer the sensors and read them out. The second technology would allow cooling the sensor in its bulk, which would alleviate the material budget of the cooling system. Alternatively, one may increase the current in the pixel array in order to improve the time resolution and readout speed or the in-pixel data processing capability. It is worth noticing that the attraction power of industrial CMOS industry irrigates also other charged particle sensing technologies, such as LGAD (low-gain avalanche detectors) and SoI (silicon on insulator) pixel sensors. The latter tend

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to integrate CMOS components and doping structures which ease their detection efficiency, radiation tolerance, and fabrication cost. This trend illustrates how powerful CMOS technology can be for particle detectors as well as the dynamics of their potential, driven in particular by the steady extension of the market of highly integrated imaging devices. Provided this trend will persist, CPS will continue push back the limits of their achieved performances and get progressively well suited to a wider panel of applications, which may go beyond tracking devices by including calorimeters.

Cross-References  High-Resolution and Animal Imaging Instrumentation and Techniques  Imaging Instrumentation and Techniques for Precision Radiotherapy  New Solid State Detectors  Radiation-Based Medical Imaging Techniques: An Overview  Radiation Damage Effects  Radiation Detection Technology for Homeland Security  Technology for Border Security  Tracking Detectors  Tumor Therapy with Ion Beams

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Virmontois C et al (2011) Total ionizing dose versus displacement damage dose induced dark current random telegraph signals in CMOS image sensors. IEEE TNS 58(6):3085–3094 Vasilescu A et al (1997) The NIEL scaling hypothesis applied to neutron spectra of irradiation facilities in the ATLAS and CMS SCT, ROSE/TN/97-2, CERN (1997) Vasilescu A, Lindstroem G (2000) Displacement damage in silicon, on-line compilation. http:// rd50.web.cern.ch/RD50/NIEL/default.html

Part III Applications of Detectors in Particle and Astroparticle Physics, Security, Environment, and Art

Astrophysics and Space Instrumentation

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Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Photon Instruments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . X-Ray Calorimeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Grazing Incidence Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Coded Aperture Masks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pair Conversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cosmic-Ray Instruments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Time-of-Flight Versus Energy Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . dE/dx Versus Total Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Magnetic Rigidity Spectrometers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Calorimeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Large-Area Composition Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Indirect Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract Instrumentation for particle and high-energy photon measurements in space must provide high levels of performance while meeting the severe constraints imposed by flight. Direct measurements are required spanning over 13 decades in energy and covering species ranging from photons to the heaviest nuclei in the periodic table. Indirect measurements increase the energy range by another five decades. Many of the detection techniques used are shared with accelerator instruments and other ground-based applications, but the implementation is often unique to

J. W. Mitchell () · T. Hams Astrophysics Science Division, NASA/GSFC, Greenbelt, MD, USA e-mail: [email protected]; [email protected] © Springer Nature Switzerland AG 2021 I. Fleck et al. (eds.), Handbook of Particle Detection and Imaging, https://doi.org/10.1007/978-3-319-93785-4_23

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space. This chapter sets the context for the required measurements and reviews representative instruments for direct measurements of photons and particles from 100 eV to 1015 eV and indirect measurements to over 1020 eV.

Introduction Instruments to measure high-energy photons, X-rays and γ-rays, and energetic particles are key tools in modern astronomy and astrophysics. High-energy photons are produced by a wide variety of processes in which particles, particularly electrons, are accelerated to relativistic velocities, or in which material is elevated to extreme temperatures. The particle acceleration processes that produce highenergy photons are also likely sources of highly energetic particles. Detected at velocities approaching the speed of light, these particles, known as cosmic rays, include atomic nuclei and electrons, as well as positrons and antiprotons. Direct high-energy photon and particle detection spans 13 orders of magnitude in energy from X-rays of ∼100 eV to particles near the “knee” of the cosmic-ray spectrum at about 1015 eV. The instrumentation required varies greatly depending on the energy and species to be observed ( Chap. 1, “Interactions of Particles and Radiation with Matter”). Indirect measurements extend more than another five orders of magnitude to above 1020 eV, see  Chap. 24, “Indirect Detection of Cosmic Rays”. In this chapter, the techniques used for high-energy astrophysics measurements from flight platforms are reviewed and representative instruments are discussed. Designers of space instrumentation face a number of special challenges. Whether for balloons, sounding rockets, or satellites, instruments must conform to strict weight, dimension, and power limits. Size is a particular issue. Larger, heavier instruments cost more to build and test. For space-based instruments, higher weight also demands more powerful launch vehicles with accompanying, often dramatic, increases in cost. Balloon payloads are limited by the capacity of the balloon vehicles and payload weight determines the altitude, and therefore the level of residual atmosphere, which can be reached. This is a compound problem because heavier payloads require stronger balloons, which themselves are heavier. Power is usually supplied by photovoltaic arrays that have limited area, supplemented by batteries whose weight has to be considered. Heat generated by the electronics of flight instruments must be dissipated by radiation to space because even at balloon altitudes (∼36 km) the atmosphere is too thin to support convective cooling. At the same time, instruments must contend with the heat load of exposure to unobstructed sunlight. Instruments must be reliable and largely autonomous while incorporating the versatility to allow reconfiguration on command to change operational modes or compensate for degradation. Space-based instruments must contend with the rigors of the launch environment including shock, vibration, and acoustic loads. Balloon instruments have to survive transportation to remote launch locations and shocks at parachute deployment and landing. For all instruments, cost is a major factor.

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Photon Instruments In this section, we review space and suborbital instrumentation for the direct measurement of highly energetic photons (X-ray, γ-ray), covering an energy range from ∼0.1 keV to ∼300 GeV. Given the large number of current instruments in this category, we can only select representative missions and discuss their instrumentation as exemplary of other missions using similar techniques. The techniques discussed include collimation (RXTE), grazing incidence focusing optics (Chandra), coded aperture mask (Swift-BAT), and pair-production tracking (FermiLAT). The need to carry out X-ray observations above the Earth’s atmosphere is apparent when considering that a 20 keV photon has an interaction length of 10 m in air. Starting in the hard X-ray range, suborbital observations become possible with balloon-borne or sounding rocket payloads. The first X-ray observations were conducted as early as 1962 (Giacconi et al. 1962) employing Geiger counters onboard a sounding rocket to demonstrate detection of an X-ray source outside the solar system.

X-Ray Calorimeters The Rossi X-Ray Timing Explorer (RXTE) is the longest operating of the currently active NASA X-ray missions. RXTE was launched in December 1995, into a 580 km circular orbit with 23 ◦ inclination, and the instrument is still providing data. The main science objective of RXTE is a time variability study of X-ray emissions in the energy range from 2 to 250 keV with microsecond time resolution and moderate energy resolution for bright sources. The RXTE spacecraft has the ability to quickly repoint the observatory to highly variable sources, such as gamma-ray bursts (GRBs). The nonimaging and nonfocusing X-ray detector system of RXTE is a good starting point for this discussion, since similar techniques (proportional and scintillation counters) had been used in earlier missions ( Chap. 11, “Gaseous Detectors,”  Chap. 15, “Scintillators and Scintillation Detectors”). RXTE employs large-area collimated X-ray detectors giving a narrow field of view of the target region and reducing unwanted background detection. RXTE is composed of three main instruments: a large-area Proportional Counter Array (PCA, in  Chap. 11, “Gaseous Detectors”) covering the range 2–60 keV (Jahoda et al. 2006), the High Energy X-ray Timing Experiment (HEXTE) (Gruber et al. 1996) with an energy range of 15–250 keV, and an All Sky Monitor (ASM) operating in the 2–10 keV energy range (Levine et al. 1996). The spacecraft can point the fixed PCA in any desired target direction except for a 30 ◦ exclusion zone in the direction of the Sun. Two star trackers provide pointing information to better than 130 arcsec and the spacecraft maintains a pointing accuracy for the PCA of better than 6 arcmin. The spacecraft can be brought on target with a slewing rate of

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HEXTE Star trackers

ASM

PCA (1 of 5) Low-gain antenna Solar-power array

Fig. 1 RXTE spacecraft

180 ◦ in 30 min. Figure 1 shows the RXTE spacecraft with location of the detector systems. The PCA is made up of five identical modules with a total collection area of 6500 cm2 . Each PCA module has two sealed gas volumes. The main detection volume is filled with Xe/CH4 gas and has four layers of proportional counters. Each layer is made up of a frame with 20 cells, each nominally 1.3 cm × 1.3 cm × 100 cm, with an anode wire in the center. The second gas volume is filled with propane and uses a single layer of proportional cells, placed on the Xe volume that serves as an entrance veto and is similar in construction to the other layers. In addition, the anode signals of the lower (fourth) layer and the outermost cells in the remaining layers of the Xe volume are used to form a three-sided anticoincidence. Both gas volumes are maintained at ∼1 atm of pressure. The sides and bottom of the PCA employ a passive graded-Z shielding of tantalum, tin, and the aluminum housing to reject cosmic rays or X-rays that do not enter through the front. The remaining 18 anode wires in each of the three Xe layers define the active detection volume of the calorimeter. Collimators in front of the PCA provide a 1 ◦ (FWHM) field of view (FOV). The entrance window to the propane volume and the divider between the propane and Xe volumes are thin aluminized Mylar. Telemetry bandwidth limits do not permit transmission of the digitized pulse heights of all anode signals. To maintain high internal background rejection and good detection efficiency, a signal encoding scheme was incorporated. The anode

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signals of the side cells and of the bottom layer are combined into a single veto signal that is sensitive both to penetrating radiation from the sides and to partially contained events. The anode wires of the propane layer are combined to build an anticoincidence to reject incident cosmic rays. In each layer, the remaining anode signals of alternate cells are combined to form a total of six signals in the active volume. Each of the six anode signals and two veto signals is individually discriminated and digitized. A nominal good event requires there to be no signal in any of the veto layers and a signal in only a single proportional cell. Incident X-rays below 60 keV predominantly lose energy through photoelectric absorption in the Xe gas. The X-ray produces a photoelectron which in turn creates electron–ion pairs in the Xe. The number of pairs is directly proportional to the energy of the incident X-ray. The proportional cell amplifies the signal and generates a measurable charge pulse on the anode wire. A pressure transducer and temperature sensor on each PCA unit record the state of the gas and thus the gas amplification. An 241 Am source in the PCA provides gain calibration. Time tagging of events is fast enough to allow for detection of microsecond-time-scale X-ray flux changes. The instrument has a sensitivity of 0.1 mCrab and an energy resolution of 18% at 6 keV. Higher-energy X-rays lose energy through Compton scattering and spread their energy deposit over a larger volume in the PCA. An increased number of proportional cells with a signal from a high-energy X-ray reduces the background rejection of the PCA and thus sets the upper energy limit of ∼60 keV. The High-Energy X-ray Timing Experiment (HEXTE), which is co-aligned with the PCA, provides high-energy measurements from 15 to 250 keV. HEXTE is divided into two clusters each employing four phoswich detectors with an effective collection area of ∼800 cm2 and a FOV of 1 ◦ . To veto charged particles entering the phoswich detectors, the sides of the cluster are surrounded by a particle anticoincidence shield of four plastic-scintillator tiles, each viewed by two photomultipliers (PMT) via wavelength-shifting light guides positioned along two sides. This anticoincidence provides prompt vetoing of spurious background from effects such as Cherenkov radiation in the PMT glass and secondary particles generated in the collimators. Each cluster can tilt off target by ±1.5 ◦ . The tilts for the two clusters are in orthogonal planes and the tilt motion always maintains one cluster on target while the other is sampling off-target background data. The ontarget dwell time is programmable between 16 and 128 s. Much like the PCA, each phoswich scintillator individually records the arrival time and energy of incident X-rays. Each HEXTE phoswich detector is contained in an opaque, sealed housing, which prevents stray light and moisture from entering and provides magnetic shielding, see  Chap. 15, “Scintillators and Scintillation Detectors”. The detector material is an inorganic scintillator, NaI(Tl) (18.29 cm diameter, 0.32 cm thick), followed by a 5.71 cm thick CsI(Na) crystal, which serves as an anticoincidence. The scintillation light is viewed by a 12.7 cm PMT. X-rays enter the detector through a Pb honeycomb collimator, restricting the FOV to 1 ◦ , and a 0.5 mm thick Be entrance window. The two scintillator materials have different characteristic rise times. NaI(Tl) emits light after roughly 0.25 μs whereas CsI(Na) has a rise time of

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0.63 μs. A pulse-shape analysis of the PMT signal can discriminate a purely fast NaI(Tl) signal (i.e., a good event) from an event with a slower CsI(Na) component. The latter class of events are rejected since they could result from an incident cosmic ray, partial energy containment in the detector by an X-ray with a Compton-scatter electron escaping the NaI(Tl) crystal, or an X-ray entering from the side. The energy resolution of the detector, 15% at 60 keV, relies on a calibration of measured PMT signal amplitude as a function of incident X-ray energy. The scintillation light yield is proportional to the X-ray energy deposit in the NaI(Tl) and the signal amplitude of the PMT is proportional to the collected scintillation light. Each phoswich module has a gain calibrator mounted in one cell of the collimator. The calibrator uses a plastic scintillator doped with a small amount of 241 Am and viewed by a 1.27 cm PMT. The plastic scintillator is placed directly in front of the entrance window. The primary decay scheme of 241 Am yields a 60 keV X-ray in coincidence with a 4 MeV alpha particle. The X-ray, leaving the plastic scintillator, provides a spectral line for gain calibration of the PMT, and the alpha, which stops in the plastic, provides a coincidence signal. To maintain uniform response across the phoswich aperture, both crystals are highly polished, optically coupled to the PMT, and wrapped in a diffuse Teflon reflector.

Grazing Incidence Optics The instruments discussed in the previous subsection do not provide imaging of X-ray sources, but rather obtain temporal or spectroscopic observations from a given region in the sky defined by the viewing angle of the collimator. Here we will discuss current X-ray instruments for astrophysical observations, which employ focusing optics. Given the strong absorption of X-rays traversing matter, refractive optics used in telescopes for visible light are not applicable. However, X-rays can be reflected off mirror surfaces provided the incident angle is shallow and the glancing angle is less than the critical angle, as Compton pointed out in 1923. For this grazing incidence technique, the critical angle depends on mirror material and X-ray energy. The critical angle is inversely proportional to the photon energy. Mirror surface materials with increasing Z have larger critical angles at the same photon energy, and most grazing-incident-angle X-ray telescopes employ high-Z gold- or iridiumcoated mirrors. The grazing incidence technique had been explored for X-ray microscopy when in the early 1950s Hans Wolter suggested three geometries for focusing X-rays. In the mid-1960s a prototype of a Wolter Type-I X-ray telescope was developed and later flown on a sounding rocket to image the soft X-rays from the Sun. The first space-based imaging X-ray telescope (Wolter Type-I) was onboard NASA’s second High Energy Astrophysical Observatory, HEAO-2. The satellite, later renamed Einstein Observatory, was launched in late 1978, collecting data for 2 years and providing, among other important studies, the first high-resolution X-ray study of supernova remnants. Focusing systems have a much higher signalto-noise (background) performance than nonfocusing systems because the X-rays collected over a large area are imaged on a much smaller sensor. As a consequence,

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focusing systems are less likely affected by spurious background events. Presently, a number of space-based grazing-incident telescopes are in operation, most notably the European Space Agency’s X-ray Multi-Mirror Mission (XMM-Newton) and NASA’s Chandra X-ray Observatory (Chandra or CXO). These latter two missions have similarities in their basic design and have complementary science goals. Here we will illustrate the technique with Chandra. Chandra, formerly known as the Advanced X-ray Astrophysical Facility (AXAF), was conceived as a large, high-sensitivity telescope serving the astrophysical community by accessing the entire sky with an availability of greater than 85% at any time, providing spectroscopy and imaging, including achieving modest energy resolution (E/ΔE≈10–50) for spatially resolved spectroscopy. The optical system achieves imaging better than 0.5 arcsec FWHM. The instrument suite covers the energy range from 0.1 to 10 keV and has an effective collection area of 800 and 400 cm2 at 0.25 and 5 keV, respectively. An artist’s view of the Chandra spacecraft is shown in Fig. 2 and instrumental details can be found on the Chandra X-ray Center website (cxc.harvard.edu). The observatory was launched into a low Earth orbit with the Space Shuttle Columbia (STS-93) in July 1999; the Inertial Upper Stage booster rocket carried the spacecraft into a highly elliptic orbit (apogee height ∼142,400 km, perigee height ∼6400 km) with a period of approximate 63.5 h (2010). The first-light image was taken of Cassiopeia A and was released on August 6, 1999. The main science components of Chandra are the High-Resolution Mirror Assembly (HRMA), which focuses incoming X-rays onto the Science Instrument Module (SIM) at the far end of the Optical Bench Assembly (OBA). The SIM contains the High-Resolution Camera (HRC) and the Advanced CCD Imaging Spectrometer (ACIS). Each instrument type is divided into an imager (-I) and spectrometer (-S) subset. The ACIS imagers have moderate intrinsic spectral resolution,

Aspect camera stray-light shade Spacecraft module

Sunshade door

Solar array (2)

Optical bench High-resolution mirror assembly (HRMA) Thrusters (4) (105Ib) Low-gain antenna (2)

High-resolution camera (HRC)

Transmission gratings (2) CCD imaging spectrometer (ACIS)

Fig. 2 Chandra spacecraft (NASA/CXC/NGST)

Integrated science instrument module (ISIM)

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but in conjunction with the Low- (LETG) or High-Energy Transmission Gratings (HETG), which can be inserted into the beam, both photosensor instruments (HRC, ACIS) provide high-resolution spectra. The science topics that can be addressed by an observatory with high availability, large collection area, and high-resolution imaging and spectroscopy are wide ranging, and these capabilities enable observation of faint sources, distant sources, or the investigation of the structure and physical processes in astrophysical objects. The HRMA utilizes a Wolter Type-I design comprised of four concentric, nested, grazing-incident X-ray mirror segments fabricated from Zerodur glass with a 330 Å iridium coating. The outer mirror segment has a diameter of 123 cm and the inner segment 65 cm. The paraboloid followed by hyperboloid mirror sections are each 85 cm long and together with the thermal pre- and post-collimator and aperture plate, the HRMA has a total length of 276 cm. The HRMA has a weight of 1484 kg and a focal length of 10 m. The precision achieved in the HRMA drives the spatial resolution of 0.5 arcsec for Chandra and provides an order of magnitude improvement over previous instruments. The ACIS is made up of 10 planar, charged-couple devices (CCDs) each with 1024 × 1024 pixels, see  Chap. 16, “Semiconductor Radiation Detectors”. An incident X-ray deposits its energy via photoelectric interaction in the CCDs. The hit pixel and the amount of charge stored characterize the incident location and energy of the X-ray. The CCDs are exposed with a frame time of ∼3.2 s and read out with transfer time of ∼41 ms. Telemetry limitations of the spacecraft permit only the transmission of data from up to six preselected CCDs. Four CCDs are arranged in a 2 × 2 array (ACIS-I) and used as an imager, the remaining six CCDs are arranged in a linear 1 × 6 array (ACIS-S) and are either used for imaging or as a grating readout. The ACIS has the capability to simultaneously acquire high-resolution images and moderate-resolution spectra. Most of the CCDs in the ACIS are front-illuminated except for two back-illuminated CCDs in the ACIS-S, which have a lower threshold. Since the CCDs are sensitive to the detection of visible light and X-ray photons, they are covered by a visible/UV-blocking filter, which is a thin composite of polyimide sandwiched between two thin layers of aluminum. The quantum efficiency of the CCDs matches the energy range of the HRMA. To achieve high-quality spectra of point and slightly extended (few arc-seconds) sources, the linear ACIS-S array is arranged in the expected diffraction direction of the transmission grating system. The ACIS instrument can be used in conjunction with the HETG or LETG, but in normal operation is mostly used with the HETG. The HETG is mounted on a support frame that can be swung into the beam behind the HRMA and contains two grating patterns: the Medium-Energy Grating (MEG) and the High-Energy Grating (HEG). The MEG, covering the range 0.4– 5.0 keV, places the grating behind the outer two mirror segments, whereas the HEG, covering the range from 0.8–10 keV, places the grating behind the inner two mirror segments. The nominal grating parameters for the HEG (MEG) are as follows: The grating lines are 5100 Å (3,600 Å) thick gold deposited on a 9800 Å (5,500 Å) thick polyimide film. The periodicity is 2000.81 Å (4,001.95 Å) and the bars have a width

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of 1200 Å (2,080 Å). The ruling patterns on the HEG and MEG form an X on the ACIS-S, allowing it to separate the different diffraction patterns. The second instrument in the focal plane of the HRMA is the High-Resolution Camera (HRC), which employs a chevron-type microchannel plate (MCP) coated with CsI to enhance photoelectric conversion and read out by a crossed-grid charge detector. The HRC has a spatial resolution of ∼20 μm. To eliminate cosmic-ray background, the HRC incorporates a plastic-scintillator anticoincidence detector. Passive tantalum shielding on the inside of the titanium housing rejects X-rays entering from the side. The HRC has two subsets, one optimized for imaging (HRC-I) and the other (HRC-S) serving as the readout for the LETG, which is similar in its function to the HETG discussed above but optimized for low-energy observations starting at 70 eV. The HRC-I provides the largest FOV (∼30 × 30 ) on the observatory, has an energy threshold below that of the ACIS, and has a good time resolution of ∼16 μs, but lacks the spectral resolution of the ACIS. In order to smooth out the pixel-to-pixel variation, the instantaneous image is spread over different pixels by dithering the spacecraft over the target in a Lissajous pattern. The amount and period of the dithering depends on the instrument in use and is 20 arcsec for the HRC and 8 arcsec for the ACIS with a nominal period of 700 s (pitch) and 1000 s (yaw). The controlled motion of the spacecraft has to be taken into account to obtain final images. Other mirrors used to focus X-rays using grazing incidence employ foil substrates instead of glass, allowing segments to be packed closer and weigh less. Foil mirrors were used in the Japanese ASCA (formerly Astro-D) satellite, which was launched on February 20, 1993, and operated for over 7 years. This mission is also noteworthy since it was the first X-ray satellite mission to use a CCD imager. New high-resolution mirrors developed for the NuStar mission (Koglin et al. 2005) use thin thermally formed glass shells with graded-depth multilayer coatings to extend focusing into the hard X-ray band from 8 to 80 keV.

Coded Aperture Masks X-ray focusing using conventional grazing incidence mirrors with single-layer coatings is technically feasible up to energies of ∼10 keV. This method provides high angular resolution (0.5 arcsec, previous section) but has a narrow field of view of ∼1 ◦ and a small collection area. In the energy range above ∼10 keV, where conventional grazing incidence focusing is less effective, and below ∼50 MeV, where pair production can be used to reconstruct the energy and direction of the incident photon, other imaging techniques are needed. One way to accomplish imaging above ∼10 keV is similar to a pinhole camera, where a position-sensitive photosensor is placed under a mask with a pinhole. A point source will illuminate a particular region of the photosensor and this location determines the arrival direction of the photons. By replacing the pinhole with a coded aperture mask, which for a given source direction casts a

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unique pattern on the photosensor, very large collection areas and good angular resolution can be achieved. To obtain the image of the source, the detected photons over the entire photosensor need to be deconvolved. Encoding incident photons can be done in one of two ways, temporally or spatially. Most present missions employ a spatial-coded aperture mask, which we discuss below. An example of current temporal encoding can be found on the All Sky Monitor (ASM) of RXTE. In the ASM three narrow FOV detectors sweep in different planes over the region of interest in the sky. Each detector records the detected count rate as a function of time (direction). The direction of a point source is marked by the time (direction) for which the photon flux is the greatest. The three scans in different planes constrain the source location. While the image in a focusing X-ray telescope is only affected by the noise of pixels in the immediate vicinity of the focused image, in the coded-aperture technique noise from the entire photosensor affects the quality of the image. Current space missions using coded aperture masks are the International GammaRay Astrophysics Laboratory (INTEGRAL) and Swift. We will use the latter to illustrate this technique. INTEGRAL was launched by the European Space Agency (ESA) in late 2002 and is an active mission. INTEGRAL is dedicated to the fine spectroscopy (E/ΔE = 500) and fine imaging (angular resolution: 12 arcmin FWHM) of celestial γ-ray sources in the energy range 15 keV–10 MeV with concurrent source monitoring in the X-ray (3–35 keV) and optical (V-band, 550 nm) energy ranges and employs a number of coded-aperture-mask instruments. Swift is the latest active mission that utilizes a coded aperture mask and has the largest mask ever deployed. This mission is conducted as an international collaboration among Italy, the UK, and the USA, funded in the USA by NASA. The main science focus of the Swift mission is to study GRBs (Gehrels et al. 2009). Swift has a complement of three co-aligned instruments to view GRBs and their afterglows at γ-ray, X-ray, ultraviolet (UV), and optical wavelengths: the Burst Alert Telescope (BAT), the X-Ray Telescope (XRT), and the Ultraviolet/Optical Telescope (UVOT) (Gehrels et al. 2004). Swift was launched on November 20, 2004, and detects ∼300GRBs/year, localizing ∼100GRBs/year. The largest instrument onboard Swift is the BAT (Barthelmy et al. 2005), which can view approximately one-sixth of the sky at any time or 1.4 sr (half-coded). The BAT can detect and acquire high-precision locations for GRBs and then relay a position estimate accurate to within 1–4 arcmin to the ground in approximately 15 s. Figure 3 shows the detector plane of the BAT instrument. The main components of the BAT are the coded aperture mask, the detector array, and the graded-Z shielding. The detector array covers an area of 1.2 m × 0.6 m and has 32,768 pixels. Each pixel is a 4 mm × 4 mm × 2 mm CdZnTe crystal operated in photon counting mode. To maintain signal uniformity across the detector plane, the detector array temperature is kept at 294 ± 1 K. The energy range of the detector is from 15 to 150 keV with an energy resolution of ∼5 at 60 keV. The coded aperture mask has a D-shape with an area of 2.7 m2 and is placed 1 m above the detector array. The approximately 54,000 Pb coding titles are 5 mm × 5 mm × 1 mm and are mounted to a composite substrate. The mask uses a completely randomized pattern (50%

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Burst alert telescope Coded mask

Tagged source (2) 44″ Loop heat pipe (2)

Detector array (16 blocks)

Thermal radiator

37″

64.5″

Fig. 3 BAT detector on Swift spacecraft

open and 50% closed) rather than the commonly used Unified Redundant Array (URA) pattern. To reduce the effect of cosmic rays on the detector array by 95%, a graded-Z shield surrounds the sides and the underside of the array. The average BAT background event rate is 10,000 events s−1 (or about 0.3 count s−1 per pixel), with orbital variations of a factor of two around this value. This yields a GRB fluence sensitivity of 2 × 10−8 erg cm−2 s−1 (15–150 keV).

Pair Conversion Above a few MeV, the dominant interaction mechanism of γ-rays with matter is their conversion to e+ e− pairs in the electric field of a nucleus or an electron. Pair production has a threshold of 1.022 MeV for interactions in the field of the nucleus and the rate of production goes as Z2 . The threshold for production by interaction in the field of an electron is ∼2 MeV and the production rate for atomic electrons is proportional to Z. Thus, in heavy materials, the interaction takes place primarily near the nucleus. Pair production can be used as the basis for a high-energy γ-ray observatory by tracking the momentum vectors of the e+ and e− and measuring their combined energy, see  Chap. 12, “Tracking Detectors.” The directions of the particles are rapidly altered by multiple Coulomb scattering, and it is important to measure the tracks before scattering has a significant effect. Provided the e+ and e− have not deviated too much from their original track before measurement, the photon momentum vector is approximately the vector sum of the momenta of the particles. Similarly, the energy of the incident photon is the small recoil energy

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plus the sum of the energies of the e+ and e− . The latter can be measured using a calorimetric technique or, at low energies, by measuring the rate of multiple Coulomb scattering. The pair-conversion telescope technique was pioneered in the NASA SAS-2 (Small Astronomy Satellite 2) instrument that flew from November 1972 to June 1973 and measured γ-rays in the 35–200 MeV range using a spark-chamber tracking system with thin tungsten plates for pair production. Energy was measured by determining the rate of multiple scattering. This was followed by the ESA Cos-B instrument that was launched in 1975 and operated for 6.5 years, ending in 1982, producing a catalog of 25 γ-ray sources, a γ-ray map of the Milky Way disc, and detection of the first extragalactic γ-ray source 3C273. Cos-B was able to add a crystal calorimeter to improve energy resolution, see  Chap. 20, “Calorimeters.” The promise of high-energy γ-ray astronomy was realized in the EGRET (Energetic Gamma-Ray Experiment Telescope) instrument on the NASA Compton GammaRay Observatory (CGRO) that launched in 1991 on the Space Shuttle Atlantis and operated until it was deorbited in 2000. EGRET used a spark chamber for pair production and tracking and had more than 20 times the geometry factor (area×solid angle) of its predecessors. The energy of the e + e − pair was measured using a NaI(Tl) crystal calorimeter. A plastic-scintillator anticoincidence dome vetoed charged-particle background. EGRET measured γ-rays from 20 MeV to 30 GeV and revolutionized γ-ray astronomy with the first all-sky survey above 50 MeV, detections of γ-ray pulsars and blazars (a class of active galactic nuclei) as well as observations of diffuse γ-ray emission, delayed emission from GRBs, and γ radiation from high-energy solar flares. The Large Area Telescope (LAT) on the Fermi Gamma-ray Space Telescope (Fermi) (Atwood et al. 2009) was designed to clarify and extend EGRET observations. Fermi (formerly the Gamma-ray Large Area Space Telescope) was launched in June 2008. Fermi-LAT was designed to provide the observations needed to understand the nature of the high-energy photon sky including identification of sources, determining the origins of the diffuse emission, understanding the mechanism of particle acceleration, using γ-rays to probe the nature of dark matter, and using γrays to study the early universe and the evolution of γ-ray sources. LAT released a catalog of 1451 sources in 2010, the largest γ-ray source catalog to date. About half the sources are either blazars (∼600) or pulsars (∼60). Other source classes, some newly discovered, include pulsar wind nebulae, supernova remnants, globular clusters, starburst galaxies, Seyfert galaxies, and X-ray binaries. In addition, the LAT has proven to be a highly effective detector for high-energy electrons with measurements of the electron spectrum to energies approaching 1 TeV. The central design goal of Fermi-LAT was to measure the directions, energies, and arrival times of incident γ-rays over a wide FOV so that much of the sky is viewed on each orbit. All of the detector technologies used were based on current practice at particle accelerators. The LAT is designed to span the energy range from below 20 MeV to above 300 GeV using a pair-conversion telescope based on a silicon-strip-detector (SSD) tracking system interleaved with thin tungsten converter layers. The energies of the e+ e− pair are measured in a fully active

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CsI(Tl) crystal calorimeter. The use of a monolithic anticoincidence limited the upper energy range of EGRET due to self-vetoing by backsplash albedo from interactions in the calorimeter. To eliminate this problem, LAT uses a highly segmented anticoincidence detector (ACD) to detect charged particles entering the FOV of the telescope. There is only a small probability of a backsplash event coincident in the same ACD tile as an incident γ-ray, and the ACD is not automatically included as a veto in the trigger. The instrument is arranged in 16 modules or towers, each incorporating both a tracking section and a calorimeter section. The tracker array is completely covered on the outside by the ACD. LAT dimensions are 1.8 m × 1.8 m × 72 cm. The instrument weighs 2789 kg and consumes 650 W. The effective area is 9500 cm2 at normal incidence and the FOV is 2.4 sr. A schematic view of the Fermi-LAT is shown in Fig. 4. The LAT converter–tracker has 18 tracking planes, each with two layers (x and y) of single-sided SSDs with 228 μm pitch and 400 μm thickness. The top 16 layers are preceded by thin tungsten converter foils with 0.03 radiation length (X0 ) thickness (0.01 cm) over the first 12 layers and 0.18 X0 (0.072 cm) foils over the last four layers. Each tracker layer has about 0.014 X0 of support and detector material. The use of thin converters in the upper layers improves the point spread function (PSF) for the lowest energies. The thicker foils at the back of the tracker enhance the effective area and FOV at high energies while reducing the angular resolution at 1 GeV by less than a factor of 2. The lowest two tracker planes do not have converter material overlaying. The detectors and foils are supported in low-mass carbon-composite “trays” with aluminum honeycomb cores. Each tray is about 3 cm thick and carries two single layers of detectors, a converter foil, and front-end electronics. A detector layer is at the top and bottom of each tray and the foil is located above the lower detector layer. The SSD strips at the top and bottom

γ

Fig. 4 Schematic view of the Fermi-LAT (Atwood et al. 2009)

e−

Incoming gamma ray

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Electron–positron pair

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of a tray are parallel, but successive trays are rotated by 90 ◦ to place x and y layers together. The tracker defines the FOV and provides the principal instrument trigger. The tracker design is compact, giving an aspect ratio for the full telescope of 0.4 to maximize the FOV. The LAT calorimeter, below the tracker, has 96 CsI(Tl) crystals in each module, each 2.7 cm × 2 cm × 32.6 cm. This gives a lateral segmentation of 1 Molière radius and a longitudinal segmentation of 1.08 X0 . The crystals are optically isolated using reflective wrapping material and are arranged in 8 layers of 12 crystals each. Each layer is rotated 90 ◦ forming an x, y hodoscope. The total depth of the calorimeter is 8.6 X0 . Combined with the converter–tracker, the full depth of the LAT is 10.1 X0 . Each crystal is read out by two photodiodes at each end, one with an area of 147 mm2 and the other with an area of 25 mm2 , to span the needed dynamic range. The relative light levels measured at the ends of each crystal give a measure of the shower position. By fitting the profile of particle cascades, the longitudinal segmentation (segmentation in calorimeter depth) allows the energy of incident particles to be measured even if the shower produced by the particle is not fully contained in the calorimeter. This technique extends the energy measurements to ∼1 TeV, although for uncontained showers the energy resolution is limited by fluctuations in shower leakage. As noted, the LAT uses a highly segmented ACD to avoid self-vetoing by backsplash from high-energy showers in the calorimeter. The ACD is required to have a very high detection efficiency for charged particles, 0.9997% averaged over the full FOV, and to impose as little interaction mass in the photon beam as possible. This was achieved using an array of plastic-scintillator tiles read out by wavelengthshifting optical fibers coupled to PMTs at the periphery of the ACD. Each tile is read out by two PMTs for redundancy. Tiles are overlapped in one dimension to eliminate gaps. The remaining gaps between tiles are closed by scintillating optical fiber ribbons with >90% detection efficiency for singly charged particles. The LAT measures γ-rays and electrons with an energy resolution ranging from 9% at 100 MeV to 18% at 300 GeV. The single-photon angular resolution ranges from 3 ◦ at 100 MeV to less than 0.15 ◦ for energies above 10 GeV. The instrument normally operates in a scanning mode in which the axis of the instrument alternates on successive orbits between +35 ◦ from zenith and toward the pole of the orbit and − 35 ◦ from zenith. For the 25.5 ◦ inclination 565 km Fermi orbit gives virtually uniform sky coverage every two orbits (3 h). The telescope can also be pointed to address targets of opportunity.

Cosmic-Ray Instruments Cosmic rays, high-energy charged particles traveling at speeds that can approach that of light, are a rich source of information on the chemical evolution of the Galaxy as well as on some of the most extreme environments and exotic processes in the universe. Cosmic rays have been detected with energies exceeding 1020 eV. Except at the highest energies, cosmic rays are isotropized by intergalactic, galactic, and

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heliospheric magnetic fields and their arrival directions do not point back to their sources. The majority of cosmic rays are atomic nuclei from hydrogen to the heaviest elements in the periodic table, with energies spanning more than 13 orders of magnitude and steeply falling spectra decreasing by a factor of ∼50 per decade in energy. Protons make up about 85% of cosmic-ray nuclei and helium about 12%. Galactic cosmic-ray (GCR) nuclei are most likely accelerated in supernova remnants and their elemental and isotopic composition probe nucleosynthesis, nuclear interactions with the interstellar medium (ISM), the distribution of freshly synthesized elements, and the mechanism of supernova explosions. Primary cosmic-ray nuclei are produced directly in nucleosynthesis processes. Secondary cosmic-ray nuclei, including Li, Be, and B, and those elements directly below Fe in the periodic table are produced mainly by fragmentation of more abundant nuclei in interactions with the ISM. Both elemental and isotopic measurements are important. Measurements of stable secondary-to-primary ratios such as B/C and sub-Fe/Fe provide important information on the path length of ISM traversed by the GCRs. Measurements of radioactive secondary GCRs such as 10 Be, 26 Al, 36 Cl, 54 Mn, and 14 C can be used as “clocks” to determine the age of the cosmic rays and the fraction of time spent in the galactic halo. The abundances of other radioactive isotopes such as 59 Ni that decay by electron capture probe the time between nucleosynthesis and acceleration. Measurements of isotopes such as 22 Ne and the abundances of elements heavier than iron probe the origins of GCRs and the mechanisms by which nuclei are selected for acceleration. The spectra of cosmic-ray nuclei reflect both source and transport effects (Strong et al. 2007). At energies above the influence of solar modulation, the GCR nuclear spectrum falls rapidly with an all-particle differential spectral index of about E−2.7 to an energy of about 1015 eV. At this point, known as the “knee,” the spectrum steepens. The reason for this is uncertain, but is commonly attributed to progressive failure of the supernova acceleration mechanism. Knee energies are at about the limit of direct measurements and most of the data comes from ground-based measurements ( Chap. 26, “Indirect Detection of Cosmic Rays”). Between 1017 and 1018 eV, an extragalactic ultrahigh-energy cosmic-ray (UHECR) component progressively becomes dominant and above the “ankle” at about 5 × 1018 eV the spectrum flattens again. Both the nature of the cosmic acceleration engines responsible for such extreme energies and the composition of the UHECRs are uncertain and are the subjects of intense study. Candidate UHECR sources include active galactic nuclei, neutron stars, galaxy clusters, and the progenitors of GRBs. UHECRs are almost certainly atomic nuclei, but models of UHECR chemical composition range from pure protons, through mixtures of light, intermediate, and heavy species, to pure Fe. Current data from the Pierre Auger Observatory favor a heavier overall composition at the highest energies, but data from HiRes do not. At energies above a few times 1019 eV, UHECRs interact with cosmic microwave and infrared background photons. The details of this interaction depend on the composition of the UHECRs. Protons interact by photoproduction, yielding pions,

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protons, and neutrons. Heavier nuclei undergo photodisintegration in which nucleons are scattered from the nucleus. Either process results in the loss of energy and causes a dramatic steepening of the cosmic-ray spectrum known as the GZK effect, named after Greisen, Zatsepin, and Kuzmin who predicted this suppression in 1966. In 2008, HiRes published the first significant observation of the GZK suppression, confirmed by the Pierre Auger Observatory. UHECRs measured with energies above the GZK cutoff must come from sources within a radius of about 100 megaparsecs of Earth. Particles at these energies have large gyroradii in extragalactic and galactic magnetic fields and their arrival directions should point back to their sources. This opens the possibility of charged particle astronomy by identifying and characterizing individual sources. The interactions that produce the GZK cutoff also produce ultrahigh-energy neutrinos, known as GZK neutrinos or cosmogenic neutrinos. The expected flux of these neutrinos depends strongly on the UHECR composition. UHECR proton interactions produce, e.g., π+ that decay to a νμ and μ which then decay to a νμ , a ν e, and an e. This process produces a spectrum of neutrinos extending to ultrahigh energies. Neutrons are also produced and can decay to produce neutrinos, but this is a minor component. Similarly, if nucleons resulting from photodisintegration of UHECR nuclei are above the pion photoproduction threshold then neutrinos are produced. The neutrino flux from this process depends on the opacity of the photon backgrounds to UHECR nuclei and the spectrum of the nuclei before photodisintegration. Oscillations over astrophysical distances result in a 1:1:1 ratio between the three ν flavors. Because the ν are not absorbed during propagation through the universe, the spectrum of cosmogenic ν arriving at the Earth should reflect the accumulated contribution of sources extending to high redshift. Other cosmic-ray components include electrons, positrons, and antiprotons. While these are largely the result of interactions of nuclear cosmic rays with the ISM, they may have other origins. Positrons and electrons can be produced directly in astrophysical objects such as pulsars, and features in their spectra can provide important insights into nearby sources. Cosmic-ray particles may also be produced directly by the annihilation of dark-matter candidates such as neutralinos and Kaluza–Klein particles. Details of the spectra of resulting particles, especially positrons, electrons, and antiprotons, provide important constraints on the nature of dark matter. The energy spectra of cosmic-ray species other than nuclei also reflect both their origins and transport to Earth. Electrons are largely secondary and the spectrum from the superposition of distant sources falls approximately as E−3 and softens rapidly above 1TeV. Electrons lose energy quickly by synchrotron and inverse Compton processes and any detected with TeV energy must have been accelerated within about 105 years and can have traveled at most a few hundred parsecs. At energies above 1 TeV, features from discrete sources might become evident in the high-energy cosmic-ray electron spectrum. A significant feature in the electron

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spectrum below 1 TeV might also indicate a nearby source of electrons, a pulsar, or dark-matter annihilation. Recent measurements of the high-energy electron spectrum differ considerably. ATIC and PPB-BETS report a feature in the 300– 800 GeV range. Measurements by Fermi-LAT and H.E.S.S. show some excess flux near 1 TeV compared to model predictions, but not a distinct feature. H.E.S.S. measurements also indicate that the spectrum steepens above 1 TeV. The positron spectrum also exhibits interesting features. PAMELA measurements show a significant excess of positrons over expectations of secondary production for energies above 10 GeV. Two general classes of explanation have been offered for the e+ excess observed by PAMELA: the signature of a nearby pulsar, or group of pulsars, and annihilation radiation from a dark-matter clump. There is ample evidence that e− and e+ pairs are produced by primary e− accelerated within pulsars and that the e− and e+ are subsequently accelerated to ultra-relativistic velocities. However, the mechanism by which the particles might escape the pulsar is unclear. Models for the dark-matter source are constrained by measurements of antiprotons from BESS and PAMELA. Most cosmic-ray antiprotons are secondaries produced by interactions of GCRs with the ISM. Production kinematics and the energy spectra of the primary cosmic rays give a characteristic secondary antiproton spectrum with a peak around 2 GeV and sharp decreases below and above the peak. The presence of an additional source such as dark-matter annihilation might be seen as a deviation from the secondary spectrum above or below the peak. Thus far, precision measurements from BESS-Polar and PAMELA have shown no significant excess. The Sun acts both as a source of energetic particles and as a modifier of the GCR flux. Particles are emitted by the Sun in the solar wind and in coronal mass ejections (CMEs). Solar energetic particles (SEPs) are accelerated by impulsive solar flares and by interplanetary shocks from CMEs. In addition, matter from the local ISM can enter the solar system as neutrals and then be ionized by the solar wind. These ions can then be picked up by the solar wind and subsequently accelerated at the solar-wind termination shock, becoming anomalous cosmic rays (ACRs). The ACRs sample matter from the local ISM. The magnetic fields entrained in the outflowing solar wind reduce the energies of GCRs entering the heliosphere. This effect, known as solar modulation, acts to redistribute the GCRs to lower energies and is often simplified as a spherically symmetric force field opposing the incoming GCRs (Fisk 1971). Solar modulation has a significant effect on the measured GCR spectrum below ∼10 GeV/nucleon. This effect is not constant, but tracks the 11-year cycle of solar activity, having its greatest influence at solar maximum. Solar modulation depends on the magnetic polarity of the Sun as well, and particles of different charge sign, e.g., electrons and positrons or antiprotons and protons, are affected differently depending on the magnetic polarity of the Sun (Bieber 1999). Understanding this charge-signdependent solar modulation is critical to developing detailed models of low-energy antiparticle fluxes.

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Time-of-Flight Versus Energy Measurements Ions with energies below a few MeV/nucleon, often reached by SEPs, CMEs, corotating-interaction-region (CIR) ions, and ACRs, can be measured with isotopic resolution using a time-of-flight (TOF) mass spectrometer ( Chap. 6, “Particle Identification”). A representative detector using this technique is the UltralowEnergy Isotope Spectrometer (ULEIS) (Mason et al. 1998) on the Advanced Composition Explorer (ACE) mission, launched in 1997. A schematic crosssectional view of ULEIS is given in Fig. 5. An ion entering the ULEIS acceptance cone passes through a series of thin metal foils, causing the emission of secondary electrons. The ion is then stopped in a solid-state detector, which measures its residual energy. The secondary electrons emitted from the foils are accelerated

ULEIS telescope cross section Typical ion path

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Fig. 5 Cross-sectional view of the ultralow-energy isotope spectrometer onboard ACE. (Mason et al. 1998 with permission from Springer)

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to ∼1 keV and deflected onto microchannel plates (MCPs) using electrostatic mirrors. The resulting MCP pulses are discriminated and the time between pulses is measured. The secondary electron optics are isochronous so that the point of impact on the foil does not influence the measured time. The first two foils give redundant start times while the last foil gives a stop. TOF is measured with ∼300 ps resolution and with a 50 cm flight path ULEIS can measure ions with energies up to a few MeV/nucleon. The lower energy of ∼45 keV/nucleon is set by the thicknesses of the foils and the front contact of the solid-state detector. The total kinetic energy of the particle, E = mv2 /2, corrected for the energy loss in the foils and detector contact, and the measured velocity v = L/t, where L is the flight path in the detector, give the mass of the ion: m = 2 Et/L2 . ULEIS cannot measure charge. Particle species are determined by comparison to solar system abundances to determine the dominant isotope among isomers (same mass but different charge). This does not contribute significant ambiguity. ULEIS uses MCPs with areas of 8 cm × 10 cm and an array of solid-state detectors with an area of 73 cm2 to give a geometric factor of 1.3 cm2 sr. Simplified implementations of this technique can reach lower energies using thinner foils. A wide range of energies can be measured in a single instrument by replacing the single solid-state detector with a dE/dx-E telescope.

dE/dx Versus Total Energy For energies below a few hundred MeV/nucleon, one of the most common techniques used for the identification of GCR or SEP nuclei is the simultaneous measurement of specific ionization energy loss, dE/dx, and total kinetic energy, E. This dE/dx-E technique, often implemented as dE/dx-total E or dE/dx-residual E methods, is capable of determining the charge, mass, and energy of incident particles. In its simplest form, a dE/dx-E telescope utilizes two detectors, usually silicon diodes, to separately measure dE/dx andE. The thickness of the entrance detector, which measures dE/dx, sets the effective lower energy limit of the device and this detector is often as thin as possible. The second detector must be thick enough to stop particles within the energy range of interest. dE/dx is approximately dE/d L sec(θ), where d L is the thickness of the entrance detector and θ is the angle of the particle with respect to the telescope axis. Similarly, the particle’s kinetic energy is approximately the energy deposited in the stopping detector if the dE/dx detector is thin. Ionization energy loss is proportional to Z2 /v2 and kinetic energy equals mv2 /2. Thus, the product dE/dx × E is proportional to Z2 m/2 and is independent of velocity. As illustrated in Fig. 6, when dE/dx is plotted against total E, the result is a series of hyperbolas in constant Z2 m/2. Elements are separated more than isotopes, so the telescope functions to determine both the charge and mass of the nucleus. In order to achieve maximum resolution, θ must be either limited by a combination of collimation and detector geometry or the trajectory of the particle must be measured. This is most commonly accomplished with position-sensitive

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Energy Loss in E1 through E3 (MeV)

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Fe Mn Cr

6000 V Ti 5000

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Fig. 6 dE/dx vs E technique used with ACE/CRIS. (Stone et al. 1998c with permission from Springer).

solid-state-detector hodoscopes, although other methods including drift chambers and scintillating optical fiber hodoscopes have also been used. The modern dE/dx-E telescope was introduced on the IMP-1 (Explorer 18) satellite, launched in 1963. This telescope used thin solid-state entrance detectors with a CsI(Tl) crystal as a stopping detector. ISEE-3, launched in 1978, incorporated two instruments that provided measurements of the incoming particle trajectory, one using a drift chamber and one with position-sensitive solid-state detectors. Since then, dE/dx-E telescopes of great sophistication have been used on many missions including Voyager (I and II), CRRES, SAMPEX, Wind, NINA, Ulysses, ACE, and STEREO. Some representative examples are discussed below. In most high-resolution solid-state telescopes, the charge and mass of detected particles are identified based on the energies they deposit coming to rest in a stack of detectors rather than in a single detector. This allows the instrument to stop particles of much higher energy than could be achieved with a single stopping detector. In addition, the resolution improves when dE/dx is measured in a detector or set of detectors whose thickness is a significant fraction of the particles range. Use of a stack of detectors allows optimization of the thicknesses of the detectors for dE/dx measurements over an extended energy range. An iterative technique for solving for mass is discussed in Stone et al. (1998a). The ULYSSES Cosmic and Solar Particle INvestigation (COSPIN) incorporated five instruments (Dual-Anisotropy Telescopes (ATs), Low-Energy Telescope (LET), High-Energy Telescope (HET), High-Flux Telescope (HFT), and Kiel Electron Telescope (KET)) measuring nuclei and electrons from 0.5 MeV to several hundred

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MeV, depending on species. The HET was designed to measure elemental and isotopic composition of nuclei from hydrogen to nickel. The lowest energy measured was about 5 MeV for protons and extended to 400 MeV/nucleon for Fe. The telescope utilized a hodoscope formed of six 1000 μm thick Li-drifted silicon (Si(Li)) detectors incorporating a multi-strip readout with position determined by voltage division. These were arranged in two groups of three detectors with successive detectors rotated by 60 ◦ , and measured both trajectory and dE/dx. The resultant resolution was about 150 μm, giving a trajectory resolution on the order of 1 ◦ . These were followed by a stack of six 5000 μm Si(Li) detectors. For particles penetrating these detectors, dE/dx was accurately measured. The stack also stopped incident nuclei and provided the total E measurement. Finally the telescope was terminated in a 1000 μm Si(Li) diode acting as a penetration detector. The full telescope was surrounded in a scintillator anticoincidence shield. The geometric factor of the HET depended on particle species and energy and ranged from about 3.6 cm2 sr at the highest energies to ∼87 cm2 sr at the lowest. ACE includes 4 dE/dx-E telescopes: the Solar Energetic Particle Ionic Charge Analyzer (SEPICA); the Electron, Proton, and Alpha Monitor (EPAM); the Solar Isotope Spectrometer (SIS) (Stone et al. 1998b); and the Cosmic-Ray Isotope Spectrometer (CRIS) (Stone et al. 1998c). SIS and CRIS both measure nuclei from He to Zn with isotopic resolution. The instruments are complementary. SIS spans the energy range from about 10 MeV/nucleon to 100 MeV/nucleon to measure nuclei accelerated in SEP events, ACRs, and low-energy GCRs. CRIS measures from approximately 100 MeV/nucleon to 600 MeV/nucleon, focusing on measurements of GCR composition. SIS uses a pair of identical telescopes composed of a stack of 17 solid-state detectors. The top two elements are 75 μm thick ion-implantedx, y (matrix) positionsensitive detectors with 34 cm2 active areas that measure energy loss and particle trajectories. Each matrix detector has 64 readout strips in x and y each 960 μm wide and separated by 40 μm. Following these are 15 ion-implanted silicon stack detectors with 65 cm2 active areas and thicknesses ranging from 100 μm for the top two stack detectors, increasing in thickness progressively to 3.75 mm. Finally, the stack has a 1 mm detector acting as a penetration counter. A collimator limits the opening angle of the instrument to 95 ◦ full angle. The SIS geometric factor ranges from 19.4 to 38.4 cm2 sr. Special care was taken in mapping both the thicknesses of the SIS detectors and the thicknesses of the dead layers. The CRIS instrument consists of a scintillating optical fiber trajectory (SOFT) hodoscope for measuring the trajectory of nuclei, and four silicon solid-state detector telescopes for measuring dE/dx andE. The SOFT system consists of a hodoscope composed of three x, y scintillating fiber planes (six fiber layers) and a trigger detector composed of a single fiber plane (two fiber layers). The hodoscope and trigger fibers are coupled to an image intensifier that is then coupled to a CCD camera for readout, and to photodiodes to obtain trigger pulses. Fully redundant image-intensified CCD camera systems view opposite ends of the fibers. Only one of these camera systems is operated at any given time because of power and bitrate limitations. CRIS contains four detector telescopes to achieve a large collecting

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area and to provide redundancy. Each consists of stacks of 15 silicon detectors. The individual detectors are 10 cm in diameter and 3 mm thick Si(Li). CRIS has a geometric factor of 250 cm2 sr for isotope measurements.

Magnetic Rigidity Spectrometers Magnetic rigidity spectrometers use measurements of the curved trajectory of charged particles in a strong magnetic field to identify incident particles by directly measuring their charge (Z), charge sign, magnetic rigidity (R = cp/ Ze, where p is momentum and Ze is electric charge), and velocity (β). This information is subsequently used to derive their p, mass (m), and kinetic energy (E k ). Magnetic rigidity spectrometers are unique in their ability to measure the charge sign and so are the principal instruments used for antiparticle (positron and antiproton) measurements and in searches for heavier (|Z| ≥ 2) antinuclei. They can also provide isotope resolution to much higher energies than dE/dx-E telescopes, limited mainly by velocity resolution, the bending power of the magnet, and multiple scattering. Magnetic rigidity spectrometers require a strong magnet to deflect incident particles and a precise tracking system to measure their trajectories. Most of the instruments built to date have used superconducting magnets and gas-based tracking systems, multiwire proportional counters or drift chambers, and have flown on balloons. However, recent advances in NdFeB permanent-magnet alloys with saturation magnetization exceeding 1.3 T coupled with silicon position-sensing detectors with resolutions of a few μm have opened the way for space-based magnetic spectrometers. This section will consider both a balloon-borne superconducting magnet instrument, BESSPolar (Balloon-borne Experiment with a Superconducting Spectrometer – Polar) (Yamamoto et al. 2011), and space-based permanent-magnet instruments, PAMELA (Payload for Antimatter and Matter Exploration and Light-nuclei Astrophysics) (Picozza et al. 2007) and AMS-02 (Alpha Magnetic Spectrometer – 02) (Kounine et al. 2010). In the 1960s, Luis Alvarez of the University of California, Berkeley, recognized that a persistent-mode superconducting magnet could be successfully operated on a balloon or space platform. Single-coil balloon-borne magnetic spectrometers were developed at Berkeley and Johnson Space Flight Center, and a spectrometer with a near-Helmholtz magnet was developed at Goddard Space Flight Center. The Berkeley group also formulated plans for a spectrometer to be flown onboard the HEAO-B mission and a prototype was developed and tested. With advances in space cryogenics for IRAS, Spacelab-2, and COBE, this led to a NASA program to develop a large superconducting magnet facility on the International Space Station (ISS), known as Astromag, which would have had provisions to refill the cryostat on orbit and to change out experiments. Astromag was terminated for budget reasons in 1990. A free-flyer version was studied, but not funded. The Astromag effort led to a new generation of balloon-borne magnetic spectrometers for studies of antimatter, elemental spectra, and light isotopes (LEAP, PBAR, SMILI, MASS, IMAX, BESS, TS93, CAPRICE, HEAT, and ISOMAX).

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PAMELA had its origin in the WiZard antimatter instrument selected for the first round of Astromag experiments. For historical context, see references in Mitchell et al. (2004). The AMS collaboration that flew the AMS-01 permanent-magnet spectrometer for 10 days on the Space Shuttle in 1998 initially included several members of the Astromag team. The AMS collaboration subsequently prepared a superconducting magnet version, AMS-02, to fly on the ISS. In light of the extended mission planned for the ISS, this was reconfigured to use the AMS-01 permanent magnet, which has no consumables. AMS-02 was successfully installed on the ISS in May 2011. During the Astromag study, a number of magnet configurations were proposed. BESS originated from a proposal to use a solenoidal superconducting magnet whose coil was thin enough for particles to pass through with minimal interaction probability, tracked by detectors within the warm bore of the magnet. This configuration maximizes the opening angle of the instrument, and hence the geometric factor, making it ideal for rare-particle measurements. Versions of the original instrument were used for nine northern-latitude flights between 1993 and 2002. In order to take advantage of the long flight durations and low geomagnetic cutoff in long-duration balloon (LDB) flights over Antarctica, a completely new version of the instrument, BESS-Polar, was developed. The BESS-Polar magnet has half the areal density of its predecessor, achieved by use of improved Al stabilized NbTi superconducting wire strengthened by cold-working and alloying the Al with Ni filaments. Cryogen lifetime was increased to >25 days by reducing heat transmission to the lowtemperature components. In addition, the outer pressure vessel was eliminated, the aerogel Cherenkov counter (ACC) ( Chap. 19, “Cherenkov Radiation”) was moved below the magnet, and a middle TOF layer was added inside the magnet bore. As a result only ∼4.5 g/cm2 is encountered by triggering particles, compared to ∼18 g/cm2 in the previous BESS instrument, lowering the effective energy threshold. BESS-Polar has a mass of 2000 kg and a geometry factor of 0.3 m2 sr. BESS-Polar I flew for 8.5 days in 2004, recording 9 × 108 cosmic-ray events. BESS-Polar II flew in 2007–2008, operating at float altitude for 24.5 days with the magnet energized and recording over 4.7 × 109 events. All versions of BESS use similar instrument configurations with detail changes reflecting the evolution of the instruments and flight-specific requirements. Figure 7 shows a schematic crosssectional view of the BESS-Polar II instrument as an example. A central JET-type drift-chamber tracking system and inner drift chambers, giving 52 trajectory points in the bending direction with a resolution of about 130 μm, are located inside the warm bore of the solenoid. R is determined by fitting the curvature of the particle track. Charge sign is determined by the direction of curvature. The horizontal cylindrical configuration of the BESS instrument allows a full opening angle of ∼90 ◦ with a resulting acceptance of 0.3 m2 sr. The thin solenoid magnet allows the incoming cosmic rays to penetrate the spectrometer with minimum interactions. Since the magnetic field is uniform inside the solenoid, the deflection distribution for particles of a given R is very narrow and the R resolution is nearly constant for all trajectories within the instrument’s geometric acceptance. The superconducting magnet can operate at 1 T and for both BESS-Polar flights a conservative 0.8 T

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TOF counters Solenoid JET chamber Inner DC Middle TOF Silica aerogel Cherenkov 0

0.5

1m

TOF counters

Fig. 7 Cross-sectional view of the BESS-Polar II instrument

was used. A maximum detectable rigidity (MDR) of 200 GV was achieved in the original BESS instrument and ∼280GV in BESS-Polar. For the BESS-TeV flights in 2001 and 2002, outer drift chambers were added to raise the MDR to 1.4TV. Arrays of TOF scintillators are located at the top (UTOF) and bottom (LTOF) of the instrument, with a TOF resolution in BESS-Polar II of ∼120 ps over a 1.48 m flight path. In BESS-Polar, developed to extend measurements to as low an energy as possible in long-duration Antarctic flights, a middle TOF scintillator array (MTOF) with resolution ∼280–380 ps is located inside the magnet bore below the lower IDC. The TOF scintillators trigger readout of particle events and measure Z and β. The p is determined from R and Z and, in turn, m is determined from p and β as illustrated in Fig. 8. BESS-Polar separates antiprotons by mass from negatively charged background particles, mainly muons and electrons, up to E k of about 1.5 GeV. At higher β, an aerogel Cherenkov ACC identifies low-m high-β background particles with a rejection power > 6000. Additional background rejection is supplied by multiple measurements of dE/dx from the JET. Antiprotons can be identified by mass and charge sign from 0.1 to 4 GeV. Elemental spectra can be measured to >100 GeV. Where BESS is designed to maximize the geometric acceptance of the spectrometer to measure rare species in balloon flights, PAMELA was conceived to accomplish the same goals as BESS by taking advantage of a long exposure in space flying on a Russian Earth-observing satellite. PAMELA was launched from Baikonur cosmodrome in June 2006. The instrument has been in stable operation since shortly after launch and has made ground-breaking measurements of highenergy positrons and antiprotons, as well as measuring element spectra and SEPs, and carrying out a search for cosmic antimatter. PAMELA is built around a permanent-magnet-based magnetic rigidity spectrometer using silicon-strip detectors. A plastic-scintillator TOF system measures the charge of incident particles, determines the direction of flight, and provides the instrument trigger. A silicon–tungsten imaging calorimeter measures the energy of incident particles, particularly electrons, and discriminates between electrons and hadrons by examining the shower topology. A plastic-scintillator anticoincidence system protects against particles arising from interactions in the material of the instrument. A plastic-scintillator penetration detector and a neutron detector below the calorimeter aid the selection of high-energy electrons. The instrument has an

25 Astrophysics and Space Instrumentation Fig. 8 BESS-Polar II Particle ID plot for singly charged particles

785

1/300

3

1/b UL

p

p d

2

t

1

−4

−2

0 Rigidity (GV)

2

4

TOF (S1) ANTICOINCIDENCE (CARD) ANTICOINCIDENCE (CAT)

TOF (S2)

z

ANTICOINCIDENCE (CAS)

x

SPECTROMETER

TOF (S3) CALORIMETER

S4 N E U T RO N DETECTOR

Fig. 9 Schematic view of the PAMELA spectrometer. (Re-drawn after Picozza et al. 2007)

overall mass of 470 kg and a geometric acceptance of 21.5 cm2 sr. PAMELA identifies antiprotons 60 MeV–180 GeV, positrons 50 MeV–270 GeV, electrons 50 MeV–400 GeV, protons 80 MeV–700 GeV, and nuclei to O up to 100 GeV. Figure 9 shows the PAMELA instrument.

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The PAMELA spectrometer is based on a magnet composed of 5 layers of NdFeB blocks, 12 in each layer, giving a mean field in the tracking region of 0.43 T. Tracking is provided by six layers of 300 μm double-sided silicon-strip detectors (SSDs) with a readout pitch in the bending direction of 50 μm and 67 μm in the nonbending direction. The tracking resolution is about 3 μm in the bending plane and 11.5 μm in the nonbending plane. The tracking layers are located above and below the magnet and between each of the magnet layers. The MDR is ∼1TV The PAMELA TOF system is made up of three layers of plastic scintillator: one (S1) at the top of the instrument and layers just above (S2) and below (S3) the magnet. The full flight distance from S1 to S3 is 77.3 cm and the timing resolution is ∼250 ps. This is adequate to separate electrons (positrons) from antiprotons (protons) to ∼1 GeV/c and to reject upward-moving particles with about 60 standard deviations. Timing resolution improves for higher charges. The SiW imaging calorimeter on PAMELA is made up of 44 layers of 380 μm thick single-sided SSDs and 22 W plates each 0.26 cm thick (0.74 X0 ). The total depth of the calorimeter is 16.3 X0 (0.6 nuclear interaction lengths). SSD layers are paired with strips on adjacent layers oriented orthogonal to one another, giving x, y positions. The W plates are interleaved between the pairs of SSD layers. The calorimeter has an energy resolution of 5.5% for electromagnetic showers. The primary goal of the calorimeter is to separate positrons and antiprotons from more abundant background particles of the same charge. Positrons must be separated from protons and antiprotons from electrons. The longitudinal and transverse segmentation of the calorimeter and the measurements of dE/dx by the SSDs identify electromagnetic showers. This allows proton background to the positron measurements and electron background to the antiproton measurements to be rejected by a factor of about 105 . In both cases the efficiency for selecting the species of interest is about 90%. AMS-02 is a large, 6900 kg, instrument designed to exploit the full capabilities of a space-based magnetic rigidity spectrometer. AMS-02 was installed on the ISS by the Space Shuttle Endeavour. As finally configured, the instrument uses the AMS-01 permanent magnet to allow for long-term operation on the ISS without the limitations of liquid-helium consumption. To preserve the performance of the instrument with the weaker permanent magnet, the tracking system was reconfigured as discussed below. AMS-02 is designed to measure cosmic-ray particles and nuclei, examine dark-matter signatures with positron and antiproton measurements, and search for primordial antimatter. It incorporates a TOF, a ringimaging Cherenkov detector (RICH) using both NaF and silica-aerogel radiators, an electromagnetic calorimeter (ECAL), and a transition radiation detector (TRD). An anticoincidence along the sides of the magnet bore rejects particles outside the instrument acceptance. The AMS-02 spectrometer employs a NdFeB permanent magnet with a 1 m diameter vertical bore, 1 m height, and 0.15 T field. The magnet is made up of ∼6000 NdFeB blocks glued together in the form of a ring dipole. The ring dipole has very little net dipole moment and so will exert negligible torque on the ISS. The tracking system has nine layers of double-sided SSDs. Position resolution is

25 Astrophysics and Space Instrumentation

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∼10 μm in the bending direction and ∼30 μm in the nonbending direction. In the original configuration for the superconducting magnet, there were eight tracking layers, one at the top of the magnet, one at the bottom, and six distributed in three pairs inside the magnet bore. For the flight configuration, parts of the tracking plane just above the magnet were moved to just above the ECAL and the plane that had been at the bottom of the magnet was moved to the top of the instrument, above the TRD, giving nine tracking layers. For particles traversing all nine tracking layers, the MDR is 2.14 TV but with a reduced geometric acceptance. The AMS-02 ECAL uses Pb absorbers interspersed uniformly with layers of 1 mm scintillating optical fibers read out at one end by multi-anode PMTs. The fibers are laid in groups or superlayers of 10 fiber layers and 11Pb foils. Each successive superlayer orientation is rotated 90 ◦ to give topological information on electromagnetic showers, improving rejection of background protons. There are five superlayers in the bending direction and four in the nonbending. The ECAL is ∼17 X0 in total and has an energy resolution of ∼2.5% and angular resolution of ∼1 ◦ . The active area is 648 mm × 648 mm and the detector is 166 mm thick. Expected proton rejection above 200 GeV is on the order of 104 . The TOF uses four layers of plastic scintillator, two located above the magnet and two below with a timing resolution of 160 ps. The RICH uses a proximity-focused design with a center 34 cm × 34 cm region of 5 mm thick NaF (n = 1.33) surrounded by an outer ring of silica aerogel (n = 1.05). Cherenkov light is imaged by an array of 10,880 photomultipliers. A 64 cm × 64 cm hole in the middle of the readout plane clears the acceptance of the ECAL. The central NaF radiator provides better resolution at lower energies and its larger refraction angle allows the Cherenkov cones produced to strike the photodetectors outside the hole. The RICH is designed to provide charge resolution up to Fe and a velocity resolution of 0.1%. The AMS-02 TRD is designed to help distinguish between positrons and protons. The TRD contains 5248 straw tubes, 6 mm in diameter, arranged in 20 layers alternating with 20 mm layers of polyethylene/polypropylene fleece radiator. The tubes are filled with a 80%:20% mixture of Xe and CO2 at 1.0 atm. The gas is cleaned by a recirculating system. The measured leak rate would give an operational life of over 24 years. Measured using 400 GeV protons, the TRD has a rejection power of 102 with an electron selection efficiency of 90%. Because this is independent of the ECAL rejection power, the result is net a hadron rejection factor of 106 .

Calorimeters In order to measure GCR protons, helium, and electrons above energies measurable by magnetic rigidity spectrometers (about 1TeV) ionization calorimetery is required. This is a standard technique for measuring electron and hadron energies at accelerators, but the constraints of balloon or space flight dictate designs that differ considerably from accelerator calorimeters. High-energy GCR calorimetry was pioneered in the Proton satellites (Akimov et al. 1970) and has been used by PAMELA (Picozza et al. 2007), ATIC (Advanced Thin Ionization Calorimeter)

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(Guzik et al. 2004), CREAM (Cosmic-Ray Energetics And Mass) (Ahn et al. 2007), Fermi-LAT (Atwood et al. 2009), and AMS (Kounine et al. 2010). In this section, we will discuss the ATIC and CREAM balloon instruments. Both instruments were designed to measure the spectra of hadronic GCRs to energies approaching the knee. ATIC has also contributed to the measurement of high-energy CR electron spectra. There are considerable similarities between the two approaches, including the inclusion of an interaction target to boost sensitivity to hadrons. However, they differ greatly in the calorimetry approach. We also briefly discuss the new CALET (CALorimetric Electron Telescope) instrument under construction for flight on the ISS (Torii et al. 2011). High-energy particles interact in material to produce particle cascades (showers) that deposit energy by ionization. The initial interaction probability and subsequent cascade development are characterized by an interaction length (λI ) for hadrons and radiation length (X0 ) for electrons and photons (and the electromagnetic component of hadronic cascades). In dense materials, λI is much larger than X0 . An ideal calorimeter fully contains the shower development of the incident particles. For space flight, however, the mass needed for such a full-containment calorimeter for hadrons is prohibitive and optimizing geometric acceptance requires a “thin” calorimeter that contains most of the development of electromagnetic showers but not hadronic showers. Thin calorimeters take advantage of the characteristic development of electromagnetic showers which peak quickly and drop to ∼1% of peak after ∼30 X0 . Energy resolutions of 1 are at a development stage past their maximum (absorption phase). The electron energy distribution follows the age-dependent power law dNe /dE ∼ E −(1+s) for E  Ec . Energy conservation leads to the track length integral: E0 =

Ec X0

 Ne (X) dX

(5)

in the approximation of constant ionization energy loss α = Ec /X0 and absence of hadronic interactions (photoproduction) or muon pair production. Mainly Coulomb scattering of electrons off air atoms leads to the lateral spread of the shower particles in em. showers. The average RMS of the deflection angle of an electron, Δθ , can be calculated in multiple scattering theory in the small-angle approximation:  Δθ 2 =

Es E

2

 ΔX X0

Es = me c2

4π ≈ 21 MeV, αem

(6)

with me and αem being the electron mass and the fine-structure constant (Molière 1948). The length scale of the lateral distribution of low-energy particles in a shower is characterized by the Molière unit r1 = (Es /Ec )X0 ≈ 9.3 g/cm2 ; see Tab. 1. Particles with E  Ec have a lateral spread reduced by the factor Ec /E. Therefore, most of the em. particles at large lateral distance have been produced by high-energy electrons or photons close to the shower axis at a depth only 2−3 radiation lengths higher up in the atmosphere. An often used analytical expression for the lateral spread is that of Greisen (1956), who parametrized the solutions of cascade equations obtained by Nishimura and Kamata (1965) with dNe Γ (4.5 − s) = Ne (X) 2 rdrdϕ 2π r1 Γ (s)Γ (4.5 − 2s)



r r1

s−2   r s−4.5 1+ , r1

(7)

now known as Nishimura-Kamata-Greisen (NKG) function. Various improvements to this parametrization have been developed; see Capdevielle et al. (2002). At very high energy, two additional processes change the characteristics of em. showers; see Risse and Homola (2007) for a review. At about E  1018 eV, subsequent interactions of photons or electrons with air can no longer be considered as independent, and the scattering amplitudes have to be added coherently (Landau and Pomeranchuk 1953; Migdal 1956). This effect is known as Landau-Pomeranchuk-Migdal (LPM) suppression of new particle production in certain kinematic regions (Stanev et al. 1982; Klein 1999). Shower-to-

26 Indirect Detection of Cosmic Rays

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shower fluctuations of em. showers increase, and the depth of maximum is shifted deeper into the atmosphere. Magnetic pair production and bremsstrahlung in the Earth’s magnetic field (Erber 1966; Stanev and Vankov 1997) become important for photons with E  1019.5 eV. Such interactions typically take place a thousand kilometers above the atmosphere. Mainly due to magnetic bremsstrahlung, a shower of more than 100 secondary photons and a few electrons is formed, which interact in the atmosphere simultaneously. Recent simulations of this effect can be found in Cillis et al. (1999); Vankov et al. (2003); Homola et al. (2005, 2007). As the primary energy is shared by many secondary particles, the LPM effect hardly influences such showers. Due to the superposition of many lower-energy em. showers, shower-to-shower fluctuations of converted primary photons are significantly reduced.

Hadron-Induced Showers The difference between em. and hadronic showers can be understood qualitatively within the model of Matthews (2005) of a simplified cascade (Heitler-Matthews model). Suppose the hadronic interaction of a particle of energy E produces ntot new hadronic particles, each with energy E/ntot . Let us further assume that two thirds of these particles are charged pions (multiplicity nch ) and one third neutral pions (multiplicity nneut ). Neutral pions decay immediately into em. particles (π 0 → 2γ ). Charged pions interact with air nuclei if their energy is greater than the typical decay energy Edec and decay at lower energy, producing one observable muon per pion. Then, the number of muons in a shower is given by  Nμ =

E0 Edec

β ,

β=

ln nch ≈ 0.86 . . . 0.93. ln ntot

(8)

The number of muons produced in an air shower increases almost linearly with primary energy and depends on the air density (through Edec ) and the charged and total particle multiplicities of hadronic interactions. Equation (8) can be improved to account for different particle types, different secondary particle energies, and an energy-dependent secondary particle multiplicity, but the overall functional form does not change (Matthews 2005; Alvarez-Muñiz et al. 2002; Kampert and Unger 2012; Grimm et al. 2018). Realistic values for β and Edec have to be determined with simulations. They depend on the modeling of hadronic multiparticle production, the zenith angle of the shower, and the energy threshold for muon detection. Examples for different hadronic interaction models can be found in Alvarez-Muñiz et al. (2002). The energy transferred from the primary hadron to the em. shower component can be calculated within the same model:

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R. Engel and D. Schmidt

Eem

  n 2 = 1− E0 , 3

(9)

where n is the number of interactions charged pions undergo before decaying. Here the assumption has been made that 1/3 of the energy is transferred to photons through π 0 decay in each interaction. For typical shower energies just above the knee, the number of generations of charged pions is about 5−6 (Meurer et al. 2006) and increases with primary shower energy up to 12. Correspondingly, the fraction of energy transferred to the em. component increases from about 70–80% at 1015 eV to 90–95% at 1020 eV. In contrast to the strong absorption seen for the em. shower component, muons reach the ground with only minor absorption. The em. shower component fed by the hadronic core behaves similar to a photoninduced shower except that it does not correspond to the full energy of the primary hadron and that the elongation rate of the depth of shower maximum is somewhat lower. The elongation rate of showers, D10 , is the amount by which the depth of maximum of a shower increases per decade of energy. (Note that sometimes also em De = ln 10D10 is used in literature. The elongation rate of em. showers is D10 = X0 ln 10.) The relation had D10 ≈ (1 − Bλ − Bn ) ln(10)X0 ln(E0 /Ec ) em ≈ (1 − Bλ − Bn )D10 ,

(10)

referred to as elongation rate theorem (Linsley and Watson 1981) approximately holds. The coefficients Bλ = −dλint /d ln E and Bn = d ln(ntot )/d ln E depend on the characteristics of hadronic multiparticle production. They are a measure of the increase of the interaction cross section and the amount of scaling violation of the secondary particle distributions. One particular implication of the elongation rate theorem is the fact that constant hadronic interaction cross sections and perfect scaling (i.e., energy-independent secondary particle distributions) lead to the maximum elongation rate of about 85 g/cm2 per decade. Again Eq. (10) can be improved by adding higher-order contributions, but the results are still very similar (Alvarez-Muñiz et al. 2002). Hadrons in an air shower exhibit a wide lateral distribution since secondary hadrons are produced at a typical, almost energy-independent transverse momentum of p⊥ ∼ 300 − 400 MeV, leading to a large angle of low-energy hadrons relative to the shower axis. Nonetheless, the lateral distribution of photons and electrons in hadronic showers is very similar to that of purely em. showers. The em. component is mainly fed by neutral pions of high energy, for which the ratio between transverse and longitudinal momentum is very small. Hence, the lateral spread of the bulk of the em. shower particles is still determined by multiple Coulomb scattering. Only at lateral distances much greater than the Molière unit, i.e., r  r1 , does the hadronically produced transverse momentum of photons begin to be important. These photons are produced by low-energy π 0 for which the longitudinal momentum is not much larger than the transverse one (Lafebre

26 Indirect Detection of Cosmic Rays

811

et al. 2009). The lateral distribution of muons is wider than that of em. particles as most of them are produced in the decay of low-energy pions for which ∼350 MeV transverse momentum leads to a large angle to the shower axis (Drescher and Farrar 2003; Meurer et al. 2006). To illustrate the typical parameters of hadron-induced showers at high energy, mean longitudinal and lateral profiles of the different shower components are shown in Fig. 3 for a proton-initiated shower of 1019 eV. The shower maximum is reached at about 1.5 km above sea level. The number of charged particles at shower maximum can be used to estimate the primary energy by multiplying it by 1.66 GeV, a relation that holds for a wide range of energies. The harder lateral distributions of muons and hadrons are clearly visible. Particles can be detected up to several kilometers from the shower core. The superposition model can be used to extend the results discussed so far to showers initiated by nuclei. The binding energy of the nucleons in a nucleus is much smaller than the typical interaction energies, allowing the seemingly crude approximation that a nucleus with mass A and energy E0 be considered as A independent nucleons with energy E0 /A. The superposition of A independent, nucleon-induced showers gives then

102 ±

μ

±

e

γ

10 1

0

20

200 10 400

7

±

600

hadrons

±

μ (x 100)

10-1 800

γ

5

3

hadrons (x 100)

10-2 10-3

e (x 5)

altitude (km)

103

atmospheric depth (g/cm2)

particle density (m-2)

(A) (p) (p) Nmax (E0 ) ≈ A · Nmax (E0 /A) ≈ Nmax (E0 )

1

1000 1

core distance (km)

0

1

2

3 4 x1010 particle number

Fig. 3 Lateral and longitudinal shower profiles for vertical, proton-initiated showers of 1019 eV simulated with CORSIKA. The lateral distribution of the particles at the ground is calculated for 870 g/cm2 , the depth of the Auger Observatory. The energy thresholds of the simulation were 0.25 MeV for γ , e± and 0.1 GeV for muons and hadrons. (From Engel et al. 2011, reproduced with permission of Annual Reviews)

812

R. Engel and D. Schmidt (A) (p) Xmax (E0 ) ≈ Xmax (E0 /A)   E0 /A β (A) Nμ (E0 ) ≈ A · = A1−β · Nμ(p) (E0 ). Edec

(11)

While the number of charged particles at shower maximum is almost independent of the primary hadron, the number of muons and the depth of maximum depend on the mass of the primary particle. The heavier the shower-initiating particle, the more muons are expected for a given primary energy. For example, iron showers contain about 40% more muons than proton showers of the same energy and reach their maximum 80−100 g/cm2 higher in the atmosphere. One of the important aspects of the superposition model is the fact that, averaged over many showers, the distribution of nucleon interaction points in the atmosphere coincides with that of more realistic calculations accounting for nucleus interactions and breakup into remnant nuclei (Engel et al. 1992). Therefore, the superposition model gives a good description of many features of air showers as long as inclusive observables are concerned such as the mean depth of shower maximum and the number of muons. However, it is not applicable to observables related to correlations or higher-order moments (Battistoni et al. 1997; Kalmykov and Ostapchenko 1989). Detailed shower simulations confirm qualitatively the energy and mass dependencies for hadronic showers discussed here (Knapp et al. 2003; Engel et al. 2011). There is a considerable uncertainty of the predicted shower parameters that stems from our limited knowledge of hadronic multiparticle production. Model assumptions are needed for extrapolating accelerator measurements to higher energies or regions of the phase space of secondary particles that are not measured in collider or fixed-target experiments. In turn, measurements of hadronic showers at these extreme energies test such assumptions and provide constraints. The measured distribution of the depth of shower maximum allows for estimation of the proton-air and proton-proton cross sections at the center of mass energies at ∼50 TeV (Abreu et al. 2012a; Abbasi et al. 2015; Ulrich 2016; Abbasi et al. 2020). Additionally, the fluctuations in the number of muons produced in air showers could be sensitive to the energy spectra of hadrons produced in the first interaction (Cazon et al. 2018). Tension exists between model predictions and measurements of the muon content of air showers. First reported in 2000 by the HiRes/MIA collaborations (AbuZayyad et al. 2000a) and since corroborated by a number of experiments (as summarized in Cazon 2020), a deficit exists in the number of muons predicted by detailed shower simulations when compared to measurements. Resolving this deficit requires an increase in the energy routed into the hadronic component of showers. This could take place in the first interactions, where exotic phenomena could play a role, or it could also take place to a much smaller extent over many generations in the shower development.

26 Indirect Detection of Cosmic Rays

813

Neutrino-Induced Showers Neutrinos interact through neutral and charged current reactions with the quarks of nuclei in air. Their interaction cross section with a nucleon can be parametrized as Glück et al. (1999)  νN σCC

= 

σNνNC =

1.10 × 10−36 (Eν /GeV)0.454 cm2 : 105  Eν /GeV  108 5.20 × 10−36 (Eν /GeV)0.372 cm2 : 108  Eν /GeV  1012 3.55 × 10−36 (Eν /GeV)0.467 cm2 : 105  Eν /GeV  108 , (12) 3.14 × 10−36 (Eν /GeV)0.349 cm2 : 108  Eν /GeV  1012

with a similar but slightly smaller cross section for antineutrinos. Although their interaction cross section rises with energy, the interaction probability in the atmosphere is only of the order of 10−5 for vertical incidence. This interaction probability can be much larger in theories with extensions to the standard model. One promising method of detecting neutrino-induced showers is that of searching for young, nearly horizontal air showers (Zas 2005; Aab et al. 2019a). The interaction of a neutrino with a nucleus is to a good approximation a pointlike scattering off a quark in which either a leading lepton (charged current (CC) interaction) or a high-energy neutrino is produced (neutral current (NC) interaction). The energy carried away by the leading lepton is of the order of 70−90%. Only for electrons or τ leptons (through the decay products) this energy might be detectable. The struck quark fragments together with the remnant of the nucleon produce many secondary hadrons. Production of high-energy charm particles is enhanced in comparison with other hadronic interactions because of the mass and coupling of the exchanged W and Z bosons. In certain kinematic configurations, one can expect to see a shower with two maxima, one coming from the hadronic shower produced by the quark fragmentation and another one from the shower initiated by the decay products of a leading τ lepton (Moura and Guzzo 2008). Neutrino interactions can be simulated with standard air shower codes if an external generator, for example, HERWIG (Corcella et al. 2001), is used for the first interaction.

Measurement Techniques and Observables A large variety of different detection techniques are applied in air shower experiments; see Kampert and Unger (2012), Schröder (2017) and Dawson et al. (2017) for recent reviews. Whereas in the early years of cosmic ray physics typically only one of these techniques was used per experiment, it is now common to combine several of them in hybrid detectors to take advantage of measuring several observables simultaneously and thereby reducing statistical and systematic uncertainties.

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R. Engel and D. Schmidt

Particle Detector Arrays Surface detector arrays consist of a set of particle detectors that are typically arranged on a regular pattern. Depending on the energy range for which the experiment is optimized, the distance between the detector stations can vary from ∼15 m (KASCADE Antoni et al. 2003a, Tibet AS-γ (Amenomori et al. 1990)) up to more than 1000 m (Telescope Array Ogio 2019, Pierre Auger Observatory Aab et al. 2015). Showers are detected by searching for time coincidences of signals in neighboring detector stations. The arrival direction can then be determined from the time delay of the shower front reaching the different detectors (see Fig. 4). The shower appears like a disk of particles that is a few meters thick in the center, increasing up to a few hundred meters at large lateral distances. Only at small lateral distances can the curvature of the shower front be approximated by a sphere. The angular resolution of the reconstructed arrival direction depends on the distance and accuracy of time synchronization between the detector stations and the number of particles detected per station (for defining the arrival time of the shower front). Air shower arrays typically reach angular resolutions of 1 − 2◦ for low-energy showers and better than 0.5◦ for those at high energies. The core position of the shower is found by fitting the signal S(r) of the detector stations with a suited lateral distribution function (LDF). Preferentially, the lateral distribution is determined from data directly using vertical showers. Because the NKG function (7) was developed to describe em. showers only, modified versions of the NKG function either  S(r) = C

r rs

−1.2   

r 2 −δ r −(η−1.2) 1+ 1.0 + , rs 1000 m

(13)

which was used for the scintillator array AGASA, or

Fig. 4 Detection principle and geometry reconstruction of air showers with surface detector arrays

26 Indirect Detection of Cosmic Rays

S(r) = C˜



815

r rs

−β 

r + rc rs + rc

−β+γ (14)

,

which is used with the water-Cherenkov detectors of the Auger Observatory (Aab et al. 2020a), are applied with other alternatives including phenomenological parametrizations such as that used at Haverah Park, namely r

¯ −(β+ 4000 m ) . S(r) = Cr

(15)

The parameters η, δ, β, γ , rc , and rs are determined from data or simulations. If several shower components are measured separately (charged particles, muons), different LDFs are used. There is a strong correlation between the arrival direction, shower curvature, core position, and asymmetry in the detector signal for nonvertical showers that has to be treated with care. The reached statistical uncertainty of the core positions varies from less than 1 m in the ideal case of a dense array and high-energy shower to up to more than 50 m for ultra-high-energy cosmic ray detectors. To reconstruct the energy of a shower, either the number of detected particles at the ground is calculated by integrating the lateral distribution or a signal density at a specific lateral distance is determined. The latter is illustrated in Fig. 5 for the Auger surface detector array. The measured signals of the detector stations of one particular

103

Signal / VEM

ropt = 1088 m S(r

102

10

opt

) = 27.4 VEM

β=1.9 β=1.7 β=1.5

1 500

1000

1500 r/m

2000

2500

Fig. 5 Example of the determination of the optimum distance for measuring the particle density of an air shower in the Pierre Auger Observatory (see text). The detector signal is expressed in units of the signal expected for vertical muons (vertical equivalent muons (VEM)). (From Newton et al. 2007, reproduced with permission of Elsevier)

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R. Engel and D. Schmidt

muon number

event are reconstructed with an NKG-like function with different values of β. A point where the differences between the fits are minimal is found at a core distance of about ropt = 1100 m (Newton et al. 2007). The signal (i.e., particle density) obtained for this distance is, to a good approximation, independent of the details of the LDF used for reconstruction and, hence, can be used as a robust estimator for determining the shower energy through comparison with Monte Carlo reference showers or cross-calibration with other calorimetric energy measurements. The optimum distance depends mainly on the spacing of the detectors and is not related to shower-to-shower fluctuations. An ideal detector configuration is reached if also the shower-to-shower fluctuations and the composition dependence of the lateral particle density exhibit a minimum at the optimum distance. This has been the case for the AGASA array with a detector distance of 1000 m and a minimum of the shower fluctuations at 1019 eV in the range of 600−800 m (Dai et al. 1988). Typical reconstruction resolutions for the signal at optimum distance or total particle number at the ground are in the range of 10−20%. The most promising surface detector approach is the separate measurement of the number of electrons and muons. The corresponding predictions for air showers simulated with the hadronic interaction models EPOS (Werner et al. 2006; Pierog and Werner 2009) and SIBYLL (Ahn et al. 2009) (interactions with E > 80 GeV) and FLUKA (Ballarini et al. 2006; Ferrari 2005b) (interactions with E ≤ 80 GeV) are shown in Fig. 6. The simulation results confirm the predictions of the superposition model; see Eq. (11), with a relative difference in the muon number between iron and proton showers of ∼40%. The difference in the number of electrons is mainly related to the shallower depth of shower maximum of iron showers relative to proton showers. The uncertainties stemming from the simulation

10

10

7

18

vertical showers at sea level

p

EPOS 1.99 SIBYLL 2.1 γ-induced

6

10 eV

Fe 17

10 eV

Fe

18

γ 10 eV

p 10

Fe

5

10 eV p

Fe 10

16

17

γ 10 eV

15

10 eV

4

p 10

5

16

γ 10 eV 10

6

10

7

10

8

electron number

Fig. 6 Predicted correlation between the number of muons and electrons of vertical showers at sea level. The simulations were done with CORSIKA using the same cutoff energies for the secondary particles as in Fig. 3. The curves encircle approximately the one-sigma range of the fluctuations. (From Engel et al. 2011, reproduced with permission of Annual Reviews)

26 Indirect Detection of Cosmic Rays

817

of hadronic multiparticle production in the showers affect the predictions for protons the strongest. With the energy transferred to the em. shower component being closely related to the number of muons at the ground, one can devise an almost model-independent estimator for the primary energy: E0 = Eem + Ehad ≈ E˜ c Ne(max),e + Edec Nμ ,

(16)

where E˜ c > Ec is a typical energy scale one has to assign to electrons to compensate for the non-detected photons. In practical applications, the energy is parametrized as ln E = a ln Ne + b ln Nμ + c, with a, b, and c being parameters determined from simulations. A similar expression can be written for ln A to find the primary mass; see Hörandel (2007). Depending on the distance of the observation level to the depth of the typical shower maximum, fluctuations in the particle numbers can be large and need to be accounted for in energy and composition reconstruction. The number of muons and electrons in a shower may be estimated from complementary measurements of particle detectors with differing amounts of overburden (Antoni et al. 2003a; Letessier-Selvon et al. 2014). In the limiting case, only muons will arrive at detectors with sufficient overburden to absorb all electrons and photons (Aab et al. 2016). Detectors with differing responses to the different particle types may also be used to deconvolve the relative signal contributions of each (Aab et al. 2016). A visualization of the signal generated by muons and electrons in a simulated water-Cherenkov detector and scintillator sampling an air shower at the same point in a shower can be seen in Fig. 7. The enhanced contribution from muons in the water-Cherenkov detector and electrons in the scintillator is visible. Other composition estimators are based on the fact that muons dominate the early part of the time signal in the detector stations (rise time method Walker and Watson 1982; Ave et al. 2003a; Aab et al. 2017b) and that the depth of shower maximum is related to the curvature of the shower front as well as the steepness of the lateral distribution (Ave et al. 2003b; Dova et al. 2004). The signal symmetry in azimuthal

Fig. 7 Signal time traces from a simulated water-Cherenkov detector (left) and scintillator (right) sampling the particles of an extensive air shower at the same position on the ground. (From Gonzalez et al. 2016, reproduced with permission of Elsevier)

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angle about the shower axis (Dova et al. 2009) has also been exploited (Aab et al. 2016a). In the early years of air shower measurements, air shower arrays have been the detectors with the largest acceptance leading to a number of fundamental discoveries. For example, using an array of hodoscope counters, Kulikov and Khristiansen discovered the knee in the spectrum of the electron number of showers in 1958 (Kulikov and Khristiansen 1958). Only a few years later, the first shower with an energy of about 1020 eV was measured with the Volcano Ranch detector, an array of 20 scintillation detectors covering 12 km2 (Linsley 1963). Larger detectors followed in the attempt to find the upper end of the cosmic ray spectrum (SUGAR Bell 1976, Haverah Park Edge et al. 1973, Yakutsk Glushkov et al. 1976, and AGASA Chiba et al. 1992). Investigations of the flux and composition of primary cosmic rays in the knee energy range have been done with a number of particle detector arrays making important contributions (i.e., CASA-MIA Glasmacher et al. 1999, EAS-TOP Aglietta et al. 2004a, KASCADE – see section “KASCADE” – and GRAPES Tanaka et al. 2008). The combination of information from electromagnetic and muon detectors has been very important for these measurements. Alternatively, surface arrays can be operated in coincidence with deep underground muon detectors providing a complementary way of deriving composition information (i.e., EASTOP with MACRO Aglietta et al. 2004b, IceTop with IceCube Abbasi et al. 2013). Detection of gamma-ray sources or source regions was achieved only within the last decade with very-high-altitude detectors including Tibet AS-γ (Amenomori et al. 1990), ARGO-YBJ (Aielli et al 2006), HAWC (Abeysekara et al. 2017b), and, most recently, LHAASO (Bai et al. 2019).

Atmospheric Cherenkov Light Detectors The large number of Cherenkov photons emitted by the charged particles when traversing a medium with refractive index n > 1 can be used for efficient detection of air showers in a wide range of energies. Imaging atmospheric Cherenkov telescopes (IACTs) can detect showers above an energy threshold of about 30 GeV (Aharonian et al. 2008a; Hinton and Hofmann 2009) but are limited in reach to very high energies due to the small effective area. Non-imaging Cherenkov detectors can be set up similar to an array of particle detectors, offering the possibility to instrument very large areas at ground level and reach very high energies (Budnev et al. 2009; Ivanov et al. 2009). Typically, only the Cherenkov light of the abundant secondary particles in an air shower is detected, but the direct Cherenkov light of the primary particle can also be measured (Kieda et al. 2001; Aharonian et al. 2007). The production of Cherenkov radiation is discussed in detail in  Chap 18, “Cherenkov Radiation.” Here we recall some important features of relevance to air shower detection. It is convenient to express the threshold of particle energy E for Cherenkov light emission in terms of the Lorentz γ -factor:

26 Indirect Detection of Cosmic Rays

γ ≥

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n(h) n(h)2 − 1

,

(17)

with E = γ m and m being the particle mass. The height dependence of the refractive index n(h) is a function of the local air density and follows approximately n(h) = 1 + 0.000283

ρair (h) , ρair (0)

(18)

where ρair is the density of air. The energy threshold for electrons and the Cherenkov angle θch in air, cos θch = 1/(βn(h)), are given in Table 1 as a function of height. Typical values at h = 10 km are θch = 0.8◦ (12 mrad) and a threshold of γ = 72, corresponding to E = 37 MeV for electrons and E = 7.6 GeV for muons. The Cherenkov light cone of a particle at 10 km height has a radius of about 120 m at the ground. This means that most of the light is expected within a circle of this radius. Due to multiple Coulomb scattering, the shower particles do not move parallel to the shower axis. The angular distribution follows in first approximation an exponential dNγ 1 = e−θ/θ0 , dθ θ0

θ0 = 0.83Eth0.67 ,

(19)

with Eth being the Cherenkov energy threshold (Hillas 1982a,b). Typical values of θ0 are in the range of 6-8◦ . The interplay of the altitude-dependent Cherenkov angle and the emission height leads to a typical lateral distribution of photons at the ground (see Fig. 8). The absorption and scattering of Cherenkov light in the atmosphere limits the detectable wavelength range to about 300−450 nm, where the upper limit follows from the λ−2 suppression of the emission of large wavelengths. One possible parametrization of the lateral distribution of the Cherenkov light is Fowler et al. (2001)  C(r) =

C120 · exp(a[120 m − r]); C120 · (r/120 m)−b ;

30 m < r ≤ 120 m , 120 m < r ≤ 350 m

(20)

with the parameters C120 , a, and b. Clear, moonless nights are required for taking data with air Cherenkov detectors resulting in an effective duty cycle of 10−15%. Also continuous monitoring of the atmospheric conditions including the density profile of the atmosphere is necessary (Bernlöhr 2000). Arrays of photodetectors are used in non-imaging Cherenkov experiments to sample the lateral distribution of light in dark and clear nights. After reconstructing the core position, the measured parameter C120 and the slope are linked to the properties of the primary article. Simulations show that the density of photons at 120 m from the core is almost directly proportional to the energy of the shower and that the slope is related to the depth of shower maximum (Hillas

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Fig. 8 Left: Illustration of the relation between production height and Cherenkov opening angle for producing the observed Cherenkov light distribution at the ground. Right: Simulated lateral distributions of Cherenkov light produced by proton-induced showers of different zenith angle (Korosteleva et al. 2003). The simulations were done for a height of 2000 m above sea level. (From Korosteleva et al. 2003, reprinted with permission)

1982b). Examples of surface arrays applying this non-imaging technique of shower detection via Cherenkov light are AIROBICC (Karle et al. 1995), EASTOP (Aglietta et al. 2004c), BLANCA (Fowler et al. 2001), Tunka (Budnev et al. 2009) and HiSCORE (Tluczykont et al. 2014) – see section “Tunka” – and Yakutsk (Ivanov et al. 2009). Over the last two decades, much progress has been made in applying the imaging Cherenkov method to the detection of high-energy gamma rays. Two or more large Cherenkov telescopes are placed at a typical distance of about 100 m, allowing the reconstruction of shower direction and energy with high accuracy from stereoscopic images. The detection principle is illustrated in Fig. 9. Using shape parameters, photon-induced showers can be discriminated from the 105 times more abundant hadronic showers. While hadronic showers of GeV and TeV energies are characterized by a rather irregular structure due to the subshowers initiated by π 0 decay, photon-induced showers have a smooth overall shape. A moment analysis of the elliptical images in terms of the Hillas parameters (Hillas 1996) provides cuts to select gamma-ray showers. The technique of imaging atmospheric Cherenkov telescopes was developed and established with the monocular Whipple telescope (Mohanty et al. 1998). The largest atmospheric Cherenkov telescopes currently in operation are H.E.S.S. (Bernlöhr et al. 2003; Cornils et al. 2003),

26 Indirect Detection of Cosmic Rays

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km 0.3 TeV γ ray

1°

1 TeV proton

20

10

100 m Fig. 9 Illustration of the stereo-detection principle of imaging atmospheric Cherenkov telescopes (Hinton and Hofmann 2009). The superimposed camera images are shown on the left-hand side. The intersection of the shower axes in this combined image corresponds to the arrival direction of the shower. (From Hinton and Hofmann 2009, reprinted with permission of Annual Reviews)

MAGIC (Ferenc 2005a; Borla Tridon et al. 2010), and VERITAS (Weekes et al. 2002, 2010) – with CTA (Actis et al. 2011) soon to follow.

Fluorescence Telescopes If the shower energy exceeds 1017 eV, fluorescence light produced by nitrogen molecules in the atmosphere can be used to measure directly the longitudinal profile of air showers. Nitrogen molecules are excited by the charged particles of an air shower traversing through the atmosphere. The de-excitation proceeds through different channels of which two transitions of electronic states, called 2P and 1N for historical reasons, lead in combination with the change of the vibrational and rotational states of the molecule to several fluorescence emission bands. The spectral distribution of the fluorescence light is shown in Fig. 10. Most of the fluorescence light emission is found in the wavelength range from 300 to 400 nm. The lifetime of the excited states of nitrogen is of the order of 10 ns. The number of emitted fluorescence photons would follow directly from the ionization energy deposited by the shower particles in the atmosphere if there were no competing de-excitation processes. Collisions between molecules are the

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Fig. 10 Left: Fluorescence light spectrum of air at 20 ◦ C and 800 hPa (Arciprete et al. 2006). The bands are labeled with the electronic transition type (2P or 1N) and the change of the vibration quantum number. Reproduced with permission of Elsevier. Right: Illustration of the detection principle of fluorescence telescopes. The arrival angle of the shower can be measured with high precision in the shower-detector plane. (Courtesy of Enrique Zas, reproduced with permission)

dominant non-radiative de-excitation processes (collisional quenching, see, e.g., Keilhauer et al. 2006). The importance of quenching increases with pressure and almost cancels the density dependence of the energy deposit per unit length of particle trajectory. These compensatory processes result in an only weakly heightdependent rate of about 4−5 fluorescence photons produced per meter and charged particle at altitudes between 5 and 10 km. In contrast to the Cherenkov yield, the fluorescence yield cannot be predicted from theory. Therefore, several experiments have been carried out to measure the yield under different atmospheric conditions; see Arqueros et al. (2008) for a review. The reconstruction of a shower profile observed with a fluorescence telescope requires the determination of the geometry of the shower axis, the calculation of the Cherenkov light fraction, and the correction for the wavelength-dependent atmospheric absorption of light. In shower observations with one fluorescence telescope (monocular observation), the arrival angle perpendicular to the showerdetector plane can be determined with high precision (see Fig. 10). The orientation of the shower within this plane, described by the angle ψ, is derived from the arrival time sequence of the signals at the camera. The angular uncertainty of the orientation of the shower-detector plane depends on the resolution of the fluorescence camera and the length of the measured track. Typically a resolution of the order of 1◦ is obtained. In general, the reconstruction resolution of ψ is much worse and varies between 4.5◦ and 15◦ (e.g., see Abbasi et al. 2007). The reconstruction accuracy can be improved considerably by measuring showers simultaneously with two telescopes (stereo observation). Showers observed in stereo mode can be reconstructed with an angular resolution of about 0.6◦ (Abbasi et al. 2007). A similar reconstruction quality is achieved in hybrid experiments that use surface detectors to determine the arrival time of the shower front at the ground (Bonifazi et al. 2005; Aglietta et al. 2007).

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Knowing the geometry of the shower axis, one can reconstruct the shower profile from the observed light intensities. While the highly asymmetric Cherenkov light has been subtracted from the light profile in the past (Baltrusaitis et al. 1985), new reconstruction methods take advantage of the Cherenkov light as additional shower signal (Unger et al. 2008) or even as dominating signal (Abbasi et al. 2018). This is possible since universality features of air showers allow a good prediction of the emitted and scattered Cherenkov light signal (Giller et al. 2005; Nerling et al. 2006; Arbeletche and de Souza 2020). The fluorescence technique allows a calorimetric measurement of the ionization energy deposited in the atmosphere. The integral over the energy deposit profile is a good estimator of the energy of the primary particle. At high energy, about 90% of the total shower energy is converted to ionization energy (Barbosa et al. 2004; Pierog et al. 2005). The remaining 10% of the primary energy, often referred to as missing energy, is carried away by muons and neutrinos that are not stopped in the atmosphere or do not interact. The missing energy correction depends on the primary particle type and energy as well as details on how hadronic interactions in air showers are modeled. As most of the shower energy is transferred to em. particles, this model dependence corresponds to an uncertainty of only a few percent of the total energy. In the case of a gamma-ray primary, about 99% of the energy is deposited in the atmosphere. Given complementary observations by fluorescence detectors and muon-sensitive detectors at the ground, the missing energy may be estimated directly from measurements (Aab et al. 2019b) as opposed to simulations alone. This results in a reduction of systematic uncertainties deriving from uncertainties on mass composition and hadronic models. The function proposed by Gaisser and Hillas (1977) gives a good phenomenological description of individual as well as averaged longitudinal shower profiles:  N (X) = Nmax

X − X1 Xmax − X1

(Xmax −X1 )/Λ

  X − Xmax , exp − Λ

(21)

with X1 and Λ = 55 − 65 g/cm2 being parameters. It is often used to extrapolate the measured shower profiles to depth ranges outside the field of view of the telescopes. A typical shower profile reconstructed with the fluorescence telescopes of the Auger Observatory (Abraham et al. 2010a) is compared to simulated showers in Fig. 11. Both the mean depth of shower maximum and the shower-by-shower fluctuations of the depth of maximum carry important composition information. The fact that the fluorescence light is emitted isotropically makes it possible to cover large phase-space regions with telescopes in a very efficient way. The typical distance at which a shower can be detected varies from 5 to 35 km, depending on shower geometry and energy. On the other hand, fluorescence detectors can only be operated on dark and clear nights, limiting the duty cycle to about 10– 15%. Furthermore, continuous monitoring of atmospheric conditions is necessary, in particular the measurement of the wavelength-dependent Mie scattering length

R. Engel and D. Schmidt

8

1200010000

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Height a.s.l. (m) 4000 2000 Number of charged particles (x109)

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Fig. 11 Profile of one shower measured with the Pierre Auger Observatory (Aab et al. 2015). The reconstructed energy of this shower is about 1019 eV. The data are shown together with ten simulated proton and iron showers to demonstrate the composition sensitivity of the depth of shower maximum. The showers were simulated with the SIBYLL interaction model (Engel et al. 1992; Ahn et al. 2009) and the CONEX air shower package (Bergmann et al. 2007)

and detection of clouds (e.g., see Abbasi et al. 2006; Abraham et al. 2010b). The density profile of the atmosphere and seasonal variations of it have to be known, too (Keilhauer et al. 2004). In 1976, fluorescence light of air showers was detected in a proof-of-principle experiment at Volcano Ranch (Bergeson et al. 1977) which was followed by the pioneering Fly’s Eye experiment in 1982 (Baltrusaitis et al. 1985). The Fly’s Eye detector was operated for 10 years, beginning with a monocular setup (Fly’s Eye I) to which later a second telescope was added (Fly’s Eye II). Fly’s Eye II was designed to measure showers in coincidence with Fly’s Eye I improving the event reconstruction by stereoscopic observation. In October 1991, the shower of the highest energy measured so far, E = (3.2 ± 0.9) × 1020 eV, was detected with Fly’s Eye I (Bird D, et al. 1995). The successor to the Fly’s Eye experiment, the High Resolution Fly’s Eye (HiRes) (Abu-Zayyad et al. 2000b; Boyer et al. 2002), took data from 1997 (HiRes I) and 1999 (HiRes II) to 2006. With an optical resolution of 1◦ × 1◦ per camera pixel, a much better reconstruction of showers was achieved. Currently, there are two fluorescence telescope systems taking data, both measuring in coincidence with a surface detector array. The Telescope Array (TA) detector (Ogio 2019) in the northern hemisphere consists of three fluorescence detector stations (Tokuno et al. 2012), each separated by approximately 35 km to form a roughly equilateral triangle, which view the atmosphere above an scintillator array of about 700 km2 area. In the southern hemisphere, the Pierre Auger Observatory (Aab et al. 2015) is taking data with four fluorescence telescope stations (Abraham et al. 2010a) and a surface array of water-Cherenkov detectors covering about 3000 km2 ; see section “The Pierre Auger Observatory.”

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Fig. 12 Left: Illustration of geomagnetic emission. The red arrows indicate the linear polarization in the shower-detector plane. Right: Illustration of charge excess emission. (Further adaptation of Huege (2016); original schematics from Schoorlemmer 2012; de Vries et al. 2012, with permission of Elsevier)

Radio Signal Detection Extensive air showers emit radiation at radio frequencies primarily due to two processes. The more dominant, termed geomagnetic emission, stems from the timedependent charge separation of electrons and positrons in the shower disk as they pass through Earth’s magnetic field (Kahn and Lerche 1966; Falcke and Gorham 2003; Huege and Falcke 2003). Depicted in Fig. 12 (left), this results in the linear polarization of the emitted radiation where the electric field vector is oriented in the direction of the Lorentz force in the shower-detector plane. The second mechanism, referred to as charge excess or Askaryan emission (Askaryan 1961, 1965), results from a time-dependent excess of electrons over positrons reaching ∼20% in the shower disk. With the passage of the shower disk, molecules in the air are ionized, and whereas the ionized electrons are swept up, the heavier, positive ions are left behind. As depicted in Fig. 12 (right), this also results in linearly polarized radiation, but with the electric field vector pointing toward the axis of the shower. Both emission processes can be coherent for wavelengths larger than the typical thickness of the shower disk of a few meters, which corresponds to frequencies smaller than ∼100 MHz. As such, the expected electric field is proportional to the number of electrons Ne . Given that Ne is proportional to the energy of the primary E0 , the power radiated by a shower therefore scales quadratically with E0 . Whereas the electric field vectors for geomagnetic emission have the same orientation regardless of the position of the observer, those of the charge excess emission do not. Depending on the position of the observer, the contributions to the radio signal can add either constructively or destructively, which results in complex asymmetries in the shower-detector plane. Additionally, due to the ultra-relativistic propagation of the shower disk and given the height-dependent index of refraction of the atmosphere, the radio radiation is collimated and results in a lateral distribution with a width comparable to that of Cherenkov light (de Vries et al. 2011). The nature of the emission processes (Askaryan 1961, 1965) leads immediately to a number of qualitative predictions that have been confirmed in detailed calculations (Engel et al. 2006; Ludwig and Huege 2011; de Vries et al. 2012). A quantitative theory of radio emission from air showers has made significant

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progress in recent years (Huege et al. 2012). In macroscopic calculations, the time variation of the charge excess and the current due to charge separation are parametrized, and the radio signal is calculated using the retarded Liénard-Wiechert potential for the effective currents (Kahn and Lerche 1966; Scholten et al. 2008; Werner and Scholten 2008; Chauvin et al. 2010; de Vries et al. 2012). A number of external input parameters are needed in these calculations to describe the path length and mean separation of e± in showers. Depending on the degree of detail of the implementation of shower features, this approach can be used to predict the radio signal only at large distance from the core and shower disk, and not too high frequencies. In contrast, adding up the radio signal from each particle during Monte Carlo simulation of a shower promises to account for all details of shower evolution and corresponding fluctuations (DuVernois et al. 2005; Engel et al. 2006; Kalmykov et al. 2009). This approach is numerically challenging and very time-consuming, but has been met with a large degree of success. The codes CoREAS (Huege et al. 2013) and ZHAireS (Alvarez-Muñiz et al. 2012), considered the state of the art, respectively, employ endpoint and ZHS formalisms in simulating radio emission from moving charges. Predictions using these two formalisms have been compared with dedicated laboratory measurements and shown to agree to within ∼5% (Belov et al. 2016). Together with differences between the air shower simulation codes in which CoREAS and ZHAireS are embedded and differences in employed atmospheric models, this results in a quantitative and qualitative agreement in the simulation of radio emission from air showers to within ∼20%. The first measurements of radio pulses from air showers were already performed by Jelley et al. (1965) in 1965 to verify the prediction by Askaryan that air showers should produce electromagnetic pulses in the radio frequency range in the atmosphere (Askaryan 1961, 1965). A review of the early attempts of exploiting this signal for cosmic ray measurements is given in Allan (1971). Data analysis was hampered by the limited power of electronic signal processing and atmospheric monitoring at the time. Less than two decades ago, new attempts of utilizing the radio signal of air showers were started (Falcke and Gorham 2003), aided by advancements in digital electronics. The first experiments in the digital era were LOPES (Falcke et al. 2005) and CODALEMA (Ardouin et al. 2005), which were both triggered by scintillator arrays and measured radio pulses in the 30−80 MHz range. The data confirmed both the approximately linear scaling of the electric field with energy and the geomagnetic emission mechanism as the dominant source of the radio signal in the MHz range (Falcke et al. 2005; Ardouin et al. 2009). A sample radio pulse measured by LOPES is shown in Fig. 13 (top). The second generation of digital detectors includes AERA (Schulz 2016) (see section “The Pierre Auger Observatory),” LOFAR (Schellart et al. 2013), and Tunka-Rex (Bezyazeekov et al. 2015) – see section “Tunka.” A sample measurement of a lateral distribution with LOFAR is shown in Fig. 14. The Cherenkov bump and asymmetries in the lateral distribution are clearly visible alongside the reproduction

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Fig. 13 Top: Radio pulse measured with LOPES in the frequency range 40−80 MHz (Apel et al. 2010b). Different lines show the signal from different radio antennas. The incoherent signal after the radio pulse (starting at −1.7 μs) stems from the particle detectors in the KASCADE array. (From Apel et al. 2010b, reproduced with permission of Elsevier). Bottom: Different antenna designs: (a) Logarithmic periodic dipole used by AERA Phase I (from Schröder 2016), (b) Butterfly antennas used by AERA Phases II and III (from Schröder 2016), (c) SALLA antenna at Tunka-Rex (from Kostunin et al. 2014), (d) low-band antenna of LOFAR. (Image credit: André Offringa)

thereof with CoREAS. Pictures of the different antenna designs used in each experiment are shown in Fig. 13 (bottom). With this second generation of digital detectors, methods of reconstructing the primary energy and the depth of shower maximum from radio measurements were matured and validated on much larger scales through cross-calibrations with other indirect detection techniques. The energy of an air shower may be estimated from its quadratic relationship with the total energy coherently radiated. The energy flux calculated from the square of the time-dependent electric field reconstructed for individual antennas may be integrated to obtain the energy fluence. The two-dimensional lateral distribution of the energy fluence may then be integrated to obtain the total radiation energy. The radiation energy for the frequency band of 30–80 MHz for showers measured by AERA is shown in Fig. 15 (left) as a function of the shower energy reconstructed by the surface detector of the Auger Observatory (Aab et al. 2016b). The expected quadratic relationship is observed.

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Fig. 14 Lateral distribution of total power as measured by LOFAR. Left: Two-dimensional lateral distribution from best-fit CoREAS simulation as a backdrop to the measurements of individual LOFAR antennas (circles). Right: One-dimensional projection of the same lateral distribution. (Adapted from Buitink et al. 2014, reproduced with permission by the American Physical Society)

The radio technique also offers sensitivity to the mass of cosmic rays through the slope of the lateral distribution. This slope has a direct and energy-independent relationship to the depth of the shower maximum (Huege et al. 2008; Kalmykov et al. 2009; de Vries et al. 2010). Shown in Fig. 15 (right) is the 1:1 correlation between the depth of shower maximum reconstructed via the slope of the radio lateral distribution as measured by Tunka-Rex with that measured by the Tunka133 Cherenkov detectors (Bezyazeekov et al. 2015). A direct comparison of the full two-dimensional lateral distribution with simulation predictions also allows for a reconstruction of the depth of shower maximum and takes full advantages of the asymmetries and Cherenkov bump. More in-depth summaries of the radio detection technique may be found in Huege (2016) and Schröder (2017). Until now, detectors of radio emission have largely relied on an external trigger from particle detectors, but efforts have been made in triggering on the radio signal directly. These have been met with limited success in regions with high rates of transient noise (Abreu et al. 2012b; Torres Machado 2013), although self-triggering may be possible in areas where such an interference is very low as indicated by measurements in Antarctica (Boser 2012) and rural China (Ardouin et al. 2011).

Examples of Air Shower Detectors In the following, some typical air shower-detector installations are reviewed. The large diversity of such detectors makes it impossible to discuss examples of all the different detection techniques in depth.

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Fig. 15 Left: Correlation of the radiation energy reconstructed by AERA with the energy reconstructed by the surface detector of the Auger Observatory. The radiation energy has been normalized to account for different angles of incidence relative to the geomagnetic field. Adaptation from Huege (2016) of original in Aab et al. (2016b), with permission of Elsevier. Right: Correlation between the atmospheric depth between observer and shower maximum as measured with atmospheric Cherenkov light by Tunka-133 and with radio emission by TunkaRex. (Adaptation from Huege (2016) of original in Bezyazeekov et al. (2015), with permission of Elsevier)

KASCADE KASCADE (Karlsruhe Shower Core and Array Detector) was a multi-detector complex combining a classic air shower array for the electromagnetic and muonic components of showers with a central calorimeter and a muon tracking detector (Antoni et al. 2003a). The KASCADE detector was located in Karlsruhe, Germany (49.1◦ N, 8.4◦ E), at an altitude of 110 m above sea level. The layout of the detector complex is shown in Fig. 16. The scintillation detectors of the air shower array are housed in 252 stations on a rectangular grid with 13 m spacing. The detector stations contain liquid scintillators (There are two scintillation detectors in each station of the outer clusters and four per inner station.) of 0.78 m2 for measuring charged particles with a detection threshold of about 5 MeV. The stations of the outer detector clusters also contain plastic scintillators of 3.24 m2 that are shielded by a layer of 10 cm of lead and 4 cm of iron for muon detection with a threshold of about 230 MeV. The central detector of 320 m2 contains a hadron sampling calorimeter (8 layers of iron slabs and liquid scintillators) with a threshold of 50 GeV (Engler et al. 1999) and a muon tracking detector (multiwire proportional chambers and a layer of limited streamer tubes) with an energy threshold of 2.4 GeV (Bozdog et al. 2001; Antoni et al. 2004). The muon tracking detector north of the central detector is built up of 3 layers of limited streamer tubes shielded by a layer of soil with a detection area of 128 m2 for vertical muons (800 MeV detection threshold) (Doll et al. 2002).

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200 m

muon tracking detector

13 m

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array cluster

electronic station detector station 0 10m 20m

Fig. 16 Layout of the KASCADE detector with an effective area of 200 × 200 m2 (Antoni et al. 2003a). The detector stations of the array are grouped in 16 clusters for triggering and readout. (Reproduced with permission of Elsevier)

The KASCADE detector began operation in 1996. In 2003, an array of 37 scintillators with a spacing of about 137 m was added (KASCADE-Grande), increasing the array size to 0.5 km2 (Apel et al. 2010a). Regular data taking finished in 2009. Both air shower arrays served as a trigger for other experiments such as LOPES (Falcke et al. 2005). Important results obtained with the KASCADE detector include the flux and groundbreaking composition measurement in the knee energy range (Antoni et al. 2003b, 2005), showing unambiguously that the composition changes toward a heavier one with increasing energy, and tests of hadronic interaction models (Antoni et al. 1999, 2001; Apel et al. 2006, 2007). KASCADE-Grande observed the second knee of the energy spectrum (Apel et al. 2013a) and a hardening in the spectrum of light nuclei around the same energy (Apel et al. 2013b). The air shower simulation package CORSIKA (Cosmic Ray Simulations for KASCADE) (Heck et al. 1998) was developed in the course of designing

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KASCADE and later continuously improved for analyzing the data taken with KASCADE and KASCADE-Grande. Nowadays, CORSIKA has become the standard tool of almost all air shower experiments worldwide.

HAWC The High-Altitude Water Cherenkov Gamma Ray Observatory, referred to as HAWC, is a large-area water-Cherenkov detector that performs continuous monitoring of the sky for gamma-ray sources with a field of view of ∼2 sr at any instant. Completed in 2015, it is situated at an elevation of 4100 m on a plateau in the Parque Nacional Pico de Orizaba in Mexico. This elevation results in a sensitivity to gamma rays at energies as low as 100 GeV (Abeysekara et al. 2017a,b). The layout of the HAWC detector is shown in Fig. 17. Covering an area of 22,000 m2 , it is comprised of 300 cylindrical steel tanks of 7.3 m diameter filled to a depth of 4.5 m with purified water. Ultra-relativistic charged particles passing through the water produce Cherenkov light, which is collected by four upwardfacing PMTs at the bottom of each tank. Not only electrons and muons contribute to the light signal. The much more abundant photons convert into electron-positron pairs in the water, which also give rise to Cherenkov light. HAWC records air showers at a rate of 25 kHz. Full detection efficiency is reached at 1 TeV, and gamma-ray measurements extend beyond 100 TeV. The angular resolution is within 1◦ around the detection threshold and improves to around 0.2◦ for the highest-energy showers. Discrimination between air showers induced by gamma rays and hadrons is done through analysis of the topology of events. The nearly purely electromagnetic air showers induced by gamma rays exhibit compact and smooth lateral distributions, whereas hadron-induced showers exhibit larger fluctuations and extend to larger distances from the shower axis. Application of these two criteria allows for a

Fig. 17 Left: View of the HAWC Gamma-ray Observatory (Image credit: Instituto Nacional de Astrofísica, Óptica y Electrónica). Right: Schematic of one water-Cherenkov detector. (Courtesy of Brian Baughman and Segev BenZvi)

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selection of photons with a minimum of 40% efficiency, while only 1 in 10 hadroninduced showers survive for the lowest-energy showers and only 1 in 1000 for the highest. A gamma-ray signal shows up as an excess of events from the direction of the source or source region. HAWC has already pinpointed a number of specific galactic sources with gamma-ray emission extending beyond 100 TeV (Abeysekara et al. 2017a,b). Also an unexpected anisotropy of cosmic rays at the level of 10−4 on scales of 10◦ has been found (Abeysekara et al. 2014).

Tunka Tunka is a classic non-imaging air Cherenkov detector for observing the Cherenkov light flashes of hadronic showers in clear moonless nights. It is located at an altitude of 680 m in the Tunka valley near Lake Baikal, Russia (51◦ 48 N, 103◦ 04 E). The initial setup of 25 detector stations (Tunka-25, 0.1 km2 ) was extended to 133 stations in 2009 and now covers an area of 1 km2 (Antokhonov et al. 2011). Each of the 133 detector stations contains an upward-facing PMT with a photocathode of 20 cm diameter. Stations are grouped into 19 hexagonal clusters of 7 detectors each. The signal is digitized by FADCs at 200 MHz. Each station is equipped with a remote-controlled protection cap that is closed during daytime to protect the PMTs. One year of operation corresponds to about 400 h data taking time under ideal conditions. Both the lateral distribution derived from the time-integrated signal and the width of the time trace recorded by the stations can be used to derive composition information for the primary particles through the dependence on the depth of shower maximum. The data of Tunka have been analyzed (Budnev et al. 2009; Prosin et al. 2016), and the mean depth of shower maximum has been derived in the knee energy range that is not accessible to fluorescence telescopes. The results give important, independent support to the composition estimate derived from ground-based particle arrays (i.e., KASCADE Antoni et al. 2005 and EAS-TOP data (Aglietta et al. 2004a)). From 2012 to 2018, an array of SALLA antennas was operated at the Tunka133 site with an additional external triggering by scintillator detectors provided from 2015 until the end of data acquisition. This setup, known as TunkaRex (Bezyazeekov et al. 2015), measured the radio signal of air showers and provided a direct cross-calibration of the energy and depth of shower maximum of extensive air showers as measured by the atmospheric Cherenkov light and radio signal detection methods.

H.E.S.S. The H.E.S.S. (High Energy Stereoscopic System) is a high-energy gamma-ray telescope of the third generation. It consists of 5 imaging atmospheric Cherenkov

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telescopes located at the Khomas Highland (1800 m a.s.l.; 23◦ 16 S, 16◦ 30 E) in Namibia. Key features of gamma-ray telescopes of the third generation are large mirror areas, cameras with very fine pixelation and a large total field of view, and stereoscopic observation. The large mirror size is required for reaching energy thresholds of ∼100 GeV and below. The fine pixelation of the camera allows a very good discrimination between photon- and hadron-induced showers. At the same time, a large field of view is of great advantage. The image of an individual shower is typically 1◦ wide, and many gamma-ray sources are extended objects on the sky. Finally, stereoscopic observation improves the reconstruction quality of showers and enables a very efficient suppression of the background from single muons. The H.E.S.S. telescopes have been designed for maximum mechanical rigidity and, at the same time, allowing full steering and automatic remote alignment of the mirror systems. The first four telescopes, comprising Phase I, began operation in the summer of 2002 and have a mirror area of 108 m2 per telescope (see Fig. 18). Each telescope has a focal length of 15 m and a mirror diameter of 12 m. The mirrors are built up of 382 individual reflectors of 60 cm diameter and can be aligned individually to minimize the point spread function of the telescope. Each camera of the telescopes – weighing almost 1 ton – consists of 960 pixels, each viewing 0.16◦ of the sky. The total field of view is about 5◦ . The telescopes can be pointed to a source with an angular precision of about 2.5 and a slew rate of 100◦ /min. The resulting performance of the H.E.S.S. array is the following. Showers can be reconstructed with an angular resolution better than 0.1◦ . Applying cuts on the Hillas parameters of the images, 50% or more gamma-ray events and less than 0.1% hadronic events are accepted. The detection threshold for gamma rays is about 100 GeV. The effective collection area exceeds 1 km2 for showers above 10 TeV. The sensitivity of H.E.S.S. can be illustrated with the Crab Nebula as benchmark source. The Crab Nebula can be detected in about 30 s at 5σ confidence level. To lower the energy threshold to 70 GeV and to increase the sensitivity of detection by a factor of 2, a giant 28 m telescope was built in the center of the original H.E.S.S. array and is operational since July 2012. The H.E.S.S. II telescope

Fig. 18 Photograph of a H.E.S.S. telescope in which the steel frame, mirror elements, and camera are visible. (Courtesy of the H.E.S.S. collaboration / MPIK Heidelberg, reproduced with permission)

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has a parabolic mirror shape with an area of 614 m2 and a focal length of 36 m. The camera contains 2048 pixels viewing a total of 3.2◦ on the sky. Many groundbreaking measurements and discoveries were made with H.E.S.S. One highlight is the galactic plane survey that resulted in more than 40 sources in a band of 60◦ < l < 280◦ of galactic longitude l, many of them being spatially extended (Aharonian et al. 2006a), and also the discovery of a new class of sources (Aharonian et al. 2005). Other outstanding results are the spatially resolved observation of galactic supernova remnants, the measurement of the local electron spectrum (Aharonian et al. 2008b), the discovery of diffuse gamma-ray emission from the galactic center ridge (Aharonian et al. 2006b), and the indirect observation of a PeV accelerator at the galactic center (Abramowski et al. 2016).

The Pierre Auger Observatory The Pierre Auger Observatory (35.3◦ S, 69.3◦ W), located at an altitude of about 1450 m in the Pampa Amarilla near the town Malargüe, Argentina, is the largest air shower detector built so far (Aab et al. 2015). It has been designed to investigate the highest-energy cosmic rays combining a surface array of particle detectors (Allekotte et al. 2008) with fluorescence telescopes (Abraham et al. 2010a) for hybrid detection. The layout of the observatory is shown in Fig. 19. An array of 1600 waterCherenkov detectors on a triangular grid of 1.5 km spacing is covering an area of about 3000 km2 . Each surface detector station contains 12 tons of purified water that is viewed by three down-facing PMTs. The PMT signals are digitized with 40 MHz electronics and stored in a ring buffer. The surface detector (SD) stations are solar-powered with backup batteries, and communication is realized as custombuilt wireless LAN in the ISM band. A central data acquisition system combines the trigger information of the detector stations and controls the transfer of signal traces from the detector stations. The fluorescence detector (FD) consists of 4 fluorescence stations, each housing 6 fluorescence telescopes with a 30◦ × 30◦ field of view per telescope (Abraham et al. 2010a). The fluorescence telescopes operate independently of the surface array. However, time traces of relevant surface detectors are read out also for triggers coming from the fluorescence telescopes. Each telescope has a 14 m2 mirror that focusses the light on a camera of 440 PMTs. The PMT signals are digitized at a rate of 10 MHz. A number of atmospheric monitoring devices are employed to ensure highquality data (Abraham et al. 2010b). These are steerable LIDAR stations (BenZvi et al. 2007), infrared cameras for cloud detection, and weather stations at each of the fluorescence telescopes, as well as two UV lasers (Fick et al. 2006) in the surface detector array. The calorimetric measurement of the longitudinal shower profiles measured with the fluorescence telescopes is used for calibrating the surface detector array that

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Fig. 19 Left: Layout of the Auger Observatory in Argentina. The green dots mark the locations of the 1600 surface detector stations; the black dots mark the different calibration and monitoring installations. The field of view of the fluorescence telescopes is indicated by lines. Also marked are the locations of the two laser facilities in the array (CLF and XLF). Right: Visualization of an AugerPrime surface detector station. (Images reproduced with permission of the Pierre Auger Collaboration)

collects data with an almost 100% duty cycle. The surface array is fully efficient for energies above 1018.5 eV (Abraham et al. 2010c), and the fluorescence telescopes can detect showers with good quality down to energies as low as 1018 eV. The angular reconstruction accuracy depends on the shower energy and arrival angle. It is typically ∼1.5◦ and improves to 0.7◦ for the highest-energy showers (Aab et al. 2020a). Due to the height of the water-Cherenkov detectors of 1.2 m, the Auger Observatory also has a good sensitivity to horizontal neutrino-induced showers (Zas 2005). Several enhancements to the baseline design of the Auger Observatory have been completed or are currently under construction. HEAT (High Elevation Auger Telescopes) comprises three additional fluorescence telescopes complementing the existing Coihueco telescopes by viewing higher elevations for reconstructing showers more reliably at ∼1017 eV. The energy threshold of the surface detector array is reduced similarly by a denser array of 24 km2 with 750 m spacing between surface detector stations, which lowers the energy with which showers can be detected at full efficiency to ∼1017.5 eV. In this denser sector of the array, buried scintillator muon counters of 30 m2 , co-located with each water-Cherenkov detector, are currently being deployed as part of AMIGA (Auger Muons and Infill for the Ground Array) (Aab et al. 2016). Furthermore, the Auger Engineering Radio Array (AERA) (Schulz 2016), comprised of over 150 autonomous radio stations covering an area of ∼17 km2 , was completed in 2015. Deployed in three phases, AERA

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serves as a test bed for different hardware including different antenna designs and detector array spacings. 24 logarithmic periodic dipole antennas comprised a dense 144 m grid (Dallier 2011), and butterfly antennas were deployed in grids with 250 m, 375 m, and 750 m spacing. The two arms of each butterfly antenna are aligned in east-west and north-south orientations and are sensitive in the 30–80 MHz frequency range. An emitting source attached to an octocopter is used to calibrate the antenna response pattern, and a beacon transmitter at one of the fluorescence detector sites of the Auger Observatory is used for time synchronization. The observatory is undergoing a large-scale detector upgrade (Aab et al. 2016; Castellina 2019) to increase its sensitivity to the mass of primary particles. Known as AugerPrime, it features a 3.8 m2 plastic scintillator and a SALLA radio antenna placed atop each existing water-Cherenkov detector. A schematic of such an upgraded surface detector station can be seen in Fig. 19. For showers with zenith angles of up to ∼60◦ , the differing responses of the scintillator and waterCherenkov detectors allow for the disentanglement of the signal contribution of muons from particles of the electromagnetic shower component. At larger zenith angles, access to the electromagnetic component of air showers is provided by the radio antennas (Hörandel 2019), as direct measurement of electrons and photons is limited due to extensive attenuation of em. particles upon reaching the ground. Used in tandem with the water-Cherenkov detectors that remain sensitive to the muonic shower component at these angles, the radio antennas extend the mass sensitivity of AugerPrime to higher declination and, hence, larger sky coverage. Highlights of results from the Auger Observatory include the confirmation of the theoretically expected flux suppression at energies higher than 6 × 1019 eV and the discovery of a new feature in the energy spectrum (Aab et al. 2020b), the observation of a correlation of the arrival direction distribution with different astrophysical classes of source candidates (Aab et al. 2018), the measurement of the depth of shower maximum (Abraham et al. 2010d) indicating a transition to a heavy composition at the highest energies, and the discovery of a large-scale dipole anisotropy in arrival directions indicating an extragalactic origin of the particles (Aab et al. 2017c). Furthermore, the searches for neutrino- and photoninduced air showers lead to the exclusion of many exotic models for the sources of ultra-high-energy cosmic rays (Aab et al. 2019a).

Open Problems and Future Experiments All indirect detection techniques of cosmic rays depend on our understanding of extensive air showers. In most cases, shower measurements can only be interpreted by comparing the data to simulated reference showers. With no calculable theory of hadronic multiparticle production available so far, hadronic interactions have to be described by phenomenological models. The limited understanding of hadronic multiparticle production constitutes currently the main contribution to the systematic uncertainty of composition measurements (Engel et al. 2011; Kampert and Unger 2012).

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While there have been methods developed to derive the energy of the primary particle of a shower with only a small dependence on the modeling of hadronic interactions, there still seems to be a systematic difference of the order of 20% in the energy assignment between different experiments. Dedicated cross-calibration measurements and the addition of radio signal measurements are expected to improve this situation. The reliable measurement of the mass composition of cosmic rays is the key challenge for the future (Alves Batista et al. 2019). Indirect measurement techniques always depend very much on simulated air showers. Therefore, in the foreseeable future, significant progress can only be achieved by accelerator measurements of hadronic interactions of relevance to air shower physics to improve the reliability of shower simulations. Model-independent, calorimetric methods of shower energy measurement rely on the detection of the em. shower component. While almost all energy is transferred to the em. component in showers of the highest energies, a fraction of less than 70% of the energy is carried by em. particles in the knee energy range. Therefore, it is necessary to measure the muonic component of intermediate-energy showers in order to estimate the primary particle energy reliably. Recent examples of ongoing upgrades include the addition of scintillation detectors and radio antennas (Haungs 2019) to the surface array IceTop (Abbasi et al. 2013) of the IceCube Observatory and AugerPrime (Castellina 2019). Current work toward new detection methods aims at developing techniques offering very large apertures to increase the statistics at the high-energy end of current experiments. One direction of research is aimed at the development of very simple and robust fluorescence detectors, for example, (Fujii et al. 2019). A promising technique is also the measurement of the coherent radio signal of air showers either with ground-based arrays (Schröder 2017) or balloon-borne instruments (Hoover et al. 2010). The vision of the Giant Radio Array for Neutrino Detection (GRAND) (AlvarezMuñiz et al. 2020) is to deploy a set of large arrays with, in total, 200, 000 radio antennas covering an area of 200, 000 km2 to achieve a sensitivity to cosmogenic neutrino fluxes on the order of 10−10 GeV cm−2 s−1 sr−1 . The design includes antennas specifically designed for the detection of near-horizontal air showers produced by Earth-skimming neutrinos or highly inclined cosmic rays and neutrinos at ultra-high energies. The collaboration’s current focus is on one of the initial phases of the project, GRANDProto300, which will consist of 300 antennas sensitive in the 50−200 MHz band to be deployed over a 200 km2 radio-quiet site in China. Deployment of this phase is expected in 2021. The construction of the full 200, 000 km2 array would take place in the 2030s. Space-borne fluorescence and Cherenkov light detectors promise even larger apertures than those achievable with giant ground arrays (Santangelo and Petrolini 2009). For example, POEMMA (Olinto et al. 2019, 2012), a system of identical telescopes on two satellites, depicted in Fig. 20, can measure in both mono and stereo modes. One such module consists of a 4-meter photometer with a 45◦ field

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Fig. 20 Visualization of POEMMA instrument in deployed state and as stowed during launch. (From Olinto et al. 2019, reproduced with permission)

of view and 1 μs and 10 ns detection capabilities respectively for fluorescence and Cherenkov light. It is planned to orbit at an elevation of 525 km. There are several new ground-based detectors planned for gamma-ray observations. Aiming at monitoring of the TeV gamma-ray sky with a large field of view is the multipurpose detector LHAASO (Bai et al. 2019) that will also measure charged cosmic rays over a wide energy range. Currently being built at an altitude of 4300 m, LHAASO will combine an array of 4901 1 m2 scintillator detectors deployed over 1 km2 with a co-located array of 1171 underground water-Cherenkov detectors for muon detection. A surface water-Cherenkov facility with a total sensitive area of ∼78,000 m2 will be located at the center of the array surrounded by 20 wide fieldof-view Cherenkov telescopes. In addition, an observatory for indirect gamma-ray detection is planned for the southern hemisphere to obtain good coverage of the galactic center. The next-generation gamma-ray telescope will be the Cherenkov Telescope Array (CTA) (Actis et al. 2011). To cover the full sky, CTA will consist of two arrays of Cherenkov telescopes, one in the northern and one in the southern hemisphere. A significant increase in sensitivity will be achieved by deploying large

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Fig. 21 Sensitivity (5σ level) of existing and planned gamma-ray experiments (Knödlseder 2016). The data for imaging atmospheric Cherenkov telescopes corresponds to 50 h of measurement time. The gray lines show the flux of the Crab Nebula for reference. For details, see Knödlseder (2016). (Reprinted with permission of Elsevier)

numbers (50–100) of Cherenkov telescopes at different distances. At the same time, an extension of the energy range in comparison with existing telescopes will be accomplished by using telescopes of different sizes. The sensitivities of existing and planned gamma-ray detectors are compared in Fig. 21.

Conclusion Indirect methods of measuring cosmic rays allow us to detect particles with energies from a few hundred TeV up to the highest energies observed in the universe (∼1020 eV). By observing the cascade of secondary particles produced by cosmic rays when interacting with nuclei of air, one can derive information on the arrival direction, energy, and mass composition of the primary particle. Sparse arrays of particle detectors or imaging telescopes are sufficient for measuring key observables because of the large number of shower particles and the large lateral extent of the particle cascade at the ground. Still, the steeply falling flux of cosmic rays makes it very difficult to cover a wide range in energy with a single detector setup. Applying the indirect detection techniques developed for charged cosmic rays to showers induced by gamma rays has proven to be an efficient way of extending the classical, satellite-borne gamma-ray astronomy into and beyond the TeV energy range.

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Acknowledgments The authors thank their colleagues from the Pierre Auger Collaboration with whom they have worked on various subjects covered in this contribution. They are also very grateful to Carola Dobrigkeit, Claus Grupen, and Andreas Haungs for valuable comments on the manuscript.

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Further Reading Aharonian FA (2004) Very high energy cosmic gamma radiation: a crucial window on the extreme universe. World Scientific, Singapore De Angelis A, Pimenta M (2018) Introduction to particle and astroparticle physics, 2nd edn. Springer, Berlin Gaisser TK, Engel R, Resconi E (2016) Cosmic rays and particle physics. Cambridge University Press, Cambridge Grieder PKF (2001) Cosmic rays at Earth: researcher’s reference, manual and data book. Elsevier, Amsterdam Grieder PKF (2010) Extensive air showers: high energy phenomena and astrophysical aspects – a tutorial, reference manual and data book. Springer, Berlin Kolanoski H, Wermes N (2020) Particle detectors – fundamentals and applications. Oxford University Press, Oxford Stanev T (2010) High energy cosmic rays, 2nd edn. Springer Praxis, Berlin

Gravitational Wave Detectors

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Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Experimental Challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Searching for Gravitational Waves – Resonant Bars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Searching for Gravitational Waves: Interferometric Detectors – The Idea . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Long Baseline Suspended Mass Interferometers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The LIGO Interferometers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Virgo Interferometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Advanced LIGO and Virgo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Detection of Gravitational Waves: The First Event . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Future Ground-Based Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gravitational Waves in Space and Pulsar Timing Array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract The Laser Interferometer Gravitational-wave Observatory (LIGO) observed gravitational waves 100 years after Einstein proposed their existence in 1916 (Abbot et al., Phys Rev Lett 116:061102, 2016). Theoretically, their existence had been controversial until about 1960, after which the challenge became an experimental one. New techniques in precision interferometry and noise reduction had to be developed, in order to achieve the sensitivity required. The experimental challenges and techniques involved in making gravitational wave detections are reviewed, as well as future plans.

B. C. Barish () California Institute of Technology and University of California, Riverside, Riverside, CA, USA e-mail: [email protected]; [email protected] © Springer Nature Switzerland AG 2021 I. Fleck et al. (eds.), Handbook of Particle Detection and Imaging, https://doi.org/10.1007/978-3-319-93785-4_49

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Introduction Newton’s Universal theory of gravity was perhaps the most successful physics theory of all time, describing a huge range of phenomena from the apple falling from a tree to the orbits of the planets. So, what motivated Einstein to make a new theory of gravity? He had solved several of the most important problems in physics in 1905. Somehow, he was so strongly motivated that he spent the next 10 years developing his theory of general relativity or theory of gravity (Einstein). It is important to note, however, that Newton’s theory of gravity was not wrong, but rather incomplete. Physics advances through evolving our understanding from a combination of experimental observations sometimes not explainable by theory, thereby motivating the development of new theories that go beyond our earlier ones. Conversely, new theories emerge that predict phenomena that must be tested experimentally. In physics, sometimes new observations lead to new theories and, sometimes, new theories lead to new observations. The immediate success of Einstein’s theory of general relativity was that after more than 200 years of success, it solved the only known problem with Newton’s theory, a ∼ 10% discrepancy in the period of Mercury around the Sun. This discrepancy had been a problem for about 50 years. The most popular view was that the discrepancy was due to not accounting for the presence of a still undiscovered object (or objects) that existed between Mercury and the Sun whose gravitational effects were responsible for perturbing the orbit of Mercury. There was strong motivation for this explanation, because of the success of an earlier planetary orbit deviation for the orbit of Uranus. That discrepancy was analyzed theoretically by Urbain Le Verrier in Paris and John Couch Adams in Cambridge who, independently, came to the conclusion that that discrepancy was due to the presence of a yet undiscovered planet that distorted the orbits of Uranus. The planet Neptune was subsequently observed exactly as predicted by Le Verrier (Levenson 2015). Motivated by the discovery of Neptune, there were many searches for objects between Mercury and the Sun in the mid-1800s. This produced several false discoveries, but all claimed observations were ruled out. In fact, by the time of Einstein, no object had been found that could explain the discrepancy, and even later, NASA did an extensive search and found no missing objects. Einstein presented his Theory of General Relativity, a new theory of gravity in 1915. Although the discrepancies in the orbit of Mercury were not the primary motivation for Einstein to develop his theory, it had the immediate success of agreeing with the observed orbit of Mercury. Einstein’s new theory had the success of correctly predicting the period of the orbit of Mercury. However, fixing this one and only known problem with Newton’s universal theory of gravity hardly warranted accepting a revolutionary new theory of gravity. It is generally considered imperative that a new theory not only solves existing problems present in an older theory but also predicts something new. This was the case for Einstein’s theory of general relativity. Einstein made a new prediction that light would bend as it passes near a massive object. Sir

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Arthur Edington dramatically confirmed that prediction in 1919, a result due to the curvature of spacetime in Einstein’s theory. He recorded the bending of light as the Hyades star cluster went behind the sun during a full eclipse, and the amount of bending of the light from those stars agreed with Einstein’s calculations. A year after introducing general relativity, in 1916, Einstein wrote a paper making another new prediction from the theory of General Relativity, the existence of gravitational waves (Einstein 1916). However, the effects of gravitational waves were so small that even Einstein was doubtful they could ever be observed. Gravitational waves were finally discovered using modern techniques that were not known at Einstein’s time. The discovery was made almost exactly on the hundredth anniversary of Einstein’s prediction of their existence in 1916. Einstein’s paper regarding gravitational waves was not immediately accepted. The original paper had not actually derived gravitational waves from General Relativity. Instead, he inferred their existence by noticing similarities between the equations of general relativity for gravity and the equations of electricity and magnetism. Since there are electromagnetic waves, he concluded that there must also be gravitational waves. However, he also noted that they would likely be impossible to detect, because the magnitude of their effect was so small. Einstein wrote a second paper (Einstein 1918) in 1918, where he fixed some numerical errors in the 1916 paper, and very importantly, showed that gravitational waves would result from accelerations of masses having a quadrupole moment (Fig. 1).

Fig. 1 Albert Einstein in 1915 at the age when he proposed gravitational waves. (Courtesy - Huntington Library)

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At this point, Einstein dropped the subject of gravitational waves. At the time, the theoretical community had not broadly accepted his proposal, because he had not derived their existence from the theory of general relativity. After emigrating to the United States, in 1930, Einstein returned to the problem of gravitational waves. He worked with Nathan Rosen, but they ran into theoretical difficulties and became concerned whether they existed or were a mathematical artifact. Einstein and Rosen wrote a paper in 1936 that upon its initial submission to Physical Review Letters was entitled “Do Gravitational Waves Exist,” where they questioned the existence. The paper underwent peer review and was not accepted by the Physical Review editor in its original form. The paper was then modified and published in the Journal of the Franklin Institute, entitled “On Gravitational Waves.” (Einstein and Rosen 1937) The published paper supported the existence of gravitational waves. However, Einstein and Rosen had not succeeded in deriving gravitational waves from the theory of General Relativity, and their existence remained controversial until after Einstein’s death in 1955. The theoretical community became convinced a few years later, beginning at a special conference in Chapel Hill, North Carolina, in 1958. At that meeting, Felix Pirani (DeWitt and Rickles 2011), a British theorist, made a convincing derivation from general relativity that established the existence of plane wave solutions for gravitational waves. Also, at the same meeting, Feynman made a physical argument that he called “the sticky bead argument” that demonstrated how gravitational waves could transfer energy. The combination of Pirani’s and Feynman’s presentations is regarded as the turning point when their theoretical existence had been demonstrated. At this point, the problem of establishing the existence of gravitational waves became an experimental one, instead of a theoretical question (DeWitt and Rickles 2011).

The Experimental Challenges Even with the theoretically uncertainties regarding the existence of gravitational waves, the formidable experimental challenges were the main reason it took so long after Einstein’s proposal, before the first detections were made. The first problem was finding a strong enough source of gravitational waves. Einstein showed in his 1918 paper that gravitational waves are created by quadrupole moments created from accelerating masses, in contrast to dipole moments that make electromagnetic waves. A simple physical picture for how one can create such a quadrupole source is to rotate a barbell. In fact, one can consider whether, using such a source, it might be possible to perform an equivalent of the Hertz experiment for gravitational waves that had demonstrated the existence of electromagnetic waves. Could such an experiment be done for gravitational waves? The idea would be to use rotating barbell as the source of gravitational waves, place a detector some distance away, and observe the gravitational wave signal. Once observed, like for the Hertz experiment, move the detector toward and away from the source to demonstrate

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the wave nature. This idea is very appealing to an experimentalist, because all the variables can be controlled. Unfortunately, the signal from such a barbell source is just much too small to contemplate such an experiment. In fact, putting in numbers for a rotating barbell and placing a detector about a wavelength away from the source gives a signal of amplitude about 20 orders of magnitude less than the black hole binary merger signals that LIGO has observed. Therefore, we must rely on nature to provide us with strong enough sources to observe gravitational waves. Fortunately, there are a number of candidate astrophysical sources and these result from very interesting astrophysical phenomena, so potentially much astrophysics can also be learned. Compact binary systems, such as merging binary neutron stars or black holes, are attractive candidate sources of gravitational waves. In fact, the first indirect evidence for gravitational waves had come from the observations of Hulse and Taylor for such a source, in their case, a binary neutron star system. They analyzed radio emissions using the Arecibo radio telescope and discovered (The Nobel Prize in Physics) the first observed binary neutron star system (PSR 1913 + 16). They were doing detailed studies of the radio emissions from a rapidly rotating magnetized neutron star (e.g., a pulsar) that has a period around its axis of 17 times per second. Precisely studying the parameters of this system, they noticed a variation that was periodic, having a period of ∼7.75 h. After establishing this effect, they interpreted their source as being due to a binary neutron star system. This was the first binary neutron star system observed. In such a system, due to the accelerations while the compact objects are orbiting each other, gravitational waves should be emitted, carrying away energy, according the Einstein’s theory of general relativity. In fact, due to this loss in energy, calculated using Einstein’s theory, the orbital period for this particular system should reduce by 76.5 microseconds per year. Physically, this implies they are slowly spiraling into each other. Weinberg and Taylor (Taylor and Weisberg 1982) measured this decay rate very precisely over 20 years and found the observations to be impressively consistent with the predictions from General Relativity. The calculated lifetime of the Hulse-Taylor binary system to final merger is ∼300 million years, at which point the two neutron stars will coalesce. It is as it approaches the final merger that the gravitational waves emitted become high enough frequency to be detectable using sensitive techniques to sense the distortions of spacetime. Long baseline suspended mass interferometric techniques were used by LIGO to make the first detections, and subsequent sensitivity improvements are enabling many more detections. There are several possible astrophysics sources for gravitational waves, but an attractive candidate is to detect Hulse-Taylor like mergers of compact binary systems. Such systems will emit gravitational waves at increasing frequency as they inspiral toward each other, and finally merge. The ground-based long baseline interferometers that I discuss in this chapter are sensitive to the gravitational wave emissions during the final merger for binary systems of black holes, neutron stars, and black hole neutron star systems. The gravitational wave discovery, as well as all

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subsequent observations of gravitational waves to date, originates from this class of sources. A second class of astrophysical sources yields “burst” signals, for example, gravitational waves emitted from the gravitational collapse of a star (a supernova). The magnitude of such a signal is difficult to estimate, because it depends on the quadrupole moment of the gravitational collapsing object, but estimates for sensitivities of present-day interferometers limit detectable signals to supernova in our galaxy, or nearby. Consequently, the rate is low, and so far, none have been detected. A third source of gravitational waves will come from spinning neutron stars or pulsars in our own galaxy. To the extent that such objects are not totally symmetrical, they will emit gravitational wave signals. At this time, no such signals have been observed in searches both for known pulsars, and in all sky searches. As the sensitivity of the detectors improve, such sources are very attractive to detect and study. They are particularly attractive to observe, because, in contrast to the transient signals from binary mergers, once a pulsar has been observed, they will produce continuous signals that can be studied in detail over time, with improved detectors, etc. Another possible source of gravitational waves are stochastic signals originating from the early universe. This would be a very exciting prospect, because such signals come from the first instants after the big bang. However, these signals are likely to be small and difficult to detect at the high frequencies of present-day ground-based interferometers. However, they may be detectable in space or in future ground-based detectors. For the remainder of this chapter, I will only consider the signals from binary inspiral systems and describe key features of the suspended mass interferometric detector technique. In general relativity, the source strength is the “strain” in Einstein’s equations, which is proportional to the amount spacetime becomes distorted by the passage of a gravitational wave. The strains, h, for the binary black hole mergers that have been observed are h ∼ 10−21 . This means that the amount of spatial distortion is L/L ∼ 10−21 . A physical interpretation of having such small strains is that spacetime distortions are very tiny from the passage of gravitational waves, even for such powerful astrophysical events. This implies that to make such an effect measurable, we must make L as large as is practical, which is why the arm lengths in the LIGO and Virgo interferometers are several kilometers.

Searching for Gravitational Waves – Resonant Bars The first technique that was employed to detect gravitational waves was resonant bar detectors. Joseph Weber, who had been at the Chapel Hill meeting, took up the experimental challenge of trying to detect gravitational waves experimentally,

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beginning in about 1965. He developed a technique based on detecting distortions that were caused by the passage of gravitational waves through a suspended resonant aluminum bar. His first detector consisted of a suspended cylinder that was 0.6 m diameter × 1.2 m long, mounted in a vacuum chamber and the bar had a resonant frequency of 1657 Hz. He mounted sensitive piezoelectric crystal detectors on the surface, around the middle of the bar, in detect tiny distortions caused by the passage of gravitational waves through the bar. In such a system, the ends of the bar act like test masses of an interferometers, while the center acted like a spring. The resonant bar technique was refined over the following years by Weber and other groups. The first big advance in the technique in searching for gravitational waves was to employ two detectors at distant locations from each other and require them to be in coincidence within the time of arrival of a gravitational wave coming from the same source. Weber’s technical work and innovations led the way experimentally, and in many ways, created the field of gravitational wave experimentation. Unfortunately, he claimed the discovery of gravitational waves several times, but none of his claims were confirmed by other, using more sensitive detectors. Weber’s first claimed detection (Weber 1967) was in 1967, and then he claimed detection again a second time (Weber 1968) in 1969 using coincidence techniques. Immediately following Weber’s initial detection claim, several more sensitive detectors were built, but none confirmed his result (Tyson 1973; Levine and Garwin 1973; Garwin and Levine 1973). For comparison, the sensitivities of Weber’s resonant bars were several orders of magnitude away from the size of the observed signals in the Advanced LIGO discovery of a black hole binary merger (Fig. 2). Resonant bar detectors continued to be improved over the next 30 years, the most important improvement was reducing the thermal noise by making the

Fig. 2 Joseph Weber and one of his resonant bar detectors. (Courtesy of – University of Maryland)

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bars cryogenic. At different laboratories around the world, different versions of cryogenic detectors were built. These detectors generally used high mechanical Q aluminum alloy put into a vacuum and cooled to 4.2 K. In addition, ground and acoustic vibrations were technically reduced as much as was practical. Finally, in the more advanced cryogenic detectors, the piezoelectric sensors were upgraded to electromechanical resonant transducers and techniques were used to make broader sensitivity in frequency. The advanced cryogenic detectors searched for gravitational waves until the much larger and more sensitive LIGO and Virgo interferometers became operational. The different cryogenic bar groups around the world formed a collaboration, where threefold coincidences between the detectors could be required to reduce false coincidences. No gravitational wave events were reported by the time these devices were superseded by interferometers near the beginning of this century. Basically, resonant bars have a serious limitation for gravitational wave detection in that they only respond to a narrow frequency band (near 1000 Hz), around the resonant frequency of the bar, while broadband interferometers respond over the audio band where the earth’s noise is the least (e.g., approximately 10 Hz to 10 KH for detectors on the earth’s surface). The lack of broadband sensitivity was a key limitation for resonant bars. They could not achieve comparable sensitivities to interferometers and have been superseded for present-day gravitational wave facilities. Another problem for the cryogenic bars was that they operated at much higher frequency than signals from black hole mergers, even with sensitivity broadened to ∼100 Hz in the most advanced cryogenic detectors. In addition, their limited length of only a few meters, compared to 4 km arms for LIGO made them less sensitive (since the signal strength for gravitational waves is proportional to L/L). Interestingly, one of Weber’s former students, Robert Forward, was the first person to make a test version of a suspended mass interferometer, while he was at Hughes Aircraft. Forward became a Science Fiction writer, instead of pursuing gravitational wave detection, however. LIGO and Virgo have inherited some very important legacies from Weber’s work, and the further developments of resonant bar detectors by others. The first important approach was that Weber performed detailed calculations of the limiting noise sources and this helped guide how sensitive the detector could be, as well as focused his laboratory work on how to reduce these noise sources. The approach for interferometer detectors is also aimed at studying and reducing the various noise sources. The second lesson learned from Weber was that he employed a coincidence between two detectors placed far enough apart to make them independent of noise sources on the Earth. This greatly reduced backgrounds by requiring a coincidence consistent with the speed of light over the distance between the detectors. Finally, Weber used a technique to determine the significance of any observed signal candidates by analyzing the data for off-coincidence as a measure of the false coincidence background levels. All three of these techniques are important features that were developed by Weber and are integral to LIGO and Virgo detections.

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Searching for Gravitational Waves: Interferometric Detectors – The Idea The idea of using interferometers to detect gravitational waves first emerged in the 1960s. Gertsenshtein and Pustovoit wrote a paper (Gertsenshtein and Pustovoit 1962) in the Soviet JETP suggesting that optical interferometers would be a more sensitive way to search for gravitational waves than detecting tension in piezoelectric crystals. Independently, a little later, Robert Forward, a student of Weber’s, built a suspended mass interferometer at Hughes Aircraft (Forward 1978), and lastly, Rai Weiss (1972), wrote an internal note at MIT where he calculated and laid out the main features that would be needed to achieve the sensitivity goals in a large-scale interferometer. This was the beginning of 20 years of R&D, where interferometric techniques were advanced toward being able to achieve the sensitivities that were expected to be necessary to detect astrophysical signatures of gravitational waves. R&D on interferometric techniques continued as well as advanced engineering to develop the proposals for large-scale interferometers, and embark on the actual building stage of LIGO in 1994. Once LIGO construction and initial commissioning were completed, the key technical team that had done the R&D and design of Initial LIGO embarked on developing the techniques that were to be used in the planned major upgrade to Advanced LIGO. R&D and technological development remains central to the pursuit of gravitational waves in LIGO, because achieving the science was dependent on the sensitivities achieved. Fortunately, technical issues in interferometry, rather than physics backgrounds limit the sensitivity of gravitational wave interferometers. Therefore, we can look toward incrementally improving the sensitivity as we look toward the future of gravitational wave science in the 2020s and beyond. The original concept had developed far enough by the late 1980s that proposals were made to funding agencies for large-scale suspended mass interferometers with sensitivities that could possibly detect gravitational waves. Proposals were submitted for large-scale interferometers in Australia, the United States, Italy, and Germany. The Australian proposal was not approved; the Scottish-German group was only approved for a smaller interferometer (GEO600) in Hannover, Germany. LIGO in the United States and the Virgo (French-Italian) in Italy were approved. The plan for LIGO (Laser Interferometer Gravitational Wave Observatory) was to build a first version, which was called Initial LIGO and was primarily built with technologies that had been proven in the R&D program, and it was designed to achieve sensitivities, where detections could be “possible.” During this phase of the project, an ambitious R&D continued on technologies were not yet mature. Ground-based interferometers are sensitive to the final merger when the frequencies become high enough to enter the audio band, and the signal strengths are largest approaching the final collision. We can estimate that the Hulse Taylor binary system will lose energy by radiating gravitational waves, and in about a

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million years, they will merge. Other binary neutron star systems are much closer to their final merger, and the frequency of the gravitational waves increases until they merge, at which point the wave frequencies enter the audio band where LIGO can make the detections, if the signal is large enough to exceed the noise in the interferometer. This expected rate was extrapolated from observations of binary neutron star systems in our galaxy and extrapolated to further distances that include more galaxies. From the number of neutron star binary systems that have been observed in our galaxy and extrapolating further into the universe estimates of the neutron star mergers was made. Such analysis is model dependent, but was used to set the target sensitivity (h ∼ 10−21 ) where estimates yielded at least one event per year. The overall strategy for LIGO was to achieve the required sensitivity goal in two steps. First, Initial LIGO was implemented, using technologies that had been proven in the laboratory. Then, after running Initial LIGO successfully, Advanced LIGO would be built designed with more advanced techniques that would enable an estimated one event of neutron star mergers per year. The two main challenges to achieve the target sensitivity were to do interferometry with a precision of ∼10−12 of the wavelength of the laser light, and to isolate the interferometer from the ground, also by a factor of ∼1012 . Neither of these goals could be achieved in Initial LIGO, although detections were still possible, because other sources might have a higher rate than neutron star mergers and have resulted in detections. But, no detections were observed in Initial LIGO or even an upgrade to Enhanced LIGO. Black hole binary mergers do have a higher rate and were detected before neutron star mergers in Advanced LIGO, but they were out of reach for the previous versions of LIGO. Initial LIGO was also unable to detect binary black hole mergers, due to poor sensitivity at low frequencies, where the signals are observed. The first detection, described below, was eventually made of a stellar mass black hole binary merger. This was a far less understood process than binary neutron mergers, so reliable predictions were not possible, in advance. Neutron star binaries were the second observed source about a year later in August 2017, and based on only a couple observed events have roughly the original estimated rates.

Long Baseline Suspended Mass Interferometers Using today’s technologies, a gravitational wave detector having sensitivity levels capable of detecting gravitational waves is a large (kilometer-scale) facility. Possible alternate technologies, like atomic interferometers, may be possible in the future, but at the present time, only conventional interferometers are practical. The LIGO facility and similarly the Virgo facility were constructed during the period from 1994 to 2000, and originally employed technologies that represented a balance between being able to reach sensitivity levels where the detections of gravitational waves are “possible,” using techniques that had been demonstrated in the laboratory. The LIGO Interferometers represented a huge extrapolation from the 30 m prototype

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Fig. 3 The LIGO Interferometer facility in Livingston, Louisiana. (Courtesy – Caltech/MIT/LIGO Lab)

interferometer in Garching, Germany, and the 40 m prototype at Caltech. These R&D devices had proven the key concepts, and this was essential considering the large investment that was being requested of the NSF (Fig. 3). In order to facilitate the planned upgrades to more advanced technologies, the Initial LIGO infrastructure was designed such that the interferometer subsystems could be evolved or replaced within the same infrastructure (e.g., vacuum vessels). After the completion and commissioning of Initial LIGO, technical improvements were incrementally made over a period of 5–7 years that substantially reduced the background noise levels. A cycle of taking data and searching for gravitational waves, then turning off and improving the detector was repeated almost once per year for over a decade. Each time, improving sensitivity and taking data runs at ever-increasing sensitivity (Fig. 4). This is an important strategy, then, and in the future, because for a gravitational wave detector the limiting factor at any given time is the sensitivity of the instrument, but the sensitivity is limited almost entirely by technical issues. As a result, achieving better sensitivity is a result of reducing technical backgrounds. The basic scheme for an interferometric gravitational wave detector uses a special high power single-line laser beam (NdYAG) that enters an interferometer, and is split at a beam splitter into two beams that are sent in perpendicular directions. The vacuum pipe is 1.2 m diameter and is kept at high vacuum (>10−9 torr). The “test” masses are mirrors that are suspended to keep them isolated from the earth. They are made of fused silica and are hung in a four-stage pendulum in Advanced LIGO.

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Fig. 4 Incrementally improvements to Initial LIGO sensitivity. (Courtesy – LIGO Laboratory Figure)

The equal length arms are adjusted such that the reflected light from mirrors at the far ends arrives back at the center at the same time. Inverting one, the two beams cancel each other and no light is recorded in a photodetector. This is the normal state of the interferometer within how well background noise sources are controlled.

The LIGO Interferometers To build a gravitational wave detector having sensitivity levels capable of detecting gravitational waves using today’s technologies requires a very large facility. Possible alternate technologies, like atomic interferometers are discussed, but at the present time, only a conventional interferometer is practical. The LIGO facility, and similarly the Virgo facility, was constructed during the period from 1994 to 2000 and employed technologies that represented a balance between being able to achieve sensitivity levels where the detections of gravitational waves might be “possible,” while using techniques that had been demonstrated in laboratory R&D programs. LIGO represented a huge extrapolation from the 30 m prototype interferometer in Garching, Germany, and the 40 m prototype at Caltech interferometers that preceded it, and especially considering the very large NSF investment, it was essential to be confident of technical success.

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Fig. 5 The noise sources that limit a suspended mass interferometer sensitivity. (Courtesy of – LIGO Laboratory)

The limiting sensitivity is different at different frequencies. As can be seen in Fig. 5, many technical sources can potentially limit the sensitivity. At the lowest frequencies (e.g., below 100 Hz), the dominant noise source limiting the sensitivity is seismic noise. This is the shaking of the earth, which falls off approximately as frequency to the fourth power. So, it is only a problem at the lowest frequencies. But, it should be noted that the first gravitational wave detections were of the merger of approximately 30 solar mass black holes, and such heavy binary systems are only detectable at very low frequencies. In the middle frequency range of 100–1000 Hz, thermal noise limits the sensitivity, and at the highest frequencies, >1000 Hz, shot noise or photo-statistics limits the sensitivity. Below these three noise sources, many other noise sources must be controlled to achieve better sensitivity. When a gravitational wave crosses the interferometer, it stretches one arm and compresses the other, causing the light from the two arms to return at slightly different times and the two beams no longer completely cancel. This process reverses itself stretching the other arm and squeezing the initial arm, back and

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forth at the frequency of the gravitational wave. The resulting light is sensed and recorded by a photo-sensor capable of recording the waveforms from the passage of a gravitational wave. The experimental challenge is to make the interferometer sensitive enough so that the incredibly tiny distortions of spacetime that come from a gravitational wave can be sensed over the various background noise sources. The spacetime distortions from the passage of an astrophysical source are expected to be of the order of h = L/L ∼ 10−21 , a difference in length that is a small fraction of the size of a proton. In LIGO, the length of the interferometer arms are as long as was practical, 4 km, and this results in a difference in length from gravitational waves that is still incredibly small, about 10−18 m. For reference, that is about a 1000 times smaller than the size of a proton! If that sounds very hard, it is!! Skipping the details, what enables achieving this precision is the sophisticated instrumentation that reduces seismic and thermal noise sources, and by effectively making the statistics very high by having many photons traverse the interferometer arms. LIGO consists of two identical interferometers, one in Livingston, Louisiana, and one in Hanford, Washington, 3002 km apart (Fig. 6). This means that when a gravitational wave intersects the earth traveling at the speed of light, the time of arrival recorded in each interferometer will be within ±10 ms of each other, the maximum difference for waves traveling at the speed of light between the two detectors. A coincidence is required between the two interferometers within this time interval, and this greatly reduces backgrounds. In addition, the difference in the time of arrival at the two sites gives information on the direction the gravitational wave was traveling.

Fig. 6 The LIGO detectors in Hanford, Washington, and Livingston Louisiana, separated by 3002 km. (Courtesy of LIGO Lab)

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The Virgo Interferometer The Virgo concept is similar to LIGO, except for a major difference in that Virgo uses a sophisticated passive seismic system, especially designed to give very good isolation at low frequencies. As a single detector, Virgo gave priority to detecting spinning neutron stars, which give a continuous signal and therefore can be done without a coincidence. There are many identified continuous sources at low frequencies, but so far none have been detected. The Virgo interferometer arms are 3 km, compared to 4 km for LIGO. In the Virgo seismic isolation system (Fig. 7), each mirror is attached to a “superattenuator.” A “superattenuator” is a chain of pendula, hanging from an upper platform and supported by three long flexible legs clamped to ground. This very

Fig. 7 Virgo Superattenuator. (From Virgo website)

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sophisticated passive seismic isolation system is extremely effective at mitigating low-frequency seismic noise above 10 Hz by a factor of 1012 .

Advanced LIGO and Virgo Following an extensive R&D program during the Initial LIGO running period, seismic isolation in LIGO was greatly improved for Advanced LIGO. This was accomplished by incorporating an integrated active and passive system. This improvement turned out to be the crucial improvement, enabling the first detections of binary black hole mergers at low frequencies. LIGO and Virgo remained as independent projects that were in competition to make the first detections. However, the value of coincidence data from both Virgo and LIGO enables accurate determination of the source direction, and motivated close collaboration over the Initial LIGO/Virgo period, including data sharing and joint analysis. Three way coincidences are important both for understanding gravitational waves, themselves, especially polarization, and at least as importantly it enables accurate determination of the direction of detected gravitational wave events. This last feature enables the possibility of alerting the astronomical community of candidate events and their direction. Joint observations are now called multimessenger astronomy. Both LIGO and Virgo underwent major upgrades to Advanced LIGO and Advanced Virgo in the period 2010–2015. A key part of the upgrade of LIGO was the addition of active seismic isolation. The various design improvements were designed to improve the sensitivity x10 over all frequencies. This translates directly to observing a factor of 10 further into the universe and thereby improving the volume and event rate a factor of 103 . For Advanced LIGO, the sensitivity improvement employing active seismic isolation at low frequency made a noise reduction of a factor of 100, giving 106 large event rate. This explains why gravitational waves were detected so quickly in Advanced LIGO, after years of observing with no detections in Initial LIGO. A comparison of Initial LIGO and Advanced LIGO technologies is shown in the table below.

Parameter Input laser power Mirror mass Interferometer topology

Initial LIGO 10 W (10 kW arm) 10 kg Power-recycled Fabry-Perot arm cavity Michelson

GW readout method Optimal strain sensitivity

RF heterodyne 3 × 10−23 /rHz

Seismic isolation performance Mirror suspensions

flow ∼ 50 Hz Single pendulum

Advanced LIGO 180 W (>700 kW arm) 40 kg Dual-recycled Fabry-Perot arm cavity Michelson (stable recycling cavities) DC homodyne Tunable, better than 5 × 10−24 /rHz in broadband flow ∼ 13 Hz Quadruple pendulum

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The Detection of Gravitational Waves: The First Event The first observed event was detected on 14 September 2015 and, after extensive tests and analysis, was announced on February 11, 2016. The gravitational wave arrived in Louisiana 6.9 ms before arriving in Hanford and combined with the amplitude information the source was located as having come up from the Southern Hemisphere within an area of ∼700 square degrees. It should be noted that with only two detectors the location is determined from the relative time of arrival at the two LIGO sites, plus phase information from the recorded signal. A third detector, Virgo in Italy, was added to the two LIGO interferometers in August 2017 and that resulted in improving the uncertainty in the direction by more than an order of magnitude. This improvement is enabling the beginning of multimessenger astronomy with astronomical telescopes. In the top pane of Fig. 8, the three phases of the coalescence (merger, coalescence, and ringdown) can be seen in the wave forms. As the objects inspiral and merge toward each other, more and more gravitational waves are emitted and the frequency and amplitude of the signal increases (the characteristic chirp signal), and following the coalescence, the final single object rings down. The second

Fig. 8 The key features of a compact binary merger. (Courtesy of LIGO Lab – PRL (Abbot et al. 2016))

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pane shows the waveforms calculated using Einstein’s theory, which looks almost identical to the data, except for the wiggles in the data from noise. The third pane shows Einstein’s calculated waveform subtracted from the observed signals in the top pane and indicates that the residual signal is consistent with noise. The bottom pane shows (the left scale) that the objects are relativistic and are moving at more than 0.5 the speed of light by the time of the final merger. On the right side, the scale is units of Schwarzschild black hole radii and indicates that the objects are very compact, only a few hundred kilometers apart when they enter our frequency band. The data fits the expectations for two heavy compact objects (black holes), each ∼30 times the mass of the sun, going around each other at relativistic velocities and separated by only a few hundred kilometers. They merge due to the gravitational radiation coming from the accelerations. Finally, the probability that this event is not a random coincidence between the two detectors was determined by comparing coincidence time slices for the two detectors, both in time (e.g., ±10 ms) and out of time. This analysis gave a false alarm rate for this event of 1 in over 22,500 years, corresponding to a probability that the observed event was accidental to be 2,000 640–2000 90–640 28–90

in many cases slowing down of fast neutrons, because the cross sections are only sufficiently high at low neutron energies. The particular interactions with other particles and the huge energy range over more than 15 orders of magnitude from ultracold neutrons below meV energies up to exceeding the TeV domain at large accelerators or in cosmic radiation are making neutron physics so diversified and cause a variety of phenomena and different detection techniques. In Table 2, there are a few common designations of neutron energy ranges. Neutrons are conventionally called slow neutrons if they are below the so-called cadmium cutoff energy at 0.5 eV and fast neutrons if they are above this value. In the terminology of the ICRP and the ICRU, neutrons of all energies are considered to be strongly penetrating radiation. Thermal neutrons are very important, because there are several efficient nuclear reactions which allow for thermal-neutron detection and because thermal neutrons induce some of the frequently used fission processes.

Basic Neutron Interactions The interactions of neutrons with other nuclei (Evans 1982; Wirtz and Beckurts 1964) can be grouped into the following processes: • • • • • •

Elastic scattering Inelastic scattering Radiative neutron capture Other nuclear reactions Fission (inclusive of spontaneous fission) Spallation

These processes are not only the base for most neutron detection mechanisms but also for neutron shielding and for the generation of any radiation hazard in biosystems. Besides elastic and inelastic scattering neutron capture and several neutroninduced nuclear reactions are of particular importance in neutron detection. The

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most important nuclear processes with thermal neutrons are listed in Tables 3, 4, 5, and 6. Because of the extremely short range of the hadronic forces, neutrons have to come very close within ≈10−15 m of a nucleus before any interaction can take place. For a neutron in normal matter, there is a lot of empty space and therefore interactions have relatively low probability and the neutron is a very penetrating particle. The probabilities of neutron interactions are characterized by their cross sections and are usually strongly depending on the neutron energy. The Q-value is a measure for the energy released to the reaction products. The higher the

Table 3 Important thermal-neutron-induced nuclear processes (Knoll 2010) Nuclear reaction 3 He (n, p) 3 H 6 Li (n, α)3 H 10 B (n, α)7 Li Cd(n,γ) 157 Gd(n, γ )158 Gd 235 U fission 197 Au(n, γ )198 Au

Q-value [MeV] 0.764 4.780 2.792

≈ 210

Cross section [barn] 5,330 940 3,840 2,450 255,000 582 98.65

Natural abundance Not applicable 7.4% 19.8% Natural Cd 15.7% 0.72% 100%

Table 4 Examples: technical data of scintillators for neutron detection Scintillator Density [g/cm 3 ] Index of refraction λmax [nm] Decay time [ns] Manufacturer

6 LiI(Eu)

4.1 1.96 470 1,400 SCIONIX

6 Li

glass 2.48–2.67 1.55–1.58 395 75–100 St. Gobain

Scintillating fiber

150 NUCSAFE Inc.

Table 5 Materials for neutron threshold activation (Wirtz and Beckurts 1964; Knoll 2010; IAEA 1974) Material Reaction 24 Mg(n, p)24 Na Mg 27 Al(n, α)24 Nas Al 27 Al(n, p)27 Mg Al 56 Fe(n, p)56 Mn Fe 59 Co(n, α)56 Mn Co 58 Ni(n, 2n)57 Ni Ni 58 Ni(n, p)58 Co Ni 63 Cu(n, 2n)62 Cu Cu 65 Cu(n, 2n)64 Cu Cu 197 Au(n, 2n)196 Au Au

Isotopic abundance [%] 78.7 100 100 91.7 100 67.9 67.9 69.1 30.9 100

Half-life [min] 900 900 9.46 153.6 153.6 2,160 103,104 9.8 762 9,792

γ Energy [MeV] 1.368 1.368 0.84–1.01 0.84 0.84 1.37 0.81 0.511 0.511 0.33–0.35

Yield [%] 100 100 100 99 99 86 99 195 37.8 25–94

Thresh [MeV] 6.0 4.9 3.8 4.9 5.2 13.0 1.9 11.9 11.9 8.6

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Table 6 Materials for slow-neutron activation (Wirtz and Beckurts 1964; Knoll 2010; IAEA 1974) Material Reaction Manganese 55 Mn (n, γ )56 Mn 59 Co (n, γ )60m Co Cobalt 63 Cu (n, γ )64 Cu Copper 65 Cu (n, γ )66 Cu Copper 107 Ag (n, γ )108 Ag Silver 109 Ag(n, γ )110 Ag Silver 113 In(n, γ )114m ln Indium 197 Au(n, γ )198 Au Gold

Isotopic abundance [%] 100 100 69.1 30.9 51.82 48.18 4.23 100

Half-life [min] 154.8 10.4 772.2 5.14 2.4 0.42 70,560 3,881

Thermal cross section [barn] 13.2 16.9 4.41 1.8 38.6 90.5 56 98.65

Q-value, the easier is detection and discrimination against gamma radiation. The most important process for fast-neutron detection and also for neutron moderation is elastic scattering on light target nuclei especially elastic n–p scattering. Spallation is an inelastic interaction of a projectile, for instance, a proton or a neutron with high kinetic energy exceeding 100 MeV with a heavy nucleus. In the first fast stage, the projectile interacts with individual nucleons of the target nucleus and several nucleons are leaving the nucleus with high energies preferably in the forward direction. In the second slower stage, the energy in the residual nucleus is distributed across the other nucleons and neutrons and other particles at a typical energy scale of several MeV are evaporated with isotropic angular distributions. Spallation is used for neutron generation in spallation sources and is also used for the detection of high-energy neutrons. Spallation target materials are for instance tungsten or lead.

Neutron Generation The main physical processes for neutron generation are fission, fusion, and nuclear reactions. The most important neutron sources or neutron-generating facilities are as follows: • • • • • • •

Reactors Accelerators (α–n) Radionuclide sources like 241 Am–Be, 239 Pu–Be, 238 Pu–Be, and 226 Ra–Be Spontaneous-fission radionuclide sources like 252 Cf Plasma neutron generators Fusion facilities Nuclear weapons

Reactors are very common as neutron sources and can deliver very high intensities. As neutrons cannot be accelerated directly by accelerators, they are

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generated by bombardment of appropriate target materials with charged projectiles. Nuclear (α–n) reactions are also important in neutron production. Especially if alpha particles are hitting 9 Be nuclei there is a large probability for the generation of a neutron and 12 C. The mixture of an alpha-emitting radionuclide with beryllium is therefore an excellent neutron source. Fusion processes are also efficient in neutron generation. Relatively new are plasma neutron generators which utilize the d–d or the d–t fusion reaction in a gas discharge tube. The former generates neutrons at energies around 2.5 MeV and the latter at about 14 MeV. Details of several of these processes and reactions are summarized below in section “Reference Neutron Radiation Fields.” Another neutron source is spent nuclear fuel. There are also significant amounts of neutrons in the secondary cosmic radiation in the atmosphere.

Neutron Moderation As there are no electric forces acting between neutrons and matter, energy can only be transferred from neutrons to other particles by hadronic interactions. As a consequence of the conservation of energy and momentum, the maximum energy transfer in elastic collisions of projectiles with target nuclei depends on the particles’ masses. The maximum energy transfer in elastic neutron scattering occurs in collisions with protons or other light nuclei. This is efficient up to the 12 C nucleus. In order to transfer kinetic energy from neutrons to other particles elastic neutron scattering on heavier target nuclei is relatively inefficient. Multiple elastic neutron scattering in a material containing light nuclei reduces the kinetic energy of incoming neutrons considerably and is called moderation. If moderated neutrons are in thermal equilibrium with the surrounding materials, they are called thermal neutrons. The mean kinetic energy of thermal neutrons is about 0.025 eV. Neutron moderation is important because thermal neutrons can easily be detected or absorbed and because thermal neutrons can induce some of the important fission processes. Good moderators are materials with a large amount of hydrogen, for instance, polyethylene or water. Deuterium is also a suitable moderator because it has a lower neutron absorption cross section than hydrogen. Of course the number of collisions required for thermalization is dependent on neutron energy. About 20 interactions are sufficient to thermalize a 1 MeV neutron in hydrogen. Beckurts and Wirtz (1964) gave a comprehensive description of neutron moderation.

Neutron Absorption and Shielding A neutron absorber is a material with which neutrons interact significantly by nuclear reactions resulting in their disappearance as free particles. As direct absorption of fast neutrons has low probabilities, efficient neutron absorbers are only existing for thermal neutrons. Therefore, neutron shielding is usually a

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combination of moderation and successive absorption of thermal neutrons. The 10 B reaction or absorption on natural cadmium, which is a mixture of several isotopes, is providing excellent thermal-neutron shielding. Cadmium of a few millimeters thickness is absorbing basically all neutrons below a cutoff energy of about 0.5 eV. The cross section of 10 B is decreasing reciprocally to neutron velocity and boron is strongly absorbing slow neutrons. Other possible reactions are listed in Table 3. Highly efficient neutron shielding for fast neutrons is either moderator material followed by layers of slow-neutron absorber or a mixture of moderating material with slow-neutron-absorbing material. Boronated polyethylene is a very useful neutron shielding material. Boron–silicone is a heat- and fire-resistant elastomer, which can be used as castable neutron shielding. Polycast is a dry mix material designed to be cast into closed containers. It is field castable, providing excellent, low-cost neutron shielding, with a hydrogen content 6% greater than that of water. Neutron putty is a nonhardening boron-loaded putty with a high hydrogen content. Neutron shielding is available as sheets, plates, rods, or pellets. Other neutron shielding materials in use are water, concrete, soil, and steel.

Metrology and Dosimetric Quantities Radiation measurements and investigations of radiation effects require the definition of radiometric quantities (ICRU 1998a). Radiation fields are characterized by radiometric quantities which apply in free space as well as in matter. The particle number Nis the number of particles that are emitted, transferred, or received. The flux is the quotient of d N/d t where d Nis the increment of the particle number in the time interval d t. One of the most important quantities in neutron detection is the fluence φ, which is the ratio of the number d N of particles incident on a sphere of cross-sectional area d a: φ˙ =

dN . da

(1)

The fluence is measured in unit m−2 . The fluence rate is defined as φ˙ =

dφ dt

(2)

and has unit m−2 s−1 . The distribution φ E represents the fluence with respect to energy where dφ is the fluence of particles of energy between E and E+ d E: φ˙ E =

dφ . dE

(3)

Dosimetric quantities should provide physical measures which are correlated with effects of ionizing radiation. The basic dose definitions are given in

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 Chap. 10, “Radiation Protection.” Operational quantities for practical measure-

ments, both for area and for individual monitoring, were introduced and further explained in ICRU Reports 39, 43, 47, and 51 (ICRU 1985, 1988, 1992, 1993). The International Commission on Radiation Protection has recommended their use in radiation protection measurements (ICRP 1991, 2007). They are based on the quantity dose equivalent and have the unit Sievert (Sv). The ICRU has provided definitions of the operational quantities at points at a depth din phantoms made out of tissue-like materials. For strongly penetrating radiation as neutrons, the depth din the phantom is 10 mm. The operational quantities for strongly penetrating radiation are for area monitoring the ambient dose equivalent H∗ (10)and for individual monitoring the personal dose equivalent Hp (10). The ICRU sphere with diameter 30 cm is the phantom for H∗ (10), while a slab phantom with dimensions 30 cm × 30 cm × 15 cmis used for the calibration to Hp (10). The ICRU material has a mass density of 1 g cm−3 and a mass composition of 76.2% oxygen, 11.1% carbon, 10.1% hydrogen, and 2.6% nitrogen (ICRU 2001). The relation between radiometric quantities and the operational quantities is established by fluence-to-dose-equivalent conversion factors. The operational doseequivalent quantities H∗ (10) and Hp (10) for neutrons are determined from the equations H ∗ (10) =



h∗φ (E)φE dE,

(4)

hp,φ (E)φE dE,

(5)

 Hp (10) =

where φE is the energy distribution of the neutron fluence and hp, φ (E) and h∗φ (E) are the corresponding energy-dependent fluence-to-dose-equivalent conversion coefficients. These coefficients were calculated by several groups and at an international level it was agreed upon the numerical values that can be found in ICRP Report 74 (ICRP 1996) and in ICRU Report 57 (ICRU 1998b). The conversion factor h∗φ (E) as a function of neutron energy is displayed in Fig. 1. The fluence response Rφ of a radiation detector is a useful quantity specifying its sensitivity for detection. For an irradiation in a homogeneous radiation field with fluence φ it is defined as (ISO 8529-1 2001) Rφ =

n , φ

(6)

where nis the total count of detected events. Fluence responses are measured in units of area, usually in cm2 . The fluence response corresponds to the area of a hypothetical detector with 100% efficiency.

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Fig. 1 Fluence-to-ambient-dose-equivalent H∗ (10) conversion coefficients for neutrons (ICRP 1996; Ferrari and Pelliccioni 1998; Sannikov and Savitskaya 1997)

A radiation detector’s response RH to dose equivalent H is defined as RH =

Rφ . hφ

(7)

Materials and Detector Types for Neutron Detection Neutron Detection Principles Ionizing radiation is a radiation consisting of directly or indirectly ionizing particles. A radiation detector is a device which in the presence of radiation provides a signal for use in measuring one or several quantities of the incident radiation. The detection of ionizing radiation usually utilizes ionization effects in detector materials. As neutrons are not directly ionizing they have to be converted into charged particles, which are then transferring their energy in direct ionization processes to the detector’s sensitive volume. The ions are subject to charge collection and sometimes to internal amplification processes. Proportional counters, Geiger–Müller counters, GEM detectors, and photomultipliers are using avalanche charge amplification sometimes at very large gains. Pulse analysis and discrimination is easier with large signals. Other detector types like ionization chambers or semiconductors are only collecting the charge. Glenn Knoll gave an excellent and very detailed overview on radiation detection (Knoll 2010).

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Active Neutron Detection Methods Gas-Filled Detectors Gas is a well-suited medium for the detection of ionizing radiation. Free electric charges are mobile in gases and their recombination probability is relatively low. The conductivity of gases is low enough that high voltages can be applied to produce sufficiently strong electric fields. Especially noble gases are well-suited components of counting gases. Quenching gas admixtures are required if avalanche gas amplification is used. This holds for the detection of all types of ionizing radiation. For neutron detection an efficient conversion process of neutrons into charged particles has to be added. There are a few gases where nuclear reactions in Table 3 provide efficient neutron conversion. The most important counting gases in neutron detection are 3 He, BF3 , methane, and hydrogen. The reactions with 3 He and 10 B have sufficiently large cross sections and high Q-values to convert slow neutrons with high probability into charged particles with enough kinetic energy to exceed detection thresholds. In hydrogen or in methane, neutrons are producing recoil protons. The neutron energy has to be not too low, because the recoil energy has also to be above detection threshold and in elastic scattering there is no energy contribution from a Q-value. In neutron detection, the most common gas-operated detector types are proportional counters, ionization chambers, and fission chambers. The working horse in neutron detection is certainly the 3 He proportional counter. Cylindrical tubes are available with diameters from a fraction of inch to several inches. There are also spherical counters and detectors with rectangular cross sections for time-of-flight spectroscopy. Tube lengths are ranging between a couple of centimeters up to several meters and 3 He filling pressures are up to 20 atm with small amounts of quenching gas. 3 He counters are rigid and can be operated at ◦ temperatures up to 200 C. The efficiencies for thermal-neutron detection are high. The 3 He(n, p) 3 H reaction releases a total of 764 keV kinetic energy as indicated by the Q-value in Table 3. According to the conservation of energy and momentum, the triton carries 191 keV and the proton 573 keV. Both particles are directly ionizing along their tracks through the gas volume and their total energy deposit is 764 keV. A typical pulse-height spectrum of a 3 He counter tube is shown in Fig. 2. with the full-energy-deposit peak at 764 keV. The tails at lower pulse heights correspond to events where one of the two decay particles has hit the counter tube’s wall and only a fraction of the full energy release is detected. Only one particle can hit the wall ◦ because the angle between both decay particles is 180 . The triton escape and the proton escape can clearly be seen in the pulse-height spectrum. All detected thermalneutron signals are exceeding a minimum energy deposit. Below this minimum, there is a gap. At very small pulse heights there are signals generated by gamma radiation. The discrimination threshold for the electronics is usually set above the gamma pulse heights and below the minimum neutron energy deposit. Detectors filled with BF3 have lower efficiencies than 3 He detectors due to the lower cross section and because the filling pressure is usually lower. But they have

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Fig. 2 Pulse-height spectrum of a 3 He counter tube with diameter 1 and filling pressure 3.5 atm

a better gamma discrimination because of the larger Q-value. Drawbacks of BF3 are that the gas is toxic and corrosive. Most BF3 counters are filled with pure boron tri-fluoride enriched to about 96% in 10 B. Boron-lined proportional counters have a similar construction to BF3 and 3 He proportional counters. However, the neutron detection is by means of a boron coating rather than boron or 3 He in a gaseous form, resulting in a higher neutron sensitivity. Typically, boron-lined proportional counters are used where the temperature limitations of BF 3 counters prevent their use. Detectors filled with hydrogen or with methane are used as recoil proton counters.

Semiconductors The following semiconducting materials have been used in neutron detection: • Silicon with 10 B coating or with 6 LiF film • Gallium arsenide with 10 B coating • Boron–carbide semiconductor diodes The advantages of semiconductors for neutron detection are mainly compact size, relatively fast timing characteristics, and an effective thickness that can be varied to match the requirements of the application. Drawbacks may be the limitation to small sizes and the relative high susceptibility to performance degradation from radiationinduced damage (Knoll 2010).

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Scintillators The following scintillators have been used in slow-neutron detection: • Boron-loaded plastic and liquid scintillators • 6 Li scintillators (LiF, LiI, LiFZnS(Ag), glass, scintillating fibers) • Gadolinium-loaded liquid scintillators Advantages of scintillators are that they can be sensitive to the amount of energy deposit and that they are fast detectors which can be used for time-of-flight measurement. Scintillators are robust, easy to be operated, and relatively cheap. Their disadvantages are aging effects and radiation damage, sometimes difficulties in the light detection, for instance, with photomultipliers in the presence of magnetic fields and some scintillators are hygroscopic. The dominant fast-neutron interaction in plastic or in liquid scintillators is the generation of recoil protons. Plastic scintillators consist out of a solid solution of organic scintillating molecules in a polymerized solvent. They are very popular because of the ease with which they can be fabricated and shaped. Typical emission is at 400 nm. They have a large light output and short decay time and are well suited for timing measurement. Many scintillator designations are following the SaintGobain-type designation. A plastic scintillator for fast neutrons would be BC-720. Plastic scintillators do not allow for a good neutron–gamma separation. The BC-501A (formerly called NE 213) is a widely used liquid scintillator with good pulse-shape discrimination properties intended for neutron detection in the presence of gamma radiation. It has extremely good timing properties and is well suited for coincidence measurements. Then there are for slow-neutron detection boron-loaded plastic scintillators (BC-454) and gadolinium (BC-521) and natural (BC-454) or enriched boron-loaded liquid scintillators (BC-523A). Also, scintillators with lithium are quite common. The lithium-iodide crystal is chemically similar to sodium iodide and also hygroscopic. Liquid scintillator with lithium is also commercially available. There are as well lithium-containing glass scintillators. A new type of a scintillation detector for neutrons is scintillating glass fibers loaded with lithium. Anthracene and stilbene also have been used for neutron detection. For neutron radiography there are scintillators with phosphor screen based on ZnS(Ag) and 6 Li (BC-704 earlier NE-426).

Superheated Emulsion Detectors Robert E. Apfel proposed in 1979 the superheated emulsion detectors, the socalled bubble technology as a new method for radiation detection (Apfel 1979). Superheated emulsion detectors are based on superheated droplets suspended in a viscoelastic gel medium, which vaporizes upon exposure to the high-LET recoils from neutron interactions. Bubbles evolved from the radiation-induced nucleation of drops give an integrated measure of the total neutron exposure. There are several different techniques to record and count the bubbles. In active devices, they can be detected acoustically, by optical bubble counting, or by vapor volume measurement. Neutron spectrometry can be performed by measuring responses at different

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temperatures or pressures. Bubble detectors are insensitive to low-LET radiation like gammas or X-rays. Acoustical recording has the issue with discrimination of bubble pulses against noise. Francesco d’Errico published overviews concerning superheated emulsion detectors (d’Errico et al. 1995, 2002; d’Errico 2001).

Passive Neutron Detection Methods Track Detectors Passive neutron detection with nuclear track emulsions is the oldest and was once the most common method for neutron personal dosimetry (Knoll 2010; ICRU 2001; d’Errico and Bos 2004). The emulsions are relatively inexpensive, but track analysis under a microscope is laborious. New developments are focusing on automated track scanning methods. Passive radiation detectors have the advantage of being able to measure also in pulsed radiation fields where active devices may suffer from deadtime losses or pulse pile-up. Thermoluminescent Dosimeters In thermoluminescent dosimeters (TLDs) (Knoll 2010; ICRU 2001; d’Errico and Bos 2004), electrons are elevated by a radiation from the valence to the conduction band and captured in trapping centers. Holes can also be trapped in analogous processes. The captured states are stable for longer periods. If a TLD is heated, the trapped electrons or holes are re-excited and emit visible photons, which can be detected by a photomultiplier. The number of photons is a measure of the dose deposit. An exposed TLD material is thus an integrating detector for ionizing radiation. There are many TLD materials. LiF has been the most widely exploited (Knoll 2010). TLDs for neutron measurement are primarily used as albedo dosimeters, which is a dosimeter capable of measuring the fraction of neutrons reflected by a human body. Thermoluminescence detectors for neutron detection utilize typically 6 LiF and 7 LiF crystals. 6 LiF is sensitive to neutrons and to photons while 7 LiF is only sensitive to photons. The neutron contribution is calculated by determining the difference of both readings. TLDs are simple, rugged, and cheap. They have a good linearity and low detection limits. TLDs are usually processed by automatic readout. Etched-Track Detectors Etched-track detectors (Knoll 2010; ICRU 2001; d’Errico and Bos 2004) are together with TLDs the most commonly used passive neutron detectors. Charged particles, like alpha particles or protons, damage the material along their tracks, which can be made visible by chemical or electrochemical etching. These secondary particles can originate from nuclear reactions both in materials adjacent to an etched-track detector and those created inside the bulk of it. Etched-track detectors are usually processed by imaging systems which analyze and count the tracks and determine the dose. This method is insensitive to photons. In particularly over the last few tens of years, polymer etched-track detectors have been used. The most

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popular detector material is polyallyl-diglycol carbonate (PADC), commercially available as CR-39. 6 Li or 10 B are mainly used as converters for slow neutrons. Their response characteristics are generally sufficiently well known for neutrons with energies up to several hundred MeV. These dosimeters are generally able to determine neutron ambient dose equivalent down to a few tenths of a mSv.

Passive Superheated Emulsion Detectors In passive superheated emulsion detectors or bubble detectors (ICRU 2001), the most immediate readout method is the visual inspection, a process that can be automated using video cameras and image analysis techniques. In the past decade superheated emulsions have achieved acceptance among the passive systems for personal neutron dosimetry. The detectors are considered to be the passive devices with the most accurate energy dependence of the response and the lowest detection threshold (d’Errico and Bos 2004). Direct Ion Storage Direct ion storage (DIS) is a relatively new technology. A small ionization chamber filled with air is in contact with the floating gate of a MOSFET transistor. The charge of the gate is initially set to a predetermined value. The charge generated by the radiation in the ionization chamber discharges partially the gate. The stored charge at the gate can be measured as a voltage without modifying its value and it is proportional to the dose. Application of DIS to neutron dosimetry is possible using pairs of detectors for the separate determination of the photon and neutron dose contribution (d’Errico and Bos 2004; Fiechtner et al. 2004). Other Passive Detectors Radioluminescent glass detectors have found limited application in neutron dosimetry. A more recent technique is optically stimulated luminescence (OSL) (McKeever 2001). This method is based on laser stimulation and does not need heating of the detector material. It seems to be a breakthrough in passive radiation detection (d’Errico and Bos 2004).

Applications of Neutron Detection Neutron Dose Measurement Introduction As a consequence of the 1990 recommendations of the International Commission on Radiological Protection, the operational quantities were newly defined (ICRP 1991). The relations between the neutron fluence and the two operational quantities, the ambient dose equivalent H∗ (10) and the personal dose equivalent Hp (10), vary widely with neutron energy. The fluence response of a well-designed instrument, which will give a reading sufficiently proportional to the operational quantities, regardless of the neutron energy spectrum should have a fluence response as a

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function of energy that is inversely proportional to the fluence-to-dose conversion coefficients (Knoll 2010) provided by the International Commission on Radiological Protection (ICRP 1996). This is the entire secret of the art of accurate neutron dose measurement.

Rem Counters The first neutron dose-rate meters based on the concept of an active thermal-neutron detector centered in an appropriate moderator with internal neutron absorbers – so-called rem counters – have been already designed in the 1960s. The Andersson– Braun counter and the Leake counter, became very popular and have been used all over the world for decades. While the Andersson–Braun counter has a cylindrical moderator and a BF3 proportional counter tube as neutron detector (Andersson and Braun 1963, 1964), the Leake counter has a spherical moderator with a reduced weight of about 5 kg and had a LiI(Eu) crystal at the center (Leake 1966). The Leake design was later improved by replacing the crystal by a small spherical proportional counter filled with 3 He gas to achieve better gamma rejection properties and increased neutron sensitivity (Leake 1968). After the publication of the ICRP60 recommendations of the International Commission on Radiological Protection (ICRP 1991), the Research Center Karlsruhe and Berthold Technologies designed a new neutron survey meter – the Berthold LB 6411 – with an energy-dependent response optimized to the then new operational quantity ambient dose equivalent H∗ (10) (Klett and Burgkhardt 1997). The rem counter utilizes a cylindrical 3 He proportional counter tube centered in a moderating polyethylene sphere with 25 cm diameter. The energy-dependent response to H∗ (10) tuned with internal perforated-cadmium neutron absorbers and with boreholes is within ±30% for neutron energies between 50 keV and 10 MeV (Knoll 2010). This is standard in gamma dosimetry but it is excellent in neutron dosimetry. The H∗ (10) response to neutrons emitted by a bare 252 Cf source is approximately 3 counts/nSv, which is very high. Figure 3 shows a drawing of the geometrical setup. Figure 4 shows the responses of several widely used rem counters to ambient dose equivalent H∗ (10) which were calculated from the fluence responses given in a technical report of the IAEA (IAEA 2001). In the United Kingdom, the radiation protection group of the Health Protection Agency together with the neutron metrology group of the National Physical Laboratory have carefully assessed the performances of several instruments (Tanner et al. 2006). For radiation protection purposes the response functions of conventional rem counters are considered to be acceptable at energies below 20 MeV. At higher energies, the responses are decreasing and the instruments are underestimating ambient dose equivalent. A growing number of accelerators with high or even very high energies and enhanced interest in dose monitoring at flight altitudes triggered novel designs of instruments for extended energy ranges (Birattari et al. 1998; Fehrenbacher et al. 2007; Klett et al. 2007). Extended-range rem counters utilize layers of lead, tungsten, or other high-Z materials to convert in spallation processes high-energy neutrons into lower-energy neutrons. Response functions of several extended-range rem counters were calculated by Mares et al. (2002).

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Fig. 3 Schematic drawing of the Berthold rem counter LB 6411

Fig. 4 Responses of several neutron survey meters to ambient dose equivalent H∗ (10)

Tissue-Equivalent Proportional Counters Tissue-equivalent proportional counters (TEPCs) allow the measurement of the probability distribution of the absorbed dose d(y) in terms of lineal energy yin

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radiation fields. The lineal energy is defined as the ratio of the energy imparted to the matter in a volume by a single-deposition event to the mean chord length in that volume. The lineal energy can be used as an approximation of the linear energy transfer LET, and the dose equivalent can be evaluated through a function Q(y) which relates the quality factor to the lineal energy. The TEPC is an important tool in microdosimetry and in some cases, the only one to provide directly dose and radiation quality information in complex radiation fields. The TEPC can be used to distinguish photon and neutron contributions with good accuracy. A tissue-equivalent proportional counter is a spherical or cylindrical detector with walls made out of tissue-equivalent material and filled with tissue-equivalent gas and operated in proportional mode. When the TEPC’s gas density and its diameter is maintained at about 10−4 g cm−2 , it can simultaneously determine the absorbed dose to the tissue and of the spectrum of the pulse heights which corresponds to the energy deposition (ICRU 2001). By far the most commonly used TEPC has been the spherical counter. It has the advantage of being isotropic with respect to external radiation, but the electric field close to the wire has unfortunately not a cylindrical geometry. In order to obtain a cylindrical electric field geometry in the volume of gas amplification, Rossi proposed the so-called Rossi counter with an auxiliary helix electrode close to the wire (Rossi and Staub 1949; Rossi and Rosenzweig 1955). The sensitive volumes of TEPCs range from a few millimeters up to several centimeters in diameter. TEPCs are operated in pulse mode to record each individual event’s energy deposit. The pulse height is proportional to the charge released in the sensitive detection volume. The measurement of lineal energies from below 100 eV/μm up to more than 1 MeV/μm requires low-noise analogue electronics with a linearity over 4–5 orders of magnitude and an appropriate ADC system. TEPCs have not only been used in dose measurements at aviation altitudes and in mixed photon–neutron fields in accelerator environments, but also in investigations in radiotherapy and radiobiology (Kliauga et al. 1995; Gerdung et al. 1995).

Active Personal Dosimeters A relatively new development now competing with and partially replacing the passive methods in individual dose monitoring are active personal dosimeters (APDs). In comparison to passive dosimeters, they have the advantages of instant reading, audible alarm, lower detection limits, data memory, and communication capabilities with other hosts. There are several neutron APDs on the market, which have one or several silicon diodes or silicon strip detectors for neutron detection. The semiconducting detectors are combined with neutron converters or with layers of material for neutron activation, for instance, silver. Some use separate photon channels for the subtraction of gamma doses. The main issue with neutron APDs is their poor energy-dependent response. There were comparisons of instruments on the market and summaries published (Bolognese-Milsztajn et al. 2004; LuszikBhadra 2007). Recent measurements with electronic personal neutron dosimeters for high neutron energies were reported by Luszik-Bhadra (2007).

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Passive Dose Measurement There is a large amount of passive dose measurement in individual monitoring of occupational exposure. The passive neutron detectors that are used are described above. A good overview about the state of art of the available techniques was given by F. d’Errico and A.J.J. Bos (2004). Dose Measurement in Pulsed Radiation Fields Many accelerators or other radiation generators operate in pulsed mode. It is well known that active radiation detectors are subject dead to time effects and exhibit limitations in pulsed radiation fields (Knoll 2010). These limitations cannot easily be overcome without the development of new active detection technologies. Measurement of pulsed radiation is usually done with passive detectors. There are now a few developments of new technologies based on the activation of radionuclides by pulsed radiation fields. One of these designs utilizes the neutroninduced activation of the nuclides 8 Li, 9 Li, and 12 B with short half-lives below 200 ms on the target nucleus 12 C in the detector materials. The decay products are detected in a time-resolved measurement. The instrument is mainly intended for radiation protection at accelerators with high energies and accomplishes the measurement of even very short and intense pulsed neutron fields (Klett and Leuschner 2007; Klett et al. 2010). Luszik-Bhadra published another design of a new monitor for pulsed fields based on the activation of silver. The device comprises four silicon diodes in a 12 polyethylene moderator sphere, two diodes covered on both sides with Ag, and two diodes covered with tin. The decay products of the activation products 109 Ag and 110 Ag are beta particles which are detected by the semiconductors. The detectors covered with silver are sensitive to neutrons and photons, while the detectors covered with tin are only sensitive to photons. The neutron dose is determined by subtraction (Luszik-Bhadra 2010; Leake et al. 2010). Examples of Neutron Dose Measurements The intensities of radiation levels at flight altitudes are exceeding-ground-level intensities by two orders of magnitude. The exposure of aircrews is comparable with or even larger than the exposure of workers classified as occupationally exposed. Primary galactic and solar particles – mainly protons – are interacting with the atmosphere and are generating secondary particles with a complicated composition. At flight altitudes of civil aircrafts about 50% of the ambient-dose-equivalent contribution is from neutrons, about 35% is from photons, electrons, and muons, and about 15% is from protons. Accurate dose measurements in these mixed fields with energies ranging from keV up to even exceeding the TeV domain is difficult. The recommendation by the International Commission on Radiological Protection (ICRP) in 1990, that exposure to cosmic radiation in the operation of jet aircraft should be recognized as occupational exposure, initiated a large number of new dose measurements onboard aircraft. A EURADOS working group has brought together all recent, available, preferably published, experimental data and results of calculations, mainly from laboratories in Europe (Lindborg et al. 2004). The

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reported results have been obtained using a variety of instrument types like rem counters, TEPCs, and Bonner sphere spectrometers. The results obtained are in good agreement almost all within ±25% of the mean values. During the time period 1995–1998 at temperate northern latitudes in 10 km altitude measured ambientdose-equivalent rates for neutrons were about 3 μSv/h and the total about 5 μSv/h. The total exposure on a typical trans-Atlantic flight is about 50 μSv (Luszik-Bhadra 2007). Another interesting example of neutron dose measurement was an international project investigating complex workplace radiation fields at European high-energy accelerators and thermonuclear fusion facilities. This study included all common types of existing neutron detection techniques in an environment with mixed radiation fields and high energies. The relevant techniques and instrumentation employed for monitoring neutron and photon fields around high-energy accelerators were reviewed with some emphasis on recent developments to improve the response of neutron-measuring devices beyond 20 MeV. It was investigated which type of area monitors to be employed (active and/or passive) and how they should be calibrated. The influence of the pulsed structure of the beam on the instruments and the needs and problems arising for the calibration of devices for high-energy radiation are addressed. The major high-energy European accelerator facilities are reviewed along with the way workplace monitoring is organized at each of them. The facilities taken into consideration are research accelerators, hospital-based hadron therapy centers, and thermonuclear fusion facilities. The issues of calibration are discussed and an overview of the existing neutron calibration facilities was provided (Bilski et al. 2006; Rollet et al. 2009; Silari et al. 2009).

Spectrometry General Neutrons appear in nature, in laboratories, or in nuclear facilities covering a very large energy range from ultracold up to ultrahigh energies at accelerators up to the TeV domain. As the interaction of neutrons with matter usually strongly depends on their energy, spectral information is needed in order to describe the occurring process. Spectrometry measurements are needed to characterize neutron fields. Commonly used measurement methods are Bonner sphere measurement, time-offlight measurement, nuclear recoil measurement, neutron-induced nuclear reactions, methods based on activation and on threshold effects, and neutron diffraction. An excellent overview about neutron spectrometry for radiation protection was provided by Thomas (2004). Bonner Spheres In 1960, the Bonner sphere spectrometer (BSS) was first described by Bramblett, Ewing, and Bonner (Bramblett et al. 1960). Of the many types of neutron spectrometers that have been developed this multisphere system has been used by more laboratories than any other. It is easy to operate, it has an almost isotropic response,

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it covers energies from thermal up to GeV neutrons, and it can be used with active or with passive detectors. A BSS is consisting of several moderating spheres with different diameters and a thermal-neutron detector which is assembled in the centers of these spheres. The spheres are usually made out of polyethylene and each sphere with the thermal-neutron detector has a sensitivity to neutrons over a broad energy range. However, the sensitivity for each sphere peaks at a particular neutron energy depending on the sphere diameter. From the measured readings of a set of spheres, information can be derived about the spectrum of a neutron field (Thomas and Alevra 2002; Thomas and Klein 2003a). Several types of thermal-neutron detectors have been used. In the original Bonner sphere spectrometer, a small 6 LiI(Eu) scintillator was used. Various cylindrical and spherical proportional counter tubes filled with BF 3 or 3 He are obvious alternatives. Several groups investigated the use of the SP9 spherical 3 He proportional counter produced by Centronic Ltd. UK. It has a diameter of 32 mm and a gas pressure of about 2 atm. The characteristics of BSSs with this detector are well established. Typical moderator sphere diameters are between 3 and 18 with the number of spheres in a set ranging between 6 and 12 spheres (Thomas and Alevra 2002). If sphere i has response function R i (E) and is exposed in a neutron field with the spectral fluence φ(E), then the sphere reading M i is obtained mathematically by folding Ri (E) with φ(E):  Mi =

Ri (E)φ(E) dE.

(8)

This integral extends over the range of neutron energies present in the field. Good approximations of Ri (E) can be obtained by simulation calculations supported by measurements in well-characterized reference neutron fields. Information about the spectrum φ(E) can be extracted by unfolding. However, because the total number of spheres is limited, the solution may provide a poor representation of the spectrum with important features smeared out. Additional a priori information on the spectrum is useful (Thomas and Alevra 2002). The PTB NEMUS system, the INFN Frascati BSS, and the NPL BSS are a few examples where detailed descriptions, measurements, and intercomparison data were published (Wiegel and Alevra 2002; Bedogni and Esposito 2009). Figure 5 shows the components of the PTB NEMUS Bonner sphere spectrometer. BSSs have an excellent energy range, good sensitivity, isotropy, and photon discrimination, simple but time-consuming operation, and poor energy resolution. According to a neutron field’s intensity and time structure, various types of active or passive thermal-neutron detectors can be selected. The data analysis requires complex unfolding of the measured data. For instance, FRUIT (Frascati Unfolding Interactive Tool), an unfolding code for Bonner sphere spectrometers, was developed under the Labview environment at the INFN-Frascati National Laboratory and is available from the authors upon request (Bedogni et al. 2007). An excellent overview on Bonner sphere neutron spectrometry was provided by Thomas and Alevra (2002).

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Fig. 5 Bonner sphere spectrometer NEMUS of the PTB with five of the ten polyethylene spheres in the back, a spherical 3 He proportional counter in the center, and parts of the modified spheres in the foreground left and right

Time-of-Flight Spectroscopy Time-of-flight spectroscopy is based on measurement of the time it takes for a neutron to travel a known distance. From this the neutron’s velocity and the energy can be calculated. The measurement needs a start and a stop signal. The former can, for instance, be derived from a pulsed neutron generation process while the latter is generated when the neutron arrives at a distant neutron detector. The indication of the start can be generated by time-pick-up signals from an accelerator, by an appropriate detector, or by a beam chopper. To minimize uncertainties time-offlight spectroscopy requires precise time measurement. Therefore, the detectors from which the time information is derived have to be very fast. Excellent timing characteristics have for instance plastic scintillators. The flight paths have to be very long and can be as long as the order of magnitude of 100 m (Fig. 6). Recoil Spectroscopy Another neutron detection technique with spectral sensitivity is based on elastic neutron scattering on light target nuclei. During the interaction a fraction of the neutron’s energy is transferred to the recoil nucleus. As the recoil nucleus is directly ionizing, it deposits its energy in the detector materials. The maximum energy Emax which can be transferred from a neutron with kinetic energy En to a recoil nucleus with mass A in units of neutron mass is (Knoll 2010): Emax =

4A (1 + A)2

En .

(9)

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Fig. 6 Neutron spectra of bare 252 Cf, moderated 252 Cf, and 241 Am–Be (IAEA 2001)

The maximum fractional energy transfer in elastic neutron scattering is 1 for hydrogen, 0.64 for 4 He, and 0.22 for 16 O. Therefore, only light nuclei are of primary interest with hydrogen being the best choice. Recoil proton spectroscopy can be performed with detectors with a substantial amount of hydrogen in the detector material. The easiest detector would be a scintillator containing hydrogen as organic crystals, plastic scintillators, or liquid scintillators. Liquid scintillators have the advantage of the possibility for neutron–gamma discrimination. Another detector type for recoil spectroscopy would be gas recoil proportional counters filled with hydrogen, methane, or with helium. The energy distribution for all scattering angles in elastic neutron–proton scattering is approximately a rectangular function. This is the detector’s response function. The neutron spectrum has to be determined by deconvolution (Knoll 2010).

Neutron Activation Analysis Neutron activation analysis (NAA) is one of the most sensitive analytical techniques to determine concentrations of many elements in a variety of materials. It is based on neutron activation and requires irradiation of the specimen with neutrons. This creates artificial radioisotopes of the elements of interest. Usually reactors are used but other types of neutron sources as previously discussed can also be used, if the energy and intensity requirements are met. The decay products of the artificial radioisotopes are then measured and analyzed. Preferably gamma spectroscopy

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allows for the identification of nuclides and for quantitative measurement of concentrations. As it is a nuclear method, NAA does not depend on the chemical form of the sample. NAA is a nondestructive technique and requires usually very small amounts of sample. Many elements can be determined at the same time (Alfassi 1990). There are a few important experimental conditions for NAA, first of all the kinetic energy of the neutrons used for irradiation. Generally, neutron activation is performed with thermal neutrons, but there are also nuclear reactions used, where higher neutron energies are required. The intensity of the neutron field and the cross sections of the selected activation processes are important parameters. The nuclear decay products can be measured during or after neutron irradiation.

Neutron Scattering There is a lot of research utilizing neutron scattering in biology, biotechnology, medicine, nanotechnology, and in research on catalysis, drugs, energy, magnetism, molecular structure, polymers, and superconductors all over the world. Some of the leading institutes are the Institut Laue–Langevin in Grenoble, the Rutherford– Appleton Laboratories in Oxford with ISIS, the FRM II reactor in Munich, the Research Center Jülich, the Paul Scherrer Institute in Würenlingen with SINQ, the KENS Neutron Scattering Facility at KEK in Japan, the Oak Ridge National Laboratory with their new spallation neutron source, and the Los Alamos Neutron Science Center LANSCE. These research centers are using special techniques like elastic and inelastic scattering, diffractometry, time-of-flight measurement, smallangle neutron scattering, reflectometry, or measurements of polarized neutrons. The international scientific community benefits from applying these sophisticated large installed detector systems, which employ physical principles and detection techniques that were discussed here. The details of these spectrometers and techniques are very elaborate and are not subject of this chapter. More information about these detector systems and research disciplines can be obtained from the Web sites of the neutron scattering laboratories.

Nuclear Medicine In radiotherapy with neutron beams, the estimation of the neutron doses to the organs surrounding the target volume is particularly challenging. For instance, at the Louvain-la-Neuve (LLN) facility, these doses were investigated. The transport of a 10 cm × 10 cm beam through a water phantom was simulated with the Monte-Carlo code MCNPX and measurements of the absorbed dose and of dose equivalent using an ionization chamber and superheated-drop detectors were performed (Benck et al. 2002). Boron neutron capture therapy (BNCT) is a cancer treatment method where after the delivery of a suitable boron compound to tumor cells, the tumor is irradiated

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with slow neutrons. The boron concentration in the tumor has to exceed the boron concentration in normal tissue considerably, which can be achieved by a number of compounds. A reactor or an accelerator has to deliver large thermal-neutron fluences of the order of magnitude of 1012 n/cm2 to get sufficient results of these irradiations (Gahbauer et al. 1997). Accurate measurements of neutron fluences and dose distributions as well as Monte-Carlo calculations are the base of treatment planning. Neutron fluence and absorbed-dose measurements were for instance performed with activation foils and paired ionization chambers (Binns et al. 2005).

Search for Illicit Trafficking Nuclear Materials Since the demise of the former Soviet Union and even more since the new terrorism, the search for illicit trafficking or hidden nuclear material became an important new application in radiation detection. In the beginning, the main focus was in gamma detection, but soon neutron detection was also included, because plutonium, a material used for nuclear weapons, is a significant source of fission neutrons (Kouzes 2005). Neutron detection is very selective for the indication of dangerous nuclear materials. Plutonium is extremely hazardous and hard to be detected, because it is not very difficult to shield the alpha, beta, and photon emissions. But the evennumbered plutonium isotopes exhibit significant spontaneous fission yields. For instance, 1 g of 238 Pu is emitting 2,660 fission neutrons per second. Therefore, a neutron detector for the search for illicit trafficking or hidden nuclear material needs a maximum of sensitivity in the fission-neutron energy region. Rem counters are for these applications not sensitive enough and perform poorly, because their “dose tuning” is based on a tremendous amount of neutron filtering and absorption. A well-designed detector’s energy-dependent response should be optimized to fission neutrons at a maximum of sensitivity. This can be achieved by a moderator of reasonable size in which a large thermal-neutron detector is located. An example of a highly sensitive handheld detector is described in Klett (1999). Neutron detection is now widely used in security applications like access and exit control of nuclear facilities, vehicle monitoring, border control, monitoring in harbors and airports, in waste storage management, and in safeguard activities. The Austrian Research Center Seibersdorf in cooperation with a team of International Atomic Energy Agency IAEA experts and supported by the World Custom Organization (WCO) and by INTERPOL has performed the Illicit Trafficking Radiation Detection Assessment Program (ITRAP). The aim of the study was to work out the technical requirements and the practicability of useful monitoring systems. International suppliers and manufacturers of radiation detection equipment from nine different countries have participated. The study covered fixed-installed monitoring instruments, pocket-type instruments, and handheld instruments. Neutron monitoring should be included in the fixed-installed systems; it was desirable for the handhelds and not necessary for the pocket-type instruments (Beck 2000).

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For the detection of special nuclear materials (SNM), there are neutron coincidence counters in use. They have arrays of neutron detectors – usually large 3 He proportional counters in moderators optimized for fission-neutron detection – covering a container from several sides. There is active interrogation and passive measurement. For active interrogation, a neutron source is used to induce fission in a fissile material under investigation. Passive measurement measures neutrons emitted by the sample without external irradiation. Homeland security applications consumed large amounts of 3 He since a decade. Since about 2008, there is now a worldwide shortage in 3 He supply and many groups are now developing neutron detection alternatives (Kouzes et al. 2010).

Reactor Instrumentation Reactor instrumentation requires mostly slow-neutron detection at high intensities and under extreme conditions of reactor operation. Neutron intensities have to be measured in core up to 1014 cm−2 s−1 and out of core up to 1010 cm−2 s−1 . There ◦ are high pressures and temperatures which can be as high as 300 C. Because of a lower gamma sensitivity, gas-filled detectors are a preferable choice. Boron ionization chambers can be tailored to measure the required range of neutron flux. Uncompensated boron ion chambers are generally used in regions of high neutron flux where the gamma flux is only a small share of the total radiation level. Fission chambers can be used in pulse or in direct-current mode. Fission chambers include a fissile material normally 235 U. The fission fragment’s large energy deposits are generating the detector signals. Fission chambers in pulse mode are ideal in mixed fields because gamma discrimination is easy in pulse mode. Socalled self-powered detectors utilize a material with a high cross section for neutron capture with subsequent beta decay. The beta decay current is measured without external bias voltage. Overviews and more details about reactor instrumentation can be found in Knoll (2010) and Boland (1970).

Fusion Monitoring Neutron spectrometry is a tool for obtaining fusion plasma information such as ion temperature and fusion power. Neutron spectrometry measurements for diagnostics at the Joint European Torus (JET) between 1983 and 1999 were reported by Jarvis (2002). A wide variety of spectrometer types with nuclear emulsions, NE213 liquid scintillators, hydrogen ionization chambers, recoil proton counters, 3 He ionization chambers, silicon detectors, and diamond detectors have been tested with varying degrees of success. Magnetic proton recoil spectrometers are successful in monitoring the d–d and the d–t reactions at 2.5 MeV and 14 MeV, respectively. Investigations about the time resolutions of several different neutron spectrometry techniques and an upgraded magnetic recoil spectrometer for ITER were recently described by Andersson (2010).

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Industrial Applications Neutron Imaging and Radiography As neutron interactions with atoms and molecules are very different from Xray interactions, the neutron is sensitive to other aspects of matter. For instance, in investigating in automotive industries with imaging techniques, X-rays would illuminate the metallic structure of an engine while neutrons would rather take a picture from the oil. Neutron imaging requires position-sensitive neutron detectors. Neutron transmission radiography (NR) is based on the attenuation of radiation passing through a sample. Details of samples can be made visible, if the attenuation is different in different materials. As neutron detectors track etch foils, a combination of a neutron converter layer (Gd, Dy) and X-ray film, or a combination of a neutron-sensitive scintillator and a CCD camera or position-sensitive 3 He detectors have been used. A new development is amorphous-silicon flat panels. They contain Gd as neutron absorber and BaFBr:Eu2+ as the agent which provides the photoluminescence. An imaging plate scanner is extracting the digitized image information from the plates by de-excitation caused by a laser signal. Humidity Measurement Because water is an excellent neutron moderator, it is possible to measure humidity with neutrons. If fast neutrons emitted by a neutron source are penetrating humid matter, there is thermalization depending on the amount of water. A typical neutron humidity measurement setup comprises a fast-neutron source and a detector for thermal neutrons close to each other. The probe is positioned in or close to the sample material, which could be coal, coke, sand, sinter, soil, or lime sand bricks. The measurement is online and continuously without direct contact with the sample. The measurement is not affected by temperature, pressure, pH value, or optical characteristics of the material and determines of the amount of water molecules, irrespective of their physical or chemical binding. Humidity measurement with neutrons is mainly used by chemical, cement, ceramics, coal, iron, and steel industries.

Reference Neutron Radiation Fields Reference neutron radiation fields are very important for the calibration of neutron detectors. The following types are commonly used: • Neutrons from radionuclide sources, including sources in a moderator • Neutrons generated by nuclear reactions with charged particles from accelerators • Neutrons from reactors These fields have usually unidirectional beams and cover neutron energies in the range from thermal up to several hundred MeV. There are quasi-monoenergetic

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neutron radiations for determining the response of neutron-measuring devices as a function of energy, and there are neutron fields with wide spectra for calibration of instruments. An instrument under calibration is placed in a free-in-air radiation field of known fluence rate and the reading is recorded. Neutron scattering from the air, by the walls, floor, and ceiling should be minimized and corrected for. The room used for irradiation should be as large as possible and measurements with a shadow cone help to take into account the scattered neutrons’ contributions. The international standard ISO 8529 about reference neutron radiations covers in its three parts the general principles, the commonly used radiation fields which are listed in Table 7, and the calibration procedures (ISO 8529-1 2001; ISO 8529-2 2000; ISO 8529-3 1998). The facilities providing neutron radiations traceable to national standards are, for instance, the Physikalisch-Technische Bundesanstalt PTB in Germany, the National

Table 7 Commonly used ISO reference neutron radiations (ISO 8529-1 2001; ISO 8529-2 2000; ISO 8529-3 1998) with fluence-averaged energies E and fluence-to-dose conversion factors h∗φ (E) according to ICRP74 (ICRP 1996) Source/Generation 252 Cf (D O 2 moderated) 252 Cf 241 Am–Be Reactor or accelerator Sc-filtered reactor beam Accelerator Accelerator Accelerator Accelerator Accelerator Accelerato Accelerator Accelerator Accelerator Accelerator Accelerator Accelerator

Half-life [years] 2.65 2.65 432

Reaction Spontaneous fission

Energy [MeV] 0.550

h∗ φ (E) [pSv cm 2 ] 105

Spontaneous fission (α, n) 9 Be(d, n)X/thermal column

2.130 4.160 2. 5 × 10−8

385 391 10.6

2 × 10−3

7.7

24 × 10−3 0.144

19.3 127

0.250

203

0.565

434

1.200 2.5 5.0 14.8 19.0 33 and 50

425 416 405 536 584

45 Sc(p, n)45 Ti 3 He

T(p, n) and 7 Li(p, n)7 Be T(p, n) 3 He and 7 Li(p, n)7 Be T(p, n) 3 He and 7 Li(p, n)7 Be T(p, n) 3 He T(p, n) 3 He D(d, n) 3 He T(d, n) 4 He T(d, n) 4 He Université Catholique de Louvain (UCL) TSL Uppsala CERN/CERF (Mitaroff and Silari 2002)

200 ) prevents an analytical maximization: the probability distribution ln P (yi |λ) depends on several components of λ. The data y are said to be incomplete. The basic idea of the EM algorithm is to postulate a so-called complete data random vector z made of independent variables such as no more than one component of λ contributes to the expectation of each element of z. Let z be a complete data random vector {{xij |j = 1, · · · , m}, qi |i = 1, · · · , n} ∈ Rn×m+n where, for detection element i, xij is defined as the number of events originating from voxel j and qi the mnumber of detected background events, with the many to one mapping yi = j =1 xij + qi (Politte and Snyder 1991). The expectations are given by E{xij } = Aij λj and E{qi } = bi . The data z follows a Poisson distribution with a log-likelihood with respect to z given by ⎛ ⎞ n m     ⎝ ln R(z|λ) = xij ln(Aij λj ) − Aij λj + qi ln(bi ) − bi ⎠ , i=1

(57)

j =1

where the terms xij ! and qi ! have been dropped. As only the incomplete data y are known, the key principle of the EM algorithm is, instead of maximizing the log-likelihood with respect to z, to maximize the expected log-likelihood with the expectation taken with respect to the unobserved complete data using a guess λ(p) of λ (Dempster et al. 1977). The EM algorithm is decomposed in two steps: the calculation of the expectation (E-step)   Q(λ|λ(p) ) = E ln R(z|λ)|y, λ(p) ,

(58)

and its maximization (M-step) λ(p+1) = arg max Q(λ|λ(p) ).

(59)

λ≥0

If we take λ(p+1) as a new guess and iterate over the E and M steps, the EM algorithm will produce a likelihood sequence L(λ(p) ) that is monotonically increasing. As L(λ) is concave, it will converge to its unique maximum. For a random vector x made of independent Poisson variables xi with mean ai , the conditional expectation is given by E{xi |

 j

ai xj = N} = N  j

aj

.

(60)

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The E-step is then given by ⎛ ⎛ ⎞ (p) n m   A λ ij j ⎝ ⎝−Aij λj + yi  Q(λ|λ(p) ) = ln(Aij λj )⎠ − bi (p) m i=1 j =1 k=1 Aik λk + bi  bi +yi m ln(bi ) . (61) (p) k=1 Aik λk + bi This expression can be analytically maximized using the Kuhn-Tucker conditions, leading for the M-step to (p)

(p+1)

λj

λj = n

n 

i=1 Aij i=1

yi

Aij m

(p) k=1 Aik λk

+ bi

(62)

or, in vector-matrix notation, λ(p+1) =

y λ(p) T , A T (p) A 1 Aλ + b

(63)

where multiplication and division between vectors are component wise, 1 is a vector of length n with all elements set to 1, and the matrix AT is the transpose of A. By analogy to the analytical operators P and P# , the matrix A corresponds to the forward projection of the image λ and the matrix AT to the backprojection of the data y. The E-step and the M-step are combined into a single step (63). The EM-ML algorithm for emission computed tomography is (0)

• Initialize λ(p=0) with strictly positive values : λj > 0 ∀ j = 1, · · · , m; • Compute the normalization image: n = AT 1; • For iteration (p) – Compute the expected data given λ(p) : E{y|λ(p) } = Aλ(p) + b; – Compute the ratio between the measured data and their expectation: r(p) = y/E{y|λ(p) }; – Backproject the ratio: c(p) = AT r(p) ; – Update the current image: λ(p+1) = λ(p) c(p) /n; – Go to next iteration. The relative simplicity of this algorithm, in particular the fact that the E and M steps are combined, also explains its popularity. If the starting image λ(p=0) is strictly positive, the algorithm ensures that the reconstructed images λ(p) are positive as long as the data y are themselves positive (if the data are pre-corrected for background events, they can be negative; negative values are then set to zero).

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The EM-ML algorithm belongs to the class of simultaneous techniques: it makes an update of the reconstructed image based on all data bins simultaneously. As a consequence, it suffers from a major drawback: it is slow to converge. To speedup convergence, accelerated algorithms have been proposed. The most popular, as it requires only minor implementation changes relative to the original algorithm, is the Ordered Subsets EM (OSEM) algorithm from Hudson and Larkin (1994). The OSEM algorithm belongs to the class of block-iterative algorithms: the measured data are grouped in ordered disjoint subsets, and the standard EM-ML algorithm is applied to each of the subsets in turn. The resulting reconstructed image of one subset becomes the starting value for the next subset. The subsets are chosen in a balanced way so that all voxels contribute approximately equally to any subset. In such case, the convergence acceleration provided by the OSEM algorithm is roughly equal to the number of subsets for the early iterations. However, for noisy data, the algorithm does not converge to the ML estimate; it cycles through a number of distinct points. This is not a major limitation as in practice the EM-ML algorithm is usually not run until convergence. Another accelerated algorithm for the ML estimate is the row-action maximum likelihood algorithm (RAMLA) of Browne and De Pierro (1996). A row-action algorithm updates the reconstructed image for each data bin separately, processing one row of the system matrix. RAMLA was inspired from the ART (algebraic reconstruction algorithm) technique of Herman and Meyer (1993), an algebraic rowaction algorithm for minimizing a least-square objective function. Let l be the index of the subiterations over the n data bin and p the index for a complete cycle over the n indices l with λ(p,0) = λ(p−1) and λ(p) = λ(p,n) . The expression of the RAMLA algorithm is given by  λ

(p,l+1)

=λ

(p,l)

+ p λ

(p,l)

Ail

yil < Ail · λ(p,l) > +bil

 −1 ,

(64)

where p is a strictly positive relaxation parameter such that p Aij ≤ 1 ∀ (i, j ), il is a permutation of the data bin, and Ai is the i th column of AT . The ordering il of the data bin is such that the consecutive vectors Ail are as orthogonal to each other as possible to accelerate convergence. The RAMLA algorithm avoids the limit cycle by using strong underrelaxation involving a decreasing sequence  of relaxation parameters p : under the conditions that limp→∞ p = 0 and ∞ p=0 p = +∞, the algorithm converges to λML . If the numerical implementation of RAMLA is such that one complete cycle over the data bin is no more computationally intensive than one EM iteration, then it is about one order of magnitude faster than EM in convergence.

ML Algorithms in Transmission Tomography For transmission tomography, an EM-ML algorithm has been derived by Lange and Carson (1984). The complete data are defined as y, augmented by the number of photons entering (uij ) and leaving (vij ) each voxel j along each projection line i.

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The expectation (E-step) is given by Q(μ|μ(p) ) =

m  n    −E{vij |yi , μ(p) }Mij μj + E{uij |yi , μ(p) } i=1 j =1

  −E{vij |yi , μ(p) } ln(1 − e−Mij μj ) .

(65)

Unlike for emission data, it does not yield a closed-form solution for the M-step. As a consequence, algorithms for resolving the M-step are slow to converge (Ollinger 1994). Algorithms more efficient than EM-ML were developed, based on direct maximization of the log-likelihood (Lange et al. 1987; Lange and Fessler 1995). One approach proposed originally by De Pierro for emission tomography is to use a surrogate function that approximates locally the objective function and is easier to minimize (De Pierro 1995). Given a current estimate μ(p) of the image, the surrogate S(μ; μ(p) ) function is tangent to −L(μ(p) ) at μ(p) and lies above −L(μ) for other positive μ: S(μ; μ(p) ) ≥ −L(μ) ∀μ ≥ 0 S(μ(p) ; μ(p) ) = −L(μ(p) ) ∇S(μ(p) ; μ(p) ) = −∇L(μ(p) ).

(66)

If the surrogate is convex, then its minimization or diminution decreases the objective function. This procedure is repeated iteratively to minimize the objective function μ(p+1) = arg min S(μ; μ(p) ). μ≥0

(67)

The convergence rate of the algorithm depends on the curvature of the surrogate. The EM-ML algorithm for emission tomography can be interpreted as a surrogate-based technique, where the conditional expectation Q(λ|λ(p) ) is an inferior surrogate function for the log-likelihood L(λ). Because the curvature of the conditional expectation at λ(p) is large compared to L(λ), the EM-ML algorithm is slow to converge. Erdogan and Fessler developed an algorithm based on a surrogate function to minimize the negative log-likelihood −L(μ) (53) in the presence of background events (b = 0): the separable paraboloidal surrogates (SPS) algorithm (Erdogan and Fessler 1999). The surrogate is chosen quadratic and separable in the voxel elements j , so that its minimization is reduced to the minimization of m 1D parabolas that depend on one voxel value μj only. The algorithm allows for simultaneous update, and the authors applied the ordered-subset principle of OSEM to SPS (OSTR) to accelerate convergence, at sacrifice of global convergence. Let k

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1309

be the index of the subiterations over the K subsets and p the index for a complete cycle over the K subsets with μ(p,0) = μ(p−1) and μ(p) = μ(p,k) . The expression of the ML-OSTR algorithm is given by  (p,k+1) μj

= max

(p,k) μj

−

K



(p,k)

i∈Sk

Mij hi

dj

 ;0 ,

(68)

where  (p,k)

hi

=

yi Ii e−

+ bi

 (p,k) − 1 Ii e−

(69)

  and dj = ni=1 Mij (yi − bi )2 /yi m j =1 Mij . An alternative is to use the OSEM algorithm with ln(Ii /yi ) instead of yi , but this is not optimal for low-count studies as the data ln(Ii /yi ) do not follow a Poisson distribution. For X-ray CT, another alternative is to assume Gaussian data. In this case, the maximization of the log-likelihood is equivalent to the minimization of a least-square function. A large class of algebraic reconstruction techniques (ART) exists to solve iteratively this type of equation (Gordon et al. 1970).

Regularization Like the FBP algorithm, the ML estimation problem is ill-conditioned: small changes in the data might result in large variations in the reconstructed ML image. The algorithm attempts to recover the underlying distribution that best matches, in a statistical sense, noisy data (Snyder et al. 1987). When the data are very noisy, the ML estimate might be too noisy for an appropriate use. Like FBP, some regularization is needed to constraint the solution and get an “acceptable” image. The meaning of acceptable depends on the practical imaging task and the criteria might differ between feature detection or quantitative estimation of a physiological parameter. There are different ways to regularize an ML-based algorithm.

Early Termination During the EM iterations, low frequencies are reconstructed first. For higher iterations number, the algorithm will essentially attempt to recover noise and yields a deteriorating “checkerboard effect” of high spatial variance in the reconstructed images (see Fig. 10). When starting from a smooth image, at some early iterations of the EM-ML algorithm, the image might “look” nicer than for higher iteration numbers. Early termination of the algorithm is one way of regularization that is commonly used in clinical studies. It has the major advantage of reducing the computation time of the image reconstruction. This also explains the popularity of the OSEM algorithm: the non-convergence of the subset algorithm is not a practical limitation. The major drawback of early termination is the nonuniform convergence

1310

C. Comtat

Fig. 10 Sagittal slice of the reconstructed images of a 2 min [18 F]-FDG brain PET scan after k iterations of the EM-ML algorithm

Fig. 11 Sagittal slice of the reconstructed images of a 2 min [18 F]-FDG brain PET scan after 1600 iterations of the EM-ML algorithm, followed by a smoothing with an isotropic 3D Gauss function of width FWHM

of the algorithm and consequently the spatially varying resolution of the image. Some parts of the image converge slower, in particular lower-count regions as opposed to higher count regions. The choice of the number of iterations is empirical and task dependent. For detection, small features should be visible and not hidden by surrounding noise. For quantitative estimations, it is important to verify that the numerical value of the parameter of interest has reached a plateau. The balance between noise level and resolution is controlled by the number of iterations.

Post-reconstruction Smoothing In order to be less sensitive to the nonstationary convergence of the EM-ML algorithm, it might be appropriate to run the algorithm for a higher number of iterations and then smooth the reconstructed image with a Gaussian kernel. This approach is related to the Grenander’s method of sieves (Snyder et al. 1987), which constrains the estimate of the image to be in a subset, called the sieve, of the space of nonnegative functions. An illustration is given in Fig. 11 for the same data set as for Fig. 10. The trade-off between noise and resolution is controlled by the width of the Gaussian kernel.

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Penalized Objective Function or MAP Reconstruction An alternative solution to resolve the ill-conditioning in the ML consists in the addition of a penalty function U (λ) directly in the objective function, and running the iterative algorithm until convergence to compute a penalized ML estimate λPML = arg max L(λ) − U (λ).

(70)

λ≥0

The log-likelihood L(λ) relates the estimated image to the data (data fitting term), whereas the penalty function U (λ) penalizes excessive noise in the estimated image by adding a roughness penalty (regularization term). The expression in (70) can also be viewed in a Bayesian framework: given some prior distribution on the image, p(λ), the posterior density conditioned on the data, p(λ|y), is maximized. The relation between these terms is given by the Bayes rule p(λ|y) =

p(y|λ)p(λ) . p(y)

(71)

The Maximum A Posteriori (MAP) reconstruction algorithm consists in the computation of the maximum estimate of the log of the posterior density: λMAP = arg max L(λ) + ln p(λ),

(72)

λ≥0

where the term p(y) has been dropped. The images are usually modeled as locally smooth, with sharp transition between different types of tissues. Two types of prior are generally considered: spatially independent priors and Gibbs priors. In the first case, voxels are assumed statistically independent and optimizations can be based on extensions of the EMML algorithm. However, these priors require information on the expected mean voxel values distribution. It can be appropriate for transmission tomography, in particular with radionuclide sources, where the mu value of the tissues is known. In the second case, more common, spatial interactions between voxels are modeled using Gibbs distributions, with the generic form p(λ) =

1 −βU (λ) e , Z

(73)

where U (λ) is the Gibbs energy function. The MAP estimate is then given by λMAP = arg max L(λ) − βU (λ),

(74)

λ≥0

where the hyperparameter β controls the weight of the prior relative to the data fidelity term.

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The Gibbs energy function is generally defined as a sum of potential functions V on the absolute difference between pairs of neighboring voxels

U (λ) =

m 



j =1 k∈Nj ,k>j

V (|λj − λk |) , dj k

(75)

where dj k is the Euclidean distance between the pair of voxels (j, k), and Nj the neighbor subset of voxel j . Typically, Nj consists in the 6 (first order) or 26 (second order) nearest voxels of voxel j . One example is the Huber prior which is quadratic for small values and switches to linear at a user-specified value δ to allow for sharp transitions

VH (t) =

if |t| ≤ δ t 2 /2 . |t|δ − δ 2 /2 else

(76)

In emission tomography, when anatomical information is available in the form of a co-registered MR or X-ray CT image, the smoothing prior can be deactivated between pairs of voxels belonging to different anatomical structures. Many optimization procedures for MAP, or equivalently PML, estimation are proposed in the literature. They can be classified into the following methods (Qi and Leahy 2006): • Gradient-based algorithms: the direction of the update is calculated from the gradient of the objective function. The preconditioned conjugate gradient algorithm is particularly efficient, although it is difficult to enforce the non-negativity constraint on the image (Mumcuoglu et al. 1994). • Coordinate-ascent algorithms: one voxel is updated in turn so as to ease the application of the non-negativity constraint. The objective function is maximized with respect to one voxel while holding the other fixed, leading to a one-dimensional problem. The algorithm is particularly efficient with a Gaussian noise model and a quadratic penalty term; the objective function is then quadratic (Fessler 1994). • Functional substitution: the original objective function is replaced at each step by a surrogate function (De Pierro 1995). An example was given in equations (66) and (67). It should be pointed out that at the time of the writing of this chapter, MAP or PML reconstructions have not yet been widely adopted, even though some manufacturers propose now MAP reconstructions for clinical applications. The favor still goes to the EM-ML algorithm or its accelerated variants (OSEM or RAMLA), with a post-reconstruction smoothing of the estimated image. This method is easy to implement and already produces satisfactory results in practice when compared to FBP.

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Fig. 12 Sagittal slice of the reconstructed images of a [18 F]-FDG brain PET scan. 360 independent acquisitions of 10 s were performed and reconstructed with the analytical 3DRP algorithm (Hann apodization window and Nyquist cut-off frequency) (top row) and with the iterative EM-ML algorithm (96 iterations, 2 mm FWHM post-reconstruction Gaussian smoothing) (bottom row). Extreme left, MR image; left, one acquisition; middle, average across the 360 reconstructions; right, standard deviation across the 360 reconstructions

Conclusive Remarks As an illustration, a comparison between the EM-ML and the FBP algorithms is presented in Fig. 12 for very noisy PET data corresponding to a 10 second acquisition. The FBP image is characterized by a high level of noise all across the reconstructed field-of-view, while the noise is more concentrated on the brain for the EM-ML image. The same acquisition was repeated 360 times and reconstructed with both algorithms, allowing for the computation of a mean image and a standard deviation image across the 360 statistically independent reconstructions. Although one replica is very noisy and difficult to examine, the average of the replicas looks similar between FBP and EM-ML, nicely showing the structures of the cortex. On the contrary, the standard deviation images are very different; quite similar to the average image for EM-ML, based on a Poisson noise model, and much more uniform spatially for FBP, based on no noise model. The choice between analytical and iterative reconstruction techniques is not obvious, although iterative algorithms allow in principle for better modeling of the scanning process and could be preferred for this particular reason. This is definitely not the end of analytical methods. The latter are linear algorithms, unlike iterative algorithms, which is advantageous for tasks like the quantitative estimation of physiological parameters. In addition, analytical techniques run much faster on a computer; one iteration of an optimization-based technique takes about the same time as one FBP reconstruction. Implementation simplicity is also a decisive advantage, in particular for the scanner manufacturers. A very accurate modeling

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of the scanning process will surely make its implementation more complex, for an hypothetical gain on image quality. This chapter presents a limited view on tomographic reconstruction techniques, focusing on some long-established techniques. Many methods and new fields were left out. Among many uncovered research fields, we can cite the active developments that are currently performed on dynamic reconstructions (4D reconstructions), including time as an additional variable to space to account for the change in the tracer kinetics or the morphological motions of patients, or even both (5D reconstruction). It is also interesting to note the new developments on analytical algorithms for X-ray CT to perform exact and stable 2D reconstruction of a regionof-interest with limited data set that were thought to be intractable before (Defrise and Gullberg 2006). The reader is encouraged to read the following chapters of the handbook related to image reconstruction in computed tomography: • • • •

 Chap. 40, “CT Imaging: Basics and New Trends”  Chap. 42, “PET Imaging: Basic and New Trends”  Chap. 41, “SPECT Imaging: Basics and New Trends”  Chap. 48, “Evaluation and Image Quality in Radiation-Based Medical

Imaging” •  Chap. 46, “Quantitative Image Analysis in Tomography” •  Chap. 5, “Statistics” Readers that do not have access to a dedicated software and wish to test iterative reconstruction algorithms for PET, SPECT, or X-ray CT data are invited to download the open source and generic CASToR reconstruction software, freely available at www.castor-project.org.

Cross-References  CT Imaging: Basics and New Trends  Evaluation and Image Quality in Radiation-Based Medical Imaging  PET Imaging: Basic and New Trends  Quantitative Image Analysis in Tomography  SPECT Imaging: Basics and New Trends  Statistics

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Multi Imaging Devices: PET/MRI

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Han Gyu Kang and Taiga Yamaya

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Why PET/MRI? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mutual Interferences Between PET and MRI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sequential PET/MRI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Simultaneous PET/MRI: PMT-Based PET/MRI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Preclinical PET/MRI with Optical Fiber Bundle and PMT . . . . . . . . . . . . . . . . . . . . . . . . Simultaneous PET/MRI: APD-Based PET/MRI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . APDs for MR-Compatible PET Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Preclinical PET/MRI with APDs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Brain PET/MRI with APDs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Whole-Body PET/MRI with APDs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Simultaneous PET/MRI: SiPM-Based PET/MRI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SiPMs for MR-Compatible PET Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Preclinical PET/MRI with SiPMs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Brain PET/MRI with SiPMs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Whole-Body PET/MRI with SiPMs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract Multi imaging devices have been playing an important role in medical imaging fields such as radiology, nuclear medicine, and interoperative surgery. In general, one standalone medical imaging device can provide only one aspect

H. G. Kang · T. Yamaya () Department of Nuclear Medicine Science, National Institute of Radiological Sciences (NIRS), National Institutes for Quantum and Radiological Science and Technology (QST), Chiba, Japan e-mail: [email protected]; [email protected]; [email protected] © Springer Nature Switzerland AG 2021 I. Fleck et al. (eds.), Handbook of Particle Detection and Imaging, https://doi.org/10.1007/978-3-319-93785-4_51

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of a patient’s information. For example, positron emission tomography (PET) provides molecular information whereas magnetic resonance imaging (MRI) provides morphological information. For an accurate diagnosis of diseases such as cancer and dementia, multiple aspects of the patient’s information are essential. Thus, multi imaging devices have evolved towards combining two different imaging modalities into a single imaging platform to provide both functional and anatomical images for better decision-making by physicians. In this chapter, one of the most modern multi imaging devices in the last two decades, PET/MRI for medical applications, is described.

Introduction Multi imaging devices have been used widely as an integral part of medical imaging. This is because one standalone medical imaging system can provide only one aspect of a patient’s information. For example, positron emission tomography (PET) can provide functional information of the patient at a molecular level (Phelps 2000) whereas x-ray computed tomography (CT) (Rubin 2014) and magnetic resonance imaging (MRI) (Grover et al. 2015) can provide structural information. From a clinical perspective, multiple aspects of disease information are essential to make the best decision for the patient’s diagnosis and treatment. Therefore, development of multi imaging devices has advanced remarkably during the last two decades. One of the most successful multi imaging devices is PET/CT which was invented by David Townsend and Ronal Nutt in 1998. PET/CT is a sequential combination of PET and CT scanners to obtain both PET and CT images in a single platform (Beyer et al. 2000). PET/CT provides a fused image of PET and CT images, enabling doctors to interpret functional information (PET image) based upon structural information (CT image) and vice versa (Kapoor et al. 2004). As a result, the accuracy of disease diagnostics has been enhanced significantly (Antoch et al. 2004). Another early improvement was to use a PET scan in place of the lengthy PET attenuation correction procedure previously done by rotating a rod shaped radioactive source around a patient (Kinahan et al. 1998). With the first commercialization of PET/CT in 2001, all the standalone PET scanners were replaced with PET/CT except for brain dedicated PET scanners. Use of PET/CT scanners has spread rapidly worldwide for cancer screening and staging (Farwell et al. 2014). In particular, fluorodeoxyglucose (FDG) PET scans which visualize the glucose metabolism of a human body have been playing an important role in the promotion of PET/CT examinations in clinical situations. FDG PET scans allow doctors to detect cancer and also to evaluate cancer progress in a quantitative manner (Boellaard 2009). FDG PET/CT scans are now one of the standard examinations for the diagnosis and staging of cancer. While PET/CT scans can provide great medical benefits for oncological examinations, there is an increasing concern about the radiation exposure from them which may increase cancer risk (Wen et al. 2013). Recent studies have shown

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that diagnostic ionizing radiation can increase the cancer risk for children who are more sensitive to radiation-induced carcinogenesis than adults (Miglioretti et al. 2013; Hong et al. 2019). Therefore, many efforts have been made to reduce the radiation dose for patients in both PET and CT examinations by using advanced detector technologies along with iterative reconstruction algorithms. Nevertheless, the radiation exposure caused by low-dose CT for children is still associated with an increased cancer risk (Rampinelli et al. 2017). Magnetic resonance imaging (MRI), on the other hand, which uses a high magnetic field and a non-ionization radiofrequency (RF) pulse, can provide anatomical information without radiation exposure to patients. Therefore, a new multimodal imaging system, PET/MRI can reduce the burden of radiation exposure for children and women who are at higher risk while providing both molecular and anatomical information for cancer diagnosis.

Why PET/MRI? Recently, neurodegenerative diseases have become a serious problem as more societies are experiencing rising numbers of the elderly. Neurodegenerative diseases are caused by slow progressive damage of neurons in the brain, which is an irreversible process since neurons normally do not reproduce themselves. Alzheimer’s disease (AD) is the most common example of a neurodegenerative disease, and the decline of cognitive ability of an AD sufferer depends on the progress of neuron damage. Since there is no cure yet for AD, its early diagnosis and prevention of further progression are crucial. For an accurate and early diagnosis of neurodegenerative diseases, targeted molecular imaging and detailed anatomical information of the human brain are important. For targeted molecular imaging, there has been a lot of studies on the development of radiopharmaceuticals which bind to biomarkers of AD selectively such as beta-amyloid or Tau protein. Subtle alterations of anatomical structures caused by a metabolic abnormality of brain, are also important information for accurate AD diagnosis. Unfortunately, however, CT scans cannot provide detailed structures of the brain with high contrast resolution. This is because the contrast of CT images comes from the density difference of the imaged objects, but brain structures such as gray matter and white matter have similar densities. On the other hand, MRI can provide excellent soft tissue contrast. In addition, MRI can visualize not only the anatomical structures but also physiological phenomena of the human body. Moreover, the contrast of brain structures can be further enhanced by employing various pulse sequences without using contrast agents. Unlike CT, MRI can provide detailed structures of the brain due to its high soft tissue contrast, and that allows doctors to detect even subtle structural abnormalities caused by diseases. Moreover, MRI does not use ionizing radiation, suggesting that the radiation dose for a patient can be reduced by half with PET/MRI compared to PET/CT. Therefore, PET/MRI offers more attractive multimodal imaging than PET/CT imaging especially for brain imaging and low-dose pediatric imaging.

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Mutual Interferences Between PET and MRI Unlike PET/CT, there are significant mutual interferences between PET and MRI (Vandenberghe and Marsden 2015), degrading the image qualities of both imaging modalities considerably. Therefore, these mutual interference issues should be resolved for the seamless integration of PET with MRI in a single platform. There are four considered here. The first mutual interference between PET and MRI is the effect of a high magnetic field on PET detectors. In conventional PET, a PET detector consists of a scintillation crystal array and photomultiplier tube (PMT). The scintillation crystal array captures gamma photons and converts them into scintillation light which carries the energy and positional information of the gamma photons. A PMT is used as a photo sensor to convert scintillation light into electrical signals. The scintillation light is converted into primary electrons by the photocathode of the PMT and then, the primary electrons are accelerated by a high voltage before they strike a series of dynodes. As a result, an amplified electrical signal can be obtained at the end of the dynode series. This electron multiplication process occurring in the PMT allows users to obtain an electrical pulse with a sufficiently high signal to noise ratio (SNR). However, when a PMT is placed nearby or inside an MRI, the electron multiplication process does not occur successfully. This is because the electrons are deflected by the Lorentz force as they travel in the high magnetic field of the MRI. As a consequence, a significant number of PMT signals is lost (Shao et al. 1997b; Vaquero et al. 2013). The second mutual interference is the RF interference between the PET electronics and MR RF coils. In MRI, a series of RF pulse chains with a Larmor frequency (i.e., 127 MHz for 3 T MRI) are generated from RF coils to excite the protons. The RF pulses generated by the body or local RF coils of an MRI device can easily interfere with PET electronics, thereby resulting in false triggering of the PET signal along with significant degradation of the energy and time resolutions. On the other hand, PET electronics containing integrated circuits can also generate electromagnetic waves which can be detected by MR receiver coils. As a result, the SNR of an MR image is reduced significantly owing to the PET operation. These mutual RF interferences can be solved by enclosing the PET electronics inside conductive materials such as copper or carbon fiber which absorb the RF pulses. However, the RF shielding materials affect the main magnetic field homogeneity, thereby causing metal artifacts and spatial distortions on the MR images. Moreover, the rapidly alternating gradient field of the MRI can induce large eddy currents on the shielding materials, causing significant distortion of MR images. Therefore, the RF shielding design of PET electronics should be optimized to minimize the eddy currents while preventing RF interference sufficiently (Truhn et al. 2011). The third mutual interference is the effect of the MR gradient field on the PET system. The quickly changing MR gradient fields in x, y and z directions with a frequency on the order of a few kHz, can generate heat and cause mechanical vibrations of the PET electronics. Therefore, the PET electronics should be designed

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so that they are able to tolerate thermal changes and small vibrations for stable PET operation. The last mutual interference is a susceptibility artifact of the MR image caused by the PET detector. In order to minimize this susceptibility artifact, the PET detector should not contain magnetic materials such as iron and gadolinium. In addition (and particularly for small animal PET), the scintillation crystal materials which are located close to the imaging object should not affect the magnetic field homogeneity (Schenck 1996). Scintillation materials such as BGO, GSO and LGSO, which contain high fractions of gadolinium material,can adversely affect the MR image quality, since gadolinium is a paramagnetic material (Yamamoto et al. 2003). Therefore, scintillation crystal materials which do not contain gadolinium, such as LSO, LYSO have been used for the development of MR-compatible PET scanners.

Sequential PET/MRI One simple way to combine PET and MRI without encountering these mutual interference problems is to place the PET scanner sufficiently far away from the MRI scanner where the magnetic field is low enough (Cho et al. 2007; Zaidi et al. 2011; Veit-Haibach et al. 2013) as illustrated in Fig. 1. In this way, the PET and MRI images can be obtained in a sequential manner without any interference and fused retrospectively. This sequential PET/MRI system design requires only a turntable rail shuttle to rotate and transfer a patient from the PET unit to the MR scanner. The main advantage of the sequential PET/MRI design is that existing PET and MRI scanners can be used without significant hardware modifications. Thus, technical challenges are small for the sequential PET/MRI design. However, there are three issues for this approach. The first one is the inaccuracy of image co-registration between PET and MRI. The PET and MRI images are obtained from two separated modalities which are spatiotemporally independent of

Fig. 1 Sequential whole-body PET/MRI design using table shuttle for patient transportation

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each other. Subsequently, a PET/MRI fusion image is generated retrospectively by using dedicated software. In such a condition, the co-registration accuracy is prone to being affected by patient motions, which eventually affects the interpretation of the PET/MRI fusion image. The second issue is that the functional information of PET is not temporally correlated with the time-resolved physiological information of MRI. Advanced MR pulse sequences such as functional MRI (fMRI) (Belliveau et al. 1991; Logothetis 2008) and functional magnetic resonance spectroscopy (fMRS) (Stanley and Raz 2018) can record physiochemical information of the human brain nearly in realtime. However, the sequential acquisition of PET and MRI data does not allow timecorrelated PET/MRI images to be obtained. The third issue is the long acquisition time which limits the patient throughput. A patient should undergo PET and MRI scans sequentially which makes the total scan time longer than that of simultaneous PET/MRI scanning. For these reasons, many research groups have focused on the development of simultaneous PET/MRI imaging systems rather than sequential PET/MRI systems. An additional advantage of simultaneous PET/MRI over sequential PET/MRI is the slightly improved spatial resolution due to the reduced positron range inside the MRI device bore. The positron range is one of the fundamental factors which limits the spatial resolution of PET images (Phelps et al. 1975; Cho et al. 1975; Levin and Hoffman 1999). High magnetic fields (5–7 T) can confine the positron range effectively as demonstrated by simulation (Iida et al. 1986) and experimental (Christensen et al. 1995) studies. It is noteworthy that the positron range measurement study inside a 5 T MRI using PMTs and long lightguides (Lucite rods with a length of 4 m) done by Christensen et al. was the first coincidence detection of positron signals in the presence of a high magnetic field. A few years later, other research groups replaced the lightguides with optical fiber bundles to keep the spatial information during the transportation of scintillation light from crystal arrays to PMTs.

Simultaneous PET/MRI: PMT-Based PET/MRI Preclinical PET/MRI with Optical Fiber Bundle and PMT In 1997, the first simultaneous PET/MRI system prototype was developed at UCLA in collaboration with UMDS (currently King’s College London). This collaborative research group developed the first prototype MR-compatible small animal PET scanner using optical fiber bundles and multi-channel PMTs (MC-PMTs) (Shao et al. 1997a). The scintillation crystals were arranged in a ring geometry placed inside a 9.4 T MRI bore. The scintillation signal produced inside the crystal array was transferred via 4-m long optical fiber bundles to the MC-PMTs which were located in the vicinity of the MRI device as shown in Fig. 2. Shao et al. were able to obtain simultaneous PET/MR images and PET/NMR data. The first advantage of this approach was that existing commercial MRI systems could be used without

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Fig. 2 Simultaneous PET/MRI system using optical fiber bundles and PMTs (left) and the first simultaneous PET/MRI images of a C-shape structural phantom (right) (Shao et al. 1997a)

MR hardware modifications and the second advantage was that mutual interference between PET and MRI could be minimized. The MR-compatibility study with the prototype PET insert showed no significant interference between PET and MRI (Slates et al. 1999). This was because the MC-PMTs and electronics which are sensitive to magnetic fields and RF pulses were placed sufficiently far from the MRI device. Moreover, the MR image quality could be well preserved since the PET electronics and its shielding box which are magnetically susceptible were moved away from the imaging object. Therefore, magnetic resonance spectroscopy (MRS) which requires an extremely uniform magnetic field homogeneity could be obtained with the 9.4 T MRI during the PET operation. However, the PET performance was significantly degraded due to the use of the 4 m long optical fiber bundles. A substantial amount of scintillation light loss was caused by the use of optical fiber bundles which resulted in the degraded energy and time resolutions of 45% and 26 ns, respectively. Moreover, this approach did not allow a multiring PET design since the optical fiber bundles were not bent at 90◦ . Nevertheless, this pioneering work of Shao et al. (1997a) on the successful demonstration of simultaneous acquisitions of PET and MR images of a rat, encouraged many other research groups to start developing various types of prototype PET/MR scanners. Other research groups also employed the optical fiber bundles as a key element for the development of MR-compatible PET scanners in combination with positionsensitive PMTs (PS-PMTs), but there was a modification of the geometry of the optical fiber bundles. For example, a collaborative research group of West Virginia University and the Thomas Jefferson National Accelerator Facility, used 90◦ bent optical fiber bundles which allowed them to extend the axial PET field of view (FOV) as shown in Fig. 3 (Raylman et al. 2006). As a result, simultaneous PET and MRI images of a rat brain were obtained successfully though the PET had limited angle geometry. A collaborative research group in Japan further improved the optical fiber bundlebased MR-compatible PET design (Yamamoto et al. 2010a). They used dual-layer LGSO crystal arrays which had different decay times to encode DOI information. The combination of slanted light guides and 75-cm long optical fiber bundles was

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Fig. 3 Simultaneous PET and MRI acquisition setup for a rat brain with 90◦ bent optical fiber bundles

Fig. 4 MR-compatible full-ring PET insert system using a slanted light guide coupled to optical fiber bundles and the PS-PMT (Yamamoto et al. 2010a)

used to transfer the scintillation light from the crystal arrays to the PS-PMT at the fringe of an open geometry 0.3 T permanent magnet as shown in Fig. 4. A full ring MR-compatible PET system consisting of 16 optical fiber bundle-based block detectors was constructed and simultaneous PET/MR images of a rat brain were obtained. A novel integrated PET/MRI system design was proposed by a research group in the University of Cambridge in collaboration with Siemens Company. The proposed PET/MRI design employed split 1 T superconducting magnets and gradients to allow the positioning of a multi-ring PET system in a 80 mm gap between the split magnet as shown in Fig. 5 (Lucas et al. 2006). The PET detectors of a commercial small animal PET system (microPET Focus-120, Siemens Medical Solutions, Inc.) were reutilized to make a PET system having an axial coverage of 7.6 cm. The scintillation light produced inside LSO crystal array were transferred to the PS-PMT via 1.1 m long optical fiber bundles. Since the PS-PMT and its electronics and shielding box were placed 1.1 m away from the imaging object, the MR image was not affected by the PET electronics. In addition, a multi-ring PET system could be integrated into the animal 1 T MRI device thanks to the large gap between the split magnets. A dedicated birdcage coil was used to transmit and

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Fig. 5 Schematic diagrams of the small animal PET/MR system using the split magnet (1 T cryogenic) and optical fiber bundle-based PET detector blocks

receive the RF signals. Simultaneous small animal PET/MR images were obtained for both a phantom and an animal without mutual interferences between PET and MRI. However, the performance of the PET system was degraded as the length of optical fiber bundles was increased from 10 cm to 1 m as compared to the original commercial small animal PET system. For example, the energy and time resolutions were degraded from 18% to 27% and 2.6 ns to 3.6 ns, respectively. Nevertheless, the PET performances were good enough to produce PET images of high resolution and high sensitivity. The main drawback of this approach was a significant modification of MRI hardware. For example, this PET/MR design required a split magnet and gradient coils to make a gap for placement of the PET hardware. In addition, this approach would not be applicable for ultra-high-field 9.4 T preclinical MRI or clinical 3 T MRI, since it is quite challenging to get a homogeneous main magnetic field with the split magnet and gradient coils at such conditions. The combination of long optical fiber bundles and PMTs opened the door for simultaneous PET and MRI imaging. Excellent MR image quality was obtained since magnetically sensitive materials of the PET detectors such as PMTs and electronics were positioned sufficiently far away from the MR FOV. However, this excellent quality came at the expense of PET performance due to the use of long optical fiber bundles. A significant amount of light loss will occur during the transport of scintillation light from the crystal arrays to the PMTs through optical fiber bundles. This significant light loss (50–80%) adversely affects the energy resolution, timing resolution and crystal identification. The scintillation light loss is a critical issue in particular for the development of MR-compatible timeof-flight (TOF) PET which requires a high light collection efficiency. Thus, some researchers developing PET/MRI devices, turned their attention from PMTs to solid state semiconductor detectors to improve the PET performance (Pichler et al. 1997).

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Simultaneous PET/MRI: APD-Based PET/MRI APDs for MR-Compatible PET Detectors Avalanche photodiodes (APDs) (Renker 2007) are promising photo sensors for the development of MR-compatible PET detectors for two reasons: magnetic field immunity and compact size. Unlike bulky PMTs, APDs are insensitive to high magnetic fields because the electron multiplication process occurs within a very short range of a few tens of micrometers. In addition, the compact size of the APDs is well suited for the development of a compact PET scanner which should be inserted into the constrained space of the MRI bore. However, compared to PMTs, the APDs have three drawbacks: low gain, poor timing resolution and temperature sensitive gain fluctuation. Therefore, development of an APD-based PET scanner is technically more challenging that development of a conventional PMT-based PET scanner. Nevertheless, the magnetic field immunity and compact size of APDs have enabled many research groups to develop high performance simultaneous PET/MR systems. The use of silicon APDs has been actively studied for the development of compact PET detectors since the mid- 1980s at Sherbrooke University (Petrillo et al. 1984; Lecomte et al. 1985, 1990 Lightstone et al. 1986). The APD-based small animal PET scanner was demonstrated as being able to provide excellent performance in terms of spatial resolution (Marriott et al. 1994; Lecomte et al. 1996).

Preclinical PET/MRI with APDs The first APD-based small animal PET/MRI scanner was developed in 2006 by a collaborative research group with members from UC Davis and Tubingen University (Catana et al. 2006). The MR-compatible small animal PET scanner consisted of LSO crystal arrays, 90◦ bent optical fiber bundles and position sensitive APDs (PSAPDs) as shown in Fig. 6. Short optical fiber bundles (10 cm long) were employed to transfer the scintillation light from the LSO crystal arrays to the PSAPDs which were still located inside the 7 T MRI bore. In this way, the metal artifacts caused by PET electronics and its RF shielding materials, could be reduced substantially while minimizing the degradation of PET performance. Therefore, simultaneous multi-slice PET/MR images of a mouse brain were obtained without mutual interference. However, Catana et al. (2006), still found slight PET performance degradation due to the sharply bent optical fiber bundles, in particular for the photopeak uniformity. But more importantly, the axial extension of the PET FOV is hardly achievable as it requires 90◦ bent optical fiber bundles which occupy a large space inside the MRI bore.

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Fig. 6 MR-compatible small animal PET insert using APDs in combination with 90◦ bent short optical fiber bundles (10 cm). (Image courtesy of Ciprian Catana)

In order to resolve these issues, a compact MR-compatible APD-based PET detector module (Pichler et al. 2006; Judenhofer et al. 2007) was introduced by another research collaboration between Tubingen University, UC Davis, Bruker BioSpin MRI, and Siemens Preclinical Solutions. The PET detector consisted of an LSO crystal arrays, a 3-mm thick light guide, a PSAPD array, and front-end electronics. The PET detector block was enclosed within two copper shielding layers (10 μm thick) to prevent RF interference from the 7 T MR RF coil. It is important to note that the RF shielding design was carefully optimized to protect PET electronics from the intense RF pulses emitted from the RF coil while minimizing the eddy current induced on the shielding material by the gradient coil (Pichler et al. 2006). An MR-compatible small animal PET insert consisting of 10 APD-based block detectors arranged in a ring shape, was inserted into the 7 T MRI bore as shown in Fig. 7 (Judenhofer et al. 2008). The simultaneous acquisition of PET and MRI images was achieved without any significant mutual interference between the two modalities. The PET electronics and shielding enclosures did not affect the MR image quality thanks to the optimized RF shielding design of the PET detector and shimming, while the MR RF pulse and gradient field did not affect the PET count rate, energy resolution and flood histogram quality which are the fundamental measures of PET performance. The well-designed compact PET detector employing solid state photomultipliers as well as the optimized RF shielding enclosures, have enabled the simultaneous PET/MR in vivo imaging without compromising the performance of both modalities as shown in Fig. 7. This approach now has become a standard method for the development of simultaneous PET/MRI scanners. However, there is room for further improvement of both PET and MRI performance by using new generation solid state photomultipliers and optimized RF shielding enclosures. A collaborative group of Brookhaven National Laboratory (BNL) and Sherbrooke University researchers has developed an MR-compatible APD-based small animal PET scanner with the similar PET/MR design but different APD readout electronics (Maramraju et al. 2011). The detector technology was based on their

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Fig. 7 APD-based MR-compatible PET insert combined with preclinical 7 T MRI, and simultaneous PET and MRI images of a mouse bearing tumor (Judenhofer et al. 2008)

previous APD-based rat brain PET scanner known as RatCAP (Vaska et al. 2004). The two distinctive features of the APD-based PET detector were its one-to-one coupling between the LSO array and the APD and use of low power consumption ASICs for the readout of individual APD channels as shown in Fig. 8. The oneto-one coupling could enhance the light collection efficiency compared to the light sharing method; however, the spatial resolution of the PET scanner was limited by the APD cell size, typically around 2–3 mm. Custom-built MR RF transceiver coils were integrated inside the PET insert. The PET insert was not shielded by conductive materials, thus, the simultaneous FDG PET and 9.4 T MRI images were obtained with significant mutual interference between the PET insert and MRI. Later on, Maramraju et al. (2012) came up with an optimized RF shielding design featuring a double-layer segmented copper shield for their PET insert system. However, the MR images were significantly affected by the copper shielding because of the short distance between the copper shield and imaging object owing to the small PET diameter of 38 mm. Moreover, the PET electronics were also affected by the RF pulse emitted from the RF coils which was attributed to the short distance (5 mm) between the custom-built RF coils and copper shielding.

Brain PET/MRI with APDs The successful development of MR-compatible APD-based small animal PET scanners has led researchers to develop human brain PET/MR scanners. The first prototype human brain PET/MR scanner employing the APD detector technology was developed by Siemens (Schmand et al. 2007) and evaluated by multiple

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Fig. 8 PET detector assembly using the LSO crystal and APD arrays (left), and the MRcompatible PET insert combined with the MR RF transceiver coil (right). (Image courtesy of David J. Schlyer)

Fig. 9 Schematic diagram of the APD-based brain PET insert with 3 T MRI and a photo of the brain PET insert combined with a slightly modified clinical 3 T MRI (Kolb et al. 2012) (right)

cooperating groups including Tubingen University, Siemens Medical Solutions, University of Tennessee Medical Center, and Max Planck Institute researchers (Schlemmer et al. 2008). An MR-compatible human brain PET insert (35.5 cm inner diameter and 19.2 cm axial FOV) was constructed using LSO-APD PET detector technology (Schmand et al. 2007; Schlemmer et al. 2008; Kolb et al. 2012). The developed MR-compatible human brain PET insert fit inside a slightly modified 3 T clinical MRI scanner (Trio, Siemens Medical Solutions USA, Inc.) as shown in Fig. 9. A specially modified head coil for less gamma photon attenuation was placed inside the PET insert for the transmission and reception of RF pulse signals and the first simultaneous PET and MR images of a human brain were obtained. The prototype MR-compatible brain PET insert and clinical 3 T MR scanner could be operated simultaneously without any significant mutual interference (Kolb et al. 2012).

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The prototype brain PET insert was also installed in a clinical 3 T MRI scanner at the Research Center Julich, Germany, for various neuroscientific research studies with both 3 T and 9.4 T human MRI systems (Shah et al. 2013). One limitation of the MR-compatible PET insert approach is that whole-body human imaging is almost impossible due to the limited space constraint inside the MRI bore. Moreover, a body coil which is essential for whole-body MR imaging cannot be used for the RF transmission as the PET detector, and its RF shielding housing blocks the RF passage from the body coil to the human body. This problem can be solved by integrating the PET detector blocks on the space between the gradient coil and body coil, but that requires a significant modification of the MRI hardware system.

Whole-Body PET/MRI with APDs In 2011, the first commercially available fully integrated whole-body PET/MR scanner using APD technology, the Biograph mMR, was released by Siemens (Delso et al. 2011). The RF shielded APD-based PET detector modules were integrated between the gradient coil and body coil of a 3 T MRI scanner (Fig. 10), thereby solving the two issues of the whole-body PET/MR design: space constraint of the MRI bore for the PET system and use of the body coil for whole-body MR imaging. The first clinical results of the integrated whole-body PET/MR scanner for oncologic diagnoses showed that PET/MR can produce clinically relevant diagnostic

Fig. 10 Schematic diagram (left) and photo (right) of the first commercially available fully integrated whole-body PET/MR with APD technology. (Photo courtesy of Siemens Healthineers, Reprinted from MReadings: molecular MRI)

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PET and MR images which are comparable to those of low-dose PET/CT scanners (Drzezga et al. 2012). The APD-based PET detector technology has enabled the successful development of MR-compatible PET scanners for both preclinical and clinical fields. However, the disadvantages of APD-based PET scanners are two-fold: poor timing resolution and necessity of a dedicated preamplifier or ASIC (Pichler et al. 2004). The poor timing resolution, on the order of a few nanoseconds, results in an increased random count rate which degrades the PET image quality. More importantly, time-of-flight information obtained from a pair of PET detectors cannot be used for the TOF PET image reconstruction to improve the SNR of PET images. Thus, the mainstream photo sensors for PET/MR development has changed from APDs to novel state-of-the-art solid-state photomultipliers possessing high gain, low noise and fast time response. In summary, APD-based PET detector technology has made a significant contribution to the development of simultaneous PET/MR scanners. For example, the two core technologies of simultaneous PET/MR systems, the compact MR-compatible PET detector design (Pichler et al. 2006) and the RF shielding techniques of PET electronics were established with the APD detectors (Peng et al. 2010, 2014; Maramraju et al. 2012).

Simultaneous PET/MRI: SiPM-Based PET/MRI SiPMs for MR-Compatible PET Detectors Silicon photomultipliers (SiPMs) (Buzhan et al. 2003), also known as G-APDs (Geiger-mode avalanche photodiodes) (Renker 2006), are excellent solid state semiconductor photo detectors for the development of truly high-performance MRcompatible PET detectors or scanners because of their high gain comparable to that of conventional PMTs, magnetic insensitivity, compact size, and low operation voltage (∼40 V). Basically, an SiPM is an array of micro APDs each of which operates in the Geiger-mode with a bias voltage higher than the breakdown voltage (Renker and Lorenz 2009). Therefore, SiPMs inherently have the same magnetic insensitivity as APDs have. More importantly, because the micro APD array operates in the Geiger-mode, the SiPMs have high gain and low noise which allow them to detect even a single photon (Otte et al. 2005). In addition, the latest SiPMs have excellent single photon timing resolution (SPTR) response ranging from 70 to 150 ps depending on their manufacturers (Gundacker et al. 2020). Therefore, the state-of-the-art TOF-PET which takes into account the arrival time difference of annihilation gamma photons for image reconstruction is easily achievable using the SiPMs in combination with fast scintillators such as LSO and LYSO crystals. The basic properties of single channel SiPMs such as gain, dark current, photon detection efficiency, and SPTR, have been characterized (Buzhan et al. 2003; Otte et al. 2005; McElroy et al. 2007; Britvitch et al. 2007; Kim et al. 2008;

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Dam et al. 2010; Vacheret et al. 2011; Seifert et al. 2012a); and they showed comparable performances to those of conventional PMTs in terms of energy resolution and timing resolution (Buzhan et al. 2003). However, SiPMs suffer from non-linearity of the output signals because of their architecture which has a limited number of micro cells (Renker 2006). Moreover, the strong temperature dependence of gain, the optical cross talk between neighboring micro cells, and the after pulse are major drawbacks for SiPM use in comparison to conventional PMT use (Eckert et al. 2010). Nonetheless, preliminary SiPM-based PET detector blocks have been reported to provide excellent energy resolution (Schaart et al. 2009) and timing resolution (Kim et al. 2011; Seifert et al. 2012b) as well as good crystal identification (Kolb et al. 2010; Yamamoto et al. 2010b). Various prototype SiPM-based small animal PET scanners have been developed in different groups and the feasibility of high resolution in vivo PET imaging was demonstrated (Yamamoto et al. 2010b; Kwon et al. 2011). The feasibility of MR-compatible SiPM-based PET detectors has also been explored by several groups in three different ways (Spanoudaki et al. 2007; Hong et al. 2008; Kang et al. 2010; Schulz et al. 2009). The first approach (Spanoudaki et al. 2007; Kang et al. 2010) placed one pair of LYSO-SiPM detectors inside an MRI without any RF shielding. The SiPM charge signals were transferred to the preamplifiers outside the MRI via long cables (300 cm) and then digitized by the data acquisition (DAQ) system in coincidence mode during the MR operation. The merit of this approach was the excellent MR image quality as PET electronics and shielding materials were removed from the MRI bore. However, the use of long cables degraded timing resolution of PET detector significantly. Similarly, the second approach (Hong et al. 2008) placed a pair of LYSOSiPM detectors without RF shielding but transferred the SiPM charge signals to the preamplifier inside the MRI bore via short cables (30 cm). The preamplifier boards were enclosed by a copper shielding box to prevent RF interference. The voltage outputs of preamplifiers were transferred to the DAQ system outside the MRI room via long cables. The coincidence data were taken during the MR pulse sequences and the MR images were not affected by the LYSO-SiPM detectors and the preamplifier boards enclosed by a shielding box. The third approach (Schulz et al. 2009) which is now commonly used for clinical whole-body PET/MR scanners placed a pair of SiPM-based PET detectors and compact electronics (ASICs, and FPGA) inside an MRI with RF shielding enclosures. The SiPM charge signals were directly digitized by the ASICs and then further processed by FPGAs which were positioned just behind the SiPM array. The MR operation did not affect the performance of the SiPM-based PET detectors in terms of energy and time resolutions because the RF shielding housing prevented the RF interference. Such successful feasibility studies demonstrating MR-compatibility of SiPMs have led other research groups to develop various SiPM-based MR-compatible PET insert prototypes with different PET detector technologies.

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Preclinical PET/MRI with SiPMs One of the first prototype MR-compatible SiPM-based preclinical PET inserts was developed in 2011 by Philips Research Europe in collaboration with researchers from Aachen University, University of Heidelberg, and King’s College London, and the Foundation Bruno Kessler (Schulz et al. 2011). The prototype MR-compatible SiPM-based PET insert had 10 RF shielded PET detector blocks each composed of 2 detector stacks. Each detector stack consisted of a 22 × 22 array of LYSO crystals (single crystal dimensions, 1.3 × 1.3 × 10 mm3 ), an 8 × 8 SiPM array coupled to an ASCI board and an FPGA board. The analog signals from the SiPM were processed by the ASIC to generate digitized energy and time information as shown in Fig. 11. The digital signals were further processed by the FPGA board which interfaced with the mainboard of the module. For the simultaneous acquisition of PET and MR data, the prototype preclinical PET insert was positioned inside a clinical 3 T MRI (3 T Achieva, Philips) and a dedicated 2-channel RF coil was used for the transmission and reception of RF signals. The simultaneous PET/MR images of a structural phantom were obtained successfully (Fig. 11). A uniform phantom was employed to evaluate the effect of PET on the MR image quality by using the B0 map which represents the spatial distribution of the main magnetic field of an imaging object. The B0 map in parts per million (ppm) indicated that the PET insert affected the main magnetic field of the PET/MR FOV with a B0 variation of ±4 ppm which slightly exceeded the recommended magnetic field drift criterion of 1 ppm for the 3 T MRI scanner. An upgraded version of the prototype SiPM-based PET combined with dedicated RF coils, called Hyperion I, was developed to obtain simultaneous PET/MR images of mouse brain (Mackewn et al. 2012) and rat brain (Weissler et al. 2014). The distinctive feature of Hyperion I was that the almost direct digitization of SiPM analog signals could be done by ASICs and FPGA boards which were placed just behind the SiPM array. In this way, the potential RF interference on the SiPM analog signals was prevented effectively. In addition, an active water cooling was employed to suppress the heating of ASICs and FPGA components. The PET/MR technology was further evolved by employing digital SiPMs (dSiPMs) (Weissler et al. 2015) in which the digitization circuits for energy and time information of individual micro cells were integrated into the SiPM photo sensor (Frach et al. 2009). Weissler et al. (2015) developed the first prototype dSiPM-based MR-compatible PET/RF insert and called it Hyperion IID (Fig. 12). The spatial resolution of the PET was improved by using a 1 mm pitch LYSO crystal array (single crystal dimensions, 0.933 × 0.933 × 12 mm3 ) that could resolve 0.8 mm diameter rods of a structural phantom as shown in Fig. 13. The main magnetic field homogeneity, namely, the B0 map quality was improved within a variation of 2 ppm by using carbon fiber shielding material and the optimized RF transceiver coils of Fig. 13. One of the first simultaneous in vivo PET/MR images was obtained by a research group at Seoul National University (SNU) in collaboration with other researchers at Eulji University (Yoon et al. 2012). The prototype MR-compatible SiPM PET insert

Fig. 11 First prototype SiPM-based preclinical PET insert for 3 T MRI (top row); and simultaneously acquired PET and MRI images of a structural phantom and B0 map of a uniform oil phantom during the PET insert operation (bottom row) (Schulz et al. 2011)

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Fig. 12 First digital SiPM-based preclinical PET/RF insert for 3 T MRI, Hyperion IID (Weissler et al. 2015)

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Fig. 13 Simultaneous PET and MRI images of a structural phantom (left top) and a mouse bearing a tumor (right) obtained with the Hyperion IID PET/RF insert; B0 maps in the coronal orientation during the Hyperion IID PET insert operation without shimming and with shimming (left bottom) (Weissler et al. 2015)

had a ring diameter of 132 mm and axial coverage of 32 mm. The PET scanner consisted of 10 detector blocks each of which was enclosed within double layer copper plates (each 18 μm thick) to prevent RF interference as shown in Fig. 14. The RF shielding boxes were connected to the electrical ground of a wall panel between the MRI and console rooms. Each PET detector block consisted of a 20 × 18 LGSO crystal array (single crystal dimensions = 1.5 × 1.5 × 7 mm3 ), an 8 × 8 SiPM array (S11064-050P, Hamamatsu) and a custom-made front-end board. The 64 channels of the SiPM anode signals were multiplexed into 4 positional signals by using a resistive network (Ko et al. 2013) to effectively reduce the number of DAQ channels. The multiplexed SiPM analog signals were fed to differential amplifiers of the frontend board. Then the outputs of the differential amplifiers were transferred to the DAQ system located outside the MRI system room via aluminum foil-screened twisted-pair cables. The required number of DAQ channels was further reduced by half thanks to the bipolar analog multiplexing circuits in which two or more SiPM analog signals shared a single DAQ channel (Yoon and Lee 2014). For an effective electromagnetic interference shielding of the PET electronics, the RF shielding boxes were electrically connected to the isolation metal panel of the MRI room through the aluminum shielding sheath of the PET signal cables to form a Faraday cage, whereas the grounds of the PET detectors and DAQ system were electrically isolated from the isolation metal panel to prevent RF noise interference on the PET signal lines. In this way, the PET system could be operated without any RF interference from the MRI.

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Fig. 14 An MR-compatible SiPM-based small animal PET insert for clinical 3 T MRI developed by researchers at SNU and Eulji University. (Image courtesy of Jae Sung Lee)

The prototype SiPM-based PET scanner was inserted inside a clinical 3 T MRI scanner (MAGNETOM Trio, Siemens), and the body coil and two loop coils (4 cm inner diameter) were used for the RF transmission and reception, respectively. The simultaneous acquisition of PET and MRI data of a living mouse was successfully performed without any significant mutual interference between the two modalities (Yoon et al. 2012). The FDG PET uptake on the kidneys of the mouse showed a good spatial correlation with anatomical structure obtained from the clinical 3 T MRI using the T2 weighted turbo spin echo (TSE) pulse sequence. The MR-compatible SiPM PET insert system had a distinctive feature of a highly multiplexed SiPM signal readout scheme. (Yoon and Lee 2014) demonstrated that this scheme reduced the number of DAQ channels substantially without a significant degradation of the PET performance and a cost-effective high-performance PET/MR system would be enabled. Moreover, the differential signaling of the SiPM analog signals from the PET detector had the ability to block the DAQ system located outside the MRI room, further mitigating the potential RF noise interference on the PET signal lines. Another distinctive feature was that the built-in body coil was used for the RF transmission. The small gap (∼2 mm) between the RF shielding boxes allowed the RF excitation pulse, transmitted from the body coil, to reach the MR imaging object with a reduced intensity. However, this work (Yoon et al. 2012) did not explore advanced MR pulse sequences such as MR spectroscopy (MRS) and functional MRI (fMRI) which can provide physiological information on animals. Moreover, the effect of the PET insert on the MR image quality was not investigated in terms of the B0 map and the B1 map which represent the spatial distribution of the main magnetic field and RF field, respectively.

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Fig. 15 A next generation SiPM-based preclinical PET insert for 7 T MRI developed by a research group at SNU. (Image courtesy of Jae Sung Lee)

A few years later, the SNU group developed a next generation SiPM-based MRcompatible preclinical PET insert for ultra-high field MRI systems (Ko et al. 2016b) and it is shown in Fig. 15. The new preclinical SiPM-based PET insert had a 64 mm inner diameter and 55 mm axial FOV (Ko et al. 2016a). The PET insert consisted of 4 rings each of which had 16 detector blocks. Each block consisted of a 9 × 9 LYSO crystal array (single crystal dimensions = 1.2 × 1.2 × 10 mm3 ), a 4 × 4 SiPM array (S11828-3344 M, Hamamatsu) and custom-made front-end board. A carbon fiber tube with a wall thickness of 1 mm was used instead of copper shielding to reduce the eddy current effect, which degrades MR field homogeneity. The PET insert was designed to be insertable into the narrow bore of a commercial 7 T preclinical MRI system (BioSpec 70/20 USR, Bruker Biospin). The simultaneous acquisition of PET and MRI was successfully performed with a mouse bearing brain tumor (Ko et al. 2016b). The next generation MRcompatible preclinical PET scanner showed high-quality PET images and excellent MR compatibility which allows for using advanced MR pulse sequences such as DWI. The B0 map obtained during the PET insert operation showed the main magnetic field variation was less than 0.28 ppm and below the manufacturer’s recommendation of 1 ppm. This PET/MR technology was later employed for a commercial preclinical simultaneous PET/MR scanner, named “SimPET” (Son et al. 2020) operating inside a 1 T cryogenic-free magnet. The collaborative group of Eulji University and SNU researchers developed the then-new prototype MR-compatible SiPM-based PET insert employing short optical fiber bundles as shown in Fig. 16 (Hong et al. 2012). The aim of this work was to build an RF transparent SiPM PET insert for simultaneous PET/MR imaging so as to use built-in body coils of a clinical 3 T MRI scanner. The MR-compatible SiPMbased PET insert had a 71 mm inner diameter and 17 mm axial coverage. The PET insert consisted of 12 detector blocks each of which were enclosed by double layer copper shielding for RF shielding. Short optical fiber bundles each with a length of 31 mm were used to transfer the scintillation light from a LYSO crystal array to

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Fig. 16 An MR-compatible SiPM-based small animal PET insert with short optical fiber bundles (31 mm) for clinical 3 T MRI. (Image courtesy of Seong Jong Hong)

the SiPM photo sensor. The front-end electronics and DAQ system originally used (Yoon et al. 2012) were reutilized. For the simultaneous PET/MR phantom imaging (Hong et al. 2012), a 3 mm diameter capillary tube containing a mixture of F-18 solution and gadolinium contrast agent, was used. The capillary tube was embedded into a cucumber and the simultaneous PET and MR data acquisitions were performed. The PET electronics were not affected by the intense RF pulse, except for the gradient field, and the PET count rate was not changed significantly. On the other hand, the PET operation did not affect the SNR of the MR images for the conventional MR pulse sequences such as T1/T2 weighted TSE and gradient echo. As a result, simultaneous in vivo PET/MR images of cucumber phantom were acquired. However, there was a significant artifact on the phantom image with the echo planar image (EPI) sequence which demands an extremely uniform magnetic field homogeneity. The MR image quality issues for the advanced MR imaging sequences such as EPI, diffusion weighted imaging and MRS, were solved with the next generation PET scanner which employed a somewhat longer optical fiber bundle (length = 55 mm) (Kang et al. 2013, 2015). There are two merits for the PET/MR design using a short optical fiber bundle. The first is that a built-in body coil can be used for the RF transmission without compromising the PET sensitivity because of the large gap between the RF shielding boxes. The second it that the RF shielding boxes which are made of a magnetically susceptible material, can be placed at a distance to the MR imaging object according to the length of the short optical fiber bundle, offering uniform magnetic field homogeneity within a variation of 1 ppm. However, there are also two major drawbacks for this simultaneous PET/MR design. There is PET performance degradation due to the light loss of around 40% during the transportation of the scintillation photons from the crystal to the SiPM photo sensor via the optical fiber bundles. Thus, this design cannot take advantage of TOF information which can improve the PET image quality significantly. The

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second drawback is that the enlarged PET outer dimensions owing to the length of the short optical fiber bundle make it difficult for this design to be used for ultrahigh field preclinical MRI scanners (over 7 T) which have narrow bore diameters of 100–120 mm. In the early 2010s, there were several pioneering research studies to develop the MR-compatible SiPM-based PET insert for small animal imaging that took slightly different approaches and used different detector designs (Schulz et al. 2011; Yoon et al. 2012; Hong et al. 2012); all demonstrated the advantages of simultaneous PET/MR imaging for preclinical research. The successful development of several prototype SiPM-based preclinical PET/MR inserts encouraged other research groups to develop their own prototype MR-compatible preclinical PET scanners employing more innovative PET detector technologies. For example, a collaborative group including researchers from the University of Manitoba, University of British Columbia, McGill University, and TRIUMF, Canada developed a prototype ultra-high-resolution PET insert operating inside the 7 T MRI using dual-layer-offset scintillator DOI technology (Goertzen et al. 2016). The PET insert was able to offer submillimeter spatial resolution with an iterative reconstruction algorithm incorporating a point spread function (Stortz et al. 2018). The development of the second-generation small animal PET insert with improved timing and count rate performance is continuing (Van Elburg et al. 2019). Another research group at the Technical University of Munich (TUM) has developed a prototype MR-compatible preclinical PET insert, called MADPET4 (Munich Avalanche Diode PET 4) (Omidvari et al. 2017). The MADPET4 features a configuration of two crystal layers and one-to-one coupling with SiPMs using individual readout; these allow for depth-of-interaction encoding and high-count rate performance, respectively. The TUM researchers are currently studying intercrystal scatter recovery to increase the PET sensitivity. Most recently, members of ETH Zurich, University of Zurich, University of Heidelberg, and University of Leeds have undertaken a research collaboration named SAFIR, Small Animal Fast Insert for mRi, and they have developed a prototype MR-compatible preclinical PET insert operating inside a 7 T MRI (Ritzer et al. 2020). The SAFIR prototype MR-compatible PET insert used one-to-one coupling between the LYSO crystal array and SiPM array with dedicated ASICs, and it provided excellent coincidence timing resolution of 194 ps, high-count rate performance and inter-crystal scatter recovery capability. In summary, for simultaneous preclinical PET/MR systems, the MR-compatible SiPM-based PET insert has become the standard design which does not require significant modification of the preclinical MRI. For the RF shielding of a PET insert, carbon fiber is being used widely because of its low eddy current induction and durability. The advancements of the MR-compatible PET detector design using SiPMs and the optimized RF shielding technique have realized the simultaneous acquisitions of PET and MRI images without significant mutual interference between the two imaging modalities. Nowadays, simultaneous preclinical PET/MR

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scanners with different magnetic field strengths are commercially available from different vendors.

Brain PET/MRI with SiPMs The simultaneous PET/MR imaging approach can utilize the full benefits on human brain imaging. The enriched molecular and morphological information, obtained respectively from PET and MRI, in the same space at the same time, can give new insight into the interpretation of human brain functions (Catana et al. 2012). One of the technical challenges in the development of the MR-compatible brain PET insert is the space constraint of a clinical 3 T MRI bore which typically has a 60 cm inner diameter. Therefore, the brain PET insert should have a compact detector design while maintaining the high performance. Another technical challenge is that bulky commercial MR head coils do not fit inside the compact MR-compatible brain PET insert. Therefore, custom-made compact MR head coils should be developed that consider the size of the brain PET insert. Moreover, the MR head coils typically positioned inside a brain PET insert increase the attenuation (photoelectric effect + Compton scattering) of annihilation gamma photons emitted from the imaging object and that degrades the PET image quality. Therefore, the MR head coils should be carefully designed to have less attenuation with regard to the 511 keV gamma photon to preserve PET image quality as well as quantification (Sander et al. 2015). The first prototype MR-compatible brain PET insert employing a SiPM photo sensor was developed in 2013 by a research group at Sogang University in collaboration with KAIST, the Korea Advanced Institute of Science (Hong et al. 2013). This prototype had a 330 mm inner diameter and 12.9 mm axial coverage and consisted of 72 detector blocks each of which had a 4 × 4 LYSO crystal array (single crystal dimensions = 3.0 × 3.0 × 20.0 mm3 ) and 4 × 4 SiPM array as shown in Fig. 17. The SiPM analog signals were transferred to preamplifiers and position encoder circuits located outside the MRI bore via a 3 m long flexible flat cable (FFC) (Kang et al. 2010). Then the analog outputs of the preamplifiers and digital outputs of position encoder circuits were fed to a FPGA-based DAQ system (Hu et al. 2012). For RF shielding of the PET detector blocks, 0.1 mm thick gold-plated conductive fabric tapes were used. The 3 m long signal lines were shielded by 0.24 mm thick aluminum mesh. The preamplifiers and position decoder circuits were enclosed in a 10 mm thick aluminum housing located outside the MRI bore. A custom-made birdcage RF head coil was positioned inside the PET gantry and used to transmit and receive the RF signals. The SiPM-based brain PET and RF head coils were positioned inside a clinical 3 T MRI (ISOL Technology, South Korea) (Fig. 17), and the simultaneous PET/MR images of a Hoffman brain phantom filled with F-18 were obtained. One of the unique features of this MR-compatible brain PET system (Hong et al. 2013) was that SiPM analog charge signals were transmitted to the preamplifier

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Fig. 17 Illustration of the first SiPM-based brain PET insert combined with clinical 3 T MRI developed by the research groups of Sogang University and KAIST: front view (left) and side view (right)

residing outside the MRI bore using a 3 m long RF shielded cable (Kang et al. 2010). In this way, the magnetically susceptible preamplifiers could be removed from the MRI bore. However, the SiPM charge signal transmission using a long cable increased the rise time of the SiPM signal, which in turn degraded the timing resolution significantly. Thus, this approach could not benefit from TOF information to improve the PET image quality. Another feature of the brain PET system has been the one-to-one coupling of the LYSO crystal and SiPM with the highly multiplexed signal readout using position encoder circuits which reduced the number of required DAQ channels (Ho Jung et al. 2010). However, the multiplexing circuit did not allow use of the light sharing method, and in turn, the PET spatial resolution was limited by the SiPM pixel size. The two limitations of this prototype brain PET insert were the short axial FOV (∼13 mm) which limits the PET sensitivity and the degradation of MR image quality caused by the large eddy current induced on the PET shielding material. (Jung et al. 2015) solved these issues with their next generation prototype MR-compatible brain PET insert which had an extended axial FOV of 60 mm and used segmented goldplated conductive fabric tapes. The next generation insert showed excellent MRcompatibility with the clinical 3 T MRI (MAGNETOM Trio, Siemens)-based on B0 and B1 maps representing the main magnetic field homogeneity and RF field distribution, respectively. A new type of MR-compatible brain PET insert was developed at Stanford University in 2015 (Olcott et al. 2015). The main goal of this work was to develop an RF-penetrable brain PET insert, enabling the use of built-in body coils and multichannel receive-only coils for high quality PET/MR imaging. The prototype brain PET had a 320 mm inner diameter and 26 mm axial FOV. The PET insert is shown in Fig. 18 (Chang et al. 2018) and consisted of 16 detector blocks each of which had a 16 × 8 LYSO crystal array (single crystal dimensions = 3.0 × 3.0 × 20.0 mm3 ) with one-to-one coupling to an SiPM array, compressed circuits (Chang et al. 2015) electro-optically coupled with nonmagnetic vertical cavity surface-emitting

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Fig. 18 RF-penetrable brain PET insert for clinical 3 T MRI (left); the PET detector module with the copper shield (middle) and without it (right) (Chang et al. 2018)

lasers (VCSELs) which convert the SiPM analog signals into near-infrared analog optical signals (Olcott et al. 2009). The analog optical outputs of the VCSELs, which carry the energy and time information of the detected gamma photon, were transferred to the FPGA-based DAQ system positioned outside the MRI room via 20 m optical fibers. The optical signals were converted into analog electrical current signals by photodiodes, and then differential voltage signals were generated by using amplifiers. The differential voltage signals were digitized by ADC boards, and then sent to the FPGA board for the generation of single and coincidence data. To isolate the PET electrical ground from that of MRI system, the PET insert was powered by two types of non-magnetic batteries, namely, low voltage batteries for the amplifiers of the compressed circuits and VCSLEs, and the high voltage batteries for SiPM biasing, respectively. For the RF shielding, each PET detector block was enclosed by a singlesided 17 μm thick copper shield as shown in Fig. 18. Unlike the conventional PET shielding method of other groups, the copper shielding and PET electronics including batteries were electrically floated relative to the MRI ground to make the PET insert RF-transparent (Lee et al. 2018a). The built-in body coil was used for both transmission and reception of RF pulse signals. The simultaneous PET/MR image of a structural phantom filled with F-18 was obtained with the prototype RF penetrable PET insert with some mutual interferences between the two modalities, namely, a maximum 11% loss on PET counts and a roughly halved SNR of MR images; these interferences were mainly due to the non-optimized RF shielding design (Olcott et al. 2015). One of the distinctive features of this MR-compatible brain PET insert was the compressed sensing circuit which multiplexed the 128 channel SiPM outputs of a detector block into 16 channels (Chang et al. 2015). This compressed sensing technique reduced the number of VESCELs, optical fiber cables and DAQ channels effectively. Moreover, the compressed sensing technique had a potential to be used for a light sharing detector for high resolution brain PET imaging although the

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feasibility was demonstrated only by a Monte Carlo simulation study (Olcott et al. 2011). A second distinctive feature of this MR-compatible brain PET insert was the electro-optical signal transmission technology which could minimize the potential RF interference on the PET signal lines during the transmission of the PET signal to the DAQ system (Olcott et al. 2009). A third distinctive feature, which was the main purpose of their PET/MR design (Olcott et al. 2015), was that the built-in body coils could be used for the transmission of MR RF signals to the image object. This was because the PET insert (including the RF shielding boxes) were electrically floated with respect to the MRI ground which allowed the MR RF pulse signals to penetrate the copper shielding housing and the PET electronics with some attenuated intensity (Lee et al. 2014, 2018a). Therefore, the combination of the built-in body coil and custommade phased array receive-only coils was used to improve the SNR of MR images as compared to the case of the custom-made birdcage transceiver coils (Lee et al. 2019). There are three limitations for this MR-compatible PET/MR design. The first is complexity of the PET detector design owing to the electro-optical signal transmission scheme. Unlike the conventional SiPM signal processing scheme, electro-optical signal transmission requires two more steps, namely, encoding of SiPM analog signals to an analog optical signal and decoding of the analog optical signal into electrical signals. As a result, additional VCSELs components, optical fiber cable, and photodiode receivers are required which increase the complexity and cost of the PET system. Moreover, VCSELs and optical fiber cables occupy a relatively large space compared to conventional compact preamplifiers or ASICs, hence the axial extension of the PET scanner would be challenging as it is constrained by the bulky size of the electro-optical signal transmission components. The second is use of bulky batteries are not practical for long operation in clinic as batteries discharge within a certain time. The third is PET performance degradation during the EPI pulse sequence because of the eddy current induced on the shielding box and PET electronics by the intense gradient switching of the gradient coils (Chang et al. 2018). To solve this issue, there is a plan to replace the RF copper plate shielding material with phosphor bronze mesh which can reduce the induced eddy current significantly (Lee et al. 2018b). Research continues on the RF-penetrable brain PET insert in Stanford University for further optimization of the simultaneous PET/MR image quality (Chang et al. 2018; Groll and Levin 2019) to obtain the simultaneous PET/MR images of a Hoffman brain phantom. One of the issues with the MR-compatible brain PET insert design is the gamma photon attenuation caused by head coils (Kolb et al. 2012; Eldib et al. 2016). In general, head coils are positioned inside the brain PET insert for RF transmission and reception. Thus, MR head coils attenuate the annihilation photons before reaching the PET detector. Moreover, the head coils occupy some space which reduces the useful FOV of brain PET/MR systems (Hong et al. 2013). Another issue with the brain PET design is parallax error owing to the relatively small inner

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Fig. 19 SiPM-based brain PET insert (1st generation) with integrated, 8-channel RF head coils between the PET detector blocks for 3 T clinical MRI and the B0 map obtained during the brain PET insert operation (Nishikido et al. 2017)

diameter compared to that of the whole-body PET scanner. The spatial resolution of a brain PET scanner deteriorates at the periphery of the FOV where the cortex region is located (Wienhard et al. 2002; Yamaya et al. 2008). In order to solve these issues, a novel MR-compatible brain PET insert design was proposed by a research group at NIRS in collaboration with Chiba University researchers in 2014 (Nishikido et al. 2014). Their idea was to integrate the RF transceiver coils on the gaps between the scintillator array blocks of a PET scanner. The prototype MR-compatible brain PET insert had a 248 inner diameter and 12 mm axial FOV (Nishikido et al. 2017). The brain PET insert consisted of 8 detector blocks and 8 RF coil elements positioned on each gap between the detector blocks as shown in Fig. 19. Each PET detector block consisted of two sets of a four-layer 19 × 6 LYSO crystal array (single crystal dimensions = 2.0 × 2.0 × 5.0 mm3 ) yielding a 20 mm total thickness. Each LYSO crystal array was optically coupled to six 4 × 4 SiPM arrays (S11064-050P, Hamamatsu Photonics) arranged in line along the radial direction. The 96 channel SiPM anode signals were multiplexed into 4 positional signals by a weighted sum circuit. The multiplexed positional signals were fed to amplifiers then transferred to the DAQ system outside the MRI room via 10-m long RF shielded cables. Each PET detector block was enclosed by a shielding box coated with a 35-μm thick copper layer to protect the PET electronics from RF interference during the simultaneous PET/MR operation. The shielding boxes and cable shielding were electrically connected to the isolation panel in the MRI room for effective RF shielding. The MR-compatible brain PET insert was placed inside a clinical 3 T MRI (MAGNETOM Verio, Siemens) and the mutual interference between the two modalities was evaluated. The MRI operation did not affect PET performance values such as spatial resolution and energy resolution, while the PET operation did not affect the main magnetic field homogeneity within a 0.8 ppm variation (Fig. 19). However, the SNR of the MR image with the T2 TSE sequence was degraded 20% because of the large eddy current induced on the copper shielding boxes. The main limitation of this prototype MR-compatible brain PET insert was the short axial PET FOV of 12 mm, which is not practical for brain PET imaging.

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Moreover, non-segmented copper shielding caused a large eddy current which deteriorated the MR SNR significantly. To address the limitations of their prototype brain PET insert, in collaboration with Hamamatsu Photonics (Nishikido et al. 2016) developed a 2nd generation MR-compatible brain PET insert combined with a head coil. The 2nd generation insert had a 275-mm inner diameter and 60-mm axial FOV as shown in Fig. 20. The brain PET insert consisted of 24 detector blocks each of which had two sets of the 4-layer 14 × 14 array lutetium fine silicate (LFS) crystal block (single crystal dimensions = 2.0 × 2.0 × 5.0 mm3 ), an 8 × 8 SiPM array (S11206-0808FC(X), Hamamatsu Photonics) and dedicated front-end board. The 128 channel SiPM anode signals were sent to four sets of the 32-channel ASIC amplifier, and then multiplexed into 4 positional signals by using a resistive network. The multiplexed positional signals were transferred through copper foil shielded cables to the DAQ system positioned outside the MRI room. For RF shielding of the PET detector, carbon fiber was used instead of copper foil to reduce the eddy current effect during switching of the MR gradient field (Peng et al. 2014). The seam of the carbon fiber plates was shielded by copper foil tapes. For the RF transmission and reception, the custom-made 8-channel head coil positioned at the gaps of the PET detector blocks was used. The performance values of the brain PET insert, such as energy resolution and the crystal map, were not affected during the operation of various MR pulse sequences such as spin echo and EPI. The 1.6 mm rod pattern of a Derenzo-like phantom filled with F-18 could be resolved clearly in PET images reconstructed with the OSEM algorithm (Fig. 20). One of the limitations of MR-compatible brain PET studies has been the lack of MR compatibility evaluation with advanced MR RF pulse sequences such as EPI, DWI and MRS which can provide physiological information of the human brain. Moreover, the B0 and B1 field homogeneities have not been investigated during the PET operation. A second limitation has been the failure to obtain simultaneous PET/MR images of a Hoffman brain phantom yet. More importantly, brain PET performance has not been evaluated in accordance with the NEMA procedure. Therefore, it would be difficult to compare the brain PET/MR inserts of Nishikido et al. (2016, 2017), for example, with other prototypes developed by other groups quantitatively (Hong et al. 2013; Jung et al. 2015; Chang et al. 2018). Lastly, the performance of the custom-made RF head coils (Tx/Rx) has not been compared with the performance of commercially available head coils such as one group did (Lee et al. 2019). The quantitative evaluation of MR image qualities with the customRF coil to those of the commercially available head coil could justify the use of custom-made RF head coil in clinical practice. Nevertheless, the distinctive MR-compatible brain PET/RF coil design that Nishikido et al. (2014, 2016, 2017) offered could eliminate the attenuation of annihilation photons on the head RF coils; thus an additional attenuation correction procedure for head coils was unnecessary for the PET image reconstruction. Recently, many groups have been working on the development of highperformance MR-compatible SiPM-based PET inserts for use with clinical MRI

Fig. 20 A second generation SiPM-based brain PET insert with integrated RF head coils (Nishikido et al. 2016)

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systems. For example, the European Union project TRIMAGE, a dedicated Trimodaility (PET/MR/EEG) imaging tool for schizophrenia, is aiming at the development of an MR-compatible brain PET insert operating inside a noncryogenic 1.5 MRI (Belcari et al. 2019). Another European research project MINDView, Multimodal Imaging of Neurological Disorders, is developing an MR-compatible brain PET insert for a 3 T MRI scanner (Gonzalez et al. 2019). In South Korea, a collaborative research group of SNU and Gachon University members is working on the development of MR-compatible brain PET insert for an ultra-high-field 7 T MRI scanner. One of the recent trends for MR-compatible brain PET detector designs is depth encoding capability to reduce the parallax error on the periphery of the brain PET FOV. For depth encoding, a staggered 2-layer pixelated crystal arrangement was chosen by several groups (Sportelli et al. 2017; Park and Lee 2019) since it does not require any special detector calibration. On the other hand, a monolithic LYSO crystal-based DOI detector which requires a special detector calibration procedure was chosen for the MINDView brain PET/MR project (Gonzalez et al. 2019). Another trend for the brain PET insert targets the TOF capability with sub500 ps coincidence timing resolution to improve the image quality (Sportelli et al. 2017; Park and Lee 2019). Recently, it was demonstrated that coincidence timing resolution of around 250 ps could improve the SNR of reconstructed PET images with the Hoffman brain phantom (Yoshida et al. 2020). However, it will be quite challenging to achieve sub-300 ps coincidence timing resolution at a system level while keeping the DOI capability with the fine crystal pitch (∼2 mm) and the long crystal configuration (∼20 mm) due to the reduced scintillation light collection efficiency. Nevertheless, the ongoing advances in SiPM performance towards higher gain, higher photon detection efficiency, and lower noise will lead to future PET detector technologies that achieve excellent TOF (sub-300 ps) and DOI (sub 5 mm) capabilities at the same time without compromising the spatial resolution and sensitivity, heralding a new era of simultaneous brain PET/MR imaging.

Whole-Body PET/MRI with SiPMs The first commercially available SiPM-based fully integrated whole-body TOF PET/MR scanner was the SIGNA developed by GE Healthcare in 2016 and it is shown in Fig. 21 (Levin et al. 2016). The whole-body SiPM-based PET/MR scanner followed the whole-body APD-based PET/MR design of the mMR scanner, in which the PET detector modules were positioned between the gradient coil and body coil of a 3 T MRI. The integrated PET scanner had a 60-cm transaxial FOV and 25cm axial FOV. It is worthwhile to mention that multiple bed positions are required to obtain whole-body PET images due to the limited axial FOV. Lutetium-based scintillation (LBS) crystal arrays (single crystal dimensions = 3.95 × 5.3 × 25 mm3 ) were optically coupled to SiPM arrays. The SiPM analog signals were processed using an ASIC board which identified the energy, timing and interaction position

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Fig. 21 The first commercially available SiPM-based whole-body PET/MR with TOF reconstruction capability (Levin et al. 2016)

of a detected gamma photon. The PET detector modules were enclosed in multilayered copper shielding to prevent RF interference from the MRI system, and at the same time, the eddy current induction on the shielding material caused by the gradient switching during the simultaneous PET/MR operation was minimized. As a result, two subsystems, namely, PET and MRI, can operate simultaneously without mutual interference. In comparison to the APD-based whole-body PET/MR scanner, the fully integrated SiPM-based whole-body PET/MR scanner features excellent coincidence timing resolution (390 ps) which allows TOF reconstruction to enhance the PET image quality significantly. Secondly, the SiPM-based scanner features the Compton scattering recovery capability for inter-block scattering events, enhancing the overall PET sensitivity roughly 20% compared with the conventional PET scanner. The state-of-the-art SiPM-based whole-body TOF-PET/MR scanner is currently being used worldwide for clinical practice. The clinical benefits of the whole-body TOF-PET/MR scanner over whole-body TOF-PET/CT in oncologic applications are still being investigated by many research groups.

Conclusions Since the 1997 introduction of the simultaneous PET/MR system employing optical fiber bundles and PMTs (Shao et al. 1997a), there have been remarkable advances in simultaneous PET/MR imaging systems using APDs which are insensitive to a magnetic field (Judenhofer et al. 2008; Schlemmer et al. 2008). The successful development of APD-based MR-compatible PET insert systems led to the first commercialization of a fully integrated whole-body PET/MR system released by Siemens (Delso et al. 2011). In the 2010s, simultaneous PET/MR systems have further evolved with the advancement of SiPM-based PET detector technology (Schulz et al. 2011) which has high gain and fast time response, allowing TOF PET reconstruction (Levin et al. 2016). Recently, many groups are working on the

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development of SiPM-based MR-compatible brain PET inserts for neurodegenerative diseases and psychiatric disorders research where simultaneous PET/MR is truly more valuable than PET/CT. Most of the major technical challenges for combining PET and MRI in a single platform have been solved from the perspective of hardware. A compact SiPMbased PET detector design with optimized RF shielding design is the key solution for the reduction of mutual interference between PET and MRI. The specially designed MR RF coils with less attenuation material reduces the attenuation and scatter fraction compared to conventional MR RF coils. From the perspective of software, various MR-based attenuation correction methods have been proposed with special MR pulse sequences which delineate the bone and soft tissue more clearly than conventional MR pulse sequences. MR-based attenuation corrections have shown comparable PET quantification accuracy with those of CT-based attenuation corrections for brain and pelvic regions. However, when it comes to thorax PET/MR, the MR-based attenuation correction showed slight but not negligible quantification error in terms of SUV values as compared to CT-based attenuation correction. Recent studies have shown a deep learning approach can provide substantially improved PET quantification accuracy for both brain (Hwang et al. 2018) and whole-body (Hwang et al. 2019) imaging even without an additional MR data acquisition, suggesting that the deep learning approach can replace the conventional MR-based attenuation correction methods. In conclusion, PET/MR multimodal imaging systems offer a unique opportunity to acquire functional and morphological information from a living subject at the same time in the same space. The radiation dose for a patient can be substantially reduced with PET/MR compared to PET/CT. In the future, PET/MR imaging will play an important role in early diagnosis of various diseases ranging from oncologic to psychiatric fields.

Cross-References  CT Imaging: Basics and New Trends  Image Reconstruction  PET Imaging: Basic and New Trends  Radiation-Based Medical Imaging Techniques: An Overview  Silicon Photomultipliers

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Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Different Types of Motion and Their Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Periodic Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Irregular Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rigid Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nonrigid Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Motion Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Internal Motion Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . External Motion Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Motion Correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Image-Based Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Projection-Based Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Event-Based Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Current Trends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Compensation of Rigid Brain Motion in PET Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . Compensation of Nonrigid Respiration-Induced Motion . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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J. van den Hoff () · J. Maus PET Center, Institute of Radiopharmaceutical Cancer Research, Helmholtz-Zentrum Dresden-Rossendorf (HZDR), Dresden, Germany e-mail: [email protected]; [email protected] G. Schramm Department of Imaging and Pathology, Division of Nuclear Medicine, KU/UZ Leuven, Leuven, Belgium e-mail: [email protected] © Springer Nature Switzerland AG 2021 I. Fleck et al. (eds.), Handbook of Particle Detection and Imaging, https://doi.org/10.1007/978-3-319-93785-4_40

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Abstract With the ever-improving spatial resolution available in single photon emission computed tomography (SPECT) and, especially, in positron emission tomography (PET), the unavoidable organ and subject motion has become one of the dominant factors limiting the practically achievable spatial resolution in the tomographic images. Moreover, uncorrected subject motion can lead to potentially severe image artifacts and compromise the quantitative integrity of the data. The latter is of special importance in PET where quantitative assessment of tracer concentrations is commonplace, both in static investigations via socalled standardized uptake values (SUVs) and in dynamic studies aiming at tracer kinetic modeling and quantification of the corresponding transport constants. Correction of the heart cycle related motion in cardiac applications has a long tradition and is covered extensively in the literature. Correction of breathing related organ motion in emission tomography, however, has attracted increasing interest in parallel to the rising importance of oncological PET, notably in the context of therapy response monitoring and radiation treatment planning. The third important area is high-precision motion correction of random head motion in brain investigations. In this chapter we give an overview of the methods employed to minimize – and possibly eliminate – the motion influence in emission tomography.

Introduction Emission tomography using radioactively labeled tracers comes in two flavors: single photon emission tomography (SPECT; see  Chap. 41, “SPECT Imaging: Basics and New Trends”) and positron emission tomography (PET; see  Chap. 42, “PET Imaging: Basic and New Trends”). Both modalities have seen much technical progress during the last decades, both in hardware (scintillation crystals, photomultipliers, avalanche photo diodes (APDs), silicon photomultipliers (SPMs), collimators, analog and digital signal processing electronics) and software (scatter correction algorithms, image reconstruction algorithms (see  Chap. 43, “Image Reconstruction”), etc.). As a result, today’s machines offer a combination of improved spatial and temporal resolution, better quantitative accuracy regarding measurement of local radiotracer concentrations, and reduced acquisition times. In PET, with state-of-the-art machines, one is able to reduce data acquisition times down to a few minutes for static investigations (i.e., those not investigating time-dependent tracer kinetic processes). This improvement is partly due to an increase of the axial field-of-view (FOV) in combination with 3D data acquisition. In addition, new scintillation materials and faster front-end electronics contribute to the improved sensitivity. A further reduction of acquisition times is principally limited by the requirement of maintaining a certain minimum level of statistical accuracy, i.e., signal-to-noise ratio (SNR) in the reconstructed images. The injected dose and thus the photon flux cannot be much increased due to radiation protection

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requirements as well as due to limitations of the count rate performance of the hardware. Thus, acquisition times remain substantial, possibly several minutes for a single image volume, and the obtained tomographic images represent “long exposure pictures” of the investigated subjects. These relatively long acquisition times increase the probability of subject motion during the course of the investigation. It is obvious that uncorrected subject motion can lead to a potentially severe image degradation and compromise the quantitative integrity of the data. The latter is of special importance in PET where quantitative assessment of tracer concentrations is commonplace, both in static investigations (via so-called standardized uptake values (SUVs) Thie (2004)) and in dynamic studies aiming at tracer kinetic modeling and quantification of the corresponding transport constants; see van den Hoff (2005, 2017) and  Chap. 47, “Compartmental Modeling in Emission Tomography” in this book. The described problems caused by subject motion become increasingly serious considering the improved spatial resolution of current clinical PET devices which can reach values below 4 mm. In this chapter we give an overview of currently employed methods to minimize – and possibly eliminate – the motion influence in the acquired data. In doing so, we will not be able to cover all aspects of the topic in equal depths due to limitations in available space. Therefore, we refer the reader to the literature where several review articles have appeared over the last years covering material partly complementary to that presented in this chapter; see, e.g., Rahmim et al. (2007) and Nehmeh and Erdi (2008).

Different Types of Motion and Their Effects There are a number of possible types of motion to be considered which differ in origin, their ultimate influence on the tomographic images, and the available options for correcting them. The latter range from straightforward approaches to quite elaborate and sophisticated algorithms. One important criterion in distinguishing different motion types concerns the temporal characteristics, namely, the question whether the motion is (semi-)periodic or irregular. The other one concerns the spatial characteristics, i.e., the distinction between rigid motions (e.g., in brain investigations) and nonrigid motion typically encountered in investigations of the trunk. In the following sections, we briefly discuss the most important aspects of the different motion types. In doing so, we focus on the description of the alterations of the effective point spread function (PSF) which characterizes the imaging process. To a good approximation, the imaging process, i.e., the translation from object space (the spatial radioactivity distribution in the case of emission tomography) to image space, is a linear operation. The cumulative motion influence during a given time interval can be considered as contributing to the effective total PSF of the imaging process, Ht , by translating the resting activity distribution to a new one which then undergoes the actual imaging process. The finally measured signal S (the image) for a given activity distribution A can then be written as

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S = Ht ⊗ A = Hs ⊗ Hm ⊗ A ,

(1)

where Hs is the PSF of the imaging system including the image reconstruction process, Hm describes the motion influence, and ⊗ denotes convolution. While Hs is time-invariant and also approximately spatially invariant across the FOV (constant spatial resolution of the device), Hm obviously is dependent on time as well as on location within the FOV, since all motions involving rotations and/or nonrigid deformations lead to a spatially variant Hm . Nevertheless, for a given motion within a given time interval, Hm is a well-defined function at each point in the FOV.

Periodic Motion Periodic motions are encountered as a consequence of the cardiac and breathing cycles. While the heartbeat-related movement obviously is only a concern when investigating this organ, breathing-related movement not only affects the lung but rather extends over most of the thorax and abdomen. Correction of breathingrelated movement thus is a very important problem in all types of whole body investigations, notably in oncology. The dominant effect of periodic organ motion is deterioration of spatial resolution. For illustration, consider the following onedimensional example where a point source executes harmonic oscillations around its origin with an amplitude a: x(t) = a · sin(ωt) . The absolute value of the source velocity is v(x) = |x| ˙ = ω · a · | cos(ωt)| = ω ·

 a2 − x 2 .

The probability dp of finding the object near position x is proportional to Including the correct normalization, the resulting probability density the motion’s PSF, Hm , and is given by Hm (x) =

1 , √ π · a2 − x 2

dp dx

1 v(x) dx.

is equal to

(2)

which expresses quantitatively the obvious fact that the object is to be found most probably near the points of maximum elongation where the velocity is small. A “long exposure picture” of the moving source will then yield an image of this probability density, Hm , convolved with the PSF of the imaging system, Hs , which is identical to the image of an ideal point source at rest:

45 Motion Compensation in Emission Tomography

Signal (a.u.)

a = 5 mm

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0

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Fig. 1 Imaging a point source executing harmonic oscillations around the origin. Signal intensity is expressed relative to the maximum of the point source image at rest. The system’s PSF, Hs , is assumed to be a Gaussian with a full width at half maximum (FWHM) of 5 mm. For motions where 2 · a (the total range of the motion) is smaller than the FWHM, the main effect is image blurring (increased width of the profile and decreased signal intensity, but only minor shape distortion). For larger motion amplitudes, shape distortions (elongation and heterogeneities) are observed as well

Fig. 2 PET image of a 1 mm point source (68 Ge, 5 min acquisition). Left: Source at rest. Right: Source oscillating along the vertical with a frequency of 0.1 Hz and an amplitude of 10 mm

 Ht = Hs ⊗ Hm =

∞

−∞

Hs (x)Hm (x − x  )dx  .

(3)

Figure 1 illustrates how such a harmonic motion modifies the total PSF, Ht , as a function of the motion amplitude. This is also demonstrated in Fig. 2, which shows results from measurements with a point source. The important point to note here is that the typical motion amplitudes occurring in patient investigations are of the same order as the reconstructed spatial resolution of current tomographs (breathingrelated motion up to about 20 mm, corresponding to amplitudes of 10 mm), which leads to a significant reduction of the effective spatial resolution. While for most of the presently installed PET systems the reconstructed spatial resolution is about 6 mm, new tomographs achieve distinctly better performance, which leads to a correspondingly larger impact of breathing-related motion.

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Irregular Motion By “irregular motion” we designate all motions due to involuntary or voluntary random subject movement. Such movements can in principle affect all parts of the body but are usually largest for the head due to practical limitations of patient fixation and the relative ease with which head movements can be executed during the investigation. The image deteriorating effects of the movement are in this case aggravated by the fact that the spatial resolution in brain investigations is for certain reasons (related to a reduced size of the relevant FOV and reduced scatter and attenuation influence) somewhat higher than in whole body investigations. The influence of irregular motions on the tomographic images is more difficult to predict than in the case of periodic motions simply because different irregular motions can have completely different characteristics. Considering a single point source, a few limiting cases of irregular motion might serve to illustrate this: Abrupt motion (“stepping”) This phenomenon occurs when the patient readjusts his position spontaneously at one or several time points during the investigation, e.g., to find a more comfortable resting position on the patient bed. Despite measures regarding patient fixation, this occurs rather frequently, notably in brain investigations. The effect on the images is a sort of double exposure effect for larger motion amplitudes leading to ghosting artifacts, i.e., structures are duplicated in the images. The relative intensity of the “ghosts” is determined by the fractional time the respective position was occupied. The total PSF (point source image) in this case is the sum of two or more Gaussians with different means and amplitudes. Random-Walk around the origin (“walking”) This idealized type of motion (approximating, e.g., motion caused by unrest or neurological disorders of the patient) leads to a Gaussian probability density of the time-averaged source position with some standard deviation σm . This is the easiest possible motion type in terms of predicting its effect. The PSF of the tomograph itself is usually well approximated by a Gaussian with a standard deviation, σs , defining the spatial resolution of the system. The convolution of this PSF with the motion’s Gaussian probability density yields a new Gaussian – the total PSF of the system including the random-walk motion – with a σt of

σt =



σs2 + σm2 .

(4)

In this idealized case, the motion leaves the shape of the PSF unaltered. It is still a Gaussian but with increased width, corresponding to a reduction of the effective spatial resolution. Note that the variances, not the standard deviations, add up in Eq. (4), making the resolution reduction moderate as long as σm is somewhat smaller than the inherent resolution of the tomograph.

d = 5 mm

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−10 0 10 20 30 40 50 −10 0 10 20 30 40 50 −10 0 10 20 30 40 50 −10 0 10 20 30 40 50

x(mm)

x(mm)

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Fig. 3 Imaging a point source executing a uniform linear motion starting at the origin. Signal intensity is expressed relative to the maximum of the point source image at rest. The PSF is assumed to be a Gaussian with a FWHM of 5 mm. For motions where d is smaller than the FWHM, the dominant effect is image blurring (increased width of the profile, but only minor shape distortion). For larger motions, shape distortions (elongations) and a center of mass shift (equal to one half of the traveled distance) become apparent

Linear motion (“creeping”) This type of motion occurs quite frequently in practice. Patients tend to slowly move out of the FOV along the patient bed leading sometimes to an overall displacement of a few centimeters. This type of idealized motion corresponds to a rectangular probability density which is centered not at the origin but rather at the midpoint of the traveled distance. The convolution with the PSF of the system in this case leads to an anisotropic blurring and a shift of the image position relative to the motion-free image. The resulting effective PSF of the imaging process along the given direction of the motion can be expressed with the help of the Gaussian error function but no longer by a simple Gaussian: for a total traveled distance d, the resulting P SF is given by      x x−d 1 Ht (x) = · erf − erf , √ √ 2 σs 2 σs 2 where 2 erf(x) = √ π

x

e−s ds. 2

0

It, therefore, rather resembles a trapezoidal shape with slopes whose width is determined by the machine’s PSF; see Figs. 3 and 4.

Rigid Motion This type of motion is more or less strictly realized in brain investigations. Otherwise it can frequently be used as a reasonable (not necessarily very accurate) approximation of local motion in sufficiently small regions.

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Fig. 4 PET image of a 1 mm point source (68 Ge, 5 min acquisition). Left: Source at rest. Right: Source moving a distance of 19 mm along the vertical during the acquisition

Rigid motions in 3D space are completely described by six parameters, the socalled six degrees of freedom. These include the three components of the translation (“displacement”) vector b and the three angles of rotation around the three coordinate axes defining the orthogonal rotation matrix R. The complete transformation restoring all object points from their motion-affected positions x back to the original positions x can be written as x = R · x + b ,

(5)

where the translation is assumed to be executed after the rotations and b and R are time-dependent functions. In the case of pure translations, all points are affected equally by the transformation (consider, e.g., the case of linear creeping motion described earlier). In the presence of rotations, however, the motion influence is position dependent, generally affecting off-center areas more than those close to the center of the FOV.

Nonrigid Motion For investigations in the thorax and abdomen, one quite generally faces the problem of nonrigid motions. This motion is mostly caused by the breathing-related organ motion which is quite strongly position dependent. In simple cases, these motions can be described by affine transformations of the image volume (see section “Image-Based Techniques”). Otherwise, more general nonlinear deformation fields might be necessary, which in turn can in principle be used to correct for the motion if they can be determined with reasonable accuracy from the available motion sensor or tomographic image data. An alternative to specifying an explicit parametrization of the deformation field for the use with image registration algorithms (section “Image Registration”) is the optical flow technique (section “Optical Flow”).

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Motion Detection In order to be able to perform any motion correction, it is of course necessary to first detect and analyze the motion. As far as the motion detection is concerned, there are two principal strategies: Internal motion detection By this we mean all methods deriving the motion information based on sole analysis of the respective tomographic image data or the primarily acquired projection data underlying the tomographic reconstruction. External motion detection By this we mean all methods using motion detection via external sensors such as video cameras or dedicated motion tracking systems.

Internal Motion Detection This approach is based on the idea of using some kind of time-resolved imaging. The subdivision of the imaging interval yields N tomographic data sets instead of a single one, thus allowing to analyze the different data sets independently with the aim of determining adequate transformations for all of them in such a way that a common object position is achieved. Two main scenarios can be distinguished. Dynamic studies Dynamic studies are frequently used in PET for assessment of tracer kinetic transport processes, not as a means of solely performing motion correction. The chosen subdivision into so-called frames is thus usually determined not by the requirements of motion correction but rather by the properties of the tracer kinetics under investigation. Nevertheless, dynamic studies still offer the ability of analyzing the images of the different frames, determining the inter-frame motion, and performing an automated mapping of all frames into a common reference frame. This approach is usually called image registration, and there exists a huge literature describing different algorithms; see, for instance, the reviews (Maintz and Viergever 1998; Hill et al. 2001). In short, the main idea is to use a certain measure of similarity between two 3D image volumes as a criterion in a nonlinear optimization. One such measure would be the covariance of the voxel intensities in both image volumes. Another one, which has proven especially valuable, is the so-called mutual information; see, e.g., Pluim et al. (2003). An overview of image registration methodology is given in section “Image Registration.” Gated studies Gated studies are used to investigate cyclic motions related to heartbeat and respiration. These are stroboscopic techniques mapping successive noncontiguous time intervals corresponding to a common phase of the cyclic motion into the same image volume. The information on the cyclic motion can be derived with systems such as an electrocardiogram (ECG) for cardiac studies or via a respiration belt (see Fig. 5). Furthermore, during recent years, methods have also

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been developed deriving cyclic motion information from the image data rather than using external devices. We will come back to this topic in section “Current Trends.” The result of a gated acquisition is a series of N image volumes (“gates”), which represent the cyclic motion time-averaged over the whole duration of the investigation. All registration techniques suitable for motion correction of dynamic studies can be applied here, too. The main difference is that in this case one quite generally is forced to use plastic, nonrigid transformations of the gates in order to achieve a common position, which can be challenging. Internal motion detection has the distinct advantage of not requiring any additional devices/sensors in order to perform motion correction. However, in emission tomography, the major drawbacks are related to the generally limited count rate statistics (low SNR) and modest spatial resolution of the tomographic images. Both factors impose limits on the available accuracy of the image registration (although it can be quite high under favorable conditions). Also affected is the achievable time resolution, i.e., the number of frames or gates which can be used without compromising tomographic image quality too much. This situation changed with the advent of integrated PET/MRI systems, which offer the possibility to utilize synchronously acquired MRI information for correction of the PET data, e.g., by using so-called navigator sequences (Ehman and Felmlee 1989; Sachs et al. 1994; Wang et al. 1996).

External Motion Detection In contrast to motion detection directly in the projection or image data, motion can also be detected with external sensors. These sensors either register the motion directly (usually visually) or provide phase information for cyclic motions which can in turn be used for subsequent motion correction. Originating in the field of computer animation, optical motion tracking devices allow to continuously monitor motion with high temporal (