CR-39 Plastic Nuclear Track Detectors in Physics Research [1 ed.] 9781628086607, 9781613244876

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Copyright © 2012. Nova Science Publishers, Incorporated. All rights reserved. CR-39 Plastic Nuclear Track Detectors in Physics Research, Nova Science Publishers, Incorporated, 2012. ProQuest Ebook

Copyright © 2012. Nova Science Publishers, Incorporated. All rights reserved. CR-39 Plastic Nuclear Track Detectors in Physics Research, Nova Science Publishers, Incorporated, 2012. ProQuest Ebook

PHYSICS RESEARCH AND TECHNOLOGY

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CR-39 PLASTIC NUCLEAR TRACK DETECTORS IN PHYSICS RESEARCH

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PHYSICS RESEARCH AND TECHNOLOGY

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CR-39 PLASTIC NUCLEAR TRACK DETECTORS IN PHYSICS RESEARCH

DAZHUANG ZHOU

Nova Science Publishers, Inc. New York CR-39 Plastic Nuclear Track Detectors in Physics Research, Nova Science Publishers, Incorporated, 2012. ProQuest Ebook

Copyright ©2012 by Nova Science Publishers, Inc. All rights reserved. No part of this book may be reproduced, stored in a retrieval system or transmitted in any form or by any means: electronic, electrostatic, magnetic, tape, mechanical photocopying, recording or otherwise without the written permission of the Publisher. For permission to use material from this book please contact us: Telephone 631-231-7269; Fax 631-231-8175 Web Site: http://www.novapublishers.com

NOTICE TO THE READER The Publisher has taken reasonable care in the preparation of this book, but makes no expressed or implied warranty of any kind and assumes no responsibility for any errors or omissions. No liability is assumed for incidental or consequential damages in connection with or arising out of information contained in this book. The Publisher shall not be liable for any special, consequential, or exemplary damages resulting, in whole or in part, from the readers‟ use of, or reliance upon, this material. Any parts of this book based on government reports are so indicated and copyright is claimed for those parts to the extent applicable to compilations of such works.

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Independent verification should be sought for any data, advice or recommendations contained in this book. In addition, no responsibility is assumed by the publisher for any injury and/or damage to persons or property arising from any methods, products, instructions, ideas or otherwise contained in this publication. This publication is designed to provide accurate and authoritative information with regard to the subject matter covered herein. It is sold with the clear understanding that the Publisher is not engaged in rendering legal or any other professional services. If legal or any other expert assistance is required, the services of a competent person should be sought. FROM A DECLARATION OF PARTICIPANTS JOINTLY ADOPTED BY A COMMITTEE OF THE AMERICAN BAR ASSOCIATION AND A COMMITTEE OF PUBLISHERS. Additional color graphics may be available in the e-book version of this book.

Library of Congress Cataloging-in-Publication Data Zhou, Dazhuang. CR-39 plastic nuclear track detectors in physics research / Dazhuang Zhou. p. cm. Includes bibliographical references and index.

ISBN:  (eBook)) 1. Nuclear track detectors. 2. Cosmic rays--Measurement. I. Title. QC787.N83Z48 2011 539.7'7--dc23 2011012598

Published by Nova Science Publishers, Inc. †New York CR-39 Plastic Nuclear Track Detectors in Physics Research, Nova Science Publishers, Incorporated, 2012. ProQuest Ebook

CONTENTS Preface

vii

List of Figures

ix

List of Tables

xiii

Introduction

xv

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Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8

Methods of LET Spectrum and Charge Spectrum Using CR-39 detectors

1

Cosmic Rays in Space and in the Earth‟s Atmosphere

51

Radiation Measured with CR-39 Detectors at Aviation Altitudes

63

Radiation Measured with CR-39 Detectors in Low Earth Orbit (LEO)

81

Ground Environmental Radiation Measured with CR-39 Detectors

127

Charge Spectra of Galactic Cosmic Rays Measured with CR-39 Detectors in LEO

133

Radiation Risk Estimation Using LET Spectrum Measured with CR-39 Detectors

141

Condensed Matter Nuclear Science (CMNS)

151

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vi Chapter 9

Contents Search for Magnetic Monopoles Using CR-39 Detectors

167 177

References

179

Index

189

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Acknowledgments

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PREFACE

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CR-39 PLASTIC NUCLEAR TRACK DETECTORS IN PHYSICS RESEARCH CR-39 plastic nuclear track detectors have proved to be one of the most useful nuclear track detectors in physics research. They have made significant contributions to research in the fields of particle radiation at aviation altitudes, in space, and in the natural environment. Other uses have included radiation risk estimation, the search for magnetic monopoles and the investigation of energetic particles generated by the low energy nuclear reactions (LENRs) in condensed matter nuclear science (CMNS). LENRs are believed to be one of the best future energy sources - cheap, clean and sustainable. The linear energy transfer (LET) spectrum method and charge spectrum method using CR-39 detectors are recognized as very dependable research tools in all of these areas of investigation. CR-39 detectors can detect heavy charged particles and low energy protons directly and detect neutrons as well as high energy protons through their secondary charged particles produced in the CR-39 and surrounding materials. CR-39 is sensitive to a wide range of LET values and can measure LET spectra and radiation quantities for complicated radiation fields. The LET calibration of CR-39 detectors can be achieved using heavy ions and protons generated by accelerators. Sensitivity fading of CR-39 detectors due to long time exposure existed can be corrected with a formula derived from experimental data. The LET spectrum method and charge spectrum method using CR-39 detectors have been used since the 1990s to measure radiation exposures for aircraft crew and astronauts and to monitor radiation inside spacecraft and the

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Dazhuang Zhou

international space station (ISS) in low Earth orbit (LEO). Radiation risk can be calculated using the LET spectrum measured for personnel exposed to radiation fields. The LET spectrum of energetic charged particles and neutrons produced by CMNS can also be obtained with the LET spectrum method. This book describes the methods and applications using CR-39 detectors in several important physics research areas and presents results obtained. Chapter 1 covers the main aspects of LET spectrum and charge spectrum using CR-39 detectors, including methods, calibrations and the correction for the sensitivity fading of CR-39 detectors with long time exposures; chapter 2 introduces the radiation fields at aviation altitudes and in space; chapter 3 presents LET spectra measured for radiation fields at aviation altitudes; chapter 4 presents LET spectra measured for radiation fields in LEO; chapter 5 reports radiation results for ground environmental alpha particles; chapter 6 presents the charge spectra of cosmic rays in LEO; chapter 7 deals with radiation risk from space radiation and ground environmental radiation; chapter 8 presents research results of CMNS; chapter 9 introduces briefly a novel approach to search for magnetic monopoles (MMs) and reports a good candidate of MMs - an unusual event with massive energy loss measured using CR-39 detectors. The recent results from LENRs research may indicate that a greater understanding of LENRs may be achieved by detail measurements and thorough quantitative analysis for the charged particles and neutrons produced by LENRs.

Dazhuang Zhou NASA-Johnson Space Center, Houston, US Universities Space Research Association, Houston, US Dublin Institute for Advanced Studies, Dublin, Ireland

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LIST OF FIGURES Figure 1. The nature of the preferential etching. Figure 2. Conical track as it appears under an optical microscope. Figure 3. Track geometry for normal incidence. Figure 4. Track geometry for a particle incident at dip angle δ. Figure 5. The nature of critical angle. Figure 6. Track geometry for a particle incident which forms top and bottom cones. Figure 7. The relationship of cone angle and etch rate ratio. Figure 8. Comparison of manual scan and automatic scan for STS and ISS missions. Figure 9. Geometry for differential flux calculation. Figure 10. Comparison of quality factors for ICRP 21 and ICRP 60. Figure 11. LET calibrations for CR-39 detectors in different oxygen environment. Figure 12. Comparison of LET calibrations for CR-39 detectors. Figure 13. Average residual range for etched cones in track detector stack. Figure 14. VT versus R for carbon calibration events. Figure 15. Relationship of range – ionization for carbon in CR-39. Figure 16. Generated calibration curves of range versus etch rate ratio. Figure 17. Generated calibration curves of gradient versus effective etch rate ratio. Figure 18. Charge identification with G-Seff method for test events. Figure 19. Charge spectra of cosmic rays. Figure 20. Differential energy spectra of GCR nuclei (solar minimum). Figure 21. Variation of cosmic rays at solar minimum and solar maximum.

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Figure 22. Geomagnetic effect of galactic cosmic rays. Figure 23. Cosmic ray induced particle cascade. Figure 24. Profile of particle intensity in the atmosphere. Figure 25. Mean free path of heavy cosmic rays in the atmosphere. Figure 26. Diagram of a stack of CR-39 detectors. Figure 27. Flight routes investigated in this study. Figure 28. Flight profile of time versus altitude. Figure 29. Integral LET spectra (dose equivalent rate) of cosmic rays at aviation altitudes. Figure 30. A comparison for dose equivalent rate measured and calculated. Figure 31. Integral LET spectra (flux) of cosmic rays at aviation altitudes. Figure 32. Integral LET spectra (dose equivalent) of cosmic rays at aviation altitudes. Figure 33. Charge distribution of Seff versus gradient for cosmic rays at supersonic altitudes. Figure 34. Charge abundance of cosmic rays at supersonic altitudes. Figure 35. A comparison of observed differential fluences and the theoretical predictions. Figure 36. The observed differential fluxes for cosmic ray nuclei (Z=2-8) at aviation altitudes. Figure 37. A comparison between experimental and theoretical results for cosmic rays at supersonic altitudes. Figure 38. A comparison of dose equivalent contributed by all particles and by HZE particles. Figure 39. Contribution of flux, dose and dose equivalent from GCR nuclei. Figure 40. Cross-section of the stack of NASA-JSC passive dosimeters. Figure 41. Differential LET spectra of flux measured with TEPC and CR39 near TEPC. Figure 42. Differential LET spectra of flux measured with TEPC and CR39 (PRDs). Figure 43. Integral LET spectra of dose equivalent measured with TEPC and CR-39 near TEPC. Figure 44. Integral LET spectra of dose equivalent measured with CR-39 (PRDs). Figure 45. Integral LET spectra of dose equivalent measured with TEPC and CR-39 PNTDs. Figure 46. Average quality factors measured with TEPC and CR-39.

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List of Figures

xi

Figure 47.(a) LET spectra of differential flux measured with TEPC and CR-39 for Expedition 12. Figure 47.(b) LET spectra of differential flux measured with TEPC and CR-39 for Expedition 13. Figure 48.(a) LET spectra of dose equivalent measured with TEPC and CR-39 for Expedition 12. Figure 48.(b) LET spectra of dose equivalent measured with TEPC and CR-39 for Expedition 13. Figure 49.(a) Average quality factors measured with CR-39 and TEPC for Expedition 12. Figure 49.(b) Average quality factors measured with CR-39 and TEPC for Expedition 13. Figure 50. Matroshka torso with poncho and hood. Figure 51. Matroshka facility outside the ISS. Figure 52.(a) Differential LET spectra of flux for Matroshka-1. Figure 52.(b) Differential LET spectra of flux for Matroshka-2. Figure 53.(a) Integral LET spectra of dose equivalent for Matroshka-1. Figure 53.(b) Integral LET spectra of dose equivalent for Matroshka-2. Figure 54. Variation of dose equivalent with LET and location. Figure 55. Differential LET spectra of fluence measured for STS-125. Figure 56. Integral LET spectra of dose equivalent measured for STS-125. Figure 57. Comparison of the integral LET spectra of dose equivalent. Figure 58. Average quality factors measured for STS-125 with low inclination. Figure 59. Integral LET spectra of dose equivalent for ISS-Expedition 1819/ULF2. Figure 60. Average quality factors for ISS-Expedition 18-19/ULF2. Figure 61. Differential LET spectra of flux for natural ground radiation. Figure 62. Integral LET spectra of dose equivalent for natural ground radiation. Figure 63. Average quality factors for natural ground radiation. Figure 64. Charge distribution of Seff versus gradient for GCR heavy nuclei. Figure 65. Charge distribution of cosmic rays (Z≥6) in LEO. Figure 66. LET spectra of dose equivalent for high LET particles in LEO. Figure 67. Cross section (the risk coefficient) as a function of LET. Figure 68. Tumor prevalence as a function of particle fluence and LET. Figure 69. Cross section of radiation risk as a function of LET. Figure 70.(a)(b) Schematics of the Pd/D co-deposition system.

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Figure 71.(a) LET spectra of differential fluence (bottom surfaces of CR39 detectors). Figure 71.(b) LET spectra of differential fluence (top surfaces of CR-39 detectors). Figure 72.(a) Energy distribution of particles (bottom surfaces of CR-39 detectors). Figure 72.(b) Energy distribution of particles (top surfaces of CR-39 detectors). Figure 73. Thiple α tracks produced in Pd/D co-deposition experiments. Figure 74. Restricted energy loss versus β for magnetic monopoles. Figure 75. Calibration of very-high restricted energy loss for CR-39 detectors. Figure 76. Photographs of the etched nuclear track in CR-39 detector. Figure 77. A diagram of the track profile for the possible magnetic monopole event.

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LIST OF TABLES Table 1. The energy intervals of nuclei detectable by CR-39 detectors as coincidence events Table 2. Radiation weighting factors as recommended by ICRP 60 Table 3. Tissue weighting factors recommended by ICRP 60 Table 4. Specified Q-LET relationships (ICRP 21) Table 5. Specified Q-LET relationships (ICRP 60) Table 6. LET calibration for CR-39 (September 2004 – September 2005) Table 7. Charge calibration results of CR-39 from carbon ions Table 8. Comparison of LET before and after correction of CR-39 sensitivity. Table 9. Radiation measured without and with fading correction for CR39 sensitivity Table 10. A comparison of radiation quantities measured with JSC-TEPC and CR-39 Table 11. Dose equivalent rates measured and calculated (aviation altitudes, ICRP 60) Table 12. Comparison of short range high LET tracks measured with CR39 detectors and neutrons calculated with FLUKA Table 13. Energies and ranges detectable for nuclei in CR-39 Table 14. Differential fluence of cosmic ray nuclei at supersonic altitudes Table 15. Information for TL/OSL dosimeters used by JSC-SRAG Table 16. Radiation measured with CR-39 (PRDs) for different locations Table 17. Radiation measured with TEPC for STS-114 and STS-121 Table 18. Radiation measured with TEPC and CR-39 PNTDs attached to TEPC

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Table 19. Radiation combined from TLDs/OSLDs and CR-39 PNTDs (STS-121) Table 20. A collection of results measured by TEPC and CR-39 PNTDs Table 21. Radiation combined from TLDs/OSLDs and CR-39 PNTDs (Expedition 12, 13) Table 22. Radiation quantities measured with CR-39 PNTDs (Matroshka) Table 23. Radiation combined from TLDs and CR-39 PNTDs (Matroshka) Table 24. Comparison of dose equivalent contributed from different LET regions Table 25. Radiation quantities measured for different inclinations Table 26. Radiation combined from TLDs/OSLDs and CR-39 PNTDs (STS-125) Table 27. Radiation measured with TEPC and CR-39 detectors (Expedition 18-19) Table 28. Radiation combined from TLDs/OSLDs and CR-39 PNTDs (Expedition 18-19) Table 29. Comparisons of radiation measured on ISS at different stage of solar activity Table 30. Radiation measured with CR-39 detectors for the radiation on the ground Table 31. Radiation on the ground measured with CR-39 detectors Table 32. The energy intervals detected by a stack of CR-39 detectors for stopping events Table 33. Number of GCR heavy nuclei measured with CR-39 in LEO. Table 34. Radiation measured with CR-39 detectors (total and HZEs) and TEPC (total) Table 35. Ten-year career limits based on three percent excess lifetime risk of fatal cancer Table 36. Events observed for different LENR experiments and detector surfaces Table 37. Energies carried by the observed particles with high LET Table 38. Very high REL calibration for CR-39 detectors Table 39. The measured and calculated physical quantities for a possible magnetic monopole

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INTRODUCTION The radiation field in LEO is mainly composed of galactic cosmic rays (GCR), solar energetic particles, electrons and protons in the south Atlantic anomaly (SAA) region of the Earth‟s radiation belts, and the albedo neutrons and protons scattered from the Earth‟s atmosphere. The radiation particles at aviation altitudes are mainly atmospheric neutrons and protons produced by the interactions between primary GCR and the Earth‟s atmosphere. The radiation particles of ground environment are mainly alpha particles from the decay of radon. Research has indicated that radiation dose equivalent is dominated by high LET particles (≥ 5 keV/µm water) for the above radiation fields. On the other hand, the radiation impact on human tissues is strongly related to the LET of particles and high LET particles dominate the impact. The radiation risk experienced by humans can be estimated using the LET spectrum measured with personal dosimeters and the cross section of radiation risk determined by radiobiology. Therefore, research of LET spectrum for high LET radiation is most important. With the chemical composition C12H18O7, most similar to human tissue and the fact that CR-39 is sensitive to high LET particles, CR-39 detectors are most suitable for simulating and representing the biological response of human tissue to radiation with high LET. At present, the suitable active personal dosimeters are not available and the best passive personal dosimeters for high LET radiation are CR-39 detectors. CR-39 dosimeters have been widely used for research on radiation in space, at aviation altitudes and on the ground. The LET spectrum method using CR-39 detectors is a powerful tool for radiation research. The method can provide complete LET spectra (differential and integral particle fluence, absorbed dose and dose equivalent) and radiation

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quantities which are needed for the full assessment of complicated radiation fields. The method is based on the strict LET calibration for CR-39 detectors and the manual scan approach for recognition of events, data scan and acquisition. The LET information can be obtained by the chemical etch of CR39 detectors in a chemical reagent. The LET calibration can be obtained by exposing CR-39 detectors to protons and heavy ions generated by accelerators. Experiments conducted in LEO for the STS (Space Transportation System) and ISS (International Space Station) space missions and on the ground showed that sensitivity fading exists for CR-39 detectors with longterm exposure and/or CR-39 detectors etched a long time after the radiation exposure. The sensitivity fading must be corrected to obtain reliable radiation quantities and can be achieved using a formula determined by experiments. In addition to the LET spectrum method, the charge spectrum method using CR-39 detectors has proved to be very successful. Particles‟ charge can be identified accurately based on the measurement of the effective etch rate ratio and the fractional etch rate gradient. The charge calibration curves are obtained by exposing CR-39 detectors to accelerator generated heavy ions. CR-39 detectors are also widely used for research in other physical areas, such as radiation risk research, research on new energy sources, and the search for the magnetic monopoles. This book introduces methods and applications using CR-39 detectors in several areas of physics research: (1) radiation dosimetry research for radiation fields in space, at aviation altitudes and on the ground; (2) radiation risk research for aircrew and astronauts due to space radiation and for the public due to ground environmental radiation; (3) LENRs research in CMNS: the LET spectrum and energy distribution for the energetic particles produced by LENRs; (4) novel approach to search for the magnetic monopoles through ultra-high REL (restricted energy loss). The book presents updated experimental results in the above research areas, including LET spectra, charge spectra and radiation risk for radiation research; LET spectra, energy distribution and charge distribution for LENR particles; and an unusual event with massive REL as a good candidate of magnetic monopoles. The LENRs are now generally believed as the best solution of energy source for the future era after the fossil-fuel: cheap, no pollution, high efficiency, strong and sustainable. A breaking-through of the CMNS research may be achieved through the strict quantitative analysis for the energetic LENR particles with the LET spectrum method using CR-39 detectors.

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Chapter 1

METHODS OF LET SPECTRUM AND CHARGE SPECTRUM USING CR-39 DETECTORS 1.1. CR-39 PLASTIC NUCLEAR TRACK DETECTORS (PNTDS)

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1.1.1. Nuclear Track Detectors Energetic charged nuclear particles produce linear regions of radiation damage in a large variety of solid insulators. In each substance these tracks can be revealed by a simple chemical treatment after which they are studied using a conventional optical microscope. It was Young who first demonstrated in 1958 that charged particle tracks existed and that they could be displayed by chemical etching of LiF [Young, 1958]. Fleischer, Price, and Walker showed the great variety of insulating materials (including glasses and plastics) that store tracks and developed a great many of the scientific and technological uses of tracks, for a review see the book by Fleischer et al. [Fleischer et al., 1975]. The technique was rapidly applied to many fields of research, including cosmic ray studies [Price et al., 1968; O'Sullivan et al., 1971, 1973]. Today, cosmic ray physics and radiation dosimetry are two areas which still make extensive use of solid state nuclear track detectors. Solid state nuclear track detection has been well documented, and the most extensive treatment of the subject is given in the book by Fleischer et al. and book by Durrani et al. [Durrani et al., 1987]. Detectors used for radiation measurement are categorized as active and passive. Active detectors for dosimetry mainly consist of Geiger-Muller

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counter, ionisation chambers, scintillation counters, Rem counters, silicon detectors and tissue-equivalent proportional counters. Active detectors can provide real time results immediately in the measurement procedure. This unique merit is useful for monitoring abrupt strong radiation, such as strong solar activity events. However they need complicated electronics and power supplies which in some cases will be inconvenient and even interfere or change the original radiation environment. Passive detectors are normally smaller sized, lighter in weight and do not interfere with the radiation field to be measured and are suitable for long-time exposure. CR-39 PNTDs sensitive to high LET particles and thermoluminescence dosimeters (TLDs) and optically stimulated luminescence dosimeters (OSLDs) sensitive to low LET particles are widely used now as personal dosimeters. Among passive detectors, track detectors are attractive for radiation dosimetry purposes because they are generally capable of providing information on charged particle fluence (measured by track density), direction (by track angle), energy loss (by track length or by track opening) and particle charge and energy (by track measurements in several consecutive detector sheets). Research already indicated that the biological impact of radiation on human tissues is dominated by high LET radiation and high LET dominates the radiation dose equivalent for both radiation at aviation altitudes and in space, therefore CR-39 detectors are the most useful detectors for personal radiation measurement. CR-39, or allyl diglycol carbonate, is a plastic polymer commonly used in the manufacture of eyeglass lenses. CR-39 is a trade marked product of PPG Industries and is made by polymerization of diethyleneglycol bis allycarbonate (ADC) in presence of diisopropyl peroxydicarbonate (IPP) catalyst. The presence of the allyl groups allows the polymer to form cross-links; thus, it is a thermoset resin. The monomer structure of CR-39 material is CH2=CH-CH2-O-CO-O-CH2CH2-O-CH2CH2-O-CO-O-CH2-CH=CH2 CR-39 detector is light weight, small volume, electronics free, easy to process and very cheap comparing to any active dosimeters. CR-39 material used by NASA (National Aeronautics and Space Administration) - JSC (Johnson Space Center) and DIAS (Dublin Institute for Advanced Studies) researchers for their research on space radiation and radiation at aviation altitudes was manufactured by American Technical Plastics. The threshold of LET for the material is ~ 5 keV/µm water.

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Methods of LET Spectrum and Charge Spectrum Using CR-39 detectors 3

1.1.2. Energy Loss Models of Charged Particles

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When charged particles with high energies pass through a solid, liquid or gas, they interact with constituent atoms, molecules and nuclei mainly by electromagnetic and nuclear processes, as a result, three basic phenomena will occur: ionization and excitation of the atoms and molecules of the material; Bremsstrahlung and Cherenkov radiation; nuclear interactions between the incident particles and the nuclei of the material atoms. All these kinds of interaction can be used to investigate particle phenomena.

1.1.2.1. Ionisation and Excitation As energies are transferred to electrons bound to atoms, their energy states will become higher and then a change in energy state may occur resulting in either ionization or transition. The ionization electrons may travel some distance away from the surrounding medium. These electrons are known as delta rays and are of significance in track formation for solid state track detectors. The detector molecules are broken resulting in the formation of chemically reactive chain scion, so that the chemical nature of the medium is different along the ion trajectory, and may result in the formation of a track which can be revealed through an etching process. The ionization process is the most important process for solid state track detectors. The ionization energy loss rate per unit path length for relativistic charged particles can be derived from relativistic quantum theory as Bethe-Bloch formula [Bethe, 1930; Bloch, 1933]

where, C 

2 n e e mc

4

2

Z eff  Z (1  exp( 

130  Z

2/3

))

is the effective charge of incident heavy particle,

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ne = electron density in detector material, m = the rest mass of electron, wmax = 2mc2β2γ2 γ = (1-β2) -1/2 β = v/c, c is the velocity of light in vacuum, I = mean ionization potential of the detector material, δ = correction of density effect for detector material at relativistic velocities, U = low velocity correction.

1.1.2.2. Bremsstrahlung and Cherenkov Radiation When a charged particle is accelerated or decelerated, it emits electromagnetic radiation; this radiation is known as Bremsstrahlung. This type of radiation is important for electrons because they have the smallest mass and can be accelerated most. Bremsstrahlung from relativistic electrons is of great significance in the field of relativistic astrophysics. When a charged particle passes through a transparent medium with a velocity greater than the velocity of light in the medium, an electromagnetic radiation is produced. This kind of radiation is called Cherenkov radiation and can be used to detect the charges and the energies of relativistic charged particles. 1.1.2.3. Nuclear Interactions In addition to electromagnetic interactions, the short-range nuclear force acting between nucleons may produce nuclear interaction as a fast ion is incident on matter. Fast ions will then lose energy in the process of penetrating matter by both electromagnetic interactions and nuclear interactions. Nuclear processes can be divided into absorption and scattering, the latter usually being subdivided into elastic and inelastic scattering. In an elastic scattering, momentum and kinetic energy of the incident particle are conserved. In an inelastic scattering, some kinetic energy of the incident nucleon is absorbed by the nucleus which is then raised to an excited state. The excited nucleus will de-excite through the emission of photons or the formation of secondary particles, known as evaporation process. These secondary particles are sometimes referred to as fragments or spallation products. In the absorption process, the incident nucleon is absorbed by the nucleus and a new compound nucleus is then formed. Usually the compound nucleus will fall to a state of lower energy with the emission of radiation and, perhaps, new particles.

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Methods of LET Spectrum and Charge Spectrum Using CR-39 detectors 5 The total energy loss should be the sum of all the energy loss processes; however, in the non ultra-high energy region relevant to our work, the portion from nuclear interaction, Bremsstrahlung and Cherenkov radiation are usually small compared with the energy losses from ionization process, so that for our purpose it's reasonable to assume that the total energy loss is approximately the same as that from ionization.

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1.1.3. Energy Loss Models for Track Formation 1.1.3.1. The Total Ionization Energy Model This model was initially promoted by Fleischer et al. [Fleischer et al., 1964] and is based on Bethe-Bloch's work. In this model, track formation depends on the total amount of energy deposited by the incident particle, i.e., dE/dx. It was soon realized that experimental data were inconsistent with the dE/dx criterion. It was shown [Fleischer et al., 1967] that relativistic iron nuclei do not produce tracks in Nixon-Baldwin cellulose nitrate. This is because the entire energy loss does not contribute to the track formation; energies transferred to high-energy delta rays may create damage too far from the track core to be effective. Therefore the model was rejected in favor of the primary ionization model. 1.1.3.2. The Primary Ionization Model This model predicts that track formation is related to the ionization produced close to the path of the incident particle, the relevant quantity, J, is given by C 1 Z eff   w max J  ln  2  I o    I o 2

   

2

   K 

where Io is the ionization potential of the most loosely bound electrons in the detector and C1 and K are the constants for the detector material [Fleischer et al., 1969]. The model gives a good fit to the results of heavy-ion irradiation experiments. However values of J are difficult to calculate and it does not take into account the effects produced by delta rays. Experiments indicate that the effects of delta rays along the track core cannot be neglected.

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1.1.3.3. The Restricted Energy Loss (REL) Model The restricted energy loss model [Benton E. V., 1970] takes into account the secondary ionizations produced by low energy delta rays. The restricted energy loss is the portion of the total energy loss that produces delta rays of energy less than some specified value, Eo and only this part of the energy loss is relevant to track formation. The restricted energy loss is given by 2

C 2 Z eff   w max E o   dE       ln  2 2  I  dx  E  E 0   

2

  U  

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where, C2 is a detector constant, the quantity Eo is chosen by calibration for different detector materials. Its value is usually taken to be 200 eV for CR-39. Both the REL model and the primary ionization model fit the experimental data and have been used successfully for many years. The quantity (dE/dx)E 20 MeV Protons, other than recoil protons, E > 2 MeV α particles, fission fragments, heavy nuclei

5 10 20 10 5 5 20

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Dazhuang Zhou Table 3. Tissue weighting factors recommended by ICRP 60

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Tissue or Organ Gonads Bone marrow (red) Colon Lung Stomach Bladder Breast Liver Esophagus Thyroid Skin Remainder

Tissue Weighting Factor wT 0.20 0.12 0.12 0.12 0.12 0.05 0.05 0.05 0.05 0.05 0.01 0.05

The equivalent dose in a tissue or organ T is weighted by the tissue weighting factor wT, which represents the contribution of tissue or organ to the total effects of uniform irradiation of the whole body. The sum of the weighted equivalent doses in all tissues and all organs of the body is the effective dose HE, given by HE 

W

T

HT

T

The values of tissue weighting factors for different tissues or organs recommended by ICRP are given in Table 3.

1.2.2. LET Spectrum Generation 1.2.2.1. Differential and Integral LET Spectrum Consider the geometry shown in Figure 9. Define a sphere of radius l unit about the point O and let the dip angle δ subtended at O, then the area dAs on the surface of this sphere which is defined by the change in θ is given by dAs = 2πl2sinθdθ

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Methods of LET Spectrum and Charge Spectrum Using CR-39 detectors 23 or by the change in δ as dAs = 2πl2cosδdδ because the solid angle is defined as dΩ = dAs/l2 hence dΩ = 2πcosδdδ By definition Fluence (F) is the number of particles per unit area, per unit solid angle, which over the plate surface is 2

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F 

d N dA p d 

In Figure 9, let dAs be the incremental area which is orientated at an angle (π/2-δ) to the plane of detector, and let dAp be the projected area parallel to the plane of the detector. The fluence over dAs is represented by 2

Fs 

d N dA s d 

where dAs = dAp sinδ as indicated in Figure 9, then Fs can be expressed as 2

Fs 

d N dA p ( 2  sin  cos  d  )

That is 2

d N dA p

 2  F s sin  cos  d 

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Dazhuang Zhou

For the situations we are interested now the radiation environment in space and at aviation altitudes as well as ground background, the radiation particles are near isotropically distributed. For an isotropic radiation field, the equal contribution of radiation is from both directions – upward and downward, thus 2

d N dA p

 4  F s sin  cos  d 

Integrate it over δ between angle δcut and π/2 dN dA p

 /2

 4 F s

 sin 

cos  d 

 cut

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where cut is the cut off dip angle above which the detection efficiency of CR39 detector is 100% (will be discussed in detail later), δcrit ≤ δcut < π/2 and δcrit is the critical angle given by 1

 crit  arcsin(

)

Vr

hence dN dA p

 4 F s

1

(1  sin

2

2

 cut )

 2  AF s cos  cut 2

Now integrate over the scanned area A

N  2  F s cos  cut 2

 dA

p

0

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Methods of LET Spectrum and Charge Spectrum Using CR-39 detectors 25  2  F s cos  cut 2

Therefore for a given etch rate ratio Vr Fs 

N 2  A cos  cut 2

Then the differential LET spectrum of particle fluence is given by 3

d N

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dA s d  d ( LET )

 ( 2 A cos  cut ) 2

1

dN d ( LET )

where cut was determined by opening up the solid angle of acceptance until the detection efficiency fell below unity, as discussed later. The integral spectrum of particle fluence is obtained by summing the differential spectrum from high LET to low LET. The method used in this analysis assumes that in order to use above LET spectrum expression, the etch rate ratio of etched track, Vr, must be constant over the total range of each particle. This of course will not be true for recoil tracks which are over etched. Because of the nature of solid state nuclear track methods of analysis, this assumption gives rise to an approximation, which though unavoidable, can be estimated to a sufficient level of accuracy for the investigation of radiation doses for the environment in space, at aviation altitudes and ground background. The method also needs a reference surface; the post etch surface is the reference surface in this investigation. All tracks that cross this surface are accepted for analysis. These include some tracks which are rounded at the bottom (over etched) which may result from very low energy recoils that have penetrated the post etch surface or from particles which stopped in the layer removed by etching. Careful visual inspection of the tracks crossing the post etch surface revealed that only ≤ 5% of the sample showed definite signs of rounded tips. The underestimate of Vr for these particles can be largely overcome by using a short etch time (≤ 20 hours) to make the bulk etch is smaller. Because of the extended period during which the detectors are employed in this investigation, background levels due to the exposure to alpha particles

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26

Dazhuang Zhou

from natural radon were not insignificant and should be deducted from the total radiation quantities measured.

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Figure 9. Geometry for differential flux calculation.

1.2.2.2. Concept of cut and Its Determination Initially it was assumed that the detection of particles for CR-39 detectors was 100% efficient between 90o and the critical angle crit. However it was found, particularly in the case of automatic scanning systems, that 100% efficiency was attainable only to an angle cut which was greater than crit [Ogura et al., 1986; Keegan, 1996]. Figure 8. in the last section is a plot of dip angle  versus etch rate ratio Vr. Data used in the Figure were scanned from CR-39 detectors exposed to space radiation with manual scan and fully automatic scan. The fall off in the density of data points near crit, which was very evident in previous work employing automatic systems is not very significant in the work where the events were scanned manually. It was noticed that dip angle is bigger and etch rate ratio is smaller for most events scanned by automatic scan while dip angle is smaller and etch rate ratio is bigger for most events scanned by manual scan. The dip angle correction for the detection efficiency of CR-39 can be realized through the quantity δcut. Thus the Figure indicates that the δcut correction is much more important for automatic scan than that for manual scan, this is a big advantage of manual scan over the automatic scan. In practical, the δcut formula can be derived conveniently from the distribution of

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Methods of LET Spectrum and Charge Spectrum Using CR-39 detectors 27 etch rate ratio S and dip angle and may be expressed as a function of critical angle arcsin(1/S):

 cut  C 1  C 2 arcsin( 1 / S ) where the fitted constants C1 and C2 could be different for the different CR-39 material. For the CR-39 manufactured by American Technical Plastics Inc. the δcut formula [Zhou et al., 2009b] can be expressed approximately as

 cut  6 . 57  0 . 91 arcsin( 1 / S ) Correction of detection efficiency could also be realized by using a cut formula as following

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 cut 



 1  g    arcsin( 2 Vr 2

 )  

where the correction factor g, g < 1.0, can be calculated from the event sample scanned by determining the minimum dip angle value appropriate to each Vr value in Figure 8. 1.2.2.3. Dose and Dose Equivalent It has been shown that the radiation field of cosmic rays in LEO and at aviation altitudes is nearly isotropically distributed [Longair, 1994; Ziegler, 1998]. For a radiation field distributed isotropically, the differential spectrum of the absorbed dose can be calculated from the differential fluence as Dose (Gy) = 4  1.6  10-9  LET  f where LET is the linear energy transfer (keV/m) in water at the centre of relevant LET bin,  means LET are contributed by delta rays with any energies, f is the differential fluence in particles cm-2sr-1 (keV/m)-1 in the same bin. The dose is calculated in Gray (Johr/kg). The differential spectrum of dose equivalent in Sievert (keV/m)-1 is then calculated by Dose equivalent (Sv) = Q  Dose (Gy)

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Dazhuang Zhou

where Q is the quality factor defined in terms of LET in water and is recommended by ICRP 21 and/or ICRP 60 and are collected in table 4 and 5. Figure 10. shows the difference between the quality factor values recommended by ICRP 21 and ICRP 60. The quality factor of ICRP 60 is higher than that from ICRP 21 when LET value is greater than about 20 keV/m in water and smaller than 200 keV/m in water - the dominant LET contribution region and above about 200 keV/m in water, the quality factor of ICRP 21 is higher than that from ICRP 60. Experiments indicate that the difference of quality factor for ICRP 21 and ICRP 60 will make a difference of about 30% for the dose equivalent of radiation at aviation altitudes and in LEO. Due to the fact that recommendations from ICRP 60 are based on more experimental research and are more reliable than those from ICRP 21, radiation results presented in the book are obtained using ICRP 60. The integral spectra of dose and dose equivalent can then be generated by summing the differential spectra from high LET to low. The average quality factor, Qave, introduced to characterize the effectiveness of radiation for a specified radiation field, is defined as

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Qave. (≥ LET∞) = integral dose equivalent (≥ LET∞) / integral dose (≥ LET∞) Q(LET) is different from Qave., Q(LETo) is the quality factor corresponding to value LETo, while Qave. is the average quality factor for the region of LET  LETo.

Figure 10. Comparison of quality factors for ICRP 21 and ICRP 60.

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Methods of LET Spectrum and Charge Spectrum Using CR-39 detectors 29 Table 4. Specified Q - LET relationships (ICRP 21) LET in water (keV/m)

Q(LET)

3.5 7 23 53

1 2 5 10 20

175

Table 5. Specified Q - LET relationships (ICRP 60) LET in water (keV/m) 100

Q(LET) 1 0.32  LET - 2.2 300/LET0.5

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1.2.3. LET Calibration for CR-39 Detectors To obtain the LET spectrum of the radiation field using CR-39 detectors, the detectors must be calibrated. The quality of the LET spectrum is strongly determined by the quality of the LET calibration for CR-39 detectors. The CR-39 detector measures linear energy transfer (LET) or the restricted energy loss. The linear stopping power s, related to LET, is contributed by atomic collision of charged particles. It is defined as (dE/dx)elec, where (dE/dx) is the energy loss in path length dx, the subscript „elec‟ specifies electronic (atomic collision). The linear energy transfer is LΔ = dEΔ/dx, where dEΔ is the energy lost by a charged particle due to electronic collisions, minus the sum of the kinetic energies of all the electrons released with kinetic energies in excess of Δ. The subscript Δ is usually in eV and LΔ is often written as LETΔ. The unrestricted linear stopping power s can be written as LET∞. According to the restricted energy loss model [Benton E. V., 1970; Henshaw et al., 1981], the restricted energy loss is the portion of the total energy loss that produces delta rays of energy less than Δ, and only this part of energy loss is relevant to track formation, while the electrons with energies in excess of Δ are not the contributors to the track formation. The value of Δ can

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be determined by calibrations for different detector materials and is usually taken to be 200 eV for CR-39 based on the experimental research. Therefore traditionally, CR-39 PNTD has been calibrated in terms of LET200 and the book follows the standard. Previous research indicated that the sensitivity of CR-39 is different for CR-39 PNTDs working in different oxygen environments. LET calibration for CR-39 detectors in different oxygen environment is needed therefore. Almost all the previous LET calibration work was carried out for CR-39 detectors in good oxygen conditions, LET calibration work for CR-39 in poor oxygen condition has not been conducted until this work. Systematic LET calibrations were carried out by DIAS group and JSC-SRAG for CR-39 detectors working in different oxygen environment and results of LET calibrations were obtained. The CR-39 material used by JSC and DIAS was manufactured by American Technical Plastics. The lowest measurable LET is ~ 5 keV/μm water for this material.

1.2.3.1. Method and Approach of LET Calibration for CR-39 Detectors Calibration exposures were carried out at the different accelerator centers (Berkeley Bevalac prior to its closure in 1993; GSI, Darmstadt between 19931997; HIMAC (Heavy Ion Medical Accelerator, Chiba, Japan), NSRL (National Space Research Laboratory, New York), BNL (Brookhaven National Laboratory, New York) and Cyclotron Institute at Texas A and M University (TAMU) from 2004. TAMU can provide heavy ions (high LET) and low energy protons (low LET), these low LET protons are very useful for obtaining calibration for CR-39 detectors at low LET region (≤ 10 keV/µm CR-39). The LET values for the LET calibrations can be extended from several to several thousand keV/µm CR-39 and satisfy the requirements for LET spectrum work. After exposure, the plates of CR-39 detectors are chemically etched in a solution of NaOH (6.25 N, 60 oC) for a time period needed. The thickness and the mass before and after etch of the CR-39 plate are measured. Detectors are scanned by either manual scan or semi-automatic scan and major and minor axes of the etched cones on the surfaces of CR-39 detector are measured and collected. The bulk etch Bt can be calculated by Henke‟s formula [Henke et al., 1985] and the etch rate ratio S can be calculated by the major and minor axes of the etched cones [Henke et al., 1971; Ali et al., 1977; Somogyi, 1977] as described in section 1.1.7.

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Methods of LET Spectrum and Charge Spectrum Using CR-39 detectors 31 The LET200 CR-39 values of the particles are calculated either by computer codes or by the energy-LET200 CR-39 relations [Benton E. V. et al., 1969]. Thus the relationship between LET200 CR-39 and etch rate ratio S is obtained and a best data fit can be found. The formula to convert LET200 CR-39 to LET∞ water obtained [Benton E. R., 2004] using Benton-Henke range-energy relations [Benton E. V. et al., 1969] is log(LET∞ water) = 0.1689 + 0.984log(LET200 CR-39)

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This formula is valid for all particles of importance in the GCR spectrum and in nuclear physics with energy between 0.8 and 2000 MeV/Nucleon.

1.2.3.2. LET Calibration for CR-39 Detectors in Different Oxygen Environments The CR-39 surface is covered by a polyethylene film (hereafter referred as PE film) when it is manufactured, in order to protect the material from damage and to decrease background radiation, mainly radon α particles. The PE film has a thickness of ~ 60 μm and a density of ~ 1 g/cm3. There are two approaches to deal with the protective film when using CR-39 detectors, one is to remove the film when preparing CR-39 stacks, and the other is to keep the film on until etch. Obviously, the former approach works in a good oxygen environment and is suitable for exposures with a higher dose, in this case the background dose is higher because the detector is unprotected by PE film. The latter approach works in a less favorable oxygen environment and is suitable for low dose exposures, in this way the background radiation is effectively reduced by the protective film. It is thought that oxygen tends to combine with ions and radicals, thus preventing their recombination and changing the sensitivity of the CR-39. Previous research indicates that the sensitivity of CR-39 detectors is different and dependent on the concentration of environmental oxygen around CR-39. The Adams group [Adams et al., 1991] and the Beaujean group [Beaujean et al., 1993] reported that their LDEF (Long Duration Exposure Facility) met low CR-39 sensitivity problem because their CR-39 detectors were exposed in vacuum while DIAS group and USF (University of San Francisco) group did not have such problem because their detectors were in a good oxygen environment. Fujii et al. (1997) did some research for the effect of the track registration on oxygen and other gases. A more recent work was conducted by Dörschel et al. [Dörschel et al., 2005]. However so far there is no systematic

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calibration research for the LET calibration of CR-39 detectors in different oxygen environments. To investigate the different response of the CR-39 in different oxygen environments, some stacks of CR-39 were designed to consist of two sheets of CR-39, in which one sheet‟s film was removed when the stack was prepared and is then in an oxygen-rich environment, while another sheet‟s film was kept on the surface of CR-39 until etch and is then in an oxygen-poor environment.

1.2.3.3. Results of CR-39 LET Calibration Table 6 is a summary of the LET calibrations for CR-39 detectors conducted up to September 2005. In the LET calibration, data with LET200 CR-39 higher than ~ 9 keV/μm are obtained from exposures to different heavy ions and data with LET200 CR-39 from ~ 3 to 9 keV/μm are from exposures to protons with energies from 3 to 10 MeV. In the table, the values of LET200 CR-39 (keV/µm) are obtained from Benton-Hankel work [Benton E. V. et al., 1969]. The results of the LET calibration for CR-39 detectors with different oxygen environment are shown in Figure 11. In the Figure, data around the solid curve are for a good oxygen environment and data around the dotted line are for a poorer oxygen environment and the two curves are best fit for experimental data. The Figure indicates that the LET response for the CR-39 detectors in good oxygen environment is from several to 745 keV/µm CR-39 with some data in low LET region from proton exposures and the LET response for the CR-39 detectors in poor oxygen environment is from ~ 14 to ~ 745 keV/μm CR-39. Experiments conducted by the JSC-SRAG confirmed that CR-39 sensitivity was influenced by the environmental oxygen. Figure 11. shows that sensitivity of CR-39 detectors in good oxygen environment is higher than those in poor oxygen environment; the lower LET value, the bigger difference of sensitivity is; above LET ~ 700 keV/μm CR-39, the difference is nearly eradicated. The sensitivity difference for CR-39 in good-oxygen and in pooroxygen environment is ~ 27%, 10%, 8% and 3% for LET = 10, 100, 300 and 750 keV/μm CR-39 respectively. A possible physical explanation is that damage trails are produced by incident charged particles in CR-39, for low LET events the damage trails of CR-39 are small and oxygen supply for the CR-39 detectors in poor oxygen environment is obviously more difficult and the recombination of the ionization for the relevant damage trails is easier and stronger, therefore the sensitivity is decreased more.

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Methods of LET Spectrum and Charge Spectrum Using CR-39 detectors 33 Table 6. LET calibration for CR-39 detectors (Sept. 2004 – Sept. 2005) Institute

Ion

NSRL (BNL) (Sept. 04) HIMAC (March 05)

TAMU (March 05)

NSRL (BNL) (July 05)

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HIMAC (Sept. 05)

O

Energy (MeV/nucleon) 1000

LET200 CR-39 (keV/µm) 9.39

Fe O Ne Ar Fe Xe Proton

1000 400 400 650 500 290 14, 10, 8, 6, 3

99.20 13.75 21.49 56.08 130.10 744.98 2.60, 3.43, 4.14, 5.25, 9.50

Si

(GeV/nucleon) 0.3, 1, 3, 5, 10

Fe O Ar Fe

3, 5, 10 0.4 0.5 0.2

49.19, 28.76, 25.73, 26.67, 28.81 88.74, 92.01, 99.37 13.75 62.37 216.30

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On the other hand for high LET events, the damage trails of CR-39 in good oxygen environment and in poor oxygen environment are probably both big and oxygen supply for these damage trails could be both good and can prevent effectively the recombination of the ionization, therefore the sensitivity of CR-39 in good oxygen environment and in poor oxygen environment is nearly the same. In addition to the influence of oxygen environment to the sensitivity of CR-39, the sensitivity of CR-39 detectors also varies with the fading time (the time from exposure of CR-39 to chemical etch) and the temperature of exposure and storage for CR-39 detectors, and for the same temperature the longer the fading time, the less sensitive is [Hardcastle et al., 1996; Enomoto et al., 1998]. Therefore to satisfy the need for experiments with different fading time, LET calibration of CR-39 corresponding to different fading time is worth investigating or a correction formula as a function of fading time for the decrease of CR-39 sensitivity should be developed.

1.2.3.4. Comparison of LET Calibrations for CR-39 PNTDs Figure 12. shows the comparison of LET calibrations for CR-39 PNTDs obtained by DIAS group and JSC-SRAG. The Figure indicates that calibration results from the two groups for the same CR-39 material manufactured by the company are very consistent. The LET calibrations for CR-39 detectors collected in the Figure can satisfy the requirements of measurements for space radiation, radiation at aviation altitudes and on the ground.

Figure 12. Comparison of LET calibrations for CR-39 detectors.

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Methods of LET Spectrum and Charge Spectrum Using CR-39 detectors 35

1.3. CHARGE SPECTRUM METHOD USING CR-39 DETECTORS

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1.3.1. Principles of Charge Spectrum Method 1.3.1.1. Particle Identification by Etch Rate and Range Cosmic ray nuclei incident on a track detector may be characterized by their charge, mass and energy. As discussed earlier, differences in these particle parameters are evident as differences in track etching parameters, such as track length and track etch rate. Particle identification depends on the relationship between the track etch rate and the ionisation rate, or the particle energy loss rate. Track detectors are employed in cosmic ray studies in stacks comprising multi detector plates. In this case two parameters of the track are measured: the track etch rate VT and the corresponding average residual range R at this point. The average residual range is defined as the distance, along the path of the particle, from the middle of the etched portion of relevant cone to the eventual stopping point. The stopping point may be identified by the presence of a round pit (test tube) which is formed at the end of the particle's path by isotropic etching beyond this point. If a test tube is not found and no cone is visible on the second surface, usually the stopping point is assumed as the point of halfway between the last cone and the next etched surface. Figure 13 shows the concept of average residual range and the geometry of etched cones in a stack of multi detector plates. The track etch rate, depending ultimately on the charge and velocity of the particle, VT can be expressed as a function of Z and . The range of a particle in a given medium is dependent on the charge, velocity and mass of the particle (Z,  and M).

Figure 13. Average residual range for etched cones in track detector stack.

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By measuring VT and R at a number of points along the particle passage, a series of equations may be established: VT (Ri) = f(Z, i ) and Ri = g(Z, M, i) which may be solved to obtain Z and M. The particle can then be identified by comparing its VT versus R response curve for the unknown particle with those curves of known ions.

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1.3.1.2. Particle Identification by Etch Rate Gradient There is a second method of particle identification involving a concept known as the fractional etch rate gradient [Fowler et al., 1977; O‟Sullivan, 1994; O‟Sullivan et al., 1971, 1973, 1984, 1995, 1996, 2004; Byrne, 1995; Byrne et al., 1995; Zhou, 1999c; Zhou et al., 1999b, 2006a,d, 2007a,f, 2009b, 2010] which is used in the case of a particle that penetrates the entire detector without stopping. Define the fractional etch rate gradient G as 1 dV T

G 

VT

dx

It is a measure of the etch rate change with respect to the distance traveled by the particle. If two etch rates, VT1, VT2, are measured at two points separated by x, then G is given by G 

2 (V T 2  V T 1 ) (V T 2  V T 1 )  x

G can be determined whether or not the residual range is known. This is the most effective method employed in identifying penetrating events. Another quantity to be defined is the effective track etch rate, given by V eff 

2V T 1V T 2 VT 1  VT 2

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Methods of LET Spectrum and Charge Spectrum Using CR-39 detectors 37 For a track with 2n equally spaced cones, the overall value of G is given by n

 ( 2 (V G 

2 n 1 i

 V i ) w i ) /(( V 2 n  1  i  V i )  x i ) 

i 1

n

w

i

i 1

where, wi  (xi)2, is a weighting factor. The overall value of Veff is V eff 

n n

 V

i

 V 2 n 1 i  /  2V iV 2 n 1 i 

i 1

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1.3.2. Charge Calibration for CR-39 Detectors Whichever method of particle identification is employed, it is necessary to compare results from experimental data with those produced by known ions. A relationship between track etch rate and ionisation of the form V T  cJ

n

has been shown to fit data over a wide range of charge and energy. The constants c and n are determined by calibration. The detector is exposed to beams of ions of known charge, energy and mass and the energy-range relations for these ions in that detector material are determined. The detector material used in the charge spectrum study is the same as that used for the LET spectrum study, i.e., CR-39. They should be exposed to heavy ions to obtain charge calibration. It was known for many years that the primary cosmic rays in the deep of atmosphere are mainly ions with electric charge smaller than 10 [Webber et al., 1967; Tsao et al., 1984; Byrne, 1995a,b; Donnelly, 1997]. Therefore for the research of charge spectrum in the atmosphere the charge calibration with high charge (Z20) such as calcium and iron ions is not suitable in view of the large extrapolation involved from high charge (Z20) to low charge (Z10).

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Figure 14. VT versus R for carbon calibration events.

It was necessary to seek calibration with ions of charge Z