Observational Studies of Photonuclear Reactions Triggered by Lightning Discharges (Springer Theses) 9811604584, 9789811604584

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Springer Theses Recognizing Outstanding Ph.D. Research

Yuuki Wada

Observational Studies of Photonuclear Reactions Triggered by Lightning Discharges

Springer Theses Recognizing Outstanding Ph.D. Research

Aims and Scope The series “Springer Theses” brings together a selection of the very best Ph.D. theses from around the world and across the physical sciences. Nominated and endorsed by two recognized specialists, each published volume has been selected for its scientific excellence and the high impact of its contents for the pertinent field of research. For greater accessibility to non-specialists, the published versions include an extended introduction, as well as a foreword by the student’s supervisor explaining the special relevance of the work for the field. As a whole, the series will provide a valuable resource both for newcomers to the research fields described, and for other scientists seeking detailed background information on special questions. Finally, it provides an accredited documentation of the valuable contributions made by today’s younger generation of scientists.

Theses are accepted into the series by invited nomination only and must fulfill all of the following criteria • They must be written in good English. • The topic should fall within the confines of Chemistry, Physics, Earth Sciences, Engineering and related interdisciplinary fields such as Materials, Nanoscience, Chemical Engineering, Complex Systems and Biophysics. • The work reported in the thesis must represent a significant scientific advance. • If the thesis includes previously published material, permission to reproduce this must be gained from the respective copyright holder. • They must have been examined and passed during the 12 months prior to nomination. • Each thesis should include a foreword by the supervisor outlining the significance of its content. • The theses should have a clearly defined structure including an introduction accessible to scientists not expert in that particular field. Indexed by zbMATH.

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Yuuki Wada

Observational Studies of Photonuclear Reactions Triggered by Lightning Discharges Doctoral Thesis accepted by The University of Tokyo, Tokyo, Japan

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Author Dr. Yuuki Wada Cluster of Pioneering Research RIKEN Wako, Saitama, Japan Laboratoire Astroparticule et Cosmologie Université de Paris/CNRS/ CEA/Observatoire de Paris Paris, France

Supervisor Prof. Aya Bamba Department of Physics Graduate School of Science The University of Tokyo Tokyo, Japan

ISSN 2190-5053 ISSN 2190-5061 (electronic) Springer Theses ISBN 978-981-16-0458-4 ISBN 978-981-16-0459-1 (eBook) https://doi.org/10.1007/978-981-16-0459-1 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 This work is subject to copyright. All rights are solely and exclusively licensed 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 Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore

Supervisor’s Foreword

“Earthquakes, thunder, fires, and an angry dad.”—says a Japanese adage, summarizing what are most feared by people. The saying is rightly respected. Among them, thunder is traditionally worshipped in Japan as a gift from gods, because the rice field hit by thunder is believed to yield good rice. In other words, thunder is one of the multitudinous gods in Japanese paganism. Indeed, one of the Japanese words to express thunder is “Ina-zuma”, which literally means the wife of rice. From the scientific point of view, lightning discharges and thunderclouds have been studied as sites of strong electric field and electron acceleration since the 1990s. It is by now understood that thunder activities are often associated with high-energy phenomena, most typically terrestrial gamma-ray flashes and gamma-ray glows, the fact of which implies that lightning discharges and thunderclouds are the strongest particle accelerators on the earth. However, it has remained a mystery how particles are accelerated up to an energy range of MeV in dense atmosphere as observed. The Ph.D. thesis of Dr. Yuuki Wada gives the definite answer to this mystery with a unique method. Thunderclouds frequently appear in the Hokuriku area during winter. They have typically low scale-heights and thus are ideal targets to investigate for the study of the particle acceleration related to thunder from the ground. Dr. Wada played a leading role in developing portable gamma-ray detectors and constructing a detector network with more than 10 sets of them in Kanazawa and Kashiwazaki, in Hokuriku. The system detected gamma rays originating from neutrons and positrons emitted immediately after the discharge of a lightning event on 6 February 2017, the iconic event which lead to a breakthrough discovery in the field of lightning science, as presented in this thesis. He made Monte Carlo simulations of the photon and particle transportation in dense atmosphere, and found with quantitative evaluations that the observed signals originating neutrons and positrons came from photonuclear reactions generating isotopes of carbon, nitrogen, and oxygen, which were triggered by lightning discharges. With detailed calculation, Dr. Wada concluded that a discharge in thundercloud accelerates electrons for which the energetics does not depend on the direction (upward or downward) and scale-height (or density of the air) of the event. v

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Supervisor’s Foreword

Studies of high-energy phenomena in lightning discharges and thunderclouds have been performed mainly from space with satellites. Although satellite-based studies have a great advantage in monitoring many thunderclouds across a wide area, the scope for the detailed study of individual events is severely limited. In stark contrast, Dr. Wada’s method of using many small detectors on the ground focuses on the detailed study of individual events with high precision, even combining simultaneous observations in other wavelengths, such as radio. Hence, his method plays a complementary role in studying electron acceleration in the atmosphere to conventional satellite-based studies. Particle acceleration is one of the fundamental physical phenomena and occurs in various places, including the atmosphere of the earth and other planets, flares on the Sun, and shocks in supernova remnants. Given that, implications and potential theoretical applications of the new insight gained in this work by Dr. Wada’s are not limited to the physics of lightning but are extended to geophysics and even astrophysics in general. The alleged relation between thunder and good rice yield may not be just folklore but may have a scientific base. Thunder ionizes oxygen and nitrogen in the air and the resultant ions permeate the rain. After a thunderstorm, the rice field underneath gets mineral-rich water and will result in a good rice yield. Dr. Wada’s discovery also implies that lightning produces not only chemical but nuclear reactions. Dr. Wada’s finding is monumental and his method presented in this thesis can be a game-changer in the field of geophysics. Based on his achievements, Dr. Wada was awarded the Student Research Prize in March 2020 by the Graduate School of Science, The University of Tokyo, and the Young Scientist Award of the Physical Society of Japan in November 2020. Tokyo, Japan December 2020

Aya Bamba

Preface

“Coup de foudre” (a stroke of lightning)—in French—expresses love at first sight. The flash of light approaching with a roaring sound must be the shock itself when you meet the person of destiny. But roar and flash, is that all about lightning? Wouldn’t the hidden, invisible, and inaudible side of lightning move the human mind? This doctoral thesis discovers a new side of lightning. That is, lightning is a natural particle accelerator and a nuclear reactor. When we think of “accelerators”, we can come up with those used in elementary particle/nuclear experiments, medical diagnosis, and radiation therapy. Radiographs use X-rays obtained from electrons accelerated by applying a high voltage in a vacuum and are an example of a familiar accelerator. If a high voltage is applied, electrons may be accelerated even in the natural world, for example, by lightning discharges. This primitive idea was published by C.T.R. Wilson in 1925, more than 90 years ago. The evidence that the electron acceleration really takes place is serendipitously found in 1991. NASA’s Compton Gamma Ray Observatory, which observes gamma rays from space, captured momentary gamma-ray bursts arriving from the Earth. This phenomenon, later named “terrestrial gamma-ray flash” (TGF), was revealed to be emitted in synchronization with lightning discharges that occurred on the Earth. That is, lightning discharges accelerate electrons to relativistic energy of several tens of MeV, and their bremsstrahlung photons reach the detector in orbit. Lightning discharges are a natural particle accelerator. In general, as the energy of a material or particle increases, their reaction transitions from the molecular level to the atomic and the nuclear levels. The gamma rays of TGFs have high energy enough to trigger nuclear reactions, and it has been predicted that they could react with nitrogen and oxygen in the atmosphere. When a phenomenon called “photonuclear reaction” occurs between gamma rays and nitrogen/oxygen nuclei in the atmosphere, neutrons and unstable nitrogen/oxygen isotopes are generated. This unstable isotope decays within minutes to tens of minutes, by emitting positrons, the antimatter of electrons. Therefore, by detecting the signals of neutrons and positrons at the same time as a lightning discharge, it can be proved that the lightning discharge works as a nuclear reactor. However, previous studies have not provided definitive observational data to support them. vii

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Preface

Since 2016, we have developed portable gamma-ray detectors and built an observation network in the coastal area of the Hokuriku region in Japan, to observe high-energy phenomena originating from lightning and thunderclouds. The Hokuriku region is world famous for its frequent lightning strikes in wintertime. On February 6, 2017, when a powerful cold wave struck the Japanese Islands, four detectors installed at the Kashiwazaki-Kariwa Nuclear Power Station simultaneously detected gamma-ray bursts originating from neutrons coincident with a lightning discharge. In addition, two of them detected gamma-ray bursts of positron origin that lasted several tens of seconds after the lightning discharge. From the epoch-making observation, we conclude that the lightning discharge caused a downward-directed TGF, triggering photonuclear reactions with atmospheric nuclei. Furthermore, by calculating particle transport and photonuclear reactions in the atmosphere by Monte Carlo simulation, we demonstrate that the number of positrons, neutrons generated by photonuclear reactions, and the number of gamma rays of the downward TGF reaching the ground can be explained consistently. These discoveries would have considerable impacts on related fields. The mainstream of TGF research is observations from space. While in-orbit observations cover a large area on the earth, they are not suitable for observing one TGF in detail. On the other hand, although there are a limited number of observations on the ground, it is possible to approach the details of one TGF by combining multiple detectors and multi-wavelength observations such as radio-frequency and optical light. It will give a new perspective to the question of “how efficiently lightning discharges accelerate and amplify electrons in a dense atmosphere”, which is still an unsolved problem. This mechanism should also give a hint to particle acceleration by electric fields in high-energy objects in the universe. It is also shown that the photonuclear reactions produce isotopes in the atmosphere. Until now, it has been thought that natural isotopes on the earth were already present at the time of the birth of the earth or were produced by cosmic rays. This study shows that lightning is the third natural source of isotopes. The Hokuriku region, which is the stage of the observations, is a gastronomic area with fresh seafood dishes such as sushi. Every year from late November to early December, the first winter thunder of the year reverberates. People call this “buri-okoshi” or yellowtail-waking thunder. Yellowtail fish, which is in season in winter, travels to the Hokuriku region with the buri-okoshi, and satisfies people’s tastes. Of course, as the Kanazawa Castle was burned down by a lightning strike in 1602, lightning is an object of awe. On the other hand, it is also an important symbol linked to food culture for the people of the Hokuriku region. And then, our journey isn’t over yet. The basic mechanism of when and how lightning begins to run is still a big mystery. This not only is an academic problem, but also, from the perspective of lightning prediction, has the social impact of reducing damage caused by lightning. Furthermore, transient luminous events in visible light synchronized with lightning discharges such as sprites and elves have been observed in various places, attracting people’s interest. In this way, lightning

Preface

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imposes a lot of homework on us. I am pleased that one of the homework is solved in this thesis. And lightning must be hiding a “stroke” that we don’t know yet. It would be revealed in the next generation of ground- and space-based observations. Paris, during the second Covid-19 lockdown December 2020

Yuuki Wada

Parts of this thesis have been published in the following journal articles: Yuuki Wada, Teruaki Enoto, Kazuhiro Nakazawa, Takayuki Yuasa, Yoshihiro Furuta, Hirokazu Odaka, Kazuo Makishima, Harufumi Tsuchiya, “Photonuclear Reactions in Lightning: 2. Comparison Between Observation and Simulation Model”, Journal of Geophysical Research: Atmospheres, Volume 125, Issue 20, e2020JD033194 (2020) DOI: 10.1029/2020JD033194 Yuuki Wada, Teruaki Enoto, Kazuhiro Nakazawa, Hirokazu Odaka, Yoshihiro Furuta, Harufumi Tsuchiya, “Photonuclear Reactions in Lightning: 1. Verification and Modeling of Reaction and Propagation Processes”, Journal of Geophysical Research: Atmospheres, Volume 125, Issue 20, e2020JD033193 (2020) DOI: 10.1029/2020JD033193 Yuuki Wada, Kazuhiro Nakazawa, Teruaki Enoto, Yoshihiro Furuta, Takayuki Yuasa, Kazuo Makishima, Harufumi Tsuchiya, “Photoneutron detection in lightning by gadolinium orthosilicate scintillators”, Physical Review D, Volume 101, Issue 10, 102007 (2020) DOI: 10.1103/PhysRevD.101.102007 Yuuki Wada, Teruaki Enoto, Kazuhiro Nakazawa, Yoshihiro Furuta, Takayuki Yuasa, Yoshitaka Nakamura, Takeshi Morimoto, Takahiro Matsumoto, Kazuo Makishima, Harufumi Tsuchiya, “Downward Terrestrial Gamma-Ray Flash Observed in a Winter Thunderstorm”, Physical Review Letters, Volume 123, Issue 6, 061103 (2019) DOI: 10.1103/PhysRevLett.123.061103 Teruaki Enoto, Yuuki Wada, Yoshihiro Furuta, Kazuhiro Nakazawa, Takayuki Yuasa, Kazufumi Okuda, Kazuo Makishima, Mitsuteru Sato, Yousuke Sato, Toshio Nakano, Daigo Umemoto, Harufumi Tsuchiya, “Photonuclear reactions triggered by lightning discharge”, Nature, Volume 551, Pages 481–484 (2017) DOI: 10.1038/nature24630

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Acknowledgements

First of all, I would like to thank Dr. Teruaki Enoto. He is the extraordinary leader of the GROWTH collaboration. I learned a lot from his great insights into sciences, ideas for observations, tough work for paper writing, and collaboration management. This work would not have been possible without his support. I would like to express my deep gratitude to my previous and current formal supervisors, Dr. Kazuhiro Nakazawa and Dr. Aya Bamba. Dr. Nakazawa demonstrated his great expertise in high-energy photon detections based on his experiences with satellite developments. It is essential for the detector development of the present work. Dr. Bamba always supports me. She provides us an ideal environment for doing research and discussions with group members. Dr. Kazuo Makishima taught me the basics of experiments, presentation, and paper writing. I was deeply impressed by his lecture when I was an undergraduate student, and decided to study high-energy astrophysics. Dr. Toru Tamagawa kindly accepted me as a junior research associate of RIKEN. The environment in RIKEN was exciting for me and impelled me to do my best. I wish to thank the members of the GROWTH experiments, Dr. Harufumi Tsuchiya, Dr. Takayuki Yuasa, Mr. Yoshihiro Furuta, Mr. Kazufumi Okuda, Mr. Takahiro Matsumoto, Dr. Daigo Umemoto, and Dr. Toshio Nakano. They have profoundly contributed to the GROWTH experiment and established a foundation for high-energy atmospheric physics. Dr. Hirokazu Odaka, the assistant professor of the Bamba Group, supported me with his great expertise in Monte Carlo simulations. Also I greatly appreciate contribution to detector development, deployment, and a lot of fruitful discussions with our collaborators, Dr. Daisuke Yonetoku, Dr. Tatsuya Sawano, Dr. Masashi Kamogawa, Dr. Takeshi Morimoto, Dr. Yoshitaka Nakamura, Dr. Gregory S. Bowers, Dr. David M. Smith, Mr. Shusaku Takahashi, Dr. Yosuke Sato, Dr. Mitsuteru Sato, Dr. Tomoo Ushio, Dr. Mamoru Kubo, Dr. Atsushi Matsuki, Dr. Hideo Sakai, Dr. Hideto Nanto, Dr. Go Okada, Dr. Shoko Miyake, and Dr. Yuko Ikkatai. I thank all my office mates, Shogo Kobayashi, Hiroaki Murakami, Zhang Zhongli, Ko Ono, Yuichi Kato, Katsuma Miyake, Yuki Murota, Hiromasa Suzuki, Manami Seino, Tomoaki Kasuga, Yuki Aizawa, Tsubasa Tamba, Satoshi xiii

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Acknowledgements

Takashima, Kosuke Hatauchi, Megu Kubota, Naoto Murata, Ryo Sasaki, Yuanhui Zhou, Guo Chengcheng, Sonoe Oda, Takaya Wakamatsu, Miho Okubo, Kento Adachi, Keisuke Uchiyama, Marina Tsutsumi, Tomoshi Takeda, Yuto Yoshida, and post-doc staff in RIKEN, Dr. Asami Hayato, Dr. Tomoki Kimura, Dr. Yuki Okura, Dr. Gu Liyi, Dr. Shinya Nakashima, Dr. Wataru Iwakiri, and Dr. Takao Kitaguchi. Especially, I would like to thank the members of Taranis XGRE and my office mates at APC in Paris, Dr. Philippe Laurent, Miles Lindsey-Clark, Eric Bréele, Damien Pailot, Ion Cojocari, Guillaume Prévôt, Ghania Fau, Hana Benhizia, Catherine Nguyen, Alin Ilioni, Matthieu Laporte, and Jean-Pierre Baronick. Je n’oublie pas le goût des frites à la cantine. The present work was performed with support from the radiation safety group of Kashiwazaki-Kariwa Nuclear Power Station, TEPCO Inc., for providing observation sites, Kenya Watarai and Kanazawa University High School, Kazuhiko Yoneguchi and Kanazawa Izumigaoka High School, Koichiro Kimura and Komatsu High School, Koji Kitano and Science Hills Komatsu, Kentaro Kono and Ishikawa Plating Industry Co., Ltd, Soichiro Kura and Kanazawa Nishi High School, Industrial Research Institute of Ishikawa, Sakaida Fruits, and Kanazawa University Noto School for detector deployment, Dr. Hiroyoshi Sakurai, Dr. Megumi Niikura, and the Sakurai Group of The University of Tokyo for providing BGO crystals, Shimafuji Electric Incorporated, Hiroshi Kato, Shigemi Otsuka, Yukio Murata, and Toru Takagaki for detector development, academist, Inc., Adachi Design Laboratory, and Makiko Maruyama for supporting crowdfunding activity, Dr. Masa Sakano for linguistic help, Dr. Tatsumi Koi for supporting Monte Carlo simulations, Dr. Nobuyuki Iwamoto for supporting extraction of JENDL databases, and Dr. Makoto Sakuda for discussion on neutron captures with gadolinium. The Monte Carlo simulations were performed on the HOKUSAI GreatWave and BigWaterfall supercomputing system of RIKEN Head Office for Information Systems and Cybersecurity. Maps utilized in this thesis are provided by Geospatial Information Authority of Japan. Data of XRAIN are obtained by Ministry of Land, Infrastructure, Transport and Tourism of Japan, and provided via Data Integration and Analysis System (DIAS), The University of Tokyo. This work is also financially supported by JSPS/MEXT KAKENHI grants 15K05115, 15H03653, 16H04055, 16H06006, 16K05555, 17K05659, 18J13355, 18H01236, 19H00683, by Hakubi project and SPIRITS 2017 of Kyoto University, by the joint research program of the Institute for Cosmic Ray Research (ICRR), the University of Tokyo, by Satio Hayakawa Fund of Astronomical Society of Japan, and by citizen supporters via the crowdfunding activity on academist. Finally, I would like to appreciate dedicated support from my parents, Yoshimi and Tetsuo, my sister Mari, and my lovely wife Shiho. Tous les chemins ménent à Paris…

Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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2 Observational and Theoretical Overview of High-Energy Atmospheric Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Terrestrial Gamma-Ray Flash . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1 Gamma-Ray Observations with Space-Borne Detectors 2.1.2 Radio-Frequency Observations of TGF-Associated Lightning Discharges . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.3 Downward TGFs Observed at Ground Level . . . . . . . . 2.2 Lightning-Associated X-Ray Emissions . . . . . . . . . . . . . . . . . 2.3 Gamma-Ray Glow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Neutron Production in the Atmosphere . . . . . . . . . . . . . . . . . 2.5 Theories of Electron Acceleration in Thunderstorms . . . . . . . . 2.5.1 Relativistic Runaway Electron Avalanche . . . . . . . . . . 2.5.2 Relativistic Feedback Processes . . . . . . . . . . . . . . . . . 2.5.3 Thermal Runaway Process . . . . . . . . . . . . . . . . . . . . . 2.5.4 Modification of Spectra . . . . . . . . . . . . . . . . . . . . . . . 2.6 Basics of Neutron Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.1 Elastic Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.2 Inelastic Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.3 Neutron Capture . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.4 Charged-Particle Production . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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3 Instrumentation and Observation . . 3.1 Winter Thunderstorms . . . . . . . 3.2 Detector Development . . . . . . . 3.2.1 Scintillation Crystals . . . 3.2.2 Data Acquisition System

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3.2.3 Compact Detectors . . . . . . . . . . . . . . 3.2.4 Stationary Detectors in Kashiwazaki . 3.3 Detector Deployment . . . . . . . . . . . . . . . . . 3.4 Detector Calibration and Responses . . . . . . . 3.5 Monitoring Posts . . . . . . . . . . . . . . . . . . . . 3.6 Radio-Frequency Measurement . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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4 Photonuclear Reactions in Lightning . . . . . . . . . . . . . . . . 4.1 Overview of Short Bursts in Two Winter Seasons . . . . 4.2 Short-Burst Event 2 on 2017 February 6th . . . . . . . . . . 4.2.1 Observational Results . . . . . . . . . . . . . . . . . . . . 4.2.2 Scenarios to Produce Positrons . . . . . . . . . . . . . 4.2.3 Atmospheric Interactions of Neutrons . . . . . . . . 4.2.4 Initial Flash Triggering Photonuclear Reactions . 4.3 Interpretation of All Detected Events . . . . . . . . . . . . . . 4.3.1 Event 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.2 Event 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.3 Event Summary . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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5 Positrons from Proton-Rich Radionuclides . . . . . . . . . . . . 5.1 Channels of Photonuclear Reactions in the Atmosphere 5.2 Monte-Carlo Simulations with Geant4 . . . . . . . . . . . . . 5.2.1 Three-Stage Simulation . . . . . . . . . . . . . . . . . . 5.2.2 Distribution of b þ -Decay Nuclei . . . . . . . . . . . 5.2.3 Spacial Distribution and Energy Spectrum of Annihilation Emissions . . . . . . . . . . . . . . . . 5.2.4 Comparison with Observation . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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6 Atmospheric Reactions of Photoneutrons . . . . . . . . . . . . . . . . . 6.1 Monte-Carlo Simulations of Neutron Propagation . . . . . . . . . 6.1.1 Photoneutron Spectrum by Terrestrial Gamma-Ray Flashes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1.2 Neutron Thermalization in the Ground . . . . . . . . . . . 6.1.3 Full Simulation of Photoneutrons in the Atmosphere . 6.2 Neutron Detection with GSO Scintillators . . . . . . . . . . . . . . 6.2.1 Responses of GSO Scintillators to Thermal Neutrons . 6.2.2 Neutron Flux in Event 3 . . . . . . . . . . . . . . . . . . . . . 6.3 Comparison Between Observations and Simulations . . . . . . . 6.3.1 Model Construction . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.2 Fitting Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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7 Downward Terrestrial Gamma-Ray Flash . . . . . . . . . . . . . . . 7.1 Verification of Dose Measurements with Monitoring Posts . 7.2 Monte-Carlo Simulation of Radiation Doses at the Ground . 7.3 Fitting of Radiation Doses at Multiple Monitoring Posts . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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8 Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1 Properties of Downward TGFs . . . . . . . . . . . . . . . . . . . . 8.1.1 Event 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1.2 Event 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1.3 Event 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1.4 Summary of Analysis . . . . . . . . . . . . . . . . . . . . . . 8.2 Origin of Possible Systematic Uncertainties . . . . . . . . . . . 8.3 Comparison with Previous Upward and Downward TGFs . 8.4 Suggestions for Future Observations . . . . . . . . . . . . . . . . 8.5 Radiation Exposures to Downward TGFs . . . . . . . . . . . . . 8.6 Isotope Production by Photonuclear Reactions . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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. . . . . . . . . . . .

137 137 137 137 138 139 140 143 147 148 149 150

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9 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 Appendix A: Wind Estimation with XRAIN . . . . . . . . . . . . . . . . . . . . . . . 155 Appendix B: Short-Burst Events in Kanazawa . . . . . . . . . . . . . . . . . . . . . 159 Appendix C: Cross Section Correction of Geant4 . . . . . . . . . . . . . . . . . . 165 Appendix D: Neutron Spectrum with JENDL/PD-2016 . . . . . . . . . . . . . . 167 Appendix E: Correlation Between TGFs and LF Pulses . . . . . . . . . . . . . 169

About the Author

Yuuki Wada Extreme Natural Phenomena RIKEN Hakubi Research Team, Cluster for Pioneering Research, RIKEN 2-1, Hirosawa, Wako, Saitama 351-0198, Japan. Appointments • Visiting Researcher, Laboratoire Astroparticule et Cosmologie, France (Sept. 2020–Dec. 2020) • Special Postdoctoral Researcher, RIKEN, Japan (Apr. 2020–present) • Visiting Researcher, Laboratoire Astroparticule et Cosmologie, France (Apr. 2018–Oct. 2018) • Special Researcher DC2, JSPS/The University of Tokyo, Japan (Apr. 2018–March 2020) • Junior Research Associate, RIKEN, Japan (Apr. 2017–March 2018) Education • Doctor of Philosophy (Ph.D.) in Physics Department of Physics, Graduate School of Science, The University of Tokyo (2020) Supervisor: Dr. Aya Bamba • Master of Science Department of Physics, Graduate School of Science, The University of Tokyo (2017) Supervisor: Dr. Kazuhiro Nakazawa

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About the Author

• Bachelor of Science Department of Physics, School of Science, The University of Tokyo (2015) Service • Reviewer for Monthly Notices of the Royal Astronomical Society, Geophysical Research Letters, Journal of Geophysical Research: Atmospheres, Scientific Reports • Member of American Geophysical Union, Physical Society of Japan, Japan Geoscience Union Major Honors and Awards • Young Scientist Award of the Physical Society of Japan (Nov. 2020) • The School of Science Encouragement Award, The University of Tokyo (March 2020) • Outstanding Student Presentation Award, Japan Geoscience Union (May 2019) • Student Presentation Award of the Physical Society of Japan (March 2019) • Outstanding Student Presentation Award, JpGU-AGU Joint Meeting (May 2017) Selected Publications • Y. Wada et al., “Photonuclear Reactions in Lightning: 2. Comparison Between Observation and Simulation Model”, Journal of Geophysical Research: Atmospheres, 125, e2020JD033194 (2020) • Y. Wada et al., “Photonuclear Reactions in Lightning: 1. Verification and Modeling of Reaction and Propagation Processes”, Journal of Geophysical Research: Atmospheres, 125, e2020JD033193 (2020) • Y. Wada et al., “High Peak‐Current Lightning Discharges Associated With Downward Terrestrial Gamma-Ray Flashes”, Journal of Geophysical Research: Atmospheres, 125, e2019JD031730 (2020)

About the Author

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• Y. Wada et al., “Downward Terrestrial GammaRay Flash Observed in a Winter Thunderstorm”, Physical Review Letters, 123, 061103 (2019) • Y. Wada et al., “Gamma-ray glow preceding downward terrestrial gamma-ray flash”, Communications Physics, 2, 67 (2019) • Y. Wada et al., “Termination of Electron Acceleration in Thundercloud by Intracloud/ Intercloud Discharge”, Geophysical Research Letters, 45, 5700-5707 (2018) Research Interests I’m interested in high-energy phenomena in the atmosphere, including terrestrial gamma-ray flashes and gamma-ray glows, and related fields such as lightning physics, atmospheric electricity, atmospheric science, and high-energy astrophysics. My research theme is to measure the physical properties of a phenomenon with instruments developed by myself. I’m a core member of the Gamma-Ray Observation of Winter Thunderclouds (GROWTH) experiment, which aims to explore high-energy phenomena during winter thunderstorms in the coastal area of Japan. I lead detector development, deployment, data analysis, Monte-Carlo simulations, paper writing, and organization of collaborative multiple-wavelength measurements. I have expertise in the development of gamma-ray and high-energy particle detectors, development of analog electronics, data analysis of high-energy particles, atmospheric electric fields, meteorological radar, radio-frequency emission, X-ray astronomy satellites such as Suzaku and NuSTAR, and Monte-Carlo simulations of particle transportation with Geant4. I have programming skills in Ruby and Python. I also lead international collaboration with colleagues in the USA, Czech Republic, and France. Especially, I participate in the development of the X-ray, gamma-ray, and relativistic electron detector (XGRE) onboard the French satellite mission Taranis. I’m mainly in charge of detector calibration and joined the calibration activity with the XGRE team during my stay in Paris in 2018 and 2020. I also participate in the Belisama project, which distributes compact radiation monitors to high schools in France as a citizen science framework.

Chapter 1

Introduction

Recent observational and theoretical studies have made us convinced that lightning and thunderstorms work as particle accelerators in nature. In 1991, the Burst And Transient Source Experiment (BATSE) detector onboard the Compton Gamma-Ray Observatory (CGRO) serendipitously detected millisecond-lasting gamma-ray bursts coming from the Earth’s atmosphere [1]. This phenomenon, later named “terrestrial gamma-ray flash” (TGF), contains gamma-ray photons with energy of >20 MeV, lasts for hundreds of microseconds to several milliseconds, and coincides with lightning discharges [2–6]. Since the gamma-ray spectra of TGFs are consistent with bremsstrahlung radiation from energetic electrons going upward into the space, it is suggested that lightning discharges can accelerate electrons up to tens of MeV. More recently, a similar phenomenon but beamed downward, called “downward TGF”, has been discovered by ground-based observations [7–11]. These findings have been establishing a new academic field called “high-energy atmospheric physics”. As proven by Benjamin Franklin in 1752, lightning and thunderstorm activities are electric phenomena. Figure 1.1 shows a schematic diagram of thunderstorms and related high-energy phenomena. There are several charged layers inside thunderclouds, and highly electrified regions can exist between two opposite charge layers. The strength of electric fields sometimes reaches 0.3–0.4 MV m−1 (Gurevich et al. [12]; converted to an equivalent value at sea level). Wilson [13] suggested that electrons can be accelerated to relativistic energies in such highly electrified regions by a process called “runaway electron”. In the dense atmosphere, electrons usually lose their energy via collisional ionization and radiative processes. If the Coulomb force of electric fields exceeds the drag force, electrons are accelerated by overcoming the energy-loss processes. The total drag force to electrons is shown in Fig. 1.2. The force gets minimum, 0.216 MeV m−1 , at 1.0 MeV in the atmosphere at sea level. When an electric-field strength of 0.4 MeV m−1 , a plausible value in thunderclouds [12], © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 Y. Wada, Observational Studies of Photonuclear Reactions Triggered by Lightning Discharges, Springer Theses, https://doi.org/10.1007/978-981-16-0459-1_1

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1 Introduction

Fig. 1.1 A schematic diagram of high-energy phenomena in thunderstorms. Photo in Sicily by the author. EOS 6D/EF24-105 mm F4L IS USM, 35 mm, 30 s, F8.0, ISO400

is assumed, the Coulomb force of electric fields exceeds the drag force at kinetic energies of electrons from 0.13 to 40 MeV. This indicates that electrons with initial energies of >0.13 MeV can be accelerated up to 40 MeV in the strong electric fields if the electric fields hold enough length for the acceleration. Gurevish et al. [12] introduced multiplication processes of electrons into this theory, by considering acceleration of secondary electrons produced by ionization. The entire process of the electron acceleration and multiplication in the atmosphere, called “relativistic runaway electron avalanche” (RREA), is now widely accepted as the basic mechanism to produce energetic electrons in thunderstorms. This mechanism to accelerate electrons in the atmosphere has been revealed to take place both in instantaneous electric fields of lightning discharges and quasistable fields inside thunderclouds. The former case corresponds to TGFs. Energetic electrons produced by e.g. cosmic rays are thought to be accelerated and multiplied by electric fields in a time scale of less than hundreds of milliseconds. However, the estimated number of electrons produced by a single TGF cannot be explained by the RREA process with seed electrons of cosmic-ray origin; much more seed electrons are needed to produce the gamma-ray fluxes of TGFs detected by satellites [15]. While several models have been proposed (e.g. Dwyer [16], Celestin and Pasko [17]), the mechanism and condition of TGF production remain a big mystery in high-energy atmospheric physics. The latter is associated with another high-energy phenomenon called “gamma-ray glow”, also referred to as “long burst”, or “thunderstorm ground enhancement” when

1 Introduction

3

Fig. 1.2 The drag force to electrons by ionization and radiation processes in the standard atmosphere at 1 atm, as a function of kinetic energies of electrons. Data are retrieved from NIST/EStar [14]

detected at ground level. It is a gamma-ray enhancement originating from electron acceleration inside thunderclouds lasting for tens of seconds to several minutes, or sometimes tens of minutes [18–20]. It has been observed by both airborne and ground experiments. Based on these initial findings, we started the Gamma-Ray Observation of Winter Thunderclouds (GROWTH) experiment in 2006 to observe gamma-ray glows during winter thunderstorms in coastal areas of the Sea of Japan. While winter thunderstorms are quite rare phenomena, they allow us to observe high-energy phenomena at sea level because winter thunderclouds develop at a lower altitude than summer ones, and hence high-energy photons reach the ground more easily. During observations over more than 10 years, we succeeded in detecting gamma-ray glows when thunderclouds were passing above our detectors. We revealed from their energy spectra that gammaray glows originate from bremsstrahlung of energetic electrons accelerated up to >10 MeV inside thunderclouds [21, 22]. Besides gamma-ray glows, another phenomenon called “short burst” has been detected by the GROWTH experiment [23]. Short bursts are gamma-ray bursts coinciding with lightning discharges and lasting for hundreds of milliseconds. While it is obvious that they are distinguished from TGFs due to their longer duration, their origin remained a mystery. At the same time, a possibility of atmospheric photonuclear reactions in lightning and thunderstorms such as 14

N + γ →13 N + n

(1.1)

has been discussed because TGFs and gamma-ray glows contain photons of >10 MeV, high enough to trigger this reaction [24–26]. The reaction emits a fast neutron and a proton-rich radioactive nucleus 13 N. Since 13 N decays with a half-life of 10 min

4

1 Introduction

and emits a positron, the annihilation line at 0.511 MeV should be detected. In fact, detections of neutrons [20, 27–29] and positrons [23, 30] have been reported, and they have thought to originate from photonuclear reactions in the atmosphere. However, such separated detections of neutrons and positrons cannot rule out possibilities of neutron productions by nuclear fusions or positron productions by pair creations. Therefore, a simultaneous detection of neutrons and positrons is the definitive way to demonstrate photonuclear reactions in lightning. In 2016, we developed compact gamma-ray detectors and started a new operation with 4 detectors at Kashiwazaki-Kariwa Nuclear Power Station. On February 6th, 2017, the four detectors caught a short burst, and furthermore, two of them detected annihilation signals lasting for tens of seconds immediately after the short burst. The present thesis verifies our hypothesis that a downward TGF coinciding with a lightning discharge triggered photonuclear reactions, and their byproducts were observed as the short burst and the annihilation gamma rays. This thesis is organized as follows. In Chap. 2, we review observations of highenergy phenomena in lightning and thunderclouds, theoretical views of electron acceleration in the atmosphere, and basics of neutron physics. Chapter 3 introduces Instruments utilized in the thesis and our observational target, winter thunderstorms in Japan. In Chap. 4, we summarize short-burst events and demonstrate photonuclear reactions in the atmosphere. In Chaps. 5 and 6, the downward TGFs which triggered photonuclear reactions are quantitatively evaluated based on observations and Monte-Carlo simulations of positrons and neutrons. The downward TGFs are also evaluated by dose measurements and Monte-Carlo simulations in Chap. 7. In Chap. 8, the evaluations of the downward TGFs by three methods (positron, neutron, and TGF dose measurements) are compared, and Chap. 9 summarizes the present thesis. The errors described in the present thesis is at 1σ confidence level unless otherwise noted. We use “thunderstorm” as a word including both lightning discharge and thundercloud. Time in this thesis is described in local time (Japan Standard Time: JST) unless otherwise noted.

References 1. Fishman GJ, Bhat PN, Mallozzi R, Horack JM, Koshut T, Kouveliotou C, Pendleton GN, Meegan CA, Wilson RB, Paciesas WS et al (1994) Science 264(5163):1313. https://doi.org/ 10.1126/science.264.5163.1313 2. Smith DM, Lopez LI, Lin RP, Barrington-Leigh CP (2005) Science 307(5712):1085. https:// doi.org/10.1126/science.1107466. http://science.sciencemag.org/content/307/5712/1085 3. Marisaldi M, Fuschino F, Labanti C, Galli M, Longo F, Del Monte E, Barbiellini G, Tavani M, Giuliani A, Moretti E et al (2010) J Geophys Res: Space Phys 115:A3. https://doi.org/10. 1029/2009ja014502 4. Tavani M, Marisaldi M, Labanti C, Fuschino F, Argan A, Trois A, Giommi P, Colafrancesco S, Pittori C, Palma F et al (2011) Phys Rev Lett 106:1. https://doi.org/10.1103/physrevlett.106. 018501

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5. Briggs MS, Connaughton V, Wilson-Hodge C, Preece RD, Fishman GJ, Kippen RM, Bhat PN, Paciesas WS, Chaplin VL, Meegan CA et al (2011) Geophys Res Lett 38:2. https://doi.org/10. 1029/2010gl046259 6. Mailyan BG, Briggs MS, Cramer ES, Fitzpatrick G, Roberts OJ, Stanbro M, Connaughton V, McBreen S, Bhat PN, Dwyer JR (2016) J Geophys Res: Space Phys 121(11):11,346. https:// doi.org/10.1002/2016ja022702 7. Dwyer JR, Uman MA, Rassoul HK, Al-Dayeh M, Caraway L, Jerauld J, Rakov VA, Jordan DM, Rambo KJ, Corbin V, Wright B (2003) Science 299(5607):694. https://doi.org/10.1126/ science.1078940. http://science.sciencemag.org/content/299/5607/694 8. Dwyer JR, Rassoul HK, Al-Dayeh M, Caraway L, Wright B, Chrest A, Uman MA, Rakov VA, Rambo KJ, Jordan DM et al (2004) Geophys Res Lett 31:5. https://doi.org/10.1029/ 2003gl018771 9. Hare BM, Uman MA, Dwyer JR, Jordan DM, Biggerstaff MI, Caicedo JA, Carvalho FL, Wilkes RA, Kotovsky DA, Gamerota WR et al (2016) J Geophys Res: Atmosph 121(11):6511. https:// doi.org/10.1002/2015jd024426 10. Tran M, Rakov V, Mallick S, Dwyer J, Nag A, Heckman S (2015) J Atmosph Solar-Terrest Phys 136:86. https://doi.org/10.1016/j.jastp.2015.10.010 11. Abbasi RU, Abu-Zayyad T, Allen M, Barcikowski E, Belz JW, Bergman DR, Blake SA, Byrne M, Cady R, Cheon B et al (2018) J Geophys Res: Atmosph 123(13):6864. https://doi.org/10. 1029/2017jd027931 12. Gurevich A, Milikh G, Roussel-Dupre R (1992) Phys Lett A 165(5–6):463. https://doi.org/10. 1016/0375-9601(92)90348-p 13. Wilson CTR (1925) Math Proc Cambrid Philosoph Soc 22(04):534. https://doi.org/10.1017/ s0305004100003236 14. National Institute of Standards and Technology. ESTAR- stopping-power and range tables for electrons. https://physics.nist.gov/PhysRefData/Star/Text/ESTAR.html 15. Dwyer JR (2008) J Geophys Res 113:D10. https://doi.org/10.1029/2007jd009248 16. Dwyer JR (2003) Geophys Res Lett 30:20. https://doi.org/10.1029/2003gl017781 17. Celestin S, Pasko VP (2011) J Geophys Res: Space Phys 116:A3. https://doi.org/10.1029/ 2010ja016260 18. McCarthy M, Parks GK (1985) Geophys Res Lett 12(6):393. https://doi.org/10.1029/ gl012i006p00393 19. Torii T, Takeishi M, Hosono T (2002) J Geophys Res: Atmosph 107(D17). ACL 2. https://doi. org/10.1029/2001jd000938 20. Chilingarian A, Daryan A, Arakelyan K, Hovhannisyan A, Mailyan B, Melkumyan L, Hovsepyan G, Chilingaryan S, Reymers A, Vanyan L (2010) Phys Rev D 82:4. https://doi.org/10. 1103/physrevd.82.043009 21. Tsuchiya H, Enoto T, Yamada S, Yuasa T, Kawaharada M, Kitaguchi T, Kokubun M, Kato H, Okano M, Nakamura S et al (2007) Phys Rev Lett 99:16. https://doi.org/10.1103/physrevlett. 99.165002 22. Tsuchiya H, Enoto T, Yamada S, Yuasa T, Nakazawa K, Kitaguchi T, Kawaharada M, Kokubun M, Kato H, Okano M et al (2011) J Geophys Res 116:D9. https://doi.org/10.1029/ 2010jd015161 23. Umemoto D, Tsuchiya H, Enoto T, Yamada S, Yuasa T, Kawaharada M, Kitaguchi T, Nakazawa K, Kokubun M, Kato H et al (2016) Phys Rev E 93:2. https://doi.org/10.1103/physreve.93. 021201 24. Babich LP (2006) JETP Lett 84(6):285. https://doi.org/10.1134/s0021364006180020 25. Babich LP (2007) Geomagn Aeron 47(5):664. https://doi.org/10.1134/s0016793207050155 26. Carlson BE, Lehtinen NG, Inan US (2010) J Geophys Res: Space Phys 115:A4. https://doi. org/10.1029/2009ja014696 27. Shah GN, Razdan H, Bhat CL, Ali QM (1985) Nature 313(6005):773. https://doi.org/10.1038/ 313773a0 28. Gurevich AV, Antonova VP, Chubenko AP, Karashtin AN, Mitko GG, Ptitsyn MO, Ryabov VA, Shepetov AL, Shlyugaev YV, Vildanova LI et al (2012) Phys Rev Lett 108:12. https://doi. org/10.1103/physrevlett.108.125001

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29. Bowers GS, Smith DM, Martinez-McKinney GF, Kamogawa M, Cummer SA, Dwyer JR, Wang D, Stock M, Kawasaki Z (2017) Geophys Res Lett 44(19):10,063. https://doi.org/10. 1002/2017gl075071 30. Dwyer JR, Smith DM, Hazelton BJ, Grefenstette BW, Kelley NA, Lowell AW, Schaal MM, Rassoul HK (2015) J Plasma Phys 81:4. https://doi.org/10.1017/s0022377815000549

Chapter 2

Observational and Theoretical Overview of High-Energy Atmospheric Physics

Since 1980s, high-energy phenomena in the atmosphere have been detected by satellite, aircraft, balloon, and on-ground experiments. As briefly mentioned in Chap. 1, they have been found to originate from electron acceleration in strong electric fields of lightning discharges or thunderclouds. This chapter reviews current observational understandings of high-energy atmospheric phenomena such as TGFs, X-ray emissions from lightning, gamma-ray glows, then theories of electron acceleration proposed to explain these phenomena. Section 2.6 introduces basic physics of neutrons utilized to interpret observation data of neutron origin.

2.1 Terrestrial Gamma-Ray Flash 2.1.1 Gamma-Ray Observations with Space-Borne Detectors Lightning discharges are known to release enormous energy via three ways, optical flashes, sonic booms, and radio-frequency emissions in various wavelengths. In addition to the three ways, gamma rays are recognized as the forth way, discovered by an in-orbit spacecraft in 1991. The Compton Gamma-Ray Observatory (CGRO), developed by National Aeronautics and Space Administration (NASA) to detect celestial high-energy emissions, was launched into a low-Earth orbit of the 500-km altitude. The Burst and Transient Source Experiment (BATSE) onboard CGRO was sensitive to X and gamma rays above 50 keV, and searched for transient emissions from the whole sky such as gamma-ray bursts. During its initial operation from April 1991 to October 1993, BATSE serendipitously detected 12 gamma-ray flashes of terrestrial origin [1]. Figure 2.1 shows count rate histories of the 12 flashes. These flashes have a duration of several hundred microseconds to a few milliseconds. The energy of their gamma-ray photons exceeded 300 keV, which is the maximum range of BATSE. When the gamma-ray flashes were detected, BATSE passed above active thunderstorms, and hence the relation between the gamma-ray flashes and thunder© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 Y. Wada, Observational Studies of Photonuclear Reactions Triggered by Lightning Discharges, Springer Theses, https://doi.org/10.1007/978-981-16-0459-1_2

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Fig. 2.1 Count rate histories of 12 TGFs detected by the BATSE detector onboard the CGRO. Reprinted from Fishman et al. [1] with permission from AAAS

storm activities was suggested. In addition, radio-frequency emissions in very low frequency (VLF: 3–30 kHz) and extremely low frequency (ELF: 50 kA [16]. Among 50 TGFs detected by Fermi, 15 events coincided with WWLLN-detected discharges within 50 µs. Estimated locations of discharges were located within 300 km from where Fermi detected the associated TGFs [21]. Reference [22] surveyed associations between TGFs and RF emissions taking place around North America using NLDN, which provides more accurate location and peak current of discharges than WWLLN. Detailed observations in LF and VHF bands give insights into individual TGFs. Lu et al. [23] for the first time succeeded in three-dimensionally visualizing a lightning discharge associated with a RHESSI TGF using a lightning mapping array (LMA [24, 25]) installed in Alabama, US. LMA is a lightning location system employing the time-of-flight technique in the VHF band. They suggested that the TGF was produced during an upward leader progression, and leader processes might be responsible for TGFs. Cummer et al. [26, 27] monitored LF waveforms from TGF-associated lightning discharges, and employed a method to estimate pulse heights of the LF sources, by identifying reflection pulses from the ionosphere and the ground [28]. Their results in the LF band also suggested that TGFs were produced in the middle of upward leader development several milliseconds after leader initiation. Cummer et al. [26] detected TGF-associated LF pulses at 11–12 km altitude, and suggested that TGFs took place in the upper part of thunderclouds. More recently, Lyu et al. [29, 30] have identified a new type of lightning discharges named “energetic in-cloud pulses” (EIPs), which are characterized by high estimated peak currents of >200 kA, and proposed a strong connection to TGFs (Fig. 2.4).

2.1.3 Downward TGFs Observed at Ground Level At present, TGFs are widely accepted as upward-beamed emissions from thunderclouds mainly observed with space-borne detectors. However, despite less common cases, TGF-like but downward-beamed emissions have been detected by onground facilities. They are now called “downward TGFs”. Downward TGFs were detected coincident with rocket-triggered lightning discharges. International Center for Lightning Research and Testing (ICLRT), University of Florida performed rocket-triggered lightning experiments, which make artificial lightning leaders by

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Fig. 2.4 LF waveforms and leader altitude progression during TGFs. Reprinted from Cummer et al. [27] with permission from Wiley Fig. 2.5 The energy spectrum of a downward TGF obtained at ICLRT. Reprinted from Dwyer et al. [31] with permission from Wiley

launching metal wires attached to a small rocket toward thunderclouds, and inducing CGs. Dwyer et al. [31] and Hare et al. [32] installed multiple sodium iodide and plastic scintillators around the launch point, and detected gamma-ray photons with energies of >8 MeV coincident with successful rocket-triggered CGs in August 2003 and August 2014, respectively. In the case in 2003 [31], 227 photons were detected during 300 µs, and its energy spectrum extended to 10 MeV, as shown in Fig. 2.5. An LMA observation in the 2014 event revealed that a downward TGF took place at the tip of an upward positive leader from the launched rocket. ICLRT and another facility of University of Florida observed other events of downward TGFs, coincident with natural lightning discharges [33, 34]. They lasted for several tens of millisecond with photons of >10 MeV. The Telescope Array (TA) experiment is performed on a wilderness at a 1400 m altitude in Utah, US, to detect ultra-high energy cosmic rays exceeding 1020 eV. It covers an area of 700 km2 with 507 surface detectors consisting of plastic scintillators, installed in a grid of a 1.2 km width [35]. Since 2010, surface detectors have observed gamma-ray signals different from those of cosmic-ray origin, coincident with lightning discharges detected by NLDN [36]. The gamma-ray signals lasted for ∼10 µs, and were simultaneously detected by several to tens of surface detecters (Fig. 2.6). An LMA installed at the TA site in 2013 observed negative leader progression of CGs or ICs associated with downward TGFs [37]. By comparing with Monte-Carlo

2.1 Terrestrial Gamma-Ray Flash

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Fig. 2.6 Waveforms from surface detectors (left) and a spatial distribution of energy deposits (right) in a downward TGF event observed by the TA experiment. Reprinted from Abbasi et al. [37] with permission from Wiley

simulations, they suggested that gamma rays of more than several MeV hit surface detectors, and 1012 –1014 photons of >0.1 MeV were produced in a downward TGF. These results presented that TA is capable of studying weak TGFs which cannot be detected by spacecrafts in detail. The Pierre Auger observatory in Argentina, aiming at detecting ultra-high energy cosmic rays likewise TA, also detected high-energy radiation events coincident with lightning discharges [38].

2.2 Lightning-Associated X-Ray Emissions Besides TGFs, another type of emissions has been recorded by ground-level measurements. In 2000, Moore et al. [39] detected X-ray and gamma-ray photons coincident with lightning discharge, by using sodium iodide scintillators installed at South Baldy Peak in New Mexico, US. The photons were produced 1–2 ms before return strokes, and some of them had energies of >1 MeV. Similar events have been detected at ICLRT [5, 40–42], at 2500-m altitude of the Pyrenees, Spain [43], and by a sealevel experiment during winter thunderstorms in Japan [44]. Dwyer et al. [5], by high-energy photon and electric-field measurements at ICLRT, revealed that X-ray photons of several hundreds of keV were emitted at each leader step, as shown in Fig. 2.7 left. This phenomenon shares characteristics with TGFs such as coincidence with lightning discharges and duration of sub-milliseconds to several milliseconds. However, energy spectra of this phenomenon have a steep cutoff at a few MeV, while those of TGFs extend to >10 MeV (Dwyer et al. [31]; Fig. 2.7 right). Therefore, it is thought that the X-ray emissions can be distinguished from TGFs, and its production mechanism should be different from those of TGFs [33].

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Fig. 2.7 X-ray pulses (left top) and associated electric-field changes (left bottom) observed at ICLRT [5], and a comparison between energy spectra of RHESSI TGFs, a downward TGF, and a X-ray emission from lightning [33]. Reprinted from Dwyer et al. [5, 33] with permission from Wiley

2.3 Gamma-Ray Glow In contrast to high-energy phenomena coincident with lightning discharges such as TGFs and X-ray bursts, X-ray and gamma-ray emissions coming from thunderclouds and lasting for more than seconds have been observed. The first report was made by Parks et al. and McCarthy and Parks [45, 46]. They equipped NASA’s F-106 aircraft with an X-ray detector and a photo-multiplier tube (PMT) without X-ray absorbers for noise monitoring. During its flights inside thunderclouds in Oklahoma and Virginia, US, X-ray bursts were detected for tens of seconds to a minute, as shown in Fig. 2.8. No lightning discharges were confirmed while the X-ray bursts were being observed. They concluded that high-energy electrons produced in active thunderstorms emitted bremsstrahlung X-rays. This phenomenon is now called “gamma-ray glow”, and has been observed inside thunderclouds by aircrafts and balloons, and below thunderclouds at mountain-top observatories. Eack et al. [47] performed a balloon flight with X-ray and atmospheric electric-field monitors. As strength of electric fields exceeded 50 kV m−1 at an 4-km altitude, a significant increase in X-rays was detected, as shown in Fig. 2.9. Since the strength of electric fields during the gamma-ray glow was less than two third of that needed for relativistic runaway acceleration [48], they speculated that there was another stronger electric fields which facilitate electron acceleration near the balloon, or an unknown mechanism to accelerate electrons even in weak electrostatic fields. Recently, airborne observations at high altitude have been performed. Kelley et al. [49] detected a gamma-ray glow at a 14 km altitude in Colorado, US, with the Airborne Detector for Energetic Lightning Emissions onboard Gulfstream V aircraft (Fig. 2.10). Based on detector responses, gamma-ray photons, whose spectrum

2.3 Gamma-Ray Glow

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Fig. 2.8 One of the first gamma-ray glow observations by airborne detectors. Reprinted from McCarthy and Parks [46] with permission from Wiley Fig. 2.9 X-ray intensity and electric-field strength measured by a balloon flight. Reprinted from Eack et al. [47] with permission from Wiley

extended to >5 MeV, propagated downward. As the aircraft was flying at the cloud top of a thundercloud during the glow detection, they concluded that electrons were accelerated downward between a positive charge layer and a negative charge layer above called “screen layer”. Kochkin et al. [50] observed gamma-ray glows lasting for 20–30 s at a 12 km altitude in North Australia, with X-ray and gamma-ray detectors onboard an Airbus A340 aircraft, and Østgaard et al. [51] observed ones at a 20-km altitude in Georgia, US, with gamma-ray and electric-field monitors onboard NASA’s ER-2 aircraft. On high-altitude mountains, on-ground observations of high-energy radiation can be performed inside or near thunderclouds. Since 2000s, cosmic-ray observatories around the world have recorded minute-lasting gamma-ray emissions associated with thunderstorm activities [53, 54]. In Japan, observatories at Mount Norikura (2770 m altitude [55]) and Mount Fuji (3776 m [56]) have recorded gamma-ray glows. The longest-lasting gamma-ray glow, lasting for ∼40 min, was observed at Yangba-

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1.5×104

(50–300 keV)/3 300–1000 keV 1–5 MeV >5 MeV

1.0×104 5.0×103 0 –5.0

0.0

5.0

10.0

s

Fig. 2.10 The brightest gamma-ray glow detected by the Airborne Detector for Energetic Lightning Emissions experiment. Reprinted from Kelley et al. [49] under the CC BY 4.0 license

Fig. 2.11 A thunderstorm ground enhancement and electric-field variation recorded at Aragats Space Environmental Center. Reprinted with permission from Chilingarian and Mkrtchyan [52]. Copyright 2012 by the American Physical Society

jing International Cosmic Ray Observatory. The highest photon energy of the glow exceeded 40 MeV [57]. Aragats Space Environmental Center (ASEC) at a 3200 m altitude slope of Mount Aragats in Armenia has continuously performed gammaray, electrons, and neutron monitoring with solar neutron telescopes and cosmic-ray monitors. They have detected increases in gamma rays and electrons associated with thunderstorms, named “thunderstorm ground enhancements” (TGEs [58, 59]). TGEs and gamma-ray glows are thought to be intrinsically the same phenomena. By comparing TGEs with electric-field perturbations shown in Fig. 2.11, Chilingarian and Mkrtchyan [52] speculated that electron acceleration and multiplication could take place in a strong electric field between a middle-layer negative charge region and a lower positive charge region. ASEC is the site where the largest number of TGEs has been registered, as ∼300 TGEs were detected there in 2008–2012. Typical summer thunderclouds have cloud bases of >3 km altitudes, and hence gamma-ray glows cannot be detected at sea level as photons and electrons are atten-

2.3 Gamma-Ray Glow

17

Fig. 2.12 A dose-rate enhancement measured by environmental radiation monitors installed at the nuclear reactor Monju during a winter thunderstorm in Japan. Reprinted from Torii et al. [60] with permission from Wiley

uated. On the other hand, low could bases of winter thunderstorms in Japan enable us to detect gamma-ray glows at sea level. Torii et al. [60], with radiation monitoring stations installed in the nuclear facility “Monju” faced on the Sea of Japan, recorded dose increases lasting for ∼1 min associated with passage of thunderclouds (Fig. 2.12). In addition, an observation with multiple monitoring stations allowed Torii et al. [61] to measure time lags of a gamma-ray glow at each station, and then to estimate the height of the gamma-ray source as ∼300 m. Since 2006, the Gamma-Ray Observation of Winter Thunderclouds (GROWTH) experiment has been performed at Kashiwazaki-Kariwa Nuclear Power Station in Niigata. Tsuchiya et al. [62] for the first time succeeded in obtaining an energy spectrum of a gamma-ray glow. The energy spectrum presenting a power-law function extending up to 10 MeV indicated that gamma-ray photons originated from bremsstrahlung of relativistic electrons accelerated in thunderclouds (Fig. 2.13). Tsuchiya et al. [63] estimated total electron numbers during their detection as 109 –1011 , and their source height as 100–700 m. Kuroda et al. [64] revealed that gamma-ray photons came from zenith during a gamma-ray glow detection, at Ohi Nuclear Power Station in Fukui with Plastic Anti-Neutrino Detector Array. Gamma-ray glows are widely thought to originate from strong electric fields inside thunderclouds, not directly associated with lightning discharges themselves. On the other hand, on-ground and airborne experiments have observed sudden termination of gamma-ray glows coincident with lightning discharges [46, 47, 49, 50, 54, 65, 66]. Since lightning discharges can be remotely observed in the RF bands, glow termination is an opportunity to observe gamma-ray glows besides high-energy bands. Chilingarian et al. [67] performed electric-field monitoring during TGEs and their termination. They revealed that negative charge layers inside thunderclouds were discharged when TGEs were terminated, and suggested that the negative layers were

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2 Observational and Theoretical Overview of High-Energy Atmospheric Physics

Fig. 2.13 Energy spectra of gamma-ray glow during winter thunderstorms and TGFs detected by AGILE and RHESSI. Reprinted from Tsuchiya et al. [63] with permission from Wiley

responsible for electron acceleration of TGEs. Wada et al. [68] observed a glow termination during a winter thunderstorm in Japan with gamma-ray, LF, and electricfield monitors. Two-dimensional lightning mapping with broadband LF receivers revealed that the gamma-ray glow was terminated by leader development of an IC which horizontally extended ∼70 km.

2.4 Neutron Production in the Atmosphere Besides electrons, X-rays and gamma rays, possibility of neutron production by lightning discharges has been discussed since 1970s. Neutron production in the atmosphere is of great importance because it leads to producing a carbon isotope 14 C, which is used for radiocarbon dating in archaeology, via a nuclear reaction 14 N + n →14 C + p [69, 70]. Shah et al. [71] reported detection of neutrons coincident with lightning discharges by cosmic-neutron monitors installed in the Himalayan region. They estimated that 107 –1010 neutrons were generated per a lightning discharge. At that time, the most probable scenario of neutron production in lightning was thought to be nuclear fusion; deutrons in vapor molecules are heated in lightning paths, and eventually trigger deutron-deutron reactions 2 H +2 H →3 He + n. In that reaction, a neutron with an energy of 2.45 MeV is produced. However, Babich [72, 73] concluded that deutron-deutron reactions are not plausible in lightning, because cross section of the reactions under the condition in lightning is too low to produce an observable number of neutrons. After the discovery of TGFs in 1994 [1], neutron production via photonuclear reactions has been discussed because energy spectra of TGFs were confirmed to extend to >10 MeV [2]. Photonuclear reaction is one of nuclear reactions that a

2.4 Neutron Production in the Atmosphere

19

Fig. 2.14 Count-rate histories of neutrons (top) and gamma rays (bottom) during a winter thunderstorm in Japan. Reprinted from Kuroda et al. [64] under the CC BY 4.0 license

photon kicks a neutron off from a nucleus. Nuclei in the atmosphere such as 14 N and 16 O are involved in the reactions 14 N + γ →13 N + n and 16 O + γ →15 O + n, with the threshold photon energies of 10.55 MeV and 15.66 MeV, respectively. Babich [72, 73] suggested that 1015 neutrons can be generated in a lightning discharge. Furthermore, Carlson et al. [74] performed a simulation study with parameters of RHESSI TGFs, and presented that 3 × 1011 –3 × 1012 neutrons per a TGF could be generated via photonuclear reactions. Several reports on neutron detection associated with thunderstorm activities have been recently made. Gurevich et al. [75] detected thermal neutrons associated with lightning discharges by 3 He neutron monitors, installed at a 3340-m-altitude cosmic-ray observatory in Kazakhstan. They reported that neutron fluxes were (3–5) ×10−2 cm−2 s−1 on average. In addition, neutrons have been detected during gammaray glows. Chilingarian et al. [58] and Chilingarian and Mkrtchyan [52] reported detection of neutrons associated with TGEs by 10 Be proportional counters of Aragats Solar Neutron Telescope. Kuroda et al. [64] also reported a neutron burst during a gamma-ray glow in a winter thunderstorm, as shown in Fig. 2.14. These two neutron bursts were not associated with lightning discharges, and hence photonuclear reactions triggered by photons of gamma-ray glows are the only possibility for neutron production. On the other hand, proton-rich nuclei such as 13 N and 15 O should be generated in such reactions. These nuclei eventually emit positrons via β + decay, with half-lives of 10 and 2 min, respectively. When photonuclear reactions take place, a signature of positrons can be detected besides neutrons. In fact, Umemoto et al. [76] reported a signature of electron-positron annihilation detected immediately after

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2 Observational and Theoretical Overview of High-Energy Atmospheric Physics

a lightning discharge. However, occurrence of photonuclear reactions in the atmosphere has never been demonstrated because simultaneous detection of positrons and neutrons has never been reported.

2.5 Theories of Electron Acceleration in Thunderstorms 2.5.1 Relativistic Runaway Electron Avalanche Wilson [48] proposed an idea that electrons can be accelerated by strong electric fields in the atmosphere for the first time. Then, Gurevich et al. [77] developed this idea into “relativistic runaway electron avalanche” (RREA) by considering acceleration of secondary electrons. As well known [78], the drag force to electrons by ionization is presented as the Bethe formula Fion = 2πre2 m e c2 ρ NA

      3 1 2 1 Z 1 4 1 m e c2 β 2 γ 2 − 1 − + − ln + ln , A β2 γ 8 γ 2I 2 γ2 γ2

(2.1) where , re , m e c2 , ρ, Z, A, NA , β, γ , I are kinetic energy of an electron, the classical electron radius, rest energy of an electron, density, atomic number and atomic weight of targets, the Avogadro constant, a ratio of electron velocity to speed of light, the Lorenz factor, and ionization energy of targets, respectively. In relativistic energies, radiative drag force also affects electrons. This force is formulated as [78] Frad = αre2 ρ NA

  2 Z(Z + 1) 4  4 ln , − A m e c2 3

(2.2)

where α the fine structure constant. The total force to electrons is the summation of ionization and radiative forces Ftot = Fion + Frad . More precise values of drag forces to electrons are provided by the EStar database provided by National Institute of Standards and Technology (NIST). The drag force in the standard atmosphere (ρ = 1.293 × 10−3 g cm−3 ) is shown in Fig. 2.15. In non-relativistic energy, drag force decreases as electron energy increases. In contrast, both ionization and radiative forces increase as electron energy increases in relativistic energy. Therefore, the drag force has a minimum at ∼1 MeV Fmin = 0.216 MeV m−1 ×

ρ . 1.293 × 10−3 g cm−3

(2.3)

When a higher electric field than this minimum exists in the atmosphere, acceleration force by the electric field and drag force are balanced at two point in relativistic energy. The lower-energy point is unstable: electrons with slightly lower energy decelerate, and those with slightly higher energy accelerate. On the other hand, the higher point

2.5 Theories of Electron Acceleration in Thunderstorms

21

Fig. 2.15 The drag force to electrons in the standard atmosphere. Data points are provided by NIST/EStar and Dwyer [79]

is stable: electrons with slightly lower energy accelerate, and those with slightly higher energy decelerate. Therefore, electrons with energy higher than the lower energy point can be accelerated to the higher energy point in the electric field. Then, acceleration of secondary electrons produced by ionization processes is considered [77]. In non-relativistic energy range, the formula of drag force is approximated as [80]   1 m e c2 2 (2.4) β . F = 2πre2 m e c2 ρ NA 2 ln β Z i In relativistic energy range as  F ≈ 2πre2 m e c2 ρ NA ln

m e c2 γ 1

 ,

(2.5)

where i = 15 eV and 1 = 270 eV. The minimum of the drag force is shown as 

Fmin ≈

2πre2 m e c2 ρ NA

m e c2 ln Z i

= 0.2 MeV m−1 × Here a non-dimensional parameter



ρ . 1.293 × 10−3 g cm−3

(2.6)

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2 Observational and Theoretical Overview of High-Energy Atmospheric Physics

δ0 =

1.293 × 10−3 g cm−3 eE E = Fmin 0.2 MV m−1 ρ

(2.7)

is introduced. When δ0 > 1, the balance equation between electric fields and drag force eE − F = 0 has two solutions, hence runaway electrons are produced. The runaway electrons produce secondary electrons via ionization processes. Assuming that primary electrons penetrate along electric fields, the angle between primary and secondary electron’s velocity vectors is given as θ , and μ = cos θ . Secondary electrons tend to be emitted into the perpendicular direction to primary electron’s velocity vector, and hence the initial value of μ is ∼0. Then velocity v and momentum angle μ of the secondary electrons are affected by the drag force and the electric field. The equation of motion of the secondary particles for their forward direction is introduced as dv = eEμ − F(v), (2.8) me dt where, m e is the electron mass. Time variation of μ = v · E/vE is also introduced as   d v·E dμ = dt dt vE     eEμ 1 F(v) eE = − sin θ (2.9) + E sin θ × E cos θ vE me me me eE eE ≈ sin2 θ = (1 − μ2 ). mev mev Here the electron velocity can be replaced by a dimension-less parameter u = v2 /c2 . In the non-relativistic case, the two equations of motion derive a differential equation of u and μ    1 ln u 2 du μu − 1 + = . (2.10) dμ 1 − μ2 δ0 ln(m e c2 /Z i ) The solution of this equation predicts the movement of secondary electrons in the μ − u plane. Figure 2.16 left shows examples of electron trajectories under a condition of δ0 = 3 and the initial value of μ = 0, calculated by the two-stage second-order Runge-Kutta method. While secondary electrons move toward μ = 1, they accelerate with higher initial velocity than a threshold, and decelerate with lower initial velocity than the threshold. The relation between δ0 and the threshold initial velocity u init is shown in Fig. 2.16 right. The threshold u init exists when δ0 is higher than 2.1. Since δ0 depends on atmospheric density and electric fields, the threshold electric-field strength where secondary electrons can run away is E th = 0.42 MV m−1 ×

ρ . 1.293 × 10−3 g cm−3

(2.11)

2.5 Theories of Electron Acceleration in Thunderstorms

23

Fig. 2.16 Trajectories of secondary electrons in the μ − u plane at δ0 = 3 (left) and the relation between δ0 and u init (right) in the standard atmosphere

The initial velocity of secondary electrons must exceed u init so that they become runaway electrons. Their kinetic energy is then 10 = 21 m e c2 u init . When energy of primary electrons far exceeds 10 , an average length λe in which a primary electron produces secondary one is u init λe = . (2.12) 2πre2 ρ NA Since the number of secondary electrons produced per a unit length is proportional to the number of runaway electrons and inversely proportional to λe , a differential equation N dN ∝ (2.13) dx λe is obtained. Ignoring the altitudinal variation of atmospheric density, the solution is N ∝ N0 exp(x/λe ), where N0 is the number of energetic seed electrons. Namely, the number of runaway electrons exponentially increases with longer length of acceleration region. This model has been developed with computer-based simulations. Dwyer [81] confirmed by a Monte-Carlo simulation that RREA processes take place with electric fields higher than the threshold E th : E th = 0.284 MV m−1 ×

ρ . 1.293 × 10−3 g cm−3

(2.14)

Babich et al. [82] independently obtained a consistent result with Dwyer (2003) [81]. The threshold field E th is higher than the runaway threshold Fmin /e, since Coulomb and Møller scatterings affect electron avalanches. Electron multiplication in the RREA process is characterized by the acceleration length λ. Electron flux F(L) is introduced as

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2 Observational and Theoretical Overview of High-Energy Atmospheric Physics

Fig. 2.17 The relation between electric-field strength and avalanche length obtained by various simulations. Reprinted from Dwyer et al. [83] under the CC BY 4.0 license



L

F(L) = F0 exp(ξ ), ξ = 0

dz λ

(2.15)

where L is a length from where electron acceleration begins, and F0 is a seed electron flux at L = 0. This formula is simplified as an exponential function F(L) = F0 exp(L/λ) when an uniform electric field is considered. The relation between electric-field strength and λ is obtained by simulation studies [81, 82, 84– 89]. Dwyer et al. [83] reviewed these results, as shown in Fig. 2.17. The relation in the standard atmosphere is empirically obtained as λ≈

7.3 MeV . eE − 0.276 MV m−1

(2.16)

Furthermore, Sarria et al. [90] inspected these results with different simulation frameworks such as Geant4 [91–93], GRanada Relativistic Runaway Simulator [94] and Runaway Electron Avalanche Model [81, 95]. The energy spectrum of electrons in RREA is thought to settle down in a steady state after accelerated for a few acceleration length. Because the electron flux f e increases e ≈ 2.71 times as electrons travel λ, its temporal evolution is expressed with an electron velocity v and the avalanche e-fold time τ = λ/v as d fe fe = . τ dt

(2.17)

2.5 Theories of Electron Acceleration in Thunderstorms

25

Fig. 2.18 Average energy of avalanche electrons in a function of electric-field strength (left) and simulation results of electron spectra in RREA (right). Reprinted from Dwyer et al. [83] under the CC BY 4.0 license

Since electrons obtain energy per a unit time d/dt = v(eE − Fd ), d d f e d fe d fe = = v(eE − Fd ) dt dt d d

(2.18)

is obtained. Therefore, the electron spectrum is formulated as  f () ∝ f 0 exp −

 . 7.3 MeV

(2.19)

Figure 2.18 left shows average electron energy in RREA, obtained by Monte-Carlo simulations. When an electric field higher than 400 kV m−1 exists in the standard atmosphere, the average electron energy is approximately 7.3 MeV, regardless of electric-field strength. Therefore, with this electric-field condition, Eq. 2.19 does not depend on electric-field strength. In fact, Monte-Carlo simulations confirmed that RREA spectrum follows an exponential function with a cutoff at ∼7.3 MeV above a few hundreds of keVs, as shown in Fig. 2.18 right. The accelerated electrons collide with ambient atmospheric nuclei, then emit bremsstrahlung. In the case of thin target, where electrons interact with the target once, a bremsstrahlung spectrum from electrons with monochromatic energy is proportional to  −1 , where  is an energy of bremsstrahlung photons, and exhibits a steep cutoff at the electron energy [96]. The bremsstrahlung spectrum from avalanche electrons Fγ is a convolution of a bremsstrahlung spectrum from monochromatic electrons and the electron spectrum. Therefore, it is approximately derived as [97]  Fγ ∝  −1 × exp −

 . 7.3 MeV

(2.20)

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2 Observational and Theoretical Overview of High-Energy Atmospheric Physics

This can reproduce the TGF spectrum obtained by RHESSI [2]. More precisely, this spectrum could be affected by atmospheric absorption and scattering. Around the RREA threshold E th , Coulomb scatterings significantly affect the RREA processes [86]. Thus, Eq. 2.16 is empirically modified around 300 kV m−1 as λ≈

5.1 MeV . eE − 0.285 MeV m−1

(2.21)

This RREA process in relatively low electric fields can be applied to discussions on gamma-ray glows. It is noted that λ becomes longer than several kilometers when electric fields are almost E th . In this case, these empirical relations cannot be applied because typical thunderstorms cannot maintain such large electric fields to realize the steady state of the RREA processes [86, 98].

2.5.2 Relativistic Feedback Processes The biggest problem of TGFs at the present is seed electrons. As in Eq. 2.15, the simple RREA process provides larger multiplication ratio with longer acceleration distance L, while longer distance than several kilometers is not plausible in thunderstorms. In fact, Dwyer [95] suggested that a multiplication factor of RREA exp(ξ ) cannot exceed 105 . In this case, the number of seed electrons is important to explain the enormous amount of energetic electrons in TGFs. However, Dwyer [97] estimated that the flux of seed electrons required for TGFs detected by RHESSI is 5 × 105 times larger than the maximum flux of atmospheric cosmic rays. Therefore, another mechanism to produce seed electrons is required. Dwyer [81] introduced the relativistic feedback model, as a complementary process of RREA. This model describes that secondary particles created in RREA supply energetic seed electrons by themselves (Fig. 2.19). Photons and electrons are thought to play a feedback role in this model. Bremsstrahlung photons emitted from runaway electrons travel to various directions, and produce energetic electrons via Compton scattering and photoabsorption. When these secondary electrons are produced in the upper of acceleration region, they can behave as seed electrons and trigger another avalanche. In the case of positron feedback, bremsstrahlung photons from avalanche electrons with energies of >1 MeV produce positrons via pair creation. In highly electrified region, they can become “runaway positrons” and move backward. Secondary electrons generated by the positrons via ionization also become seed electrons. These processes recursively increase the number of runaway electrons, not depending on the number of initial seed electrons in the atmosphere. Therefore, the relativistic feedback processes are a candidate to solve the seed-electron problem of TGFs. Let us consider a temporal evolution of electron flux by the relativistic feedback processes FRF [95]. As shown in Eq. 2.15, electron flux in normal RREA is FRREA = Fseed exp(ξ ). Introducing an e-folding time τ , FRF at a time point t is a sum of total

2.5 Theories of Electron Acceleration in Thunderstorms

27

Fig. 2.19 Examples of electron avalanches and relativistic feedback. Reprinted from Dwyer et al. [83] under the CC BY 4.0 license

runaway electrons generated by the feedback Fn (t), formulated as FRF =

t/τ

Fn (t),

(2.22)

n=0

where n is the generation of feedback. Fn (t) is included in a recursion formula with feedback parameter γ

t

Fn+1 (t) = γ

D(t − t  )Fn (t  )dt  .

(2.23)

0

The transportation function D(t − t  ) is approximated with the Dirac delta function σ as D(t − t  ) = σ (t − τ − t  ). Therefore, using the relation Fn+1 (t) = γ Fn (t − τ ),  0 (t < nτ ) Fn (t) = n γ Fseed exp(ξ ) (t ≥ nτ ) and FRF = Fseed exp(ξ )

t/τ

γn

(2.24)

(2.25)

n=0

are obtained. The formula of sequence summation t/τ

n=0

 γ = n

γ (t/τ )+1 −1 γ −1

γ = 1

(t/τ ) + 1 γ = 1

(2.26)

derives

FRF

⎧   ⎪ ⎨ Fseed exp(ξ ) exp(t/τ )/(γ − 1), τ ≡ τ/ ln(γ ) γ > 1 = Fseed (t/τ ) exp(ξ ) γ =1 ⎪ ⎩ γ 300 kV m−1 with enough acceleration distance exist around the streamers. A streamer is calculated to produce 1019 electrons s−1 . Assuming that 106 streamers are produced in the tip of a stepped leader, 1016 electrons with energies of several tens of keV can be produced in 1 ns. If these electrons are accelerated to MeV or tens of MeV, the number of energetic electrons is comparable to that in TGFs (∼1017 [102]) without any further avalanche processes. In addition, if ambient electric-field potential surrounding streamers reaches 300 MV, the electron spectrum in the thermal runaway electron process approximately follows exp(/6 MeV), whose bremsstrahlung spectrum is consistent with observed TGF spectra (Fig. 2.23 [99]).

2.5.4 Modification of Spectra Even in lower electric fields than the RREA threshold, charged particles in secondary cosmic rays can be accelerated against atmospheric attenuation [103, 104]. When electric fields are weaker than the runaway (0.216 MV m−1 at sea level) and avalanche (0.284 MV m−1 ) threshold, they cannot produce runaway electrons nor trigger avalanches. However, the electron spectrum of secondary cosmic rays extending to several hundreds of MeVs can be changed by the electric fields. This process is called “Modification of Spectra” (MOS [105, 106]) Chilingarian et al. [105, 106] and

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2 Observational and Theoretical Overview of High-Energy Atmospheric Physics

Fig. 2.23 Electron and gamma-ray spectra produced in potential drops around electron-seeding streamers. Reprinted from Celestin et al. [99] with permission from Wiley

Fig. 2.24 Gamma-ray spectra of secondary cosmic rays and an excess component created by MOS. Reprinted from Chilingaian et al. [106] with permission from Europhysics Letters

Cramer et al. [98] performed Monte-Carlo simulations that they input the cosmic-ray spectrum provided by EXPACS/PARMA model [107, 108] into a weak electric field. Figure 2.24 shows a comparison between an original cosmic-ray-induced gamma-ray spectrum and an excess component by MOS. The excess component is ∼10% of the original component, and extends to several tens of MeVs. This model is thought to be applied to gamma-ray glows and TGEs with low gamma-ray fluxes. This mechanism is also considered for acceleration and deceleration of muons. In fact, Hariharan et al. (2019) [109] demonstrated an existence of 1.3 GV potential inside a thundercloud by monitoring muons with the muon telescope GRAPE-3 installed in India.

2.6 Basics of Neutron Physics

31

Fig. 2.25 Cross sections of neutron reactions as a function of neutron kinetic energy, extracted from JENDL-4.0 [110]

2.6 Basics of Neutron Physics This section describes neutron reactions utilized in the present thesis. Here neutron energy is considered to be non-relativistic, which is justified by the fact that the typical energy of photoneutrons is less than 20 MeV, much lower than the neutron rest-mass energy of 940 MeV. Considering reactions with relatively light elements in the atmosphere or soil, there are four major reactions with neutrons: elastic and inelastic scatterings, neutron capture, and charged-particle production. Figure 2.25 shows cross sections of these reactions with nuclides considered in the present thesis such as 1 H, 14 N, 16 O, 27 Al, 28 Si, and 40 Ar.

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2 Observational and Theoretical Overview of High-Energy Atmospheric Physics

Fig. 2.26 Diagrams of an elastic scattering with a neutron in the laboratory frame and in the center-of-mass frame

2.6.1 Elastic Scattering Elastic scattering is the most major reactions with neutrons. Here kinetic energy of scattered neutrons is considered based on expertises in radiation engineering [111, 112]. Let us consider the situation shown in Fig. 2.26: a neutron is elastically scattered with an angle of θ L in the laboratory frame, or θ in the-center-of-mass frame. Considering the laws of conservation of energy and momentum, the ratio of kinetic energies of a neutron before (E) to after (E  ) the scattering is A2 + 1 + 2 A cos θ E = , E (A + 1)2

(2.28)

where A is the ratio of the neutron mass to a mass of a target nucleus. When θ = π , E  becomes its minimum as  E min =



A−1 A+1

2 E = α E,

(2.29)

where α = [(A − 1)/(A + 1)]2 is the collision parameter. Also E  becomes its max = E when θ = 0 (i.e. no collisions occur). Considering the relation imum as E max between the laboratory and center-of-mass frames, θ L is expressed as cos θ L = √

A cos θ + 1 A2

+ 1 + 2 cos θ

.

(2.30)

In the center-of-mass frame, the scattered neutron is emitted isotropically. Namely, the probability d P of neutron emission per unit steradian is dP =

sin θ dθ . 2

(2.31)

2.6 Basics of Neutron Physics

33

By differentiating Eq. 2.28,

and hence,

2 A sin θ dP = E, dθ (A + 1)2

(2.32)

dP dθ dP (A + 1)2 × = const. = = d E dθ d E 4 AE

(2.33)

are obtained. Namely, the energy distribution is constant in the range of α E ≤ E  ≤ E, like a square-wave shape. Therefore, the average of E  is calculated as

E =

E

E

αE

  dP 2A  . d E = E 1 − d E (A + 1)2

(2.34)

It is convenient to introduce the lethargy ξ = ln E/E   to consider averaged neutron energies after multiple elastic scatterings. By utilizing the equations derived above, E 

ξ = ln E/E  =

E dP d E E d E dP  αE d E d E

ln E

αE

=1+

A−1 (A − 1)2 ln 2A A+1

(2.35)

is obtained. When considering nuclei with a large atomic number A, ξ can be approximated as 2 ξ≈ . (2.36) A + 2/3 Therefore, when a neutron with an initial energy of E 0 is elastically scattered n-times, its expected energy after nth scatterings E n is expressed as E n = E 0 exp(−nξ ).

(2.37)

2.6.2 Inelastic Scattering As well as elastic scatterings, inelastic scatterings can also occur when kinetic energy of incident neutrons is higher than the lowest excitation level of target nuclei. In this case, the kinetic energy of incident neutrons are distributed not only to kinetic energies of the scattered neutron and nucleus, but also to excitation energy of the target nucleus. The excited nucleus immediately goes back to the ground state by emitting de-excitation gamma-ray lines.

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2 Observational and Theoretical Overview of High-Energy Atmospheric Physics

Table 2.1 De-excitation gamma-ray lines from neutron captures with 14 N, 27 Al and 28 Si 14 N 27 Al 28 Si Energy (MeV) Ratio (%) Energy (MeV) Ratio (%) Energy (MeV) Ratio (%) 1.678 1.885 2.000 2.520 3.532 3.678 4.509 5.269 5.298 5.533 5.562 6.322 7.299 8.310 10.829

26.66 62.86 13.76 18.69 29.94 48.63 55.96 100.00 71.10 65.57 35.77 61.05 31.45 13.80 47.89

0.031 0.983 1.408 1.623 2.108 2.283 2.59 2.821 3.034 3.465 3.591 3.849 4.133 4.260 4.691 4.734 4.903 5.134 7.693 7.724

100.00 15.77 11.11 16.49 10.04 16.85 15.05 13.98 31.54 25.09 16.85 11.11 24.73 24.37 16.49 19.71 11.11 10.75 11.83 96.06

1.273 2.093 3.539 4.934 6.38 7.199

24.05 27.85 100.00 93.50 16.04 10.04

2.6.3 Neutron Capture One of the major reactions which absorb neutrons is neutron captures. In this reaction, a target nucleus absorb a neutron, and transforms into an isotope. Furthermore, the produced isotope is excited by the binding energy of the neutron, and immediately goes back to the ground state by emitting de-excitation gamma-ray lines. The energy of de-excitation gamma rays corresponds to excitation levels of the produced isotope. Table 2.1 summarizes energies and branch ratios of de-excitation gamma rays by neutron captures with 14 N, 27 Al and 28 Si.

2.6.4 Charged-Particle Production It is possible that another nucleon is emitted when a neutron is absorbed by a target nucleus. The reaction absorbing a neutron and emitting a proton is called chargedparticle production. Only 14 N is capable of charged-particle production with low-

2.6 Basics of Neutron Physics

35

energy neutrons among nuclides considered in the present thesis. 14 C, the product of charged-particle productions by 14 N, is an important isotope for radiocarbon dating. They are usually produced by neutrons of cosmic-ray origin.

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Chapter 3

Instrumentation and Observation

Since 2006, we have been performing the Gamma-Ray Observation of Winter Thunderclouds (GROWTH) experiment, an on-ground observation program for highenergy phenomena during winter thunderstorms in Japan [1–4]. In 2015, we launched a mapping observation program; observation network with compact gamma-ray detectors has been constructed in coastal areas of the Japan Sea [5–10]. Because of gamma-ray attenuation in the atmosphere, a single detector can cover only an area within 1–2 km from its location. It is therefore important to deploy multiple gamma-ray detectors for covering wider area and for increasing the number of event detections. In addition, detections of an identical event by multiple detectors allow us to examine more detailed nature of the event such as spatial distribution of gamma-ray fluxes than by a single detector.

3.1 Winter Thunderstorms Winter thunderstorms in coastal areas of the Sea of Japan provide unique features comparing to other thunderstorms in the world (e.g. Rakov and Uman [12]), and they have been studied by sferics and radar observations since 1970s. During winter seasons in Japan, seasonal northwest winds are provided by Siberian Anticyclone staying on the Eurasian Continent and depressions on the Sea of Okhotsk and the Pacific. When these dried and cold winds pass over the Sea of Japan, water vapor is provided by the Tsushima Warm Current, which flows in the Sea of Japan from west to north. Then the winds bring heavy snow in coastal and mountainous areas in Japan. If ascending air currents take place in coastal areas, the winds also provide thunderstorms. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 Y. Wada, Observational Studies of Photonuclear Reactions Triggered by Lightning Discharges, Springer Theses, https://doi.org/10.1007/978-981-16-0459-1_3

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Fig. 3.1 A contour map of lightning density around Japan in winter (from November to March). Provided by Franklin Japan Co., Ltd. [11] Density of lightning is the number of lightning discharges JLDN recorded in a region. The data is accumulated in 10 years from 2010–2019. Copyright 2020 Franklin Japan Co., Ltd

Fig. 3.2 Contour maps of thunder days (left) and lightning density (right) around Japan. Provided by Franklin Japan Co., Ltd. [11] Thunder day is defined as the number of days that Japanese Lightning Detection Network (JLDN) recorded one or more lightning discharges in a region. Density of lightning is the number of lightning discharges JLDN recorded in a region. The data is accumulated in 10 years from 2010–2019. Copyright 2020 Franklin Japan Co., Ltd

3.1 Winter Thunderstorms

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Fig. 3.3 Comparison of thundercloud structures in summer and winter. Reprinted from Kitagawa and Michimoto [15] with permission of Wiley

Figure 3.1 presents a contour of lightning density around Japan during winter seasons (from November to March). While most parts of the main land of Japan are rarely struck by lightning discharges in winter seasons, a lot of discharges occur in the coastal areas of the Sea of Japan. Figure 3.2 also shows contours of thunder days and lightning density. Notably, lightning flashes occur in more than 40 days per year in the coastal region. The Japan Meteorological Agency reports that Kanazawa City, Ishikawa Prefecture in the Hokuriku area shows the greatest number of thunder days in Japan: 42.4 days per year on average from 1981 to 2010 [13]. On the other hand, the number of lightning strikes in Kanazawa is not as many as those in other regions. This indicates that winter thunderstorms frequently take place in Kanazawa, but each thunderstorm hosts a smaller number of lightning discharges in its lifecycle than summer ones. This unique feature of winter lightning is called “single-flash thunderclouds”, as Michimoto [14] reported. Winter thunderstorms taking place in coastal areas of the Sea of Japan have some unique features which do not appear in summer thunderstorms. The most important one is the cloud structure developed at a lower altitude than summer [15, 16]. Figure 3.3 shows structures of summer and winter thunderclouds. Typical thunderclouds have a tripolar structure of charges produced by collisions of ice crystals and droplets [17]. The altitude with a temperature of −10 ◦ C, where a negative charge region forms, is 5–6 km in summer, while ∼2 km in winter. The cloud top is at ∼15 km in summer while 5–7 km in winter, and cloud bases in winter also get lower around 0.2–0.8 km [18]. The lower altitude of cloud bases makes several distinctive features: In winter thunderstorms, the ratio of positive lightning, which discharges

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3 Instrumentation and Observation

positive charges in thunderclouds to the ground, to negative lightning is higher than in summer [19]. Upward lightning also frequently occurs, whose leaders develop from a tip of tall buildings into thunderclouds [20]. The lower cloud bases of winter thunderclouds make on-ground radiation measurements feasible. Electron ranges in the standard atmosphere at sea level are 3.8 m and 40.2 m at 1 MeV and 10 MeV, respectively, while mean free paths of gamma-ray photons are 122 m and 380 m at 1 MeV and 10 MeV, respectively. Since electrons and gamma rays generated above 1-km altitudes are absorbed before reaching the ground, gamma-ray glows produced in summer thunderstorms, whose cloud bases are higher than a 3 km altitude, cannot be detected at sea level. On the other hand, gamma rays generated in winter thunderstorms lower than 1 km can reach the ground. Based on these facts, on-ground radiation measurements during winter thunderstorms in Japan have been performed by Torii et al. [21–23], Yoshida et al. [24], and Kuroda et al. [25] besides the GROWTH collaboration.

3.2 Detector Development The present thesis employs original compact gamma-ray detectors with scintillation crystals which are sensitive to photons of several to tens of MeVs. We developed these detectors for the mapping observation program.

3.2.1 Scintillation Crystals We employ inorganic scintillation crystals as the main gamma-ray detection unit. Specification of representative inorganic crystals such as NaI, CsI, BGO (Bi4 Ge3 O12 ), GSO (Gd2 SiO5 ), LaBr3 , and a plastic scintillator EJ-200 for comparison is shown in Table 3.1. When gamma-ray photons enter scintillators, either photoabsorption,

Table 3.1 Specification of scintillation crystals [26–28] Type (doped element) NaI (Tl) CsI (Tl) BGO Density (g cm−3 ) Refractive index Decay time (ns) Light output (photons MeV−1 ) Peak wavelength (nm) Deliquescence

GSO (Ce) LaBr3 (Ce)

EJ-200

3.67 1.85 230 38,000

4.51 1.80 680 65,000

7.13 2.15 300 8,200

6.71 1.85 56 9,000

5.08 1.9 16 63,000

1.02 1.58 2 10,000

415 Yes

540 Slightly

480 No

440 No

380 Yes

425 No

3.2 Detector Development

45

Fig. 3.4 Probability of photoabsorption, Compton scattering, and pair production with gamma rays in 2.5-cm-thick scintillators, extracted from NIST/XCOM [29]

Fig. 3.5 A schematic view of Type 1 BGO, a cuboid of 25.0 × 8.0 × 2.5 cm3

Compton scattering or pair creation takes place stochastically. Figure 3.4 shows reaction probability between gamma rays and scintillators of 2.5 cm thickness. In general, scintillators including heavy nuclei such as Bi and Ge have large cross section of photoabsorption. In the present study, three types of scintillators, BGO, NaI, and GSO are employed. We utilized two types of shape for BGO crystals. Type 1 is a cuboid of 25.0 × 8.0 × 2.5 cm3 , shown in Fig. 3.5. The crystals are coupled with two photomultipliers (PMTs: Hamamatsu R1924), and shielded by 3-mm-thick aluminum.

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3 Instrumentation and Observation

Fig. 3.6 Cross sections of neutron capture with Gd isotopes, extracted from JENDL-4.0 [30]

Fig. 3.7 Probability of neutron capture in 5-mm-thick GSO scintillators, calculated with JENDL-4.0 [30]

They are provided by Sakurai Radioactive Isotope Group, RIKEN Nishina Center and Nuclear Experiment Group, The University of Tokyo. Type 2 is a cylinder of φ7.62 cm × 7.62 cm, coupled with a PMT (Hamamatsu R6231) and shielded by 3-mm-thick aluminum. BGO crystals are suitable for detection of ≥10 MeV gamma rays due to large cross section and high density, although light output is only 22% of NaI. In addition, they are not suffered from high humidity in winter because they are not deliquescent. A NaI scintillator used in this study is also a cylinder of φ7.62 cm × 7.62 cm, coupled with a photo-multiplier (Hamamatsu R1306) and shielded by 3-mm-thick aluminum. GSO scintillators are a cuboid of 2.0 × 2.0 × 0.5 cm3 , which are spares for the Hard X-ray Detector onboard the X-ray Astronomy Satellite “Suzaku”. These are connected with a photo-multiplier of Hamamatsu R7600U. GSO scintillators are employed for neutron detection, rather than photon detection. Figure 3.6 shows cross sections of neutron-capture reactions with 155 Gd, 156 Gd, 157 Gd and 158 Gd included in GSO crystals. Among Gd isotopes, nuclei containing an odd number of neutrons have a large cross section to neutrons, and they have been utilized as neutron detectors [31–33]. When the Gd nuclei capture a neutron, they emit de-excitation gamma rays; 155 Gd mainly emits gamma-ray lines at 88.97 and 199.22 keV, and 157 Gd at 79.51 and 181.94 keV. Since the de-excitation gamma-ray lines are self-absorbed in the GSO scintillators, the large cross section of GSO scintillators to neutrons allowed us to use them as thermal neutron detectors. Neutron-capture probability of 5-mm-thick GSO scintillators used in this study is shown in Fig. 3.7.

3.2 Detector Development

47

3.2.2 Data Acquisition System Minimizing data acquisition (DAQ) system is a key to develop compact gamma-ray detectors, because other components such as scintillators have to be as large as possible to enlarge effective areas to gamma rays. Therefore, we developed a dedicated DAQ system for the mapping observation program. It consists of three components: a field-programmable gate array/analog-to-digital converter (FPGA/ADC) board, an analog processing board to be connected with PMTs, and a small Linux computer Raspberry Pi. A summary of the DAQ system is shown in Fig. 3.8. The GROWTH FPGA/ADC board was developed by Dr. Takayuki Yuasa and Shimafuji Electric Incorporated [34]. Two 12 bit/2 ch flash ADC chips (Analog Devices AD9231; 4 ch in total) and an FPGA chip (Xilinx Artix-7 XC7A35T-2FTG256C) are onboard. The dimension of the FPGA/ADC board is 9.5 × 9.5 cm2 . This board obtains pulse signals by self-triggered and event-by-event schemes. Input signals (±5 V) are buffered by a differential amplifier, digital-sampled by a 50 MHz ADC. The digitized signals are then sent to the FPGA. The FPGA always store 20 samples (for 400 ns at 50 MHz sample rate). When the FPGA detects a signal exceeding a trigger threshold in the 20 samples, it stores following 500–1000 samples (10–20 µs at 50 MHz). Two types of trigger thresholds are employed: fixed thresholds and differential thresholds based on running average. In the stored samples, detection time, triggered channel, trigger number, the maximum, minimum, first, and last values are extracted. The trigger number counts up every detected event. If a pulse event is triggered but not properly transferred to Raspberry Pi, the corresponding trigger number is not registered in the event list. Detecting the unrecorded trigger number is utilized for the dead-time correction.

Fig. 3.8 An overview of the DAQ system. Left-top: the GROWTH daughter board on the GROWTH FPGA/ADC board. Left-bottom: the GROWTH FPGA/ADC board with a Raspberry Pi. Right: a schematic diagram of the system

48

3 Instrumentation and Observation 100 pF 100 pF

51 kOhm 100 kOhm

input

3

20 kOhm

200 pF 1

3

2

10 kOhm

LM6172

5 kOhm 1

2 LM6172

10 kOhm

3 1 2 LM6172

Acharge

amplifier

shaping amplifier

output 50 Ohm

gain adjuster

Fig. 3.9 A circuit diagram of the charge and waveform-shaping amplifiers onboard the GROWTH daughter board

The FPGA can be connected with a global positioning system (GPS) receiver, and calibrate the detection time with better than 1 µs accuracy. The extracted data by the FPGA is transferred to a Raspberry Pi computer by the Universal Asynchronous Receiver/Transmitter (UART) protocol via a USB driving device FT2232HL. The theoretical maximum rate of data transfer is 36 kHz with the maximum speed of UART (8 Mbps). However, an effective transfer rate is limited up to ∼10 kHz because the processing ability of Raspberry Pi is not enough to receive all event packets. In addition, another ADC (Microchip Technology MCP3208) and digital-analog convertor (DAC; Microchip Technology MCP4822) chips controllable by Raspberry Pi with Serial Peripheral Interface (SPI) are onboard. This ADC is connected to onboard current sensors, and monitors power supply modules to record housekeeping data of the DAQ system. For analog processing, we utilize the GROWTH daughter board to read signals from PMTs with the GROWTH FPGA/ADC board. The daughter board was developed and designed by the author, manufactured and soldered by p-ban.com Corp. Its dimension is 9.5 × 9.5 cm2 , and can be stacked on the GROWTH FPGA/ADC board (the left-top picture of Fig. 3.9). On the daughter board, 4 ch charge amplifiers, waveform-shaping amplifiers, and high-voltage (HV) supply modules to PMTs are mounted. A circuit diagram of the charge and waveform-shaping amplifiers is shown in Fig. 3.9. The amplifiers consist of 3 channels of operation amplifiers (Texas Instruments LM6172). The time constants of charge and waveform-shaping amplifiers are 10 and 2 µs, respectively. We employ Matsusada OPTON-1.5PA-12 as a HV module for PMTs. Their output voltage is controlled by reference voltage or a potentiometer from 0 to 1500 V. In the present case, the reference voltage was produced by the Raspberry-Pi-controlled DAC and connected to the HV module via a buffer circuit. Besides the amplifiers and HV modules, a GPS receiver (Global Top FGPMMOPA6H), a small liquid-crystal display and an environmental sensor recording humidity, temperature, and pressure (Bosch Sensortec BME280) are onboard. Signals from these devices are transferred to the FPGA/ADC board and Raspberry Pi. The FPGA/ADC board, daughter board, HV module and Raspberry Pi consume 3.1, 1.7,