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Springer Series in Plasma Science and Technology Shunjiro Shinohara High-Density Helicon Plasma Science From Basics to Applications Springer Series in Plasma Science and Technology Series Editors Michael Bonitz, Kiel, Germany Rudolf Neu, Garching, Germany Tomohiro Nozaki, Tokyo, Japan Jozef Ongena, Brussel, Belgium Hideaki Takabe, Faculty of Engineering, Osaka University, Osaka, Japan Zensho Yoshida, National Institute for Fusion Science, Toki, Gifu, Japan Plasma Science and Technology covers all fundamental and applied aspects of what is referred to as the “fourth state of matter.” Bringing together contributions from physics, the space sciences, engineering and the applied sciences, the topics covered range from the fundamental properties of plasma to its broad spectrum of applications in industry, energy technologies and healthcare. Contributions to the book series on all aspects of plasma research and technology development are welcome. Particular emphasis in applications will be on high-temperature plasma phenomena, which are relevant to energy generation, and on low-temperature plasmas, which are used as a tool for industrial applications. This cross-disciplinary approach offers graduate-level readers as well as researchers and professionals in academia and industry vital new ideas and techniques for plasma applications. Shunjiro Shinohara High-Density Helicon Plasma Science From Basics to Applications Shunjiro Shinohara Tokyo University of Agriculture and Technology Tokyo, Japan ISSN 2511-2007 ISSN 2511-2015 (electronic) Springer Series in Plasma Science and Technology ISBN 978-981-19-2899-4 ISBN 978-981-19-2900-7 (eBook) https://doi.org/10.1007/978-981-19-2900-7 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 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 Preface Plasma exhibits many interesting phenomena from earth to space in an unusually wide range of density and temperature parameters. Often, drastic changes in structural formation can be attributed to inherent nonlinear behaviors, and therefore, several practical applications based on fundamental understandings have been accomplished. From the end of the 20th century, remarkable progress has been witnessed in plasma science, and this has contributed to enriching our daily lives. To this end, the development of plasma sources is crucial for further advanced studies and applications. The helicon wave plasma source is a promising candidate among the many developed sources of plasma. The helicon source has attracted considerable research attention, and several research studies focused on the fundamental to industrial application fields have been conducted; this is because we can easily achieve a high electron density (~ 1013 cm−3) with flexible external operation parameters. A helicon wave can be excited in a radio frequency region in the pres- ence of external magnetic fields under a relatively low fill gas pressure. Although this advantage of helicon plasmas is well-recognized, to the best of my knowledge, there are no book that have studied helicon plasma science in a unified manner, despite some review papers published, including ours. In this book, bearing the contemporary helicon plasma advancements, I attempted to survey the up-to-date results over a wide area of basic understandings and applications, including our research, which exhibited a mixed feature of a textbook, specialized book, and monograph. This book is organized as follows: In Chap. 1, general plasma characteristics that exist universally in our whole world are explained for a non-specialist, a beginner of plasma science, or an undergraduate student, as an introduction. Then, descriptions of a variety of plasma and its waves, stressing the importance of plasma sources, especially the helicon plasma source, are mentioned. Furthermore, in Chap. 2, the fundamentals of plasma are presented for a review and confirmation of basic plasma understanding. Plasma diagnostics tools are included briefly but extensively for practical use. The lists of useful and convenient constants v vi Preface and formulas are also provided. Considering some of the difficult points for begin- ners, I have attempted to insert some essential descriptions that are not provided in several textbooks, neatly and carefully. Readers without background knowledge on introductory plasma physics can go through the succeeding chapters that focus on helicon science by reading the first two chapters and the beginning part of Chap. 3. Here, relatively wide but not very deep descriptions have been provided considering the objectives and length of the book. Therefore, I believe that the first two chapters benefit from introducing plasma science independently, regardless of the succeeding chapters on helicon plasma. When further interests arise, readers can investigate many journal papers and information listed in the Reference section of every chapter. For a quick study, most of Sects. 2.4, 2.5.2–2.5.7, and 2.7.2–2.7.4 can be saved. If readers have sufficient knowledge of the fundamentals of plasma, they can skip Chaps. 1, 2, Sect. 3.1 and move to the main contents of helicon plasma science. In Chap. 3, the cold plasma dispersion relation and its wave characteristics are introduced. Then, helicon wave physics from basic features and highly efficient production mechanism, which has been controversial, are described. Some of the essential characteristics of helicon plasma sources are introduced, for example, plasma size and dependencies on external operational parameters. As an Appendix, I briefly present the experimental Radio Frequency (RF) system after the ray tracing technique, where geometrical approximation can be satisfied. This is practically important because experimental results obtained using this system can be compared with the theoretical/numerical results. In Chap. 4, miscellaneous examples of helicon plasma sources with characteriza- tion are provided; these plenty of examples include basic wave characteristics, control of plasma behavior, and torus experiment, followed by common plasma phenomena of mode transition, neutral density effect, and various instabilities. Then, several applications are presented, including plasma thrusters, nuclear fusion, and industrial applications. Finally, in Chap. 5, various helicon plasma performances described so far from Chaps. 1 to 4 are summarized. The future aspects from the fundamentals to applications in the helicon plasma science are discussed, and a final concluding remark is provided; these indicate the promising future in expanding helicon science. This book, which provides content covering the basics to the applications of extensive helicon plasma science, is useful for various readers (e.g., scientists, researchers, industry experts, and students) interested in this attractive field that has global perspectives. Experimental and practical viewpoints, sometimes with careful and detailed descriptions, have been added. Further, I have provided physical interpreta- tions, with an attempt to present a broad view, and/or mentioned other related fields when necessary. As mentioned previously, some essential contents/points described in this book are not provided in general textbooks. These points are helpful for diversified readers, and occasionally, I have inserted a reference so that readers can confirm the provided content and review the related articles. In this book, I attempted to use SI unit unless otherwise specified; however, mixed expressions with CGS unit may be present at some instances because of customary Preface vii use and the cited references and graphs. Further, a list of symbols and abbreviations of physical quantities has been provided before Chap. 1 and the definitions are given repeatedly for easy recognition; in addition, you can refer to the index provided at the end of the book. I have strictly distinguished frequency from angular frequency because there is a large difference of 2π between the two in the calculations; this is not considered in most textbooks. I believe that there are almost no books describing the recent review on extensive helicon plasma science in a unified manner. I also believe that most of this content will be useful over a long time because the essential physics is also included. This book has been written based on my rich and broad experiences in the University of Tokyo, Kyushu University, and Tokyo University of Agriculture and Technology in Japan with many domestic and international research collaborations: from low- temperature (such as fundamental plasma physics partly aiming at plasma application, including broad helicon science and helicon utilized thruster using many kinds of linear machines) to high-temperature plasma (such as the nuclear fusion field, using tokamaks and reversed field pinch devices). Several of my discussions with people from myriad areas of science were also helpful. Professor R. Boswell has made a great contribution to helicon studies from the early phase, and remarkable progress has been found by many researchers and their collaborators, who are mentioned in this book; these researchers include, in the alphabetical order but excluding us, Profs. A. Ando/K. Takahashi, C. Charles, F. F. Chen, C. S. Corr, T. Klinger/O. Grulke, M. Krämer, J. Scharer, E. Scime, T. Shoji/Y. Sakawa, and G. Tynan/S. C. Thakur, and by research groups, e.g., in Ad Astra Rocket Company and Oak Ridge National Laboratory. I hope that this book will be valuable for readers interested in helicon plasma science (and for those who need only fundamental knowledge on plasma physics presented in Chaps. 1 and 2). I believe that the general method of thinking over plans and performing research presented will benefit readers’ miscellaneous advancements through this book. In writing this book, I would like to thank many people for their continuous encouragement, crucial discussions, and comments. First, I appreciate the fruitful, collabo- rative research on helicon science executed with late Dr. K. P. Shamrai; late Prof. K. Toki, who was a good friend of mine since high school; Prof. Em. T. Tanikawa; Prof. Em. T. Hada; and Prof. A. Fruchtman. Next, I greatly appreciate the research discus- sion and contributions provided by my team members, including the above people, for our Helicon Electrodeless Advanced Thruster (HEAT) project, supported by the Grants-in-Aid for Scientific Research (so-called “KAKENHI”), the Japan Society for the Promotion of Science: Profs. I. Funaki, H. Nishida, and D. Kuwahara, Drs. F. Otsuka, T. Matsuoka, T. Motomura, T. Nakamura, S. Isayama, and T. Furukawa, and many others. Furthermore, I wish to acknowledge the graduate and undergraduate students in my past laboratories at the University of Tokyo, Kyushu University, and Tokyo University of Agriculture and Technology for their tireless efforts, which contributed to fruitful research studies. viii Preface In addition, I would like to thank Prof. Em. F. F. Chen and Dr. V. Godyak for their continuous encouragement and kind advice, and my past mentors, late Prof. Em. K. Miyamoto, late Prof. Em. H. Toyama, late Prof. Em. N. Inoue, and Prof. Em. Y. Kawai, for their guidance in exploring the fascinating plasma science fields with enthusiasm and encouragement. I am also grateful for the intensive and extensive discussions and information exchanges with numerous researchers during many conferences and my domestic and oversea visits; they have helped me improve myself. In writing this book, I would like to thank again Profs. Fruchtman, Tanikawa, Hada, and Kuwahara, Drs. Isayama and Furukawa; and Prof. S. Nishimura, for their valuable comments and information to improve the present book. Needless to say, the considerable efforts invested by Dr. A. Tokuno (the editor of this book) must be appreciated, in addition to Ms. K. Raghunathan and Mr. A. Vinoth (project coordinators of the book). Without any help and support from the people mentioned above, this book would not have been published. Finally, I wish to thank my whole family, especially my wife, Hiroko Shinohara, who supported me for a long time and ensured that ideal surroundings were main- tained to enable me to do my best. At the very end, I would like to dedicate my book to my late father Chimaki Shinohara and my late father-in-law Yukio Nose. Both continue to enjoy their lives in another world, after publishing individual books in fields different from my own, a long time ago. Tokyo, Japan Shunjiro Shinohara On a Pleasant Spring Day in 2022 Contents 1 Introduction ................................................... 1 1.1 Plasma World .............................................. 1 1.2 Plasma Waves .............................................. 4 1.3 Importance of Helicon Plasma Source ......................... 7 References ..................................................... 8 2 Fundamentals of Plasma and Its Diagnostics ...................... 11 2.1 Basic Plasma Properties ..................................... 11 2.1.1 Plasma Oscillation ................................... 12 2.1.2 Debye Sheath ....................................... 13 2.1.3 Plasma Conditions and Definition of Temperature ........ 14 2.2 Plasma Generation .......................................... 16 2.3 Motion of Charged Particles ................................. 17 2.3.1 Cyclotron Motion .................................... 18 2.3.2 Drift Motion ........................................ 19 2.3.3 Magnetic Moment ................................... 21 2.4 Plasma as Fluids ........................................... 26 2.4.1 Kinetic Description and Maxwell Transport Equation ..... 27 2.4.2 Magnetohydrodynamic Equations ...................... 29 2.4.3 Simplified Magnetohydrodynamic Equations ............. 33 2.5 Transport Process .......................................... 36 2.5.1 Collision and Resistivity .............................. 37 2.5.2 Diffusion Parameters ................................. 41 2.5.3 Ambipolar Diffusion ................................. 42 2.5.4 Diffusion Across the Magnetic Field .................... 43 2.5.5 Diffusion in a Cylinder and Recombination .............. 45 2.5.6 Anomalous Diffusion ................................. 47 2.5.7 Wall Conditions ..................................... 49 2.6 Equilibrium and Stability .................................... 52 2.6.1 Plasma Equilibrium .................................. 53 2.6.2 Plasma Instabilities ................................... 56 ix