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Effects of Secondary Electron Emission on the Plasma Sheath Effects of Secondary Electron Emission on the Plasma Sheath and Local Electron Energy Distribution with Application to Hall Thrusters by Kapil Umesh Sawlani A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Nuclear Engineering and Radiological Sciences) in The University of Michigan 2015 Doctoral Committee: Associate Professor John E. Foster, Chair Professor Alec D. Gallimore Professor Ronald M. Gilgenbach Professor Mark J. Kushner Yevgeny Raitses, Princeton Plasma Physics Laboratory \If you want to inform yourself only roughly about something, present a paper about the subject; but, if you want to gain an in-depth knowledge about it - you have to write a book." - Richard Kieffer © Kapil Umesh Sawlani 2015 All Rights Reserved To my parents and uncle Jay Datwani. Thank you for the constant support and believing in me. ii ACKNOWLEDGEMENTS The journey to achieve this degree has been a very interesting one. From the kid who didn't really want to study to the high school student who was very interested in everything mechanical and wanted to be a rocket scientist some day. Having been through various peaks and valleys of academic environment and expectations, I would like to say the overall journey was worth it. This achievement would not have been even remotely possible had it not been through the support, guidance and encouragement from various people. This section lists only a few of them but there are so many many more that I will always remember and thank for what they did in order to shape my success at different points. Firstly, I would like to thank Prof. John E. Foster, my dissertation advisor as well as mentor, who has been encouraging me to succeed through out the journey as well as has been patient with me. Before being my thesis advisor, he was the first professor whose class (NERS 471 - Introduction to Plasma Physics and Controlled Fusion) I enrolled in at the University of Michigan. My desire to learn more about space propulsion existed since my undergraduate days and being presented an opportunity to discuss and work on this project was rewarding. With Prof. Foster I had the opportunity to work on many other projects over the years which will definitely help me through my career. All I can say is, thank you for all the opportunities provided to me. The number of skills learned in the duration would not have been possible at any other place or time. Secondly, my committee members who have been supportive through out the iii Ph.D. process - Prof Gallimore, Prof. Gilgenbach, Prof. Kushner and Dr. Raitses. There was a lot I learned from you in classes that you offered and our personal interactions, as well as part of my PhD experience. The guidance helped me think better about tough problems. In addition to the academic faculty, having good colleagues and friends made the journey a lot easier. The members from Plasma Science and Technology Laboratory - Aimee, Ben, Brad, Brandon, Eric, Sarah, Alex - It was enjoyable working with you and learning from your experiences. The new group - Janis, Yao, Adrian, Neil, Selman, Kenneth and Karl, it was a pleasure meeting you all and working with you for a short duration. I hope I was able to part some of the knowledge I received from the previous PSTL members. I would also like to thank the undergraduate students (some of who are now graduate students) who worked with me making it truly a good teaching and learning experience - Athena, Yen Ying, Alison, Patrick, Joowon, Zachary, Joshua, Abraham, and Alexader and Nate. Thank you all !! In addition, I would like to thank a lot of other group members from PEPL, NGPD, CPSEG, and many others from NERS and EECS. From building electronic circuits and understanding automation systems from Aaron Borgman and David McLean to trying my hands at the art of glass blowing with Harold Eberhart, and learning how to machine and how to machine efficiently from Kent Pruss and Marv Cressey was one of the best experiences of graduate school. I cannot thank you all enough for all the support and guidance you have been. The friendship that developed as part of working with you all would be something I would definitely miss in the months and years to follow. I also must thank many staff members in NERS who have helped me to get required hardware or software in short term notice, or for ordering lab equipment as well as providing administrative support throughout for academic and non-academic issues. Ed Birdsall, James White, Caroline, Cherilyn, Peggy, Rose, Sheena and others, iv I will always remember your support and friendship. A special shout out to Rachel for all her support throughout graduate school and making me realize the size of UM libraries. I would also like to thank many friends I made at the UM libraries over the years. To my relatives and friends, thank you for being there and keeping me in the loop even though there were times I got too caught up with graduate school related tasks. I would also like to thank you for the good wishes. Finally, I would like to say special thanks to my parents and uncle Jay Datwani. The guidance and wisdom they offered helped me remain calm and focus on the task. It would not have been possible without the love and support provided. There are so many others that deserve acknowledgement for their support at different times in my life that allowed me to reach this stage. I apologize for not having you listed here. Kapil Umesh Sawlani 2015 v TABLE OF CONTENTS DEDICATION :::::::::::::::::::::::::::::::::: ii ACKNOWLEDGEMENTS :::::::::::::::::::::::::: iii LIST OF FIGURES ::::::::::::::::::::::::::::::: x LIST OF TABLES :::::::::::::::::::::::::::::::: xv LIST OF ABBREVIATIONS ::::::::::::::::::::::::: xvi LIST OF SYMBOLS :::::::::::::::::::::::::::::: xviii ABSTRACT ::::::::::::::::::::::::::::::::::: xxi CHAPTER I. Introduction .............................. 1 1.1 Problem Statement . 1 1.2 Crossed Field Plasma Devices . 2 1.3 Research Objectives and Goals . 2 1.4 Dissertation Hypothesis . 3 1.5 Dissertation Organization . 4 II. Theoretical Considerations ..................... 7 2.1 Introduction . 7 2.2 Plasma Material Interaction . 9 2.2.1 Basic Plasma Physics . 10 2.2.2 Need for Plasmas . 11 2.2.3 Reaction Rate . 12 2.2.4 Influence of Magnetic Fields . 16 2.2.5 Plasma Sheath Theory . 18 2.2.6 Electron Energy Distribution Function . 25 2.3 Secondary Electron Emission . 33 vi 2.3.1 Energy Loss of Primary Electrons . 34 2.3.2 Secondary Electron Emission Yield . 35 2.3.3 SEE in Vacuum . 36 2.3.4 Influence of SEE on Plasma Sheath . 38 2.3.5 Influence of SEE on Plasma EEDF . 39 2.4 Space Propulsion . 40 2.4.1 Different Propulsion Technologies . 44 2.4.2 Why Electric Propulsion? . 44 2.4.3 Hall Thruster Design . 46 2.4.4 Hall Thruster Operation . 47 2.4.5 Complex Interactions . 50 2.4.6 Magnetic Shielding . 52 2.5 SEE and Hall Thrusters . 52 III. Bench-top Experimental Apparatus and Setup . 54 3.1 Introduction . 54 3.2 Vacuum Facilities . 56 3.2.1 Tall Cylindrical Chamber . 57 3.2.2 `Rocket' Chamber . 57 3.3 Variable Magnetic Field Bench-top Apparatus . 58 3.3.1 Helmholtz Coil . 58 3.4 Impact Angle . 64 3.5 Plasma Sources . 66 3.6 Electron Beam Source . 66 3.7 Materials: Preparation and Surface Characterization . 69 3.7.1 Copper . 69 3.7.2 Graphite . 73 3.7.3 Boron Nitride (HP Grade) . 73 3.8 Manufacturing and Assembly . 77 3.9 Computer Programs for Data Acquisition and Control . 79 IV. Plasma and Electron Beam Diagnostics . 83 4.1 Langmuir Probes Diagnostics . 83 4.1.1 Orbital Motion Limited Theory . 87 4.1.2 Electron Energy Distribution Function . 87 4.1.3 Sheath Size in Langmuir Probe Operations . 88 4.1.4 Plasma Parameters . 90 4.1.5 Second Derivative of a Langmuir Probe . 91 4.1.6 Numerical Smoothing and Differncing Schemes . 92 4.1.7 Multi-Component Plasma Environment . 105 4.1.8 Experimental Approach . 107 4.1.9 Langmuir Probe Construction and Circuit . 109 4.1.10 Sample Langmuir Probe Data Analysis . 110 vii 4.1.11 Problems with Langmuir Probes . 115 4.2 Emissive Probe Diagnostics . 121 4.2.1 Theory of Emissive Probes . 122 4.2.2 Probe Construction Techniques . 123 4.2.3 Emissive Probe Methods for Plasma Potential Deter- mination . 123 4.2.4 Emissive Probe Construction . 126 4.2.5 Experimental Procedure and Electrical Circuit . 127 4.2.6 Sample Analysis of Emissive Probe Data . 128 4.2.7 Influence of Magnetic Field on Emissive Probes . 128 4.3 Retarding Potential Analyzer . 130 4.3.1 Probe Design . 133 V. Low-Cost, Low-Energy, High-Current Electron Gun . 136 5.1 Introduction . 136 5.2 Thermionic Emission . 138 5.2.1 Richardson-Dushman Equation . 140 5.2.2 Cathode Coatings . 142 5.3 Experimental Setup . 144 5.3.1 Electrical Circuit for the Electron Gun . 146 5.4 Electron Beam Characterization in Vacuum . 147 5.4.1 Beam Perveance . 147 5.4.2 Spatial Profile of Beam . 148 5.4.3 Beam Energy Characteristics using RPA . 151 5.5 Electron Beam Operation in Plasma . 153 5.5.1 Beam Energy Characterization using RPA . 153 5.6 Electron Beam Characterization in a Uniform Magnetic Field in Vacuum . 156 VI. Results and Discussion . 160 6.1 Discharge Characterization . 160 6.2 Presence of SEE . 166 6.3 Sheath Behavior in Presence of SEE . 168 6.4 EEDF Behavior in Presence of SEE . 187 6.5 Post Operation Material Analysis . 198 VII. Conclusion and Future Work . 204 7.1 Summary of Research Intent .
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