To my Grandmother… ii “Understanding is a personal achievement, won only at the cost of constant intellectual struggle and reflection.” – Preface to Statistical and Thermal Physics by H. Gould and J. Tobochnik. iii Acknowledgement This research has been made possible through financial support from Busek Co. Inc., Worcester Polytechnic Institute (WPI), the Massachusetts Space Grant Consortium (MASGC), the National Aeronautics and Space Administration and the Department of Defense (DoD). This experience has changed the trajectory of my career and my life, for that I am forever grateful to have been afforded this opportunity. I would not have been able to complete this work without assistance and support from a number of people. First and foremost, I would like to thank my advisor, Prof. John Blandino, for taking me on as a PhD candidate and his sustained support throughout the duration of this work. His guidance and seemingly limitless patience were directly responsible for my growth as a scientist, as a teacher and as a person, and the success of this research effort. I would like to thank the members of my committee; Prof. Nikolaos Gatsonis and Prof. Michael Demetriou from WPI and Dr. James Szabo from Busek Co. Inc., for their time and valuable comments. Dr. Szabo, his guidance and commitment to experimental research demonstrated that persistence might be the best tool a researcher can have in their toolbox. I am grateful to Vlad Hruby and the entire Busek Co. Inc. family for their support throughout my journey over the past six years. Special thanks to Lauren Lee for her continued support, guidance and encouragement throughout my time at Busek. Mike Robin, for all his help getting the cathode to operate on iodine and everything else iodine related. Chris Grenier for always keeping me honest and all his help machining parts and fabricating test setups. Dan Courtney, for his invaluable guidance and numerous discussions, and more specifically, his assistance with the uncertainty analysis for my measurements. There are so many others at Busek who always provided their assistance including, but not limited to, Surjeet Paintal, Larry Byrne, Chas Freeman, Bruce Pote, Yu-Hui Chiu and Lynn Olson. During my time as a full time graduate student I would like to thank Barbara Edilberti, Barbara Furhman and Donna Hughes for all their help. I would like to thank WPI for three degrees, and all of the Fluids iv and Plasma Dynamic Laboratory (FPDL) students and professors who I worked with throughout my years as a full time graduate student. I am grateful to Adriana Hera for her constant willingness to help me with my MATLAB code. And to Sergei Averkin, although our work together did not make it into my thesis, I appreciate all of our long lunchtime discussions and coffee breaks. I am also grateful to Dan Asselin for getting me started in the FPDL at WPI and for his continued friendship. Although Dan moved on to another university to continue his PhD, he remained a constant source of support and encouragement, always lending an ear even though he was going through his own, similar struggles. It is difficult to overstate his contributions my growth personally and professionally. Throughout this journey I have been fortunate to have the lifelong support of my friends and family. To my parents, thank you for everything from never missing a hockey game to helping me turn the garage into a science project construction site, you have been nothing but encouraging. My siblings, Jared and Amanda, you are two of the most inspiring people I know and are changing the world one young person at a time. You two have been more than encouraging, but rather a foundation for me to grow from— knowing that you would always be there to support me provided me great confidence. To my grandmother, for whom this work is dedicated, I am forever indebted to you for all of the love, time and support you have given me throughout my entire life. You are the anchor that my entire support network is derived from, which gave me the ability to lead my best life. Thank you. v Table of Contents Acknowledgement ...................................................................................................................................... iv Table of Contents ....................................................................................................................................... vi List of Tables ............................................................................................................................................ viii List of Figures .............................................................................................................................................. x List of Symbols .......................................................................................................................................... xv Abstract ................................................................................................................................................... xviii Chapter 1 Introduction ......................................................................................................................... 1 Chapter 2 Background ......................................................................................................................... 7 2.1 Electrostatic Propulsion ................................................................................................................ 8 2.1.1 Ion Engines ........................................................................................................................... 8 2.1.2 Hall Effect Thrusters ........................................................................................................... 10 2.2 Hollow Cathodes ......................................................................................................................... 12 2.3 Iodine as a Propellant for Electrostatic Thrusters ....................................................................... 23 2.4 Plasma Physics ............................................................................................................................ 28 2.4.1 Electodynamics and Single Particle Motion ....................................................................... 28 2.4.2 Sheaths ................................................................................................................................ 32 2.4.3 Plasma Characteristics ........................................................................................................ 38 2.4.4 Distribution Functions......................................................................................................... 39 2.4.5 Collision Processes ............................................................................................................. 43 2.4.6 Iodine Literature Review .................................................................................................... 51 Chapter 3 Experimental Methods ..................................................................................................... 60 3.1 Emissive Probes .......................................................................................................................... 60 3.1.1 Theory of Operation—Floating Point Technique ............................................................... 60 3.1.2 Uncertainty Analysis ........................................................................................................... 63 3.2 Langmuir Probes ......................................................................................................................... 67 3.2.1 Theory of Operation ............................................................................................................ 67 vi 3.2.2 Plasma Density .................................................................................................................... 70 3.2.3 Druyvesteyn Method ........................................................................................................... 73 3.2.4 Second Harmonic Method .................................................................................................. 76 3.2.5 Uncertainty Analysis ........................................................................................................... 78 Chapter 4 Experimental Instrumentation and Apparatus .............................................................. 84 4.1 Emissive Probe ............................................................................................................................ 84 4.2 Langmuir Probe .......................................................................................................................... 87 4.3 Hexaboride Cathode Experimental Setup ................................................................................... 92 4.4 BaO Cathode Experimental Setups ............................................................................................. 95 4.4.1 BaO Cathode – Configuration 1 .......................................................................................... 95 4.4.2 BaO Cathode – Configuration 2 ........................................................................................ 100 Chapter 5 Results .............................................................................................................................. 103 5.1 Hexaboride Cathode Study ......................................................................................................