Performance Scaling of Gas-Fed Pulsed Plasma Thrusters John Kenneth Ziemer A DISSERTATION PRESENTED TO THE FACULTY OF PRINCETON UNIVERSITY IN CANDIDACY FOR THE DEGREE OF DOCTOR OF PHILOSOPHY RECOMMENDED FOR ACCEPTANCE BY THE DEPARTMENT OF MECHANICAL AND AEROSPACE ENGINEERING June, 2001 Performance Scaling of Gas-Fed Pulsed Plasma Thrusters Prepared by: John K. Ziemer Approved by: Professor Edgar Y. Choueiri Dissertation Advisor Professor Robert G. Jahn Dissertation Advisor Professor Szymon Suckewer Dissertation Reader c Copyright by John Kenneth Ziemer, 2001. All rights reserved. Abstract The performance scaling of gas-fed pulsed plasma thrusters (GFPPTs) is in- vestigated theoretically and experimentally. Analytical models of the discharge current suggest that close to critically damped current waveforms provide the best energy transfer efficiency. A characteristic velocity for GFPPTs that depends on the inductance-per-unit-length and the square root of the capacitance-to-initial- inductance ratio is also derived in these models. The total efficiency is predicted to be proportional to the ratio of the exhaust velocity to the GFPPT characteristic velocity. A numerical non-dimensional model is used to span a large parameter space of possible operating conditions and suggest optimal configurations. From the non-dimensional model, the exhaust velocity is predicted to scale with a non- dimensional parameter called the dynamic impedance parameter to a power that depends on the mass loading prior to the discharge. To test the validity of the predicted scaling relations, the performance of two rapid-pulse-rate GFPPT designs, PT5 (coaxial electrodes) and PT9 (parallel-plate electrodes), has been measured over 70 different operating conditions with argon propellant. The performance measurements are made in a recently renovated fa- cility that uses liquid nitrogen cooled baffles and a micro-thrust stand capable of measuring impulses < 20 Ns within <10%. The measurements demonstrate that the impulse bit scales linearly with the integral of the discharge current squared, as expected for an electromagnetic accelerator. The measured performance scaling in both electrode geometries is shown to be in good agreement with theoretical pre- dictions using the GFPPT characteristic velocity. Normalizing the exhaust velocity and the impulse-to-energy ratio by the GFPPT characteristic velocity collapses al- most all the measured data onto single curves that represent the scaling relations for these GFPPTs. i Acknowledgments When I look back at my time at Princeton, I can think of the many things I’ve learned and the many friends I’ve gained. I am very fortunate to have been advised by two experts in the field, Prof. Edgar Choueiri and Prof. Robert Jahn. They have taught me more about electric propulsion and basic research than I ever thought possible. Eddie, I will always be amazed by your ability to dive into a new subject and master it. I look forward to more late-night discussions on baseball, squash, philosophy, art, macs, and just about anything else. Prof. Jahn, your insights into difficult problems are profound and legendary. I was happy to be on the receiving end of your wit and wisdom on more than one occasion. To both, I can’t thank you enough for your advice, mentorship, and faith in my abilities. I would also like to thank Prof. Szymon Suckewer for his comments on my dissertation, as well as Prof. Harvey Lam, Prof. Sam Cohen, and Prof. Nat Fisch for their involvement in my research and graduate instruction. For Dr. Daniel Birx, I truly wish he could be here to see this. This dissertation is dedicated in his memory. My friends at Princeton made all the difference in the time I spent there. I’ll always remember the cooking and the midnight plasma sessions with Ted Cubbin and Paolo Gessini. Patrick Mahoney taught me all I really know about computers and barbecuing. Sheff, Harris, Cowles, and Bob Anderson were my roommates at one time or another in 3Q. I’ll always remember the times at the D-Bar, reunions, our friend FH, spokey, the recycled furniture, mattress surfing, long nights at the Queen’s Tavern, in New York and Philadelphia, Jimmy’s Fat Cocoa, late night runs to the Wa, Sunday afternoon Taco Bell runs, Neon Lady, four-wheeling in the rental car, the golf, the olds, the horizon and the jetta, the top hat incident and the night that led up to it, movies with Maria, the noises of the Hibben, cybertubes, softball, all those lunches at George’s and Tex-Mex, the playground, the squishy-side, the tour, and all the laughs–we sure laughed a lot. To the band: Bob, Mike, Geoff, Brad, and Scott, I never knew I had it in me–some will argue that I still don’t–but when we were in the grove, there was nothing like it. Craig Woolsey is one of the most sincere people I know who tried his best to make the department a fun place to be while we were there. We all owe him a lot for that. Craig, I wish you and Sarah all the best. Best wishes also go out to my friends Armelle, Deborah, Irena, Cristin, Amy, Jill, Heather, Mike, Dave, and Tony who always were the life of the party. To everybody in the EP lab, you are my good friends and more. Kevin Diamant, George Miller, and Bob Sorenson taught me how to build an experiment that works the first time, or at least how to fix it when it didn’t. Vincent Chiravalle is a model of perseverance with a personality and heart that fills the room–literally. Vince, take care always, and I know you’ll go far (probably in first class!). Andrei Litvak left a legacy of hard work that gave the lithium thruster its first legs and me a ii better understanding of dedication. Kamesh Sankaran is someone I could always share new ideas with easily, no matter how crazy they seemed. Kamesh, I think I still owe you for crawling down into that DP. Tom Markusic, a fellow PPT fanatic, always challenged me to be a better scientist. Tom, I think we both look forward to learning even more from each other in our new jobs at NASA. Say hello to Christa, Elena, and Nate for me. I never saw much of Andrea Kodys and Gregory Emsellem as they always seemed to be just coming in when I was leaving the lab and visa versa. When we did see each other though, we had a great time! Andrea, come out and visit JPL as soon as you can, we need your expertise. To the new guys: Lenny, Kurt, Jack, and Slava, congrats on passing your general exams–now get back to work, slackers! In all this effort, I had the support of my entire family. Mom, Dad, Grams, Christine and Scott, your support meant the world to me. When I needed someone to lean on and talk to, you were there with understanding. Sometime in the future, I hope I can be there for you in a similar way. To my long time friends that have been with me the whole way: Jeff, Jason, Kris, Jeff, Arjay, and Liz, you’re the best, and I’ll see you all soon. To my new family members: Al, Mary, Michael, Laura, and Matt, thanks for taking me in during this crazy time. I look forward to the good times to come. To the true love of my life, Lisa Taneyhill Ziemer, I say what everyone around you knows already, you’re amazing. How could I have ever gotten through this without you? Your love and support gave me my reason to stay in Princeton, to keep working the long hours, and finally to give this one last push and finish all together. You could never know how happy it makes me to be with you and to know that for the rest of our lives, we’ll be together. (Well, us and the MKT, that is!) I love you very much. Professional Acknowledgments This research has been supported by the Air Force Office of Scientific Research (grant number F49620-98-1-0119), the Program in Plasma Science and Technology at the Princeton Plasma Physics Laboratory, Science Research Laboratory, Inc., and NASA Jet Propulsion Laboratory. This dissertation carries the designation 3016-T in the records of the Depart- ment of Mechanical and Aerospace Engineering. iii Contents Abstract ....................................... i Acknowledgments ................................ ii Table of Contents ................................. iv List of Symbols .................................. vii 1 Introduction 1 1.1 Spacecraft Mass Distribution and Optimization ............. 4 1.1.1 Mission Requirements ....................... 5 1.1.2 The Optimal Exhaust Velocity ................... 6 1.2 Missions Where GFPPTs Would Be Useful ................ 7 1.2.1 Orbit Raising and Station Keeping Maneuvers ......... 8 1.2.2 Small Satellites ........................... 9 1.2.3 Power-Limited Deep Space Missions ............... 10 1.3 The Mass of a GFPPT System ....................... 11 1.3.1 Achieving the Maximum Payload Mass ............. 12 1.3.2 Characteristic GFPPT System Velocities ............. 13 1.3.3 Balancing Performance, Lifetime, and System Mass ...... 14 1.3.4 The Need for a Performance Scaling Law ............ 15 1.4 Background of GFPPT Development ................... 16 1.5 Dissertation Outline ............................ 20 2 The Dynamics of a GFPPT Discharge 21 2.1 Discharge Description ........................... 21 2.1.1 Initiation ............................... 21 2.1.2 Propagation ............................. 22 2.1.3 Expulsion .............................. 23 2.2 Effective Models for the GFPPT Discharge ................ 23 2.2.1 The Equivalent Circuit and Snowplow Model ......... 24 2.2.2 Energy Distribution in GFPPTs .................. 26 2.3 The Efficiency of a GFPPT ......................... 28 2.3.1 Propellant Utilization Efficiency, pu ............... 30 2.3.2 Accelerator Efficiency, a ...................... 31 iv 2.3.3 Energy Transfer Efficiency, energy ................