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Investigation of High Frequency Instabilities in the Plume of the Vx-200 Magnetic Nozzle

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Investigation of High Frequency Instabilities in the Plume of the Vx-200 Magnetic Nozzle INVESTIGATION OF HIGH FREQUENCY INSTABILITIES IN THE PLUME OF THE VX-200 MAGNETIC NOZZLE ----------------------------------------------------- A Dissertation Presented to the Faculty of the Department of Physics University of Houston ----------------------------------------------------- In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy ----------------------------------------------------- By Matthew Giambusso May 2018 INVESTIGATION OF HIGH FREQUENCY INSTABILITIES IN THE PLUME OF THE VX-200 MAGNETIC NOZZLE ___________________________________ Matthew Giambusso APPROVED: ___________________________________ Dr. Edgar A. Bering III, Chairman ___________________________________ Dr. Gemunu H. Gunaratne ___________________________________ Dr. Lawrence S. Pinsky ___________________________________ Dr. George F. Reiter ___________________________________ Dr. Demetre J. Economou Cullen College of Engineering ___________________________________ Dr. Mark D. Carter Ad Astra Rocket Company ___________________________________ Dean, College of Natural Sciences and Mathematics ii ACKNOWLEDGEMENTS In May of 2009, I was trying to figure out how to transition from being a Navy submariner to a plasma rocket scientist. I am still working on this transition, but I wish to thank some of the people who have helped me so far. I sincerely thank Dr. Edgar A. Bering III for being my dissertation advisor, and particularly for his words of encouragement nine years ago; they have changed my life. I thank my dissertation committee, for their guidance and patience during my learning process. My gratitude goes to the physics and math instructors who have taught and challenged me at the University of Houston, particularly Drs. Kevin Bassler, Lowell Wood, George Reiter, Ed Hungerford, David Wagner, and the late Drs. Michael Gorman, Bambi Hu, and Kwong Lau. I also thank my classmates, particularly Mr. Luis Ackermann and Dr. Cameron Williams, who answered many naïve questions of mine and helped me through some difficult coursework. I owe a great deal to the men and women of Ad Astra Rocket Company, who have employed me for most of my graduate career. I am honored and thrilled to be part of their team. I particularly thank Drs. Franklin Chang-Diaz, Jared Squire, and Mark Carter, and Messrs. Greg McCaskill and Lawrence Dean, for teaching me about VASIMR ®, plasma, space propulsion, electronics, manufacturing and countless other subjects. I thank Mrs. Yamaris Lopez-Nieves and Ms. Miranda Chang for their expressions of confidence in the successful conclusion of this dissertation. I also thank the former employees of Ad Astra who have since moved elsewhere, including iii Dr. Benjamin Longmier, Mr. Maxwell Ballenger, and particularly Dr. Christopher Olsen, whose Ph.D. thesis was a foundation for my own. Lastly, I thank my family. To my parents and my sisters, I am grateful for all the ways they have helped grow into the person I am. To my daughters, Rosalie and Liliana, and to my unborn daughter, I am grateful for their inspiration; they make me want to be better in every way. I thank them also for their generous forfeiture of play time for the sake of this research. Being their father is more than I deserve. To my wife Angela, I owe such a debt of love and sacrifice as I don’t yet know how to repay. I am working on this as well. I thank her, with all my heart, for steadfastly supporting me in this endeavor, and for being my partner in life. iv INVESTIGATION OF HIGH FREQUENCY INSTABILITIES IN THE PLUME OF THE VX-200 MAGNETIC NOZZLE ----------------------------------------------------- An Abstract of a Dissertation Presented to the Faculty of the Department of Physics University of Houston ----------------------------------------------------- In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy ----------------------------------------------------- By Matthew Giambusso May 2018 v ABSTRACT During testing of the Variable Specific Impulse Magnetoplasma Rocket (VASIMR ®) VX-200 device, high frequency (HF) harmonics of the ion cyclotron heating (ICH) stage were measured in the radial component of the electric field along the upstream edge of the plasma exhaust. The oscillations were low amplitude and electrostatic, existing in a limited region of the plasma plume. The perpendicular electron density gradient in this portion of the plume could allow growth of the lower hybrid drift instability (LHDI) or the modified two-stream instability (MTSI), but the perpendicular DC electric field is generally not strong enough to support these drift waves. It is theorized that the ICH power excites the unstable drift waves; the amplified ICH harmonics are the ones whose frequencies are close to the theoretical frequency of the instability. In a separate but related approach, the stability of the exhaust jet is examined under the assumption of cold, homogenous, and uniformly magnetized plasma. A Clemmow Mullaly Allis (CMA) diagram for singly ionized Argon is drawn and annotated with scans through the plasma plume. Finally, a two- dimensional particle-in-cell model of the exhaust plume is developed, simulating a trans-Alfvénic plasma jet, the ion kinetic Beta transitioning from less than one to greater than one. In future works, beyond the scope of this dissertation, this simulation model will test theories about wave physics and detachment in the exhaust plume. vi TABLE OF CONTENTS I. Introduction ............................................................................................. 1 A. Organization of this Dissertation ....................................................... 4 II. Background ............................................................................................. 6 A. VX-200 Experiment ......................................................................... 6 B. Instabilities Observed During Detachment Study .............................. 7 C. Theory of the Lower Hybrid Drift Instability .................................. 12 III. Stability Analysis of Experimental Data ................................................ 15 A. LHDI Stability Analysis ................................................................. 15 1. Experimental Measurements of Plasma Properties ...................... 15 2. Finding Perpendicular Gradients ................................................. 21 3. Calculating the Minimum Electric Field for the LHDI ................. 28 4. Comparing the Minimum Field to the Measured DC Field .......... 31 5. Connecting Observed Oscillations to the Drive Frequency .......... 33 B. MTSI Stability Analysis ................................................................. 36 1. Experimental Measurement of Ion Temperature .......................... 37 2. Minimum Electric Field for the MTSI ......................................... 39 C. Distinguishing Between LHDI and MTSI ....................................... 40 D. Cold, Uniform Plasma Dispersion Analysis .................................... 41 1. Recreation of the Stix CMA to validate the method ..................... 43 2. CMA diagram for Singly Ionized Argon ..................................... 51 3. CMA with VX-200 Plume Scans................................................. 52 4. Tracking ICH Harmonics through the Plume ............................... 55 IV. Development of Magenetic Nozzle PIC Simulation ............................... 58 A. Review of PIC Method in Plasma Physics ...................................... 58 B. Review of Previous Local Simulation Efforts ................................. 60 1. Summary of Corey Henderson’s Work ........................................ 60 C. Development of Simulation Technique ........................................... 62 1. Simulation Boundary Conditions................................................. 63 2. Background Magnetic Field ........................................................ 66 3. Initial Simulations – Good Plume, Bad Beta................................ 70 D. Campaign to Validate Code against other Simulations .................... 73 1. An Alternate Simulation Technique – Two Fluid ........................ 73 2. Compare Ion Streamlines of Two-fluid to PIC ............................ 75 vii V. Simulation of Trans-Alfvénic Plasma .................................................... 79 A. Simulation Assumptions and Constraints ........................................ 81 1. Cylindrical Axisymmetry ............................................................ 81 2. Artificial Ion-to-Electron Mass Ratio .......................................... 82 3. Single Nozzle Coil at Plasma Entrance ........................................ 83 4. Model a Super-Alfvénic Transition ............................................. 83 5. Model a Realistic Magnetization ................................................. 84 6. Ensure Several Grid Cells in any Debye Area ............................. 85 B. Implicit Determination of Simulation Inputs ................................... 85 1. Emitter Parameters ...................................................................... 86 2. Simulation Time Step .................................................................. 89 3. Number of Simulation Particles................................................... 90 4. Summary of Simulation Inputs .................................................... 92 C. Assessment of Simulation Goals ..................................................... 93 1. Stability of Plasma Flow and Particle Populations ......................
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