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Experimental and analytical investigation of a ring cusp ion thruster: Discharge chamber physics and performance

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Experimental and analytical investigation of a ring cusp ion thruster: Discharge chamber physics and performance

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Content EXPERIMENTAL AND ANALYTICAL INVESTIGATION OF A RING CUSP ION THRUSTER: DISCHARGE CHAMBER PHYSICS AND PERFORMANCE Copyright 2005 by Anita Sengupta A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (AEROSPACE ENGINEERING) December 2005 Anita Sengupta Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. UMI Number: 3220154 Copyright 2005 by Sengupta, Anita All rights reserved. INFORMATION TO USERS The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleed-through, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. ® UMI UMI Microform 3220154 Copyright 2006 by ProQuest Information and Learning Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. ProQuest Information and Learning Company 300 North Zeeb Road P.O. Box 1346 Ann Arbor, Ml 48106-1346 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. DEDICATION This work is dedicated to Abe, my mom, and friends, who provided me with a never ending supply of encouragement and praise. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ACKNOWLEDGEMENTS I would like to acknowledge Dr. Dan Goebel, A1 Owens and Dr. Dennis Fitzgerald from the Jet Propulsion Laboratory, Professor’s Dan Erwin, Tom Katsouleas, Joe Kune, Mike Gruntman and Phil Muntz from USC, and Professor’s George Tynan and Russ Doemer from UCSD. I am thankful for all the guidance, insight, and assistance they have provided me during the course of my research program. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. iv TABLE OF CONTENTS DEDICATION....................................................................................................................... ii ACKNOWLEDGEMENTS................................................................................................iii LIST OF TABLES............................................................................................................... vi LIST OF FIGURES............................................................................................................vii ABBREVIATIONS............................................................................................................xii ABSTRACT........................................................................................................................xx I. INTRODUCTION..............................................................................................................1 A. Overview.......................................................................................................................3 B. Current Research in the Field................................................................................... 10 C. Research Description................................................................................................ 15 II. BACKGROUND........................................................................................................... 18 A. Ion Thruster Performance.........................................................................................18 B. Ion Thruster Theory..................................................................................................24 C. Plasma Diagnostics Theory...................................................................................... 34 III: ANALYTICAL MODEL OF THE ION THRUSTER DISCHARGE PLASMA.............................................................................................................................46 A. Plasma Production....................................................................................................46 B. Plasma Confinement.................................................................................................49 C. Analytical Model Development.............................................................................. 64 IV: EXPERIMENTAL SETUP AND PROCEDURES................................................74 A. Test Facility And Engine......................................................................................... 74 B. Procedures and Operation.................................................. 87 V: EXPERIMENTAL RESULTS....................................................................................93 A. Nominal Configuration: Case V I ...........................................................................96 B. Enhanced 4 Ring Cusp: Case V 2 .......................................................................... 127 C. Enhanced 4 Ring Cusp: Case V 3 .......................................................................... 137 D. Enhanced 3 Ring Cusp: Case V 4.......................................................................... 148 E. Discharge Loss Versus Propellant Utilization Efficiency Measurement 158 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. V VI: DISCUSSION OF THEORY WITH EXPERIMENT..........................................161 VII: LIFETIME AND SYSTEMS ENGINEERING IMPLICATIONS................... 185 A. Improving Performance..........................................................................................185 VIII: CONCLUSION........................................................................................................202 IX. REFERENCES...........................................................................................................206 APPENDICES A: Xenon Cross Section Data.............................................................. 213 Appendix A: Xenon Cross Section D ata....................................................................213 Appendix B: Publications List..................................................................................... 218 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. vi L ist o f T a b l e s Table 2-1. Approximate Particle Parameters in the Ion Thruster Discharge.............. 33 Table 2-2. Neutral-Xenon Transition Data...................................................................... 45 Table 3-1. Typical Cross Section Values for an Ion Thruster Discharge Plasma 49 Table 4 -1 .1 6 x 5 Sensitivity Test Matrix Based on Taguchi M ethod........................ 89 Table 4-2. NSTAR Throttle Table.................................................................................... 92 Table 5-1. Summary of NSTAR Engine Tests................................................................93 Table 5-2. Nominal (VI) NKOl and FT2 Performance................................................ 97 Table 5-3. Cusp Strengths for Nominal Configuration................................................. 98 Table 5-4. BOL engine sensitivities to flow and beam current at full power 118 Table 5-5. Cusp Strengths for Nominal Configuration............................................... 128 Table 5-6. Enhance 4-Ring Cusp NSTAR Performance.............................................131 Table 5-7. Cusp Strengths for V3 Configuration.......................................................... 138 Table 5-8. 4-Ring Cusp V3 NSTAR Performance.......................................................141 Table 5-9. Cusp Strengths for V4 Configuration.......................................................... 149 Table 5-10. 4-Ring Cusp V3 NSTAR Performance.................................................... 152 Table 6-1. Comparison of TH15 Performance for the 4 Configurations Investigated.........................................................................................................................163 Table 6-2. 0D Model Input Parameters..........................................................................171 Table 7-1. Predicted NSTAR Performance Summary at TH15 Operation................185 Table 7-2. NSTAR and Enhanced NSTAR Mass Breakdown.................................... 186 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. v ii L ist o f F ig u r e s Figure 2-1. Principle o f Ion Thruster Operation.............................................................. 18 Figure 2-2. Functional Diagram of a Ring Cusp Ion Thruster..................................... 24 Figure 2-3. Typical Langmuir Probe Trace.....................................................................35 Figure 2-4. Neutral Xenon Energy Level Diagram.........................................................44 Figure 2-5. Partial Neutral Xenon Energy Level Diagram............................................ 44 Figure 4-1. NKO NSTAR Thruster in the Test Facility.................................................75 Figure 4-2. FT2 NSTAR Thruster in Test Facility..........................................................76 Figure 4-3. Endurance Test Facility at the Jet Propulsion Laboratory.........................76 Figure 4-4. NKOl in the Endurance Test Facility at the Jet Propulsion Laboratory.............................................................................................................................79 Figure 4-5. Seven Axial probe locations as seen from outside the NKO engine) 80 Figure 4-6. Seven Axial probe locations as seen from inside the NKO engine (optics removed).................................................................................................................. 81 Figure 4-7. Typical Translation Profiles versus time......................................................81 Figure 4-8. Probe Mount and Junction Box on Stage.....................................................82 Figure 4-9. Cylindrical Langmuir Probes.........................................................................84 Figure 4-10. Flat Plate Langmuir Probe........................................................................... 84 Figure 4-11. Optical Fiber Probe....................................................................................... 86 Figure 5-1. NSTAR Nominal (VI) Magnetic Contour Plot.......................................... 98 Figure 5-2. NSTAR Nominal (VI) Magnetic Field Lines............................................. 99 Figure 5-3. Comparison of cylindrical probe IV characteristics................................. 102 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. v iii Figure 5-4. Cylindrical Probe Electron Temperature Profiles at TH15..................... 103 Figure 5-5. Cylindrical Probe Electron Number Density Profiles at TH15...............103 Figure 5-6. Electron Current Density Profiles at TH15 for VI Configuration......... 107 Figure 5-7. Electron Number Density Profiles at TH15 for VI Configuration........ 108 Figure 5-8. Electron Temperature Profiles at TH15 for VI Configuration............... 109 Figure 5-9. Plasma Potential Profiles at TH15 for VI Configuration........................ 110 Figure 5-10. Ion Saturation Current Density Profiles at TH15 for VI Configuration......................................................................................................................I l l Figure 5-11. Normalized Radial Profiles of Photon Flux at 823.2 nm......................114 Figure 5-12. Relative Neutral Density Profiles at TH15 for the VI Configuration......................................................................................................................116 Figure 5-13. Discharge-Loss Sensitivity at Full Power (TH15)..................................119 Figure 5-14. Discharge-Voltage Sensitivity at Full Power (TH15)...........................120 Figure 5-15. Discharge-Current Sensitivity at Full Power (TH15)........................... 120 Figure 5-16. Discharge-Loss Sensitivity at Half Power (TH8).................................. 122 Figure 5-17. Discharge-Voltage Sensitivity at Half Power (TH8)............................ 123 Figure 5-18. Discharge-Current Sensitivity at Half Power (TH8).............................123 Figure 5-19. Discharge-Loss Sensitivity at Minimum Power (TH0)......................... 124 Figure 5-20. Discharge-Voltage Sensitivity at Minimum Power (TH0)...................125 Figure 5-21. Discharge-Current Sensitivity at Minimum Power (TH0)................... 125 Figure 5-22. Discharge-Loss Sensitivity to Beam Voltage at All Power Levels.... 126 Figure 5-23. 4 Ring Cusp NSTAR (V2) Magnetic Contour Plot................................129 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ix Figure 5-24. 4 Ring Cusp NSTAR (V2) Magnetic Field Lines.................................. 130 Figure 5-25. Electron Number Density Profiles at TH15 for V2 Configuration 133 Figure 5-26. Electron Temperature Profiles at TH15 for V2 Configuration 134 Figure 5-27. Plasma Potential Profiles at TH15 for V2 Configuration....................... 135 Figure 5-28. Ion Saturation Current Density Profiles at TH15 for V2 Configuration..................................................................................................................... 137 Figure 5-29. Magnetic Contours for Case V3................................................................139 Figure 5-30. Magnetic Field Lines for Case V3............................................................140 Figure 5-31. Electron Number Density Profiles at TH15 for V3 Configuration 144 Figure 5-32. Electron Temperature Profiles at TH15 for V3 Configuration 145 Figure 5-33. Plasma Potential Profiles at TH15 for V3 Configuration......................146 Figure 5-34. Ion Saturation Current Density at TH15 for V3 Configuration 147 Figure 5-35. Magnetic Contours for Case V4................................................................150 Figure 5-36. Magnetic Field Lines for Case V4............................................................151 Figure 5-37. Electron Number Density at TH15 for V4 Configuration.....................154 Figure 5-38. Electron Temperature at TH15 for V4 Configuration........................... 155 Figure 5-39. Plasma Potential at TH15 for V4 Configuration.................................... 156 Figure 5-40. Ion Current Density at TH15 for V4 Configuration...............................157 Figure 5-41. Discharge Loss Curves for Cases V I, V3, and V4.................................160 Figure 6-1. Ion Current Density Radial Profile Comparison 2cm Downstream of Cathode Exit.......................................................................................................................162 Figure 6-2. Ion and Electron Number Density Radial Profile Comparison 2 cm Downstream of Cathode Exit for case V I......................................................................165 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. X Figure 6-3. Ion Current Density Comparison for 14cm downstream of cathode (near grid region) showing mirror image of data from 0 to -15cm............................169 Figure 6-4. Ion Current Density Comparison for 6 cm downstream of cathode (conical region).................................................................................................................. 170 Figure 6-5. Comparison of Measured to Predicted Discharge Loss at TH15 for the Nominal Configuration V I.........................................................................................173 Figure 6-6. Comparison of Measured to Predicted Discharge Loss at TH15 for Case 174 Figure 6-7. Comparison of Measured to Predicted Discharge Loss at TH15 for Case V4............................................................................................................................... 174 Figure 6-8. Comparison of Predicted Discharge Loss at TH15.................................. 175 Figure 6-9. Primary Electron Utilization as a Function of the Magnetic Confinement Length for Different Discharge Voltages............................................... 178 Figure 6-10. Ion Loss Fraction as a Function of the Closed magnetic Contour Strength for Different Anode to Contour Spacing........................................................ 178 Figure 6-11. Volume Averaged Electron Temperature at TH15 as a Function of Closed Contour Strength...................................................................................................181 Figure 6-12. Volume Averaged Primary to Total and Maxwellian to Total Electron Density Ratio at TH15 as a Function of Closed Contour Strength for a 2 cm Gap........................................................................................................................... 181 Figure 6-13. Volume Averaged Electron Temperature at TH15 as a Function of Propellant Utilization for Various Closed Contour Strengths..................................... 182 Figure 6-14. Volume Averaged Primary to Maxwellian Electron Number Density Ratio at TH15 as a Function of Propellant Utilization for Various Closed Contour Strengths............................................................................................... 183 Figure 7-1. Insert Life Plotted as A Function of Discharge Current.......................... 190 Figure 7-2. Comparison of 30,000 Hr ELT insert surface (top) and an un-used insert surface (bottom).....................................................................................................192 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. xi Figure 7-3. Comparison of Extended Life Test Accelerator Grid Aperture Enlargement to Normalized Beam Current Density Profile........................................ 196 Figure 7-4. Normalized Accelerator Grid Aperture Erosion Rate Versus Beamlet Current.................................................................................................................................197 Figure 7-5. Predicted Propellant Throughput Versus Peak Beam Current Density.................................................................................................................................198 Figure 7-6. Total number of thrusters versus propellant throughput......................... 200 Figure 7-7. Total IPS mass versus propellant throughput............................................201 Figure A -l. Excitation Cross Section as a Function of the Primary Electron Energy.................................................................................................................................214 Figure A-2. Ionization Cross Section as a Function of the Primary Electron Energy.................................................................................................................................214 Figure A-3. Maxwellian Averaged Ionization Cross Section as a Function of Te. .215 Figure A-4. Maxwellian Averaged Excitation Cross Section as a Function of Te. . 215 Figure A-5. Maxwellian Averaged Ionization Rate as a Function of Te................... 216 Figure A-6. Maxwellian Averaged Excitation Rate as a Function of Te................... 216 Figure A-7 Excitation Cross Section (823.2 nm) as a Function of the Primary Electron Energy.................................................................................................................217 Figure A-8. Maxwellian Averaged Excitation (823.2 nm) Cross Section as a Function of Te.................................................................................................................... 217 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. x ii ABBREVIATIONS NEP Nuclear Electric Propulsion SEP Solar Electric Propulsion EP Electric Propulsion ELT Extended Life Test of the DS1 Flight Spare Ion Thruster NSTAR NASA Solar Electric Propulsion Application Readiness Program DS1 Deep Space 1 JIMO Jupiter Icy Moons Orbiter NASA National Aeronautics and Space Administration JPL Jet Propulsion Laboratory SOA State of the Art FT Flight Thruster NKO NSTAR Knock-Off Thruster EM Engineering Model PPU Power Processing Unit IPS Ion Propulsion System DCIU Digital Control and Interface Unit DAQ Data Acquisition and Control THO Throttle Level 0 (0.51 kW) TH8 Throttle Level 8 (1.5 kW) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TH15 Throttle Level 15 (2.3 kW) OD Outer Diameter ID Inner Diameter NA Numerical Aperture IR Infrared Radiation EEDF Electron Energy Distribution Function OLM Orbital Limited Motion AV Exhaust Velocity Ue Measure o f Energy (to Reach Desired Orbit/ Planetary Body Isp Specific Impulse go Gravity Constant M0 Initial Spacecraft Mass Mi Mass of Propellant V b Beam Voltage VA Accelerator Grid Voltage Vnk Neutralizer Keeper Voltage sB Discharge Loss Cathode Mass Flow Rate ^c a th o d e Neutralizer Mass Flow Rate m „eu< Main Mass Flow Rate Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Jb Beam Current J b , actual Beam Current Modified for Double Ion Content F total Thrust Uncorrected for Off Axis Thrust Losses F on-axis Thrust Corrected for O ff Axis Thrust Losses 0 Beam Divergence Angle a Percentage of Doubles to Singles J+ Single Ion Current r Double Ion Current f P Flatness Parameter J b, avg Average Beam Current Density J b,peak Peak Beam Current Density fie le c Electrical Efficiency f iu Propellant Utilization T it Total Thruster Efficiency V th Thermal Velocity V e Maxwellian Electron Velocity vp Primary Electron Velocity Vi Ion Bohm Velocity V ± Velocity Perpendicular to Magnetic Field v l l Velocity Parallel to Magnetic Field Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. XV V 0 Initial Velocity VDiag Diamagnetic Drift Velocity VExB Drift Velocity B Magnetic Field Strength Bsaddle Magnetic Field Strength At Saddle Point B cusp Magnetic Field Strength at Cusp R l Larmor Radius R l ,p Primary Electron Larmor Radius RL,ion Ion Larmor Radius RL,max Maxwellian Electron Larmor Radius R l ,Hybrid Hybrid Larmor Radius C0c Cyclotron Radius Lcusp Magnetic Cusp Length Lconfine Electron Confinement Length Ae,therm Los Area for Primary Electrons Pm om Magnetic Moment ©LOSS Loss Cone Angle Te Electron Temperature T, Ion Temperature To Neutral Temperature Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. x v i Ji Photon Flux for state i U i Excitation Potential for state i to j U e x c ite Threshold Excitation Potential for Xel Collision Cross Section for Excitation from state i to j < 'C * ex citeV m '> Excitation Volumetric Rate Coefficient Jij Photon Production Rate D ij Excitation Rate V Volume of Discharge Chamber K Percentage of Xel Atoms Excited to State j that Release a Photon U jo n First Ionization Potential for Xe ^ io n Collision Cross Section Ionization of Xel to Xell <C ionV m :> Ionization Volumetric Rate Coefficient A.j Einstein Coefficient E ji Change in Electronic Energy S i j Degeneracy of Stage i or j eP Primary Electron Energy v D Discharge Voltage Vc Cathode Loss Voltage Jion Total Ion Current Ja Ion Current to Anode Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Jp Primary Electron Current Jd Discharge Current Jm Maxwellian (Secondary) Electron Current Ji,loss Ion Current Lost to the Anode P i.loss Probability of Ion Loss to Anode Jp,loss Primary Electron Current Lost to the Anode P p,loss Probability of Primary Electron Loss to Anode < t > i Ion Transparency 4* o Neutral Transparency Ag Area of Grid Js Screen Current Mi Ion Mass me Electron Mass ntot Total Electron Number Density nP Primary Electron Number Density nM Maxwellian Electron Number Density ni Ion Number Density no Neutral Number Density V j-o Ion Neutral Collision Frequency Ci-o Ion Neutral Momentum Transfer Cross Section Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. XV1U A .m Mean Free Path x Collision Time Da Ambipolar Diffusion Coefficient Dj,e Diffusion Coefficient pj e Mobility Coefficient Mo Chemical Symbol For Carbon C Chemical Symbol For Barium Ba Chemical Symbol For Barium Xe Chemical Symbol For Xenon Xel Neutral Xenon Xell Singly Ionized Xenon Xelll Doubly Ionized Xenon s0 Permittivity of Free Space danode Radial Distance to Anode From Maximum Value Closed Contour Pin Input Power Pexcite Power for Excitation P m a x w e l l i a n Power for Maxwellian Electrons Pion Power for Ionization P W aii Power Lost to Walls < j ) Bias Potential Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Ie Electron Current Ie,sat Electron Saturation Current Ii,sat Ion Saturation Current D/t Aspect Ratio Ap Probe Area A Diffusion Area E Electric Field e Coulomb q Charge eV Electron Volt k Boltzmann Constant Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ABSTRACT XX Analytical and experimental magnetic plasma confinement studies were performed on the state-of-the-art NSTAR ion thruster. The goal of this research was to determine the dependence of plasma confinement and plasma uniformity on the strength and shape of the imposed ring-cusp magnetic field. Four primary cases were investigated to parametrically determine the individual effects of adding an additional magnetic cusp, increasing the magnitude of the highest value closed magnetic contour line, and varying the magnetic field free volume in the discharge chamber. A laboratory model NSTAR engine was retrofitted with additional magnets to allow experimental investigation o f both enhanced 3 and 4 ring cusp geometries. The performance of each configuration was determined from bulk discharge electrical parameter measurements, as well as Langmuir probe sweeps and Xenon optical spectroscopy to determine plasma parameters. A zero dimensional analytical model was developed to provide predictions of thruster performance, based on only the geometry and magnetic field configuration of a proposed thruster design. The results of the experimental studies and analytical model development confirm that increasing the magnetic strength of the highest valued closed Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. x x i contour line significantly reduces ion loss to the anode walls. Increasing the contour line strength enhances magnetic confinement of the secondary electron population and electrostatically confines the ion population. It was also demonstrated that, increasing the field free volume in the near-grid region, improved plasma uniformity and produced a flattened beam profile. The major finding of the study is that a reduction in ion loss to the anode walls through electrostatic confinement significantly reduces the discharge power, required to produce and extract beam ions from the thruster. The enhanced 3 and 4 ring cusp geometries demonstrated a 20% reduction in discharge loss and up to a 40% reduction in peak beam current density, at the NSTAR full power throttle point. The reduction in discharge power and peak current density is also estimated to increase the total throughput per NSTAR engine by a factor of 1.8, by reducing wear mechanisms that limit thruster life. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1 I. INTRODUCTION Ion engines offer the potential for orders of magnitude performance improvement over traditional chemical propulsion systems, resulting in shorter trip times, reduced launch vehicle costs, and with the push for the Nuclear Electric Propulsion (NEP) Mission Architecture, far more ambitious science return than ever before. In spite of the tremendous advantages the technology offers, actual use of the state-of-the-art ion thruster technology on NASA science missions has been limited, due to its insufficient electrical efficiency, high fabrication and test costs, and reliability/lifetime issues. Without significantly improving the ion thruster’s efficiency and lifetime, use of this technology on NASA science missions will never take hold. The current inefficiencies of the state-of-the-art ion engine are directly related to the production and confinement of the discharge plasma in the engine’s discharge (ionization) chamber. Poor plasma confinement is directly related to thruster lifetime, as non-uniform plasma production increases wear of the ion engines electrodes and electron source. Therefore an understanding of plasma production and confinement is critical to increasing efficiency, life, and reliability, of the ion thruster. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2 The objective of this research is to use a combined approach of analytical model development of the bulk discharge plasma in conjunction with spatially resolved experimental measurements inside of an operating ion thruster, to quantitatively understand and improve upon the confinement and production of the discharge plasma. The experimental investigations included Langmuir probe, optical probe, and emissive probe measurements as a function of location, operating condition, and magnetic field design, inside an operating 30-cm diameter NSTAR thruster. The analytical model provides experimentally validated predictions of ionization efficiency, total thruster efficiency, and plasma parameters, as a function of the magnetic field design, thruster geometry, and throttle point settings. The end result of the research program is an experimentally validated enhanced NSTAR thruster design that improves ionization efficiency by 20% and plasma uniformity by 50%, significantly increasing the efficiency and lifetime of the NSTAR thruster. The model development in conjunction with experimental measurements, also details the physics of magnetic electron and ion confinement, in a ring cusp geometry. The analytical model may be used as a design tool for larger thrusters at different operating conditions, as it has no empirical based formulations, and only depends on a given thrusters geometry, magnetic circuit design, and throttle point. Finally, lifetime and performance Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 3 predictions of the enhanced NSTAR engine are used to show the systems engineering advantages o f the enhanced NSTAR engine for a variety of mission classes. A. Overview Ion engines are a promising and potentially attractive propulsion system alternative for near term and far term interplanetary and earth orbiting science missions. Although ion engines were originally developed in the 1950’s by Kaufman, it is only in the past decade that the technology has been flight qualified as a primary propulsion alternative to traditional chemical thrusters1 ,2 . Ion engines fall into a class of propulsion technology known as electric propulsion. Electric propulsion differs from traditional chemical propulsion, in that the kinetic energy transferred to the propellant is transferred via electrostatic or electromagnetic acceleration as opposed to the release of chemical energy and subsequent acceleration due to thermal expansion. Electric propulsion (EP) is an attractive alternative to traditional chemical propulsion due to its high mass utilization efficiency, reducing total propellant mass consumed and total feed system mass on the spacecraft. The acceleration imparted to a charged particle in an EP thruster is directly related to the amount of electrical energy available Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4 on board the spacecraft, for example solar array or a nuclear reactor power converted into electrical energy. There is of course a theoretical and practical limit on energy that can be imparted, but such a limit is several orders of magnitude greater than that contained in a chemical reaction. Therefore the exhaust velocity of ions released from an EP device is a factor of 10 to 100 greater than that of traditional solid or liquid propellant-powered chemical engines, which directly translates into a factor of a 10 to 100 increase in specific impulse. Although ion engines have been around since the 1960’s, it was the development of the technology for use on NASA flight programs, performed by both NASA and industry in the late 1980’s and throughout the 1990’s, that has served to flight qualify the technology for NASA science missions. Specifically in the 1990’s NASA’s Solar Electric Propulsion Technology Application Readiness (NSTAR) program, developed the current state-of-the art engine, known as the NSTAR engine. The program focused on flight qualifying the 30- cm-diameter ion thruster technology through a series of wear tests and subsequent design changes to mitigate wear mechanisms that were discovered during the extended duration testing3,4,5’ 6’ 7 ’ 8 . After a series of engineering model (EM) thruster re-designs, two flight unit thrusters, FT2, and FT1, were finally built by Hughes Electron Dynamics to serve as the primary propulsion system Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. on NASA’s Deep Space Mission9,10. DS1 was a technology demonstration mission, the purpose of which was to demonstrate and flight qualify several advanced technologies to benefit future NASA science missions1 1 . Although the primary purpose of DS1 was not science return, the spacecraft was equipped with several imaging and diagnostic devices and returned an extensive amount of science data during its rendezvous with the Comet Borelly and Asteroid Braille. The FT1 engine was installed on the DS1 spacecraft and operated for a total of 16,000 hours and processed 80kg of Xenon propellant on its two year journey1 2 ,1 3 ,1 4 ,1 5 . The engine performed flawlessly for the duration of the mission. The flight spare engine, FT2, was the subject of an extended life test at the Jet Propulsion Laboratory, where it operated for 30,000 hours and processed 235kg of Xenon propellant, making it the longest operation of an ion engine to date1 6 ,1 7 . The findings of the various wear tests of the EM NSTAR engines and the extended life test of the flight engine have resulted in an extensive amount of research in the community, focusing on understanding the physics that drive the primary thruster wear mechanisms. The primary wear mechanisms for the NSTAR ion thruster are wear of the accelerator grid, due to charge exchange sputter erosion, erosion of the keeper electrode that protects the hollow cathode electron source in the engine’s discharge chamber, and depletion of the source material inside the hollow cathode. The operation of these engine components will be described in detail in chapter 2, but it suffices to say that extensive wear Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 6 of these three components can and have led to thruster failure over the past decade of testing, and therefore understanding the plasma physics that drives these failures is critical to mitigating them in improved engine designs. The current and past research on the NSTAR ion thruster has predominantly focused on improving lifetime by understanding the wear mechanisms that lead to thruster failure for the nominal NSTAR thruster configuration. Research focused on understanding the physical processes and/or plasma physics inside the thruster to improve overall performance and life, has however, been less emphasized. In many ways, these two research areas are intrinsically linked, in that design changes to improve thruster performance may impact thruster life, and vice versa. Over the past several decades the design of ion engines has been largely based on empirical data and relations and the desire to use heritage designs that have demonstrated sufficient life and reasonable performance. Although this may have been an acceptable method for designing laboratory model or technology- demonstration engines for the DS1 mission, today’s NASA science mission climate has changed. Today’s missions are largely driven by cost constraints, therefore higher efficiency, longer life, and increased propellant utilization ion engines are required to compete in the propulsion system “market”. Although R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. 7 ion engines, in principle, have the capacity for orders of magnitude improvement in propellant utilization efficiency over traditional chemical systems, they are expensive by comparison from a fabrication, test, and reliability standpoint. Therefore in order for ion engines to compete with traditional, low-cost, reliable, chemical alternatives, their efficiency must be such that propellant and subsystem mass savings (launch cost savings) significantly outweigh the high-cost of the subsystem itself. Therefore, mitigating perceived risk by developing longer-lasting engines is not sufficient to ensure the technology a secure place in the spacecraft design world. As stated previously, much of the experimental and theoretical research on ion thrusters has focused on improving thruster lifetime, however, there has not been an extensive amount of experimental and analytical work performed on improving the efficiency of ion thrusters. This is an area of critically needed work, as the current State-of-the-Art NSTAR ion thruster is highly inefficient over the majority of its 0.5 kW-2.3 kW throttle range. In addition, the current near term and far term NASA NEP exploratory missions will require maximum use of propulsion system power in the range of lOOkW to 1 MW demand efficiencies of greater than 70%, and ion thrusters capable of operating for up to 10-15 years or 100,000 hours of operation. In addition, improving the performance of the NSTAR thruster also has a direct impact on thruster life. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Removing the non-uniformity of the plasma produced in the discharge chamber offers the potential to increase grid life by a factor of 2, which would increase the overall lifetime of the thruster and the total impulse that could be acquired per unit engine, requiring fewer engines to do the same mission. Similarly, improving the ionization efficiency of the thruster can reduce the discharge power requirements to run the hollow cathode, which in turn reduces the temperature at which it operates, increasing life of the emitter, and thereby increasing life of the thruster. These lifetime implications will be discussed in chapter 7. It is therefore a challenge with the potential for great rewards to the EP engineering community to improve the performance of the SOA NSTAR thruster. The state-of-the-art ion thruster, used on both the DS1 Mission and to be used on the Dawn mission, as mentioned above, is the 30-cm-diameter NASA NSTAR thruster9,18. The NSTAR thruster is characterized by a -60% total efficiency, 3000s Isp, and a lifetime of 235 kg of Xenon propellant throughput or 30,000 hours of operation1 9 . The life of the NSTAR thruster is primarily limited by erosion of the accelerator grid electrode, erosion of the discharge cathode keeper, and depletion of the electron emitter source material. Accelerator grid erosion is inherent to the operation of an ion thruster, and is due to the production of charge exchange ions immediately downstream of the screen grid. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 9 Although this is a severe life limiter for the NSTAR thruster, this erosion mechanism is well understood both analytically and experimentally2 0 ,2 1 ,2 2 ’ 2 3 ’ 24. As accelerator grid erosion is linearly dependent on ion current density, reducing the peak ion density by flattening out the beam profile can increase grid life. Alternatively, a change o f the grid material, to sputter resistant carbon-carbon composite, can mitigate this wear mechanism and extend grid lifetime by a factor of three25,26. Although a material change may be a good engineering solution to the problem, flight qualification of a new manufacturing approach, vendor, and technology is a multi-year and multi-million dollar process. Therefore, a more basic modification to the heritage design is in fact the most desirable solution in the near term, and lends itself to direct infusion into the current SEP mission architecture. Erosion of the discharge cathode keeper is not a well understood wear mechanism, and is the subject of much experimental and computational research in the EP community. The discharge cathode keeper is an electrode surrounding the discharge cathode (the electron source in the discharge chamber); in part to help maintain the electrical discharge that enables primary electron emission from the surface of the cathode, but primarily to protect the cathode from ion bombardment from the discharge plasma. The 30,000 hour life test of the DS1 NSTAR thruster verified that erosion of the discharge keeper from discharge Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 10 plasma ion bombardment was likely to cause near term cathode failure, which would result in absolute thruster failure1 6 . At this time, there are several NASA and academic research projects focused on this wear process, as the source and mechanism by which the discharge plasma ions obtain sufficient energy to 27 28 29 30 31 sputter erode the discharge keeper are not well understood ’ ’ ’ ’ . The performance of the NSTAR thruster is limited by its inefficient discharge chamber design, leading to unnecessary loss of neutral propellant and primary electrons, poor confinement of ions, and a non-uniform / peaked beam profile. The result is a remarkably high energy cost associated with producing ions that get extracted through the grids/electrodes, to produce thrust. It is these areas that are the focus of the proposed research and are discussed in more detail in the following sections. B. Current Research in the Field The bulk of the current discharge plasma/chamber research has been the experimental determination of the plasma parameters in the vicinity of the hollow cathode, in an attempt to understand the source of high-energy ions that bombard and erode the discharge cathode keeper electrode. The erosion of the keeper electrode led to the severe erosion of the cathode orifice plate, in the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 11 30,000 Hr life test of the DS1 flight spare ion thruster. The implication of this erosion is the eventual failure of the cathode and thus the failure of the thruster1 6 . Current and past research techniques and activities aimed at measuring and understanding the plasma environment have included single Langmuir probing, double Langmuir probing, LASER induced fluorescence and retarding potential analyzers, primarily in the near cathode part o f the discharge plasma. The most recent investigation of the near discharge cathode keeper plasma in a 30cm- NSTAR thruster was performed by Herman et al. at the University of Michigan29,30. Utilizing the IV traces of double and single Langmuir probes in the near discharge cathode region, these researchers have made plasma parameter measurements, assuming a Maxwellian distribution of electrons and a high-density plasma or operation in the thin sheath regime for the collected electron probe current. Their results indicate electron temperatures in the range of 2 to 7 eV and plasma densities on the order of le i 1 to l e i 3 cm-3 in this region of the plasma out to the anode wall. Williams et. al from NASA GRC used LASER induced fluorescence to map out the ion energy distributions in the near cathode region, also in an attempt to understand the energy and source of the high energy ions that erode the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 12 discharge keeper in a 30-cm NSTAR thruster. They too found electron temperatures on the order of 5 eV in the near keeper region, using the • 28 32 assumption of a Maxwellian population of electrons ’ . Goebel et al. from the Jet Propulsion Laboratory have used an axially reciprocating single Langmuir probe to measure the plasma parameters both in the insert/orifice region of a hollow cathode and up to several centimeters downstream of the cathode, along the centerline using a mock anode. Using a Maxwellian with a primary tail EEDF assumption, they too found electron temperatures on the order of 5-6 eV and plasma densities on the order of l e i 3 to le l2 cm-331’ 33. Older references in the research area which have focused on improving discharge chamber performance in smaller ring cusp ion thrusters, include Hayakawa et al., who used single Langmuir probes to measure the EEDF variation in a Japanese 14cm-diameter Ring Cusp Ion Thruster, and Brophy who generated and experimentally validated a single node analytical model of a 12cm-diameter ion thruster’s performance. Hayakawa used single Langmuir probes of varying geometries, inside a 14cm- diameter-engine, to determine the electron energy distribution function and its Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 13 variation at a total of twenty locations in the discharge chamber. These researchers discovered that for their baffled-hollow-cathode discharge chamber geometry, the measured EEDF was not a single Maxwellian electron population, but two populations corresponding to a high energy population of primary electrons emanating from the hollow cathode, and a lower energy population that was more representative of a Maxwellian distribution. The implication here being that the 30-cm-diameter NSTAR engine, the subject of the current research, may also have an electron distribution function that varies significantly from Maxwellian34. Brophy generated a single node, power balance model of a 13cm diameter, filament-style electron source, ring cusp ion thruster. He analytically determined the dependence of discharge loss as a function of the discharge voltage, mass propellant utilization, and 4 unknown quantities: the fraction of ion current that contributes to thrust, fraction of ion current lost to the walls (fA), the primary electron utilization factor (C0 ), and the baseline plasma ion energy cost (sp ). These independent variables are a function of the magnetic field, thruster geometry, and plasma properties, but they were assumed to be a constant for a given thruster design, and extracted from thruster operational data. With empirically derived values for these four unknown parameters, the model predicted the dependence of thruster performance loss solely on mass propellant Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 14 utilization. Brophy validated the model with determination of the four factors above, from test data, and measurement of discharge loss and plasma parameters in a 12-cm diameter ion engine operated without beam extraction. His model 35 yielded results that compared remarkably well with his experiments . The primary limitation of his model was the lack of analytical functional relationships for electron confinement, ion confinement, and plasma properties, allowing the model to be used only with pre-existing thruster designs with an empirically determined C0, £p* , and fA . The assumption of a constant electrical propellant utilization factor is not correct, as electron temperature and ion production changes with mass utilization; however, the power balance approach he took was valid and lends itself to further examination. Therefore, explicit determination of the magnetic confinement theory and plasma parameter dependence on magnetic confinement, combined with the power balance approach could lead to a fully explicit thruster design tool, allowing predictive performance of any ring cusp thruster without any major assumptions on plasma properties, plasma confinement, or demonstrated performance. Wirz, Mikellides, and Katz are developing two-dimensional axis-symmetric computer models of the bulk discharge plasma and hollow cathode discharge plasma for an NSTAR type engine. These models require the input of boundary condition neutral number density and plasma parameters, as well as engine Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 15 operating set-points, thruster geometry and magnetic field, to spatially resolve electron trajectories and ionization of the propellant gas. The end goal of these models is to map out the plasma parameters and plasma potential, and discover the source of the high energy electrons that cause discharge keeper erosion3 6 ’ 37. C. Research Description It is the purpose o f the current research to experimentally and analytically characterize the discharge chamber performance and discharge plasma of a ring cusp NSTAR ion thruster. The research has demonstrated improved discharge chamber efficiency and illustrated its dependence on operating conditions, geometry, and magnetic circuit design. The detailed understanding of the discharge plasma and chamber performance was obtained via the following activities: 1. Experimental characterization of discharge plasma performance as a function of operating conditions on an NSTAR type thruster. These studies determined the sensitivity of engine discharge voltage, current, and loss to variation primary electron input, neutral density input, and electric field strength between the electrodes. 2. Experimental characterization of the discharge plasma of an NSTAR ion thruster using Langmuir probes providing spatially resolved plasma Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 16 density, electron temperature, and plasma potential measurements for the nominal and enhanced NSTAR engine configurations. 3. Development of a diagnostic technique to measure the neutral number density in the discharge chamber of an ion thruster. Using this technique, spatially resolved relative neutral number density profiles in the discharge chamber have been obtained. This data provides insight into the areas of poor ionization efficiency and neutral depletion that can be used to tailor future NSTAR thruster designs to improve propellant utilization efficiency and minimize the production o f double charged ions. 4. Development of a zero dimensional analytical performance model to predict an ion thruster’s performance as a function of geometry, magnetic field, and operating conditions. This performance model provides analytical relations to predict electron and ion production and confinement as a function of magnetic field geometry. The performance model also predicts plasma parameter variation as a function of operating condition and magnetic field. 5. Experimental studies on how magnetic field strength/geometry affects electron confinement, ion confinement, propellant utilization efficiency, plasma uniformity, and plasma properties. These studies have demonstrated an enhanced NSTAR engine designs that improve Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 17 ionization efficiency 20% and improve plasma uniformity 40%, with respect to the nominal NSTAR engine. The studies have validated the 0D performance model, providing a quantitative understanding of how varying the thruster’s magnetic field improves electron and ion confinement. A secondary motivation for performing the above work is the addressing of failure modes and wear mechanisms in the NSTAR engine. Improving plasma uniformity has the ability to reduce accelerator grid wear and increase total propellant throughout per NSTAR engine. Improving plasma confinement reduces the discharge power requirements for the hollow cathode enabling it to operate at a lower temperature, also increasing the engine’s lifetime. The enhancements to the NSTAR engine experimentally investigated are presented in terms of their systems engineering benefits in chapter 7. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. II. BACKGROUND 18 A. Ion Thruster Performance Noutrali/er Cathode Discharge Chamber Discharge Cathode t * * High Velocity Ion Beam Figure 2-1. Principle of Ion Thruster Operation3 8 . An ion thruster is a propulsion device that utilizes the principle of electrostatic acceleration to accelerate charged particles (ions); thereby producing thrust (Figure 2-1). Ion engines are a particularly useful type of thruster as their specific impulse is related to the square root of the accelerating voltage applied between the electrodes. The energy imparted by the applied electric field is equal to the kinetic energy of accelerated ions by the following relation: Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. \ 2 — M U exhaust ~ * 1 ^ b eam (2-1) 19 U exhaust ieam The specific impulse is defined as follows: I u exhaust s p (2-3) O Having a high specific impulse essentially means high propellant utilization efficiency. This is desirable as less propellant and a lower mass propellant feed system need to be carried for a given spacecraft with a particular AV requirement, where AV is the integration over time of the acceleration produced by the propulsive device required to perform a particular mission. The farther the target orbit is from earth or the more massive a payload to be delivered, the larger the AV required to accomplish the mission objectives. Lower mass means lower launch vehicle costs and increased payload fraction. The rocket equation relates Isp and AV as follows: (2-4) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2 0 As can be seen from this equation, high AV missions to the outer planets and beyond can only be accomplished with either high Isp or a very low mass fraction. Reducing the mass fraction can be accomplished by staging, where a rocket propulsion system has multiple propulsion stages, and each is released from the vehicle after it has been used to reduce the total vehicle mass over time, but there is a physical limit to this approach. For example, for a mission into deep space you would need on the order of 20 stages, which is not only impractical but impossible to launch into orbit with modem day launch vehicles. Therefore, increasing specific impulse is the only feasible approach for enabling large AV missions. Although ion engines are low thrust devices (mN to N range) they thrust (accelerate the spacecraft) for many tens of thousands of hours, significantly reducing trip times for long distance missions, which is yet another advantage of the technology. Ion thrusters are limited by the amount of electrical power available to a spacecraft. For nearer to earth missions, solar power from arrays is the typical power source for ion thrusters providing from 2 to 10 kW o f power per thruster. These missions are typically called Solar Electric Propulsion or SEP missions. In theory, ion thrusters are well suited for the SEP mission class, as they can be Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 21 operated or throttled over multiple power levels, enabling maximum utilization of solar array power as a function o f distance from the sun. Examples of such missions include NASA’s Deep Space One mission, which utilized a 30cm- diameter NSTAR ion thruster for its primary propulsion system, Boeing’s 702 Communications satellites which use four ion thrusters for orbit-raising and station-keeping operations, and the upcoming Dawn Mission, which will utilize three NSTAR engines for its primary propulsion from earth to Vesta, and from Vesta to Ceres. For deep space missions, where the solar irradiance decreases as the reciprocal of the distance from the sun, nuclear power from a space-based reactor may be used to provide power from lOOkW to the MW range. The Jupiter Icy Moons Orbiter (JIMO) mission, proposed to launch in the next decade is considering the use of 6 ion engines as its primary propulsion from the Earth to the Jovian system39. The electrical efficiency of an ion thruster is the ratio of the beam power to the total electrical power. n- ^ J V + p \ s J ^ J B B T 1 other ^ B B The denominator of equation 2-5 represents the total electrical power expended by the ion thruster. Po lh e r is the power required to operate the neutralizer and accelerator grid supply. The product of the beam current, Jb, and beam voltage, Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 22 V b , defines the beam power. s B is the discharge loss or cost to produce a beam ion and is typically referred to in units of eV/ion or W/A. V J s B = (2-6) J B The discharge loss includes the power expended in ionization and excitation of the propellant. It is typically on the order of 150 to 260 W/A or eV/ion, compared to the ionization potential which is only 12.1 eV for Xe. As can be seen, the discharge loss is the parameter that controls the electrical efficiency of the ion thruster. As will be discussed in great detail, in this dissertation, reducing the discharge loss is essential to improving the performance of the ion thruster. Another efficiency term is the mass propellant utilization efficiency. This represents the ratio of beam current produced to the mass flow rate. n. = r / ‘ T T - < 2-7> m +m m " * c V e The total efficiency is equal to the product of the discharge and electrical efficiencies, and a correction factor, for beam divergence and doubles production in the beam. Off-axis thrust losses must be accounted for in the total efficiency calculation as the beam is divergent and the ion optics are domed. The beam divergence is typically quantified by the divergence angle,9. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The percentage o f double ions, a , in the beam must also be accounted for as they reduce the total number of charge carriers, whilst producing the same apparent beam current. J a B, actual 1 + V 0 5 r _ r 1 + r r (2-9) An empirical relation for a , was developed in reference 40 for a ring cusp ion thruster geometry similar to NSTAR as a function of throttle level. This relation is used in the standard NSTAR throttle table to compute the total thruster efficiency. The total thruster efficiency is then written as follows. Thrust Power Electrical Power = (acos@)2r/ur/e le c (2-10) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2 4 B. Ion Thruster Theory M agnetic Field Perm anent M agnets Ion Optics Propellant Flow ' Discharge C athode Propellant Flow Anode D ischarge Supply P ropellant Flow * N eutralizer C athode N eutralizer K eeper Supply A ccelerator G rid Supply Beam Supply Figure 2-2. Functional Diagram of a Ring Cusp Ion Thruster The thruster is comprised of four major functional components: the discharge chamber, the discharge-cathode assembly, the ion-optics (accelerator) assembly, and the neutralizer assembly (Fig 2-2). An ion thruster operates by ionizing neutral Xe gas in the discharge chamber via inelastic electron collisions with neutral propellant atoms. The positively ionized Xe propellant is then focused Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 25 and electrostatically accelerated through a two-grid electrode system, the ion optics. The neutralizer cathode acts as a plasma bridge between the neutralizer and the beam; supplying electrons to charge-neutralize the ion beam. The discharge or ionization chamber consists of a conical and a cylindrical segment, with the discharge cathode mounted to the base of the conical segment and the ion-optics assembly mounted to the downstream end of the cylindrical segment. The discharge chamber body is typically referred to as the anode. The anode is electrically isolated from ground potential, and from the ion optics, and is typically floating ~650-1100V above ground potential for NSTAR. The magnetic circuit consists of three rings of samarium-cobalt magnets located at the base of the cathode assembly and encircling the downstream and upstream cylindrical discharge chamber segment. The 3-ring cusp field provides a magnetic field strength of 20-120 Gauss at the cathode keeper and 1000-3 000G at the magnet surfaces. The NSTAR magnetic-circuit design closes the 20-Gauss contour line throughout the discharge chamber. The purpose of the magnetic circuit is to confine primary and secondary electrons, increasing the probability of an ionization collision prior to their loss to the anode wall. It also produces a preferential drift o f the ions toward the ion optics, improving the overall thruster efficiency. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2 6 Ionization occurs within the discharge chamber of an ion thruster by electron- neutral inelastic collisions with the injected propellant xenon. The discharge cathode assembly serves as the electron source for the NSTAR thruster. The discharge hollow cathode utilizes a thermionic emitter (insert) to provide electrons for ionization in the discharge chamber. The insert consists of a porous W matrix impregnated with a Ba-Ca-A^C^ compound in a 4:1:1 ratio. This compound produces a low work function on the tungsten surface, enabling thermionic electron emission from the surface. When heated, barium diffuses to the surface of the insert forming a barium oxide monolayer. The barium oxide monolayer forms a dipole potential at the surface, which reduces the potential barrier allowing thermionic emission. The electrons emitted from this surface ionize neutral Xe propellant flowed through the cathode tube. The rate at which the Ba source material diffuses and eventually depletes is a function of its temperature, which is directly related to the electron current generated by the device41. A keeper electrode and plate, concentric to the hollow cathode, is used to aid in cathode ignition and protect the cathode from discharge-plasma ion bombardment. The keeper electrode is tied to the anode through a 1 kQ resistor, resulting in a keeper potential 3 to 5 volts above cathode common. Nominally, the potential between the discharge chamber (anode) and the cathode is 24 to 26 V, and is referred to as the discharge voltage. The discharge voltage is typically Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2 7 a few volts below the actual plasma potential, measured with respect to cathode common. Figure 2-2 also details the electrical circuit of the NSTAR thruster. A two-grid molybdenum (Mo) ion-optics assembly is attached to the downstream end o f the discharge chamber. The screen grid, is the innermost grid, and is biased above ground or spacecraft potential. The outer grid, the accelerator grid, is biased negative of ground or space potential. A cold grid-gap of 660 p (0.026 in.) is nominally established between the grids prior to operation. The electric field between the grids provides the electrostatic acceleration needed to extract and focus the ions through the ion optics. The applied high voltage of typically -1000 V is used to accelerate the ions to achieve a sufficiently high exhaust velocity. The screen grid is electrically connected to cathode common potential to prevent collection of electrons on the screen-grid upstream surface. In addition, ions created in the discharge chamber that are at the plasma potential, 25V or so above cathode common potential, are subjected to an axial electric field, giving them a preferential drift velocity to the grid region. The accelerator grid, located downstream of the screen grid, is electrically connected to neutralizer common. The accelerator grid is nominally biased 150 V to 250 V below ground potential to prevent electrons in the beam plasma from backstreaming into the discharge chamber, which would negatively 19 22 impact thruster efficiency ’ . Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2 8 The neutralizer hollow cathode assembly, attached externally to but electrically isolated from the discharge chamber, provides electrons to neutralize the ion beam. With the exception of its larger smaller diameter, the neutralizer hollow cathode is identical to the discharge cathode. The neutralizer also employs a separate keeper supply to maintain the discharge. The neutralizer common potential is the reference potential for the NSTAR thruster. Neutralizer common is typically 10 to 12 V below ground potential and provides an indication of how well the neutralizer plasma is coupled to the thruster-beam plasma. The discharge chamber is enclosed in a perforated plasma screen to prevent beam-neutralizing electrons from reaching high-voltage surfaces. The plasma screen is electrically connected to ground or spacecraft potential. Further details of the NSTAR flight thruster design can be found in reference1 0 ,4 2 . 1) Plasma Formation: In an electron bombardment ion engine, such as the NSTAR engine, ions are created by inelastic collisions with electrons. The discharge cathode described above is the source of primary electrons. Primary electrons have been assumed to have a relatively narrow distribution function, and an average energy of some fraction of the discharge voltage. Although this is an over simplification, this Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2 9 model has been proven to be valid34. Primary electrons can do one of four things, have a collision with a neutral, an ion, or electron, or be lost at a thruster surface. It is assumed in the model development of chapter 3, that electron-ion collision frequency is negligible compared to electron neutral collisions, as the discharge plasma is only 10% ionized. It is also assumed that primary electron- electron and primary electron-secondary electron collisions are negligible compared to electron neutral collisions. As electron-neutral elastic collisions do not change the energy of the impacting particle, only direction, it is assumed that electron-neutral inelastic collisions and loss of primary electrons to the anode, represent the sinks for primary electron loss, and all other loss mechanisms are negligible. Inelastic collisions of primary electrons with neutral Xe atoms can either excite or ionize the Xe atom. The probability for excitation of Xe is a function of primary electron energy and is documented in the literature43, therefore the cross section for excitation may be directly calculated for primary electron excitation. The probability for ionization of Xe atoms to create either Xell, Xelll, etc. is also well documented in the literature, and the cross section for ionization may also be directly calculated for primary electrons. The excitation and ionization cross section as a function of primary electron energy and averaged over a Maxwellian EEDF are contained in Appendix A. The sum of the excitation and Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 30 ionization cross sections therefore represents the total inelastic cross section for Xe atoms at a particular energy level. a o = ° \ +Ecr, (2‘ n ) After a primary electron has an inelastic collision its energy is reduced and it is assumed to thermalize rapidly to become part of the secondary electron population. The secondary electron population is populated by all primary electrons that have undergone at least one inelastic collision and electrons released in the ionization process. As the secondary electron collision frequency is high it is assumed that the population is thermalized on a time scale shorter than the ion-Xe collision time. The result is a Maxwellian population of secondary electrons that can either be lost to the anode or have inelastic collisions with neutrals or ions. Similar to primary electrons, secondary inelastic collisions with ions are assumed to be negligible compared to inelastic collisions with Xe atoms. Therefore, secondary electrons contribute to the production of ions and excited Xe atoms in the discharge plasma. The Maxwellian population has an electron temperature on the order of 5eV, whereas the ionization potential of Xel is 12.13 eV, and excitation 10.1 eV, therefore electrons at the tail of the distribution that have sufficient energy to ionize and excite Xel. Similarly the primary electron dependent cross section data may be averaged over a Maxwellian distribution function to formulate ionization and excitation rate coefficients as a function of electron temperature (Figure 2-5, 2-6). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 31 1 8 For the neutral density in the NSTAR ion thruster which is on average 3x10 m' 3 at TH15, the mean free path is on the order of 2 m, whereas the chamber radius is only 15 cm (Table 2-1). Therefore, if unconfined, very few primary electrons would ever have an inelastic collision prior to being lost to the anode. Therefore, a magnetic field is employed to increase the confinement time of the primary and secondary electrons. The electrons then cyclotron gyrate about the field lines at their larmor radius, rL , and at the cyclotron frequency, co c. mv x R, = — ^ (2-12) l eB coc = — (2-13) m „ The cyclotron gyration increases the probability that they have a collision with a Xe atom prior to be collected by the anode. The larmor radius of an electron in the bulk of the discharge plasma would be ~0.4 cm for a 20G magnetic field with a thermal velocity at an electron temperature of 5 eV. Typical properties of plasma particle in the ion thruster discharge chamber are summarized in table 2- 1. Therefore, electron cyclotron gyration increases the mean free path of an electron and thus increases the probability that an electron will have a collision before being lost to the anode wall. The exact analytical relationship between the magnetic field strength and confinement of electrons has thus far not been well understood for ion thrusters, and is in itself one of the primary motivational aims of this research project. Therefore, a more detailed theoretical discussion is Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 32 included in chapter 6 in the context of observed experiment and the analytical model development. As stated previously, the discharge plasma is only partially ionized, therefore neutral propellant loss from the engine is a factor in total engine performance, as neutral loss does not contribute to thrust and represents wasted propellant mass. There is a tradeoff between mass utilization efficiency (reducing mass flow rate) and thruster wear, preventing the increase in ionization, simply to reduce neutral propellant loss. As neutral propellant rate is reduced, the discharge voltage increases resulting in an increase in the production of both singly and doubly ionized (Xell and Xelll). Increasing the double ion content is undesirable as Xelll have sufficient energy to sputter erode discharge chamber surfaces, and can therefore limit thruster life. Therefore, increasing discharge voltage must be balanced with the wear of sensitive discharge chamber and cathode surfaces. Neutral propellant is introduced into the engine through a perforated ring in the cylindrical segment of the discharge chamber. The propellant injection ring is oriented such that propellant is introduced in the upstream direction, however, the bulk flow velocity and pressure is sufficiently low, that neutral atom movement is essentially free molecular, or random, assuming it does not become ionized. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 33 PARTICLE V t h [M/S] R l [CM] Primary Electron 300,000 0.0085 (B=2kG) Maxwellian Electron 120,000 0.37 (B=20G) Singly Ionized Xe 382 26.1 (B=20G) Neutral Xenon 219 N/A Table 2-1. Approximate Particle Parameters in the Ion Thruster Discharge Ion motion and confinement are also areas of limited analytical understanding. Although Xe ions are charged particles they are massive and thus their larmor radii are so large that they are essentially un-magnetized. As the plasma is assumed to be quasi-neutral, electric fields do not manifest themselves in the bulk of the discharge plasma, only in the sheath regions, such as at the anode and cathode potential surfaces. For ions in the vicinity of cathode potential surfaces they experience a preferential drift velocity due to an axial electric field. Ions in the bulk of the plasma have no preferred direction and are more likely to be lost to anode potential surfaces, as opposed to through the grids, due to the large anode surface area. Ion motion in the bulk of the discharge chamber interior, and ion diffusion to anode is not well understood, leading to a lack of knowledge on design changes needed to reduce ion loss to the anode, a large source of the discharge inefficiencies of the ion thruster. The confinement of ions was also a major part of the research, and will be discussed in greater detail in chapters 3 and 6. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C. Plasma Diagnostics Theory 34 A large part of the experimental portion of this research work utilizes plasma and optical diagnostic devices to quantitatively and qualitatively understand the discharge plasma and its dependence on operating conditions, magnetic field, and location within the discharge chamber. The physical experimental setup will be described in chapter 4, but the theory, assumption, and limitations of each diagnostic technique are discussed below. 1) Langmuir Probe: Langmuir probes are commonly used in the experimental plasma physics world to spatially resolve plasma parameters in low-temperature plasmas. Langmuir probes are electrostatic devices that make use of the Debye shielding principle to measure collected current of charges particle to a biased object inserted into a plasma44. Debye shielding is a fundamental property of any plasma. When a charged object is inserted into plasma, charge carriers within the plasma will tend to shield out any electric fields produced by the localized charge disturbance. A Langmuir probe is a typically a cylindrical or planar electrode that is placed into the plasma, and is biased with an external power supply, through a range of potentials negative and positive of the plasma potential. The Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 35 current to the probe is measured as a function of the applied bias voltage generating a current-voltage characteristic or IV curve for a particular location within the plasma. The Langmuir probe surface is cold relative to the plasma temperature and therefore collects charge carriers in accordance with its potential relative to the plasma potential. With the assumption that the plasma of interest is essentially collisionless, for large positive potentials, all ions are repelled and the current saturates with electrons, defining the plasma potential. For large negative potentials, all electrons are repelled and the measured current is defined as the ion saturation current from which the ion density can be obtained. Figure 2-3 is a representative Langmuir probe trace with labeling of the floating Dotential. olasma ootential. and resions of interest. 0.4 0.3 < t> p i ■ I 0 10 30 50 - 0.1 Bias Voltage [V] Figure 2-3. Typical Langmuir Probe Trace Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 36 Region A is called the ion saturation region, where the probe is biased negative of the cathode common potential to repel electrons and collect ions. When biased sufficiently negative, the ion current to the probe saturates. When the flux of ions and electrons to the probe are equal the measured current is zero, and the associated potential is called the floating potential, < j > f i o a t- This potential marks the start of region B, known as the retarding region of the IV characteristic. Region B corresponds to a bias potential range in which electrons are retarded and collected by the probe. As the probe is biased increasingly positive of the cathode common potential, electrons of increasing energy are collected by the probe, and all ions propelled. In this region, the electron energy distribution function (EEDF) is proportional to the second derivative of the probe current with respect to the bias potential45. EEDF o c —~ J me (2-14) Ape V 2e d< j)B I A S In the ion thruster discharge plasma, the electrons are assumed to follow the Maxwell-Boltzmann law, representing a plasma in thermal equilibrium. In a Maxwellian plasma, the electron-retarding region of the probe trace is proportional to the Gaussian distribution at the electron temperature46. 1 , SkTe iinS = T”«VJ exp 4 V Tim. kT (2-15) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 37 (2-16) Therefore, a simple exponential curve fit or linear curve fit to the natural log of the current trace, may be used to obtain the associated plasma electron temperature, Te. Region C of the probe trace in Figure 2-3, is known as the saturation region, where electron current to the probe saturates, as the probe is at a potential above the plasma potential. As sheaths form in a plasma, the effective probe area is equal to the physical area, plus any the area due to sheath formation about the probe. Therefore, with increasing potential above the plasma potential, the electron current is not truly saturated, and monotonically increases as shown in region C. Nevertheless, the plasma potential, < j ) p, can be determined from the knee in the curve, corresponding to potential at which the collected current saturates, and no more current is collected. There are several methods for obtaining the plasma potential. The traditional method for obtaining the knee is by plotting the probe trace on a semi-log graph. For Maxwellian plasmas, as both the retarding and saturation regions of the probe trace are represented by exponential (Maxwellian) distribution functions, on a semi-log scale, the intersection of linear curves fits to each region, is defined as the plasma potential46. Another method for obtaining the plasma potential is by computing the first derivative of the probe trace47. The peak of the first derivative then corresponds to the knee and therefore the plasma potential. As Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 38 the discharge plasma is not purely Maxwellian, the first derivative method was used for the studies in chapter 5. It does not rely on linear curve fits, and can be genetically applied to any type of electron distribution, which eliminated curve fitting errors for the semi-log method. A Maxwellian fit to region B was used to calculate the electron temperature, Te, even though the plasma electron population is not purely Maxwellian. As will be discussed in chapter 6, emission of primary electrons from the hollow cathode, violates the assumption of a pure Maxwellian plasma. However, as primary electron comprise less than 10% of the total electron population, and are primarily located in the cathode plume, the error introduced is viewed as acceptable for the purposes of analyzing plasma parameter data, in the context of understanding the physics of plasma confinement. Calculation of EEDF from the second derivative of the probe trace with use of equation 2-14 was attempted but abandoned due to large numerical error introduced by the relatively noisy probe trace. Therefore, the Maxwellian data analysis approach was used exclusively for the determination of electron temperature and plasma density. The electron number density was obtained from the measured electron saturation current and electron temperature, from the measured electron saturation current, l e . s a t , at the plasma potential according to equation 2-17. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 39 4 / e,sat n (2-17) eA p Although the plasma is assumed to be quasi-neutral, explicit determination of ion density can also be determined from the probe characteristic. Ion density can be determined from ion saturation region of the probe trace and the electron temperature. The ion current density needed to form a stable sheath is as follows. The ion density can be directly obtained and compared to the measured electron density. Any differences in the measurement can then be attributed to probe effects. Two different probe geometries were investigated for this research activity, cylindrical and planar. In the case of the cylindrical probes, the effect of sheaths surrounding the probe must be accounted for sheath thicknesses on the order of the probe radius. In low density plasmas, as the bias potential to the probe is increased, the sheath, d, grows according to the child Langmuir law for potentials greater than the electron temperature. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 4 0 For plasma densities of the 101 0 cm'3, or less, the sheath thickness is on the order or greater than the probe radius. Electron saturation cannot occur as the radially expanding sheath will collect current proportional to the surface area that it occupies. For this regime of operation, the Orbital Limited Motion theory must be applied to determine the electron saturation current to the probe, as the probability that an electron will miss the probe is increased for expanding sheath thickness48. As much of the discharge plasma falls in density regime, necessitating the use of the OLM theory, it was decided to use planar probes to examine this region. The advantage of planar probes is that sheath expansion is only in the direction normal to the surface and does not increase the total current collection area for increasing bias voltages. Assuming the aspect ratio of a planar probe is sufficiently large to ignore end effects, the planar probe can be saturated in low density and high density regions, allowing a full mapping of the discharge plasma utilizing the equations above. 2) Optical Probe: Optical emission spectroscopy was used to spatially resolve the relative Xe neutral density in the discharge plasma. A fiber optic probe, based on the work of Yun and Tynan, was developed to measure photon production at specific Xel R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 41 downward transitions5 1 ,5 2 . The rate of production of excited Xel atoms, going from state i to j, is related to the plasma parameters as follows. J,j = nena < <r,v > V (2-20) The production of photons emitted from the downward transition of j to i, is related to the Xel production rate as follows. Jji = KJtj = Knena < rr,v > V = Kn0VD„ (2-21) Where the excitation rate is: D ij = n e < a ijv > (2-22) If the photon production rate (flux) can be measured optically for a small volume of the plasma, the neutral number density can be computed from equation 2-21, assuming prior knowledge of the excitation collision cross section for the particular transition, EEDF, electron number density, and K the percentage of excited neutrals that emit a photon. K J : nD = J — (2-23) < cr v > Vne Plasma number density and electron temperature for the same spatial location through which the optical probe translates may be obtained from Langmuir probe traces utilizing the methods discussed in section 2.3.1. Xenon fluorescence line cross section measurements exist in the literature as a function of energy from a monoenergetic source53. In order to obtain the excitation rate, R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 42 Dij, the cross section data is integrated over a Maxwellian distribution of electrons at the measured electron temperature, Te. The factor K represents the functional dependence of photon emission on the plasma properties and transition of interest. Photons can be released due to spontaneous de-excitation or collisional de-excitation. The probability of spontaneous radiative de-excitation per unit time is defined by the Einstein coefficient A jj. The Einstein coefficients are well documented in the literature for most Xel transitions relevant to spectroscopic diagnostics5 4 ’ 55. The standard method for estimating the collisional de-excitation probability per unit time, with prior knowledge of the excitation rate, Dij, is to assume a detailed balance applies in thermal equilibrium between the two electronic levels. The de excitation rate is then a function of the excitation rate, difference in electronic energy between i and j, electron temperature, and degeneracy (statistical weight) of states j and i 56. D j, = — D# exp g i AE (2-24) For Aji»Djj, K can be assumed to be constant, as spontaneous radiative de excitation occurs on a timescale orders of magnitude less than collisional de excitation. If K is a constant, for relative neutral density profiles, it can be removed from equation 2-23. For Ajj~Djj, K is a function o f the plasma R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 43 properties, and varies as a function of spatial location in the plasma, and therefore cannot be omitted from equation 2-23. As K = K(neTe) is an unknown quantity, the optical determination of relative neutral density is only valid for plasmas and transitions where spontaneous radiative depopulation is strong relative to collision de-excitation. Figure 2-4 is an energy level diagram for Xel. Figure 2-5 is a partial energy level diagram showing the two transitions of interest for the measurement technique developed 55. Specifically, the 828.0 nm (6p[3/2]2 to 6s[3/2]°i) and 823.2 nm (6p[l/2]oto 6s[3/2]°2) transitions are of interest in optical spectroscopy 53 52 due to their relatively high intensity, as measured by other experimenters ’ . The 823.2 nm transition is a metastable state. As a result, transition from 823.2nm to the ground level is forbidden. The 828.0 nm state has a transition to the ground level, at 147.0 nm. The Einstein coefficients, degeneracy, and electronic energy, excitation rates, and A/D ratio for the 823.2 nm transition is shown in Table 2-2. Spontaneous radiative de-excitation occurs on a time scale three orders of magnitude shorter than collisional de-excitation. Therefore, the assumption of constant K, is justified for the optical probe technique used. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 4 4 aoooo' '7 5 0 0 0 1 U 1 70000 65 0 0 0 - W ll/SK 8280A 1470A ti/aa» 6 s[3 /a] Ssja-e; ( S 1 - . Q'"» * » "» e~*w 6p ( SQ ) FIG. 2-1. Parti*] «*f*y-fcvei diagram of xenon. Figure 2-4. Neutral Xenon Energy Level Diagram 54 110000 £ ™ 1 O s ' ..* 9 3 * Xeil 100000 ■ 6 d £ i5d' 90000 6p‘ *7S 5d 80000 - < 70000 60000 FIG. A -t. Neutral-xenon energy-level diagram. Figure 2-5. Partial Neutral Xenon Energy Level Diagram5 4 . R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 45 Transition 823.2 nm A« (1/s) 2.39e7 Ei (Te ) 9.82 a 5 Ei(Te ) 8.31 a 5 Dij 3.1e3 Djj 4.19e3 Aji/Dji 5.7e3 Table 2-2. Neutral-Xenon Transition Data5 4 ” 5 5 . Although both the 828.0 and 823.2 nm transitions were valid for the optical probe technique, and were detected in the plasma, the 823.2 nm transition was chosen for the analysis. The 823.2nm transition was stronger, providing the highest signal to noise ratio. Measurements of both transitions were found in the literature54. The cross section for exciting Xel to 823.2 nm as a function of primary electron energy is contained in Appendix A, Figure A-7. As with the Xel total inelastic cross section discussed in section 2.2, the differential excitation cross section was also integrated over a Maxwellian distribution and is shown in figure A-8. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 46 III: ANALYTICAL MODEL OF THE ION THRUSTER DISCHARGE PLASMA A zero dimensional analytical discharge performance model was developed to predict the thruster performance as a function of geometry, magnetic field, and operating conditions, without the need for empirical data or prior thruster testing. The model also details the physics of magnetic confinement of ions and electrons. The model explicitly defines plasma properties by their functional dependence on the throttle conditions, geometry, and magnetic field. The goal was to create a model that is by definition scalable to larger thrusters, therefore serving as a predictive design tool to determine and optimize thruster performance. A. Plasma Production There are several assumptions in the model to simplify the analytical formulations for a zero dimensional approach. It is assumed that there are two populations of electrons in the discharge chamber, a primary electron population emitted from the discharge cathode, and a Maxwellian population comprised of primaries that have undergone an inelastic collision and secondary electrons R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 4 7 released in the ionization process. The primary electron current can be represented analytically by a monoenergetic electron distribution at the primary electron energy, cp 35. The primary electron energy is the difference between the discharge voltage and the cathode region plasma potential, V o ep =VD-V c (3-l) Primary electrons can lose their energy by collisional excitation, ionization, or recombination. Primary electron collisions with other electrons are assumed to be negligible, as the ion engine discharge is only partially ionized. Similarly, energy loss due to inelastic primary collisions with ions, are also assumed to be negligible. Energy loss from elastic primary electron collisions with neutrals and ions are also ignored, as such energy transfer is proportional to the ratio of the colliding particle masses. For Xenon this ratio is ~10'6 57. Primary and Maxwellian averaged cross sections for ionization and excitation in a typical ion thruster discharge plasma are shown in table 3-1. In low pressure, partially ionized plasmas, ion-electron recombination occurs at the walls, and recombination in bulk plasma can be ignored. This is justified as the ion- electron collision frequency is an order of magnitude lower than the neutral- electron collision frequency, as the plasma is only 10% ionized. Consequently, volume electron-ion recombination is ignored, however both electrons and ions are assumed to be lost to thruster surfaces. Both the Maxwellian and primary electrons undergo inelastic collisions with neutrals, resulting in the production R eproduced with perm ission o f the copyright owner. Further reproduction prohibited without perm ission. 48 of Xe ions and excited Xe neutrals and ions. It is however assumed, that energy loss associated with the production of multiply charge Xe (Xelll.XelV) and excitation of multiply charged Xe is negligible. This assumption is also valid as the threshold energy for electron impact Xell and Xelll production is 35 V and 70 V respectively44. In the model, ionization or excitation of Xel may only result from primary or secondary electron inelastic collisions with a neutral Xe. It is assumed that electron-ion ionization/excitation is negligible due to the low number of ions relative to neutrals in the discharge chamber. It is also assumed that the plasma is quasi-neutral, namely the ion density is equal to the total electron density. nu* = ni = nM + np (3-2) The final two assumptions are that ions are cold relative to electrons, with a temperature of 0.05eV, and that volume averaged double ion production in the discharge plasma is negligible1 9 , and as such is ignored in the calculations. The latter assumption is marginal, at high propellant utilization efficiencies where the discharge voltage may increase, but elimination from the analytical model was made to allow for explicit determination of all parameters. As ion engines are typically operated at 90% propellant utilization efficiency, where the primary electron energy is well below the threshold voltage for double ionization, this assumption is valid44. Although there are no measurements of ion temperature in the NSTAR thruster, ions are assumed to be bom with the gas R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 49 temperature during ionization. The gas temperature is essentially the wall temperature, 300°C, therefore an ion temperature of 0.05 eV is reasonable1 9 . Inelastic Collisional Parameter PRIMARY MAXWELLIAN Xel Excitation (m2) 3.23e'2 U 2.77el0-2 1 Xel Ionization (m2 ) 2.06e'2 U 5.11el0"2 1 O 'odteV m ax (cm /s) 7.61el0'y V ionizeV m a x (cm3 /S ) 1.3el0'8 Table 3-1. Typical Cross Section Values for an Ion Thruster Discharge Plasma4 3 . B. Plasma Confinement Before the analytical model was developed, the theory for electron and ion confinement in the discharge plasma was formulated. A primary motivation for this research project was the lack of such a theory applicable to ion thruster design and operation. In the 1970’s and 1980’s however, there was an extensive amount of basic plasma physics research in magnetic confinement for high power fusion containment. As such, this area was revisited for application to the low temperature and density plasma regime of an ion thruster. R eproduced with perm ission o f the copyright owner. Further reproduction prohibited without perm ission. 1) Electron Confinement: 5 0 In an electron bombardment ion engine, electrons are confined in a ring cusp magnetic field geometry. The magnetic field lines which originate and terminate at the cusps confine both the primary and Maxwellian electron populations. Electrons spiral around and along the field lines according to their Larmor radius as defined by equation (2-2) until they eventually find and are lost to the magnetic cusp. As mentioned previously, the primary electrons are assumed to be mono-energetic with an energy that greatly exceeds the plasma electron temperature, allowing them to interact with the magnetic field in a single particle manner. By definition they aren't part of the Coulomb-collision- produced Maxwellian distribution of the plasma electrons, and the plasma electrons and ions are assumed to not significantly affect their motion. As such the primary electrons are treated as a group of independent particles constrained to the field lines lost at a different rate than that of the maxwellian electron population. In a multi-pole cusp confinement engine, primary electrons are lost to the magnetic cusps in an area equal to twice the Larmor radius times the cusp length58. The magnetic cusp length is equal to the total circumference of all the magnet ring cusps inside the ion thruster. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 51 A , = 2h L c p 0 -3 ) The total time the primary electrons spend in the discharge chamber is therefore a function of the volume of the containment device, the velocity of the electron, and the confinement area. V tP=- T — (3-4) Apvp The total distance traveled by a primary electron is thus equal to the product of the confinement time and electron velocity. VeB L r = v t = -------------- (3-5) c o n fm e p p 2m v L e p cusp Due to the presence of the neutral population, there is a probability of collision with a neutral, the mechanism by which ions are formed in the discharge chamber. Therefore, the probability that a primary electron is lost to the cusps is a function of the energy dependent total inelastic collision cross section, neutral density, as well as the electron confinement due to the ring cusp magnetic field. The probability that a primary electron is lost to the magnetic cusp may be computed from a differential equation approach. To determine the probability of electron loss as a function of time, a differential equation can be written to represent a differential diffusion of electrons in an increment o f time, dt. Such an incremental diffusion is proportional to the inelastic collision frequency. P,LOST = J P ,L O S T V inelastic ^ ( 3 " 6 ) R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 52 Integrating equation 3-39 leads to the following. l n J P = V lnelaSlJ + C Which is: J = J e '1 4 = J e~V i" e ,‘s ,ic ‘ 13-71 J P,LOST u p o ^ D ' ) The inelastic collision frequency is defined as follows. ^inelastic inelastic^prime Therefore, equation 3-7 m aybe rewritten as follows. r j - n , P 0 vp m r t / t _ q \ P,LOST D V J v ) An additional substitution can be made, recognizing that the product of vprim et is simply the electron confinement length developed in equation 3-5. Therefore, equation 3-9 may be rewritten as follows. JpMKt = J De n °°°L ^ (3-10) Equation (3-10) indicates an exponential decrease with increasing neutral density, cross section, and confinement length. It is desired to minimize the loss of primary electrons to the anode as such losses reduce electrical efficiency, as the energy expended in creating the primaries does not contribute to the formation of ions. For a given engine operating point, the neutral density and cross section are fixed values. Therefore, to improve electrical efficiency the total confinement length must be increased, as primary loss has an exponential R eproduced with perm ission o f the copyright owner. Further reproduction prohibited without perm ission. 53 reduction in on confinement length. Confinement length has a linear dependence on the magnetic field strength at the cusps. In fact, equations 3-5 and 3-10 show us, that for NSTAR conditions, a cusp field strength of 2000 G is sufficient to contain 99% of all primary electrons. Such field strength is within the capability of commercially available permanent magnets. The secondary or the Maxwellian electrons are confined according to the hybrid radius59. The hybrid radius is the square root of the product of the ion and Maxwellian electron Larmor radius. R-L,Hybrid = V ^ L .io n ^ L .e le c ( 3 " H ) The magnetic cusp loss area for primary electrons is equivalent to twice the co hybrid diameter times the total cusp length . e,therm H ybrid^cusp 1 ^ ) Unlike primary electrons, due to their significantly lower energy (velocity) as a result of energy exchange with ions during inelastic collisions, the plasma electron population motion is affected by the ion population and hence gyrates at the hybrid larmor radius. At the large hybrid radius described above, cross-field radial diffusion across field lines can occur for the secondary electron population if the magnetic field is not sufficiently strong. This will be discussed further in section 3.2.2. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 54 Magnetic mirroring was also investigated to see if electron primary loss was reduced by mirroring. A magnetic mirror is based upon the invariance of the magnetic moment ( /j.m o m ) of a particle and conservation of kinetic energy. The supposed mirror for a particle would be defined by the saddle point magnetic field between cusps, and the stronger magnetic field at the cusps. Particles traveling on field lines between those areas could then conceivably be mirrored back from the cusps (throat). Conservation of and energy requires that as particle moves from an area of weak magnetic field to stronger magnetic field, its perpendicular velocity component must increase and parallel component decrease. Therefore, for mirroring to occur, v{ goes to zero at the throat, and the particle is reflected back towards the saddle point. Not all particles in a magnetic mirror, however, are confined. There is a region of velocity space called the loss cone, inside of which particles are lost the magnetic cusp. Manipulation of equations 3-13 and 3-14 leads to the definition of the angle the loss cone. mom saddle arcsin LOSS R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 55 For the ion thruster, the loss cone angle is on the order of 5 degrees which suggests that a large number of electrons should be magnetically mirrored from the cusp region. Therefore the primary electron confinement length calculated previously can be interpreted as the number of bounces it must make before being lost to a cusp. 2) Ion Confinement: Enhancing magnetic ion confinement is vital to minimizing overall discharge loss as reducing the number of ions lost to the walls reduces the discharge power requirements. Ions are charged particles, but due to their relatively large mass, their larmor radius in the 20-50 G magnetic field in the chamber interior is on the order of the discharge chamber dimensions. Therefore, ions are not magnetically constrained to the field lines, as are the primary and secondary electron populations. Although ions are lost to the magnetic cusps, ion diffusion to the anode wall is the primary mechanism for their loss. Diffusion in a plasma is driven primarily by particle density gradients. In the absence of a strong electric field, ions will tend to drift to low density regions in the plasma, eventually making their way to the anode where the plasma density is zero. Although there is an axial electric field, established by the difference between the plasma potential and cathode common potential of the screen grid, its R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 56 magnitude is not sufficient to prevent the loss of ion current to anode walls in the nominal NSTAR thruster. The rate at which diffusion occurs depends on many factors, including the degree of ionization of the plasma, the presence and strength of a magnetic field and the mass and charge of the diffusing particle. Classical and neoclassical diffusion in a magnetic field are not relevant to the ion thruster discharge plasma, as those constructs assume only coulomb collisions, and have no functional dependence on neutral-charged particle momentum transfer collisions. Therefore, only relations for diffusion in partially ionized plasmas are relevant. In the absence of a magnetic field, ions can diffuse via random walk collisions with a step length equal to their mean free path and as a result of ambipolar electric fields brought about by localized density gradients in the Maxwellian electron population. In the absence of a magnetic field, the random walk diffusion coefficient for an ion, is derived from the single fluid MHD equation, and is a function of the collision frequency, v jo n _neut, for momentum transfer collisions and the ion temperature. dv mn = qnE - kTVn - mn v^0v - 0 (3-16) dt v ,. k l L ^ Y l (3-17) m iv i-o m iv i-o n R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. The mobility and diffusion coefficients are defined allowing simplification of equation 3-17. These coefficients are valid for electron or ions. kTa < Die= — (3-19) m i,e V i-o (3-20) m v i,e i-o v = D E - £ i — (3-21) n The implication here, being that momentum transfer collisions reduce the diffusion coefficient. For the relevant thruster discharge parameters, the diffusion coefficient would be on the order of 5x102 m V . The ambipolar diffusion results in quasineutrality in the plasma. As electrons are more mobile, they tend to leave the plasma faster, leaving behind a charge imbalance. This charge imbalance sets up an electric field that accelerates ions and decelerates electrons diffusing to the wall. Quasineutrality requires that the flux of electrons and ions must be equal to one another. Therefore, from equation 3-17, the following can be written. R eproduced with perm ission o f the copyright owner. Further reproduction prohibited without perm ission. 58 Flux = vtn = D tEn - jutVn = DeEn - //e , V« = + Vn (3-22) F i + F e Equation 3-22 defines the ambipolar diffusion coefficient, D a , as a function of both the ion and electron mobility and diffusion coefficients. D = F P e + F e _ D , ( 3 . 2 3 ) F i + F e For the relevant ion thruster discharge parameters, the ambipolar diffusion coefficient is on the order of 2.5xl04 m V1 . Assuming that the electron mobility is significantly greater than the ion mobility, equation 3-21 reduces to the following. A , “ A (1 + ^ 0 (3-24) Therefore, in the absence of a magnetic field, the ambipolar electric field T increases ion diffusion by a factor (1 + . This is a significant diffusion loss mechanism for cold-ion plasmas. If the ambipolar diffusion coefficient above is applied to the NSTAR ion thruster plasma, a simple calculation using Fick’s Law predicts an ion flux two orders of magnitude greater than the measured average ion current density in the NSTAR engine. r, = A ^ * A - y (3-25) dr R R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 59 Therefore, it is clear that the magnetic field plays a major role in the confinement of ions by reducing the rate of diffusion. The effect of the magnetic field must therefore manifest itself in the random walk diffusion process and/or in the ambipolar electric fields generated by the Maxwellian electron population. As the ion larmor radius is on the order of the discharge chamber diameter, the probability that an ion will have a collision prior to its recombination at the anode wall is virtually zero, suggesting that the cyclotron gyration of the ion does not reduce radial diffusion to the anode wall. However, as will be shown in chapter 5, ion confinement is highly dependent on the magnetic field strength and geometry. Therefore magnetic confinement of ions must be due to the requirement of quasineutrality in the discharge plasma. As electrons are light, their motion is governed by electron cyclotron gyration about the field lines as they drift towards the magnetic cusps. As electrons leave an area, the deficit of negative charge will set up an electric field that will attract ions. Therefore, ions will follow electrons in their magnetically constrained motion in order to shield out electric potentials that would otherwise exist due to electron magnetic confinement. The ion and electron number density profiles presented in chapter 5 support this physical explanation. In more simplistic terms, the fact that ions are electrostatically confined by the plasma electrons is simply the requirement that diffusion of the plasma must be ambipolar. R eproduced with perm ission o f the copyright owner. Further reproduction prohibited without perm ission. 6 0 In order to develop an analytical formalism for the electrostatic confinement of ions by the secondary electrons, we can recognize that random walk diffusion does apply to the secondary electron population. As shown experimentally by Koch and Matthieussent, the plasma electrons, in the presence of ions and a magnetic field actually gyrate at the hybrid gyro-radius59. R-L,hybrid ~ y ] J o n ^L ,max ( 3 " 2 6 ) As ions are confined to the electrons, it is intuitive to think of the motion as an ion-electron pair walking in the direction opposite the density gradient. The random walk process is dependent on the magnetic field. Specifically, due to the presence of a magnetic field, the fluid equation of motion can be used to solve for the perpendicular velocity component60. dv i \ mn = en\E + v x B J -k T V n -m n v ^ v = 0 (3-27) dt vu = M i D : Vn v&B+v + - ExB ' DlAG,i f X \ 2 (*■ ) 2 n 1 + 1 + 1 + V ) I ) (3-28) Comparing equation 3-21 to 3-28, we see that the perpendicular diffusion and mobility coefficients are reduced by the factor 1 + \ R L d J , in the presence of a R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 61 magnetic field. Therefore, the diffusion and mobility coefficients are proportional to B 2 and may be rewritten as follows for R, » Xm, where Am is 2.48 m and RL is a 1 to 7cm, depending on the closed contour strength. kT v2 D ± = 2' mvv 1 + V Rl j vna R \vna = R \v = ^ (3-29) KnvRLj Mi = qR ]na qR2 Lv qR\ mvv 1 + ( ; ^ m 2 \ R L,i J vnu v2z y n°RU J It is clear that mobility coefficient is orders of magnitude less than the diffusion coefficient, due to the presence o f V2 in the denominator. It is also clear that increasing the magnetic field strength, will reduce both plasma electron and ion diffusion, by reducing the effective larmor radius. In terms of the random walk mechanism, the electron-ion motion now walks at a path length equal to the hybrid larmor radius. As the charge particle is confined to gyrate about a field X line N — times until it has a collision, the step length between collisions is r l the Larmor radius. Depending on where in the discharge chamber the ion is, the value of the magnetic field, and thus the larmor radius differs. In order to calculate a OD effect of magnetic ion confinement, a design parameter for the magnetic field must be chosen to calculate the probability that ions produced in the discharge chamber are lost to the walls by diffusion across magnetic field R eproduced with perm ission o f the copyright owner. Further reproduction prohibited without perm ission. 6 2 lines. The minimum closed magnetic contour is used to define the radius of gyration for the approach developed in this research program. The software MAXWELL 2D was used to model the magnetic field of the NSTAR thruster for both the nominal and modified magnetic field designs investigated. Random walk electron-ion diffusion is governed by a step length between collisions that is the hybrid larmor radius not the elastic scattering mean free path6 0 . The probability that an ion diffuses an incremental area, dA, in a collision time, x, can be represented by a differential equation. Using equation 3-32 and substituting equation 3-29, the probability an ion diffuses an area A is as follows. a w = J - ^ - d A (3-30) D l t Integrating equation 3-31 leads to the following. ln JU L oss = D ±t A + c (3-31) i,LOSS which is: = J ioe~D lV i (3-32) i,LOSS = exp R L, Hybrid A (3-33) R eproduced with perm ission o f the copyright owner. Further reproduction prohibited without perm ission. 63 The area A, that the ion must diffuse to be lost, is not intuitive. However, if we think of diffusion as ID process to the wall, in an incremental distance dx, we can rewrite equation 3-30 and redo the integration as follows. Rr » Xm, linear ion diffusion and loss is purely a function of the effective (hybrid) larmor radius and the distance it must travel before it reaches the wall, assuming its motion is obeying that of the magnetically confined secondary electron population, due to electrostatic attraction. As will b e . shown with experimental data in chapter 5, this is indeed the case. The use of equation 3-35 has been shown to be empirically valid, via accurate comparison o f the model to experimental discharge loss curves as will be shown in chapter 6. It is also interesting to note that use of equation 3-35 results in diffusion with a ~ dependence, which has been shown empirically to be the case for diffusion in the presence of a magnetic field by other plasma physics researchers60. ^i-L O S S i.LOSS ~ D dx (3-34) anode L,Hybrid (3-35) Equation 3-35 shows us that under the pretext of a 0D model, and in the limit of R eproduced with perm ission o f the copyright owner. Further reproduction prohibited without perm ission. C. Analytical Model Development 6 4 The model developed is based on a steady state electrical power and particle balance to the discharge plasma. The input power to the discharge chamber is equivalent to the output power that leaves the chamber. The power into the chamber is derived from the primary electron input into the chamber, which is related to the discharge supply output less the power needed to operate the hollow cathode. P i n = J o i V D - V c ) (3-36) Energy from the primary electrons is either lost due to recombination with the anode walls or it is transferred to the propellant by ionization and excitation. Following a collision, the remaining energy goes into the Maxwellian population. Pin = P ' w n + Pexcite + P w A U + PMAXWELLIAN (3 “3 7) Each one of these terms can be explicitly defined in terms of known quantities. The power expended in ionization and excitation is as follows. P i o n = U ionJ wn (3-38) P m u = Z U j J j (3-39) As various excitations can occur, a summation over all possible states is required. This is the most useful representation as the total excitation cross R eproduced with perm ission o f the copyright owner. Further reproduction prohibited without perm ission. 65 section data for Xel is readily available in the literature43. The power expended in primary electron loss to the wall is as follows. P p X O S T = J I’, LOST ( K j ~ K : ) (3-40) Substituting in equation 3-9 for primary electron utilization, we see that power loss due to primary electron loss has an exponential dependence on neutral density, the inelastic collision cross section, and the electron confinement length. W ={VD- V c ) j l> e - ' ’-L ~’- (3-41) The remaining power from the primary electrons that do have an inelastic collision is assumed to go into a secondary Maxwellian electron population. FMAXWELLIAN = M (3 "42) The Maxwellian population of electrons has two sources, primary electrons that have undergone any inelastic collision, and electrons released in the ionization process. Therefore, the Maxwellian electron current may be written as follows. J m = + U d - - W W , . + (3-43) All equations must now be written in terms of known variables, namely the throttle point settings, VdJb, mm , r\u, and the dependent variable S b. Equations for excitation and ionization production rates can be written as follows. ^io n = noVe(nm((Tio „vm) + npa io n vp) (3-44) R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 6 6 •J«cae = n0Ve(nm U o ex citevm) + n Hc7ex citevp) (3-45) Equations 3-44 and 3-45 may be rewritten in terms of the percentages o f the two electron populations relative to the total plasma density. J io n = (o-ionV » } + — a ionV p ) (3-46) As the plasma is assumed to be quasi-neutral the following is also true. n,o t = ni = np + nm (3-48) n nn -1 sl = \--J L . (3-49) Returning to equation 3-37, the new formulations may now be entered. JD(VD-V c) = Ui0 n n0n,0tVe n„ n r \ ° i o n V m ) + O’to.V \ n ,o» n ,ot J + Z U e x c U e nontolVe \ nto , Z {(Jexci,eV m) + -JL ^°exci,eV \ (3-50) + J + / ^ n o°oLco„fme ^ J io n ^ J K - )+-4 , \ t , + J d ( l - e ' - ’-'™*- )f T. To simplify the equation further it is time to re-introduce the dependent parameter, eb, the discharge loss. et = J V (2-6) J R R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 67 The discharge loss represents the energy expended in the production of ions that contribute to beam current. Beam current is only a fraction o f the total ion current that is actually produced, in equation 3-46. The total ion current, J;o n may leave the thruster as beam current, or may recombine on cathode potential surfaces, or recombine on anode potential surfaces. The ion current can therefore be written as follows. J ^ = JB+ J A+ J C = J B+ J A + JK + Js (3-51) Ion current to cathode potential surfaces (Jc) is the sum of current to the keeper (JK ) and to the screen grid (Js). Ion current to the keeper is negligible, less than 1% of the total current, so it is ignored in this analysis. Ion current that passes through the optics assembly, as opposed to recombining on the screen grid, is a function of the grid transparency to ions. The transparency of the optics assembly to ions is a thruster design parameter, and may be taken as an input to the model. For the NSTAR grids, the value is approximately 0.8 as calculated by CEX2D code6 1 and as measured during the ELT1 9 . The transparency to ions is defined as follows. 4 s — (3-52) J B + J s Therefore, the ion current may be written in terms of the anode and beam current only. < 3 - 5 3 ) A R eproduced with perm ission o f the copyright owner. Further reproduction prohibited without perm ission. 6 8 The following formulation will also be useful later on. J ion { <t> i (3-54) V J ion J As discussed in the previous section, the probability that an ion is lost to the anode is a function of the ion larmor radius. Therefore, substituting equation 3- 35, the ion current can be written as follows. | _ K L,Hybrid V j (3-55) In order to obtain an expression for the discharge loss, equation 3-50 may now be written in terms of sb. eb^b f, B Vc - U io n Jio„ + ^ U e x c ite Je x c ite +sBJBe + 1 t j . + — 2 e excite J T tUlt ll/rt - C A C K C C A L U C U U T T V D V » B ^ B _ ^ ~ n0< T o^confme ^ n o°o^conflne I (3- 56) Dividing equation 3-57 by Jio n leads to the following expression. £ B ^ B £ B ^ B y _ T T I v n J excite , £ B J B „ ~ no o 'A ™ /™ - - - - V C ~ U ion _ t " excite ' J V J J ion v D J ion _ ^C£B^B p L c o n /in j- ! SbJB vD Ji o n V J v D ion J excite j £ B ^ B J. J- ion ion ( i - e-n ^ L ^ j r e (3-57) Solving for £b and substituting in equations 3-56, 3-44, and 3-45, leads to the following. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. The remaining unknown variables are now n0, Te, J a , v p , nm /nto t, and L C O nfme- The Maxwellian averaged excitation and ionization reaction rates are functions of Te and can be determined if Te is explicitly defined. The Maxwellian averaged inelastic reaction rates from experimental cross section data are detailed in Appendix A. The primary electron velocity determination is straightforward. The neutral density may also be written in terms of known parameters, derived from neutral particle flux in free molecular flow. Relating this to total Xe mass flow rate through the grids and propellant utilization is also straightforward as described in reference 57. particles R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 7 0 m m ,.„Ja \2kTr 4 V m W l v„ * J t m = 'Jl*L JB+ F!ux * Agtjtg = 'J1M LL + ^ _ J ^ Aj g = ^ lJL (3_61) Xe Substituting equation 2-27, and solving for n0 yields equation 3-62. . _ 4J , ( 1 - , , ) eA„ 2 kT0 T )u (3-62) m Xe The primary to total electron density ratio may also be solved in terms of the known parameters. From quasineutrality, we know the ion current density is equivalent to the total electron density. From reference 63 we have the following expression for the beam current. kT J B = 0 .6nte A J.\— - (3-63) m Xe Taking equation 3-46, substituting in equation 3-63, and recognizing that nj = ntot, yields the following expression. 0.6eA„ 1 kT„ m Xe f \ = noV< \ J ION J n„ 1 *- n tot cr v ) H — —a. v ) (3-64) ion m ion p J V / n • * • tn i Yl J Solving for —- and substituting r A from equation 3-55 leads to the J ION following. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Substituting for n0 from equation 3-62 leads to equation 3-66. 0.6 eAs% k jT X ion m m X e V 7-------- 1---------------- (3'66) From equation 3-66 and 3-49, we can easily compute the Maxwellian to total density ratio. 0.6eA g2 ^k^fjf„ 1 - i . ion m anode L , H yb rid mX eV { ° i o n V p - { ° i o n V m ) ) (3-67) Dividing equation 3-66 and 3-67, we can compute the primary to Maxwellian density ratio. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. An expression for Te is not as straightforward as the previous terms. Instead a derivation of the Maxwellian averaged ionization reaction rate is obtained. Equation 3-46 may be rewritten by solving for \crio n vm ) and dividing by nm . / °ionV m) = J,. \ — cr+ vD n n Vc \ n Pno y (3-69) Substituting in equation 3-55 leads to the following. cr v ion m anode L , H ybrid cr. v n „nVe (3-70) R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 73 In order to determine Te, equation is 3-68 is solved for (crjo n vm ) and set equal to equation 3-70. Using a polynomial curve fit for (<Jio n vm ), in terms of Te, a Newtonian solver can be used to explicitly determine the value of Te for a given thruster geometry, operating point (Vd,JB, fiu), and magnetic field design. The prediction of Te, as a function of the minimum closed magnetic contour is discussed in Chapter 6. The prediction of Te as a function of r|u, for specific magnetic field designs is also discussed in Chapter 6. The functional dependence is clear, as the magnetic field is increased, ion loss reduces and the bulk plasma electron temperature is reduced. For a given magnetic field design, as the propellant utilization is improved, Te increases. With an explicit determination of Te, all remaining parameters may be calculated, including plasma density ratios and discharge loss. All formulations will be discussed in chapter 6. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 7 4 IV: EXPERIMENTAL SETUP AND PROCEDURES A. Test Facility And Engine All plasma diagnostic experiments were performed on a laboratory model NSTAR engine, referred to as the NKOl thruster (Figure 4-1). The parametric engine testing (sensitivity testing), was performed on the FT2, DS1 flight spare ion engine, as a part of the ELT program (Figure 4-2). Both the NKOl engine and FT2 engine are functionally identical to the NSTAR engine description in chapter 2, the differences being higher fidelity and longer lasting hardware for the flight engine (FT2). A comparison of the laboratory model and FT2 engine performance is documented in Table 5-2. The engines were operated and tested in the Jet Propulsion laboratory’s Endurance Test Facility (Figure 4-3). The 3- m-diameter by 10-m-long vacuum chamber is pumped by three 1.2-m-diameter CVI cryopumps and three Cryomech Xe cryopumps, for a total Xe-system pumping speed of 100 kL/s. The pumping system provides a base pressure of 1x10-5 Pa (1x10-8 Torr) and about 5x10-4 Pa (4x10-6 Torr) at the NSTAR full- power flow rates. The walls of the vacuum chamber were lined with graphite panels to reduce the amount of facility surface material back-sputtered onto the engine surfaces and diagnostics. Graphite was used because carbon (C) is more R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 75 resistant to sputter-erosion than the steel tank wall material25. A quarts crystal microbalance was used to measure the amount o f facility material back- sputtered into the plan of the engine. Figure 4-1. NKO NSTAR Thruster in the Test Facility. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 7 6 Figure 4-2. FT2 NSTAR Thruster in Test Facility. Figure 4-3. Endurance Test Facility at the Jet Propulsion Laboratory. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 77 The propellant-feed system consisted of two Unit Instruments mass flow meters in each of the main, cathode, and neutralizer flow lines. The main flow meter had a range of 0 to 100 seem and the cathode flow meters had a 0- to 5 seem range. The downstream flow meter in each line was used to measure the flow rate to an accuracy of ±1%. All flow meters were mounted on a temperature- controlled plate inside a thermally insulated box. The upstream meter in each line was used as a flow controller. The signal from each upstream meter was used to actuate a solenoid valve, which maintained the flow rate at the desired set point in each line. The solenoid valves were also mounted on a temperature- controlled plate installed in an evacuated flow box. Flow calibrations were performed periodically as engine performance was highly sensitive to change in flow rate. Laboratory power supplies with similar capabilities to the DS1 flight power- processing unit (PPU) were used to run both FT2 and NKOl. A POWERIO supply was used for both the discharge supply and the cathode heater supply. It was computer-controllable, with a maximum output of 20 A at 50 V. A computer-controlled isolated switch was used to change from heat mode to discharge mode following cathode ignition. A Spellman high-voltage supply was used to provide the screen and accelerator voltages. The voltage set-points are varied manually via a pot attached to the isolation module. R eproduced with perm ission o f the copyright owner. Further reproduction prohibited without perm ission. 78 A Labview-based computer data acquisition and control system was used to monitor facility and engine conditions as well as control the power supplies. High-voltage signal isolation was provided by OPTO 22 modules, which use fiber optic transmission lines to transfer 0-5V signals between the grounded DAQ system and the high voltage engine output and supplies. The data acquisition (DAQ) system measured engine electrical parameters to within ±0.5%. The NKOl engine was configured to allow the translation of 7 probes providing radial profiles from the anode wall to just past the thruster centerline for both the cylindrical and conical chamber regions. Seven 0.75 cm diameter holes were cut into the anode wall to allow the translation of various probes. The probe locations provided a spatially resolved discharge plasma characterization, from 1 cm to 14 cm downstream of the discharge cathode keeper (2 cm upstream of the screen grid), in the axial direction. The axial locations of the probes were 1, 2, 3, 4, 6, 10, and 14 cm downstream of the keeper electrode (Figure 4-4 to Figure 4- 6). Higher spatial resolution was required in the near keeper plasma as density 30 and potential gradients are known to be highest in the vicinity of the cathode . The probes were inserted into and retracted from the discharge chamber by a high speed linear translation stage (Figure 4-4). A Kollmorgen brushless servomotor in conjunction with a Servostar CD driver was used to drive a R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 79 Velmex lead screw stage. The computer controllable motor was able to operate at a variety of speeds, with a maximum speed of 50.8 cm/sec. This enabled a 16.5cm probe insertion and retraction operation to be less than 0.8 sec. There was a 0.1 sec dwell period between the stage at 16.5 cm and the subsequent retraction. A sample translation profile is shown in Figure 4-7. The stage was fitted with a home switch and two limit switches to bring the stage back to the same starting point and prevent operation outside of the desired range. Position relative to home was recorded with a NOVOTEC 0-10 cm travel linear position transducer, which was essentially the voltage output of a voltage divider. I riiiisiliioct* Figure 4-4. NKOl in the Endurance Test Facility at the Jet Propulsion Laboratory. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Conical Segment Figure 4-5. Seven Axial probe locations as seen from outside the NKO engine). Figure 4-6. Seven Axial probe locations as seen from inside the NKO engine (optics removed). R eproduced with perm ission o f the copyright owner. Further reproduction prohibited without perm ission. 81 1 8-i 1 6 - e 1 4 - O o 1 2 - C T 3 1 0 - 0 3 0 > 03 03 0.25 0.30 0.35 0.15 0.20 0.05 0.10 0.00 Tim e [s] Figure 4-7. Typical Translation Profiles versus time. The probes were mounted to the stage on the probe mount shown in Figure 4-8. Teflon spacers and setscrews were used to hold the alumina tube probes in a fixed position on the probe mount. Alignment and insertion into the engine were accomplished by a thruster probe mount, which housed each probe in stainless steel collar inserted into the anode wall that protruded up to 0.76 cm into the discharge chamber (Figure 4-6). Precision alignment of the system was accomplished via fine adjustment screws on both the probe mount and thruster probe mount. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 82 Figure 4-8. Probe Mount and Junction Box on Stage. During each translation, a combination of single Langmuir probes, optical probes, and emissive probes translated into the discharge chamber. Both cylindrical geometry and flat disc geometry single Langmuir probes were used, as density variations in the discharge chamber warranted their use. Each cylindrical Langmuir probe consisted of a thoriated tungsten cylindrical rod spot welded to a stainless steel wire that was fed through either a single or double bore alumina tube with an OD of 0.48 or 0.51 cm respectively (Figure 4-9). Each Tungsten rod extended 0.6 to 0.64 cm beyond the ceramic. The stainless steel wire extended 15 to 20 cm beyond the ceramic and was fitted with coax R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 83 connection to electrically connect each probe to the junction box. The position of the wire was maintained with several layers of high temperature shrink tubing affixed at the end of each alumina rod. Tungsten rod diameters of 0.1 cm and 0.15 cm were used primarily to investigate the effect of varying the effective sheath to probe radius on plasma parameter measurement consistency, and limitations of the use of OML theory data analysis in low-density plasmas. Flat plate geometry Langmuir probes consisted of a 0.4 cm diameter tungsten disk spot welded to at 0.05 cm diameter Ta wire, that was fed through first a single bore alumina tube with a 0.1 cm OD inserted into a single bore ceramic with a 0.48 cm OD (Figure 4-10). This dual-ceramic, necked down configuration was chosen to minimize perturbations due to insertion of a large insulating surface into the plasma. A similar necked down configuration could not be used for the cylindrical probes due to the large OD of the tungsten rod. The Ta wire extended 8 to 10 cm beyond the ceramic and mated to a flexible copper wire 10 to 20 cm in length to minimize torsional loads on the comparatively rigid Ta wire. The position of the Ta wire inside the ceramic tube, was maintained with several layers of high temperature shrink tubing affixed at the end of each alumina rod. The copper wire was fitted with coax connection to electrically connect each probe to the junction box. Each Langmuir probe coax output connection was fed into a shielded junction box (Figure 4-4). The junction box could take up to 5 probe electrical connections. The output signals from the junction box were R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 84 routed through the vacuum chamber to a combination of ISI SHV10 and standard coaxial vacuum feedthroughs. The ISI feedthroughs were rated to lOkV isolation with respect to ground, and the standard coaxial feedthroughs were rated to 2kV isolation. The vacuum feedthroughs and the air-side cabling shields were electrically connected facility ground to reduce signal noise. Figure 4-9. Cylindrical Langmuir Probes. Figure 4-10. Flat Plate Langmuir Probe. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 85 51 52 The optical probe was modeled after a technique developed in references ’ . Each optical probe consisted of a 0.48 numerical aperture (NA) optical fiber fed through a 0.51 cm OD alumina rod. The optical fiber, purchased from Thor labs, was chosen for its large aperture size and sensitivity to the visible near-IR range. The fiber consisted of a quartz cylinder surrounded by silicon cladding. As an optical fiber can see light in all directions, it was necessary to limit the light it saw to a small volume of plasma at the probe tip location. This was accomplished by inserting into the alumina tube, a thin walled stainless tube with a window cut into it with a solid cap spot welded to the end (Figure 4-11). The optical fiber was then fed into the stainless tube, and recessed 1 cm from the window. The stainless steel tube was aligned so that the window extended just beyond the alumina housing, only allowing light from the window into the optical path of the fiber optic. The light from each fiber optic was passed through a tunable spectrometer. The output of the spectrometer was received by a HAMAMATSU H5784-20 infrared-extended, multialkali photocathode, with enhanced sensitivity in the 300 to 900 ran spectral range. The photon flux is converted to a voltage output within the electronics of the device, to allow for low noise signal output. Due to the high sensitivity o f the device, it was necessary to house it in a light tight box fitted with a computer programmable shutter. The electronic shutter allowed minimum exposure to light and high precision exposure times from as low as 6 ms. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 86 Figure 4-11. Optical Fiber Probe. A separate LABVIEW data acquisition system was used to control the translation stage, electronic shutter, probe power supplies, and record current/voltage data from each probe. A high-speed data acquisition card, with a sampling rate o f up to 2 MHz for analog input and 1kHz for analog output was used to record current-voltage waveform data, linear position output, PMT output, and provide control voltages for the bias power supply, electronic shutter, and high-speed stage. A bipolar power supply was used to bias the Langmuir probes +/- 50V with respect to cathode common. The voltage waveform was a saw tooth ramp, cycled at 100 Hz typically for a duration of 1 second. The bias supply was placed in series with the probe and cathode common, and allowed to float at the thruster potential with respect to ground. As the data acquisition system was at ground potential, and the thruster operating up to 1100 V above ground potential, it was necessary to isolate the probe signal and control voltage for the bias power supply. This was accomplished via the use of two fiber optic link modules. The fiber optic link module consisted of a R eproduced with perm ission o f the copyright owner. Further reproduction prohibited without perm ission. 87 separate transmitter and receiver module connected to one another by a fiber optic cable with standard SMA fittings. Each module either receives from or transmits to the complementary module, optically, a via linear 0-5V signal. The current through each probe was measured across a 2-Ohm current shunt. The voltage output from the shunt was conditioned using a low-pass RC filter circuit, and then routed through a fiber optic link module, to be read by the grounded data acquisition system. The control voltage for the bias supply was transmitted in the reverse manner from ground to high voltage through a fiber optic link module. High voltage and ground potential equipment were physically isolated from each other using fiberglass and glO boards mounted in a standard rack. AC power was provided to the floating bias supply through a lOkV isolation transformer with the high voltage side referenced to cathode common B. Procedures and Operation Several types of experiments were performed as part of this research program. Parametric engine tests, also known as sensitivity tests were performed on the FT2 engine, nominal configuration. Discharge loss versus propellant utilization measurements and plasma diagnostic studies were performed on the NKOl engine for several magnetic field configurations. For each test, a detailed procedure to start the engine and throttle it to the desired operating point was R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 88 followed. The test procedures were developed for the ELT, and were followed for all engine tests below. 1) Sensitivity Tests: Experimental characterization of the discharge chamber performance as a function of operating condition was performed on the FT2 NSTAR ion engine via a series of sensitivity tests. Sensitivity tests were used to determine the functional dependence of plasma production, ionization efficiency, and hollow cathode efficiency on the extracted ion fraction (JB ), primary electron input (Jd), and neutral density input to the discharge chamber and hollow cathode (main and cathode flow rates). Specifically, a matrix of sensitivity operating points was generated to map out the sensitivity of discharge voltage, discharge current, double ion production, and discharge loss to variations in main and cathode flow rate, beam current, applied electric field, and power level. The discharge chamber sensitivity to ±3% variation in main flow, cathode flow, and beam current, and to ±5% variation in beam and accelerator voltage, was determined for the minimum- (THO), half- (TH8), and full-power (TH15) points. For each power level investigated, 16 high/low operating conditions were chosen to vary the flows, beam current, and grid voltages in a matrix that mapped out the entire R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 89 parameter space in accordance with the Taguchi theory o f experiments (Table 4- l ) 64. Experiment • m mam (seem) • m ca,h (seem) • m neu, (seem) V B (V) Jb (A) 1 +3% -3 % -3 % +5% -5 % 2 -3 % -3 % -3 % -5 % -5 % 3 +3% -3 % +3% +5% -5 % 4 -3 % +3% +3% +5% +5% 5 +3% +3% +3% -5 % +5% 6 -3 % +3% -3 % -5 % +5% 7 +3% -3 % -3 % -5 % +5% 8 -3 % -3 % -3 % +5% +5% 9 +3% +3% -3 % +5% +5% 10 -3 % +3% +3% -5 % -5 % 11 +3% -3 % +3% +5% +5% 12 -3 % -3 % +3% +5% -5 % 13 +3% -3 % +3% -5 % -5 % 14 -3 % -3 % +3% -5 % +5% 15 +3% +3% -3 % -5 % -5 % 16 -3 % +3% -3 % +5% -5 % Table 4-1.16 x 5 Sensitivity Test Matrix Based on Taguchi Method The engine was allowed to reach steady state operation at each of these off nominal conditions before the discharge electrical parameters were recorded. The 16x5 matrix of data generated was used to determine the sensitivity of the dependent parameters— discharge voltage, discharge current, and discharge loss,—to the variations in the independent parameters— main flow, cathode R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 9 0 flow, beam current, and beam voltage. The sensitivities or partial derivatives of each dependent parameter with respect to each independent parameter were determined using a least-squares fit routine. The results will be discussed in Chapter 5 in context with the actual plasma parameter measurements. 2) Discharge Loss Curves: Experimental determination of the discharge loss, the energy expended in creating ions that contribute to thrust, as a function of propellant utilization was required for validation of the analytical model to be discussed in chapter III. Discharge loss may be calculated in a straightforward manner from thruster electrical measurements as follows. VjyJ J (2-6) B The procedure involved in making the measurement was measuring the discharge electrical parameters in equation 2-6, and calculating the discharge loss as a function of the propellant utilization. The propellant utilization efficiency is defined below. 7. = T - ^ T - ^ (2-7) e m m + mc A propellant utilization of 100% would mean that all xenon atoms are converted into beam ions, and conversely, a utilization of 0% would mean no ionization is R eproduced with perm ission o f the copyright owner. Further reproduction prohibited without perm ission. 91 occurring. For a fixed beam current (thrust), the utilization can be changed by varying the main or cathode flow. The NSTAR nominal operation point is at 90% utilization, which results in a compromise between minimizing the production of X elll and maximizing the use of propellant to produce thrust. In order to make this measurement, and allow direct comparison to the analytical model, the discharge voltage, Vd, and beam current, Jb, were held constant, as they are input parameters into the model. Maintaining a fixed beam current is nominal operation for the NSTAR thruster, as the discharge supply is in a current control mode and is controlled by the computer to operate at a fixed beam current set by the operator. This is the desired mode of operation to prevent fluctuations in thrust. Holding the discharge voltage constant, however, is not normally done, as it requires adjusting the cathode flow rate to match the desired discharge voltage. Normally the cathode flow is fixed for a given throttle point, based on the NSTAR throttle table (Table 4-1), giving the 90% utilization discussed above. Therefore, in order to change the propellant utilization, at a fixed beam current, the main flow rate was reduced to increase the utilization, and cathode flow rate increased to maintain the discharge voltage. The converse is also true. This procedure used was to measure the discharge loss dependence on propellant utilizations from 75 to 95%, for TH15 and TH8 operation as will be discussed in the following chapter. R eproduced with perm ission o f the copyright owner. Further reproduction prohibited without perm ission. 92 THROTTLE LEVEL Power (kW) VB (V) Jb (A) v a (V) V n k (V) • m mam (seem) • (seem) • m neu, (seem) THO 0.52 650 0.51 -150 2.0 5.98 2.47 2.40 TH 1 0.66 850 0.53 -150 2.0 5.82 2.47 2.40 TH 2 0.75 1100 0.52 -150 2.0 5.77 2.47 2.40 TH 3 0.91 1100 0.61 -150 2.0 6.85 2.47 2.40 TH 4 1.02 1100 0.71 -150 2.0 8.30 2.47 2.40 TH 5 1.12 1100 0.81 -150 2.0 9.82 2.47 2.40 TH 6 1.24 1100 0.91 -150 2.0 11.33 2.47 2.40 TH 7 1.34 1100 1.0 -150 2.0 12.90 2.47 2.40 TH 8 1.46 1100 1.1 -180 1.5 14.41 2.47 2.40 TH9 1.58 1100 1.2 -180 1.5 15.98 2.47 2.40 TH10 1.72 1100 1.3 -180 1.5 17.22 2.56 2.49 TH11 1.85 1100 1.4 -180 1.5 18.51 2.72 2.65 TH12 1.96 1100 1.49 -180 1.5 19.86 2.89 2.81 TH13 2.08 1100 1.58 -180 1.5 20.95 3.06 2.98 TH14 2.2 1100 1.67 -180 1.5 22.19 3.35 3.26 TH15 2.33 1100 1.76 -180 1.5 23.43 3.70 3.60 Table 4-2. NSTAR Throttle Table R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 93 V: EXPERIMENTAL RESULTS The experimental results section contains bulk performance and plasma parameter measurements for four separate NSTAR thruster magnetic field designs. For each case, the NKOl thruster was physically modified by the addition/replacement of permanent magnets. The goal of the magnetic studies was to determine the dependence of plasma confinement and plasma uniformity on the strength and shape of the imposed ring-cusp magnetic field. As a full factorial test matrix is impractical four primary cases were investigated to parametrically determine the individual effects of the following: 1. Adding an additional cusp 2. Increasing the magnitude of the minimum closed magnetic contour line 3. Varying the magnetic field geometry with respect to the anode wall. CASE NUMBER OF RINGS CLOSED CONTOUR (G) MEASUREMENT SUMMARY VI (baseline) 3 20 Parametric, Discharge Loss, Plasma Parameters, Relative Neutral Density V2 4 30 Discharge Loss, Plasma Parameters V3 4 50 Discharge Loss, Plasma Parameters V4 3 50 Discharge Loss, Plasma Parameters Table 5-1. Summary of NSTAR Engine Tests R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 94 The nominal case, V I, is the 3-ring cusp engine configuration that was used for the DS1 mission and extended life test. This is the baseline configuration, against which all other configurations are compared. Cases V2 and V3 are 4- ring cusp versions of the NSTAR thruster. In case V2, a magnet ring was added to the center o f the conical section of the discharge chamber. In order to maintain alternating polarity between the cusps, the cathode magnet ring was also replaced with one of opposite polarity. The middle and front magnet rings were left unchanged from the nominal configuration. This design closed the 30G contour, a 10 G improvement over V I. The primary purpose of this configuration was to measure the effect that adding another cusp and pushing the minimum closed contour closer to the anode wall had on plasma uniformity. Case V3, in addition to having a conical segment magnet ring and a new cathode ring, also strengthened the middle ring cusp magnetic field by adding a ring of magnets directly over the existing middle ring. The resultant magnetic field closes the 50G contour. Case 3 is used to determine the effect of increasing the closed contour value, but trading it with a smaller magnetic field free region than V2. Case V4 is a 3-ring cusp NSTAR engine, but with a strengthened middle magnet ring (as in V3), allowing closure of the 50G magnetic contour line. V3 uses the nominal cathode and front magnet ring of the V I, and does NOT have a conical magnet ring. V4 is used to separate the effects of physically R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 95 adding an additional cusp from increasing the magnetic contour closure and increasing the field free volume. For each of these cases, a 2D map of the magnetic field and magnetic contours was computed with the software MAXWELL 2D. The test sequence was then to retrofit NKOl for the new magnetic circuit, measure the individual cusp magnetic field strengths with a Gauss meter, and then install the engine in the test facility for experimentation. Experimental data collected included performance parameters, discharge loss curves, and spatially resolved measurements of electron density, electron temperature, plasma potential, and ion density with Langmuir probes. Measurements were taken for the TH15 operating point for each configuration. Performance data and ion saturation profiles were also taken at the THO and TH8 operating points. Relative neutral number density measurements were made with the optical probe technique for case V I. Discharge loss curves were generated for TH15 operation, to allow comparison of the actual performance to the predicted performance of the analytical model for all cases in investigated. This data set is used to determine the validity of the ion and electron confinement model developed in chapter IV. Additional data was collected for the nominal configuration on the FT2 engine, as part of the Extended Life Test (ELT). Parametric engine tests to determine the R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 96 functional dependence and sensitivity of thruster performance on main flow rate, discharge current, and total accelerating voltage were performed. The summary of all measurement made is found in table 5-1. A. Nominal Configuration: Case VI 1) Overall Performance: The performance, as a function of runtime and power level of the nominal NSTAR thruster, is well documented in references 17 and 19. Table 5-2 compares the performance of the nominal NKOl during the experiments and the FT2 engine after 1000 hours of operation during the Extended Life Test (ELT). Discharge power varies with thruster wear, as erosion of the accelerator grid hole pattern leads to increased neutral loss8. Therefore the 1,000 hour mark for FT2 operation was chosen as a representative point for comparison between the engines, as they exhibited a similar degree of accelerator grid wear. Performance data is presented for TH15, TH8, and TH0 operation. As can be seen, the laboratory model engine is not identical but certainly representative of the flight thruster performance. Variances between the two can be related to minor differences in the axial cathode location and nominal grid gap of the optics assembly. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Figure 5-1 and 5-2 are MAXWELL 2D plots of the field lines and lines of constant magnetic strength. From these plots we can see that the nominal thruster configuration closes only the 20G contour line and the field free volume in the cylindrical segment is significantly smaller than the physical volume. Although the cusp strength is sufficiently high to minimize primary electron loss, it is likely that secondary electrons and thus ions are not well confined due to the weak magnetic field. Table 5-3 summarizes the measured cusp field strength. These values are used in the performance model to calculate primary electron confinement. Primary electron loss, calculated from equation 3-10, is on the order of 10%. Although this is by no means insignificant, it is clear that ion loss to the walls is the primary source of electrical inefficiency in the nominal configuration. Although not shown in figure 5-2, the magnetic field lines emanating in the vicinity of the cathode are essentially axial, suggesting a high degree of ionization due to magnetic confinement of primary electrons to the thruster centerline region. DISCHARGE PARAMETER NKOl (VI) FIf2 (1KHRS) TH15 TH8 TH0 TH15 TH8 TH0 Jb (A) 1.76 1.10 0.51 1.76 1.10 0.51 Jd (V) 14.8 8.3 5.3 14.3 8.4 5.3 VD(V) 24.65 26.2 25.70 24.7 25.1 25.5 Sb(V) 207.3 198.3 267.1 201 192.2 265.8 T |t0 t 0.609 0.603 0.391 0.612 0.606 0.392 Table 5-2. Nominal (VI) NKOl and FT2 Performance. R eproduced with perm ission o f the copyright owner. Further reproduction prohibited without perm ission. 98 CUSP LOCATION CUSP STRENGTH [G] Cone N/A Middle 1230 Front 1100 Table 5-3. Cusp Strengths for Nominal Configuration B [ T ] 7 . 0 0 0 0 e - 0 0 3 6 . 0 0 0 0 e - 0 0 3 5 . 0 0 0 0 e - 0 0 3 4 . 0 0 0 0 C - 0 0 3 3 . 0 0 0 0 e - 0 0 3 2 . 0 0 0 0 6 - 0 0 3 X . 0 0 0 0 e - 0 0 3 — ~ y . Figure 5-1. NSTAR Nominal (VI) Magnetic Contour Plot. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 99 B[T] ? . 0 0 0 0 6 - 0 0 3 6 .0 000e-003 S . 0 0 0 0 e - 0 0 3 4 . 0 0 0 0 C - 0 0 3 3 . 0 0 0 0 e - 0 0 3 2 , 0 0 0 0 e - 0 0 3 1 .0 000e-003 1 I Figure 5-2. NSTAR Nominal (VI) Magnetic Field Lines. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 1 0 0 2) Plasma Parameters: The following sections detail measurements of electron temperature, plasma density, ion saturation current, plasma potential, and relative neutral density. The measurements were made with cylindrical and flat plate Langmuir probes, and fiber optic probes. Measurements are presented for TH15 operation only. a) Cylindrical Probe Data: A total of 5 cylindrical probes were used in this study. The axial locations of the cylindrical probes were 1, 2, 4, 6, and 10 cm downstream of the keeper electrode (Figure 4-5 and Figure 4-6). Higher spatial resolution was required in the near keeper plasma as density gradients are known to be highest in the vicinity of the cathode30. The radial expanse of each probe was from the anode wall to just past the thruster centerline. Initial data reduction of the probe IV characteristics, indicated that the sheath surrounding the probes in the low density cylindrical region of the discharge chamber was greater than the probe radius itself. This prevented electron saturation from occurring as the increasing sheath thickness increased the total probe collection area with increasing bias voltage. Without electron saturation accurate measurements of plasma parameter measurements could not be acquired in the low plasma density region. In the conical region the R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 101 thickness of the plasma sheath surrounding each probe was 5% of the probe radius, and its effect could be ignored. A comparison of the probe traces in the two regions is presented in Figure 5-3 for illustration of the probe sheath problem. Probe 1 was 5 cm downstream of the cathode keeper exit. Probe 5 was 10 cm downstream of the keeper exit. As discussed in chapter 2 the plasma sheath grows according to the child Langmuir law in the presence of a potential. Therefore, the probability that an electron will miss the probe surface and instead orbit the probe in the plasma sheath surrounding the probe, increases for increasing sheath thickness in accordance with the OLM theory. Although OLM theory can deal with this type of situation, it was decided that flat plate probes would be a better solution and allow calculation of the plasma parameter in all regions of the discharge plasma, to be presented in section 5b. Therefore the results presented here are only for the conical section o f the discharge chamber. Figures 5-4 and 5-5 present the electron temperature and electron density in the region 1 to 6 cm downstream of the discharge cathode exit, corresponding to the conical region of the discharge chamber. In this region of the plasma, axial variation in the electron temperature ranged from 6eV to 4eV and radial variation, from 5 to leV. The maximum electron temperature was on the centerline 1 cm downstream of the cathode, and minimum recorded at 1 cm from the anode wall. This is consistent with the density gradients in the plasma. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 102 - 2 Electron number density was found to vary axially from 2.25el2 cm' to le l2 cm'3, from 1cm to 6cm downstream, respectively. Radial variation indicated that density gradients decreased in magnitude with distance from the cathode, with a minimum of 5el0 cm'3. The plasma parameter measurements indicate that the plasma current density is peaked on axis, consistent with a high degree of ionization within the cathode plume. Radial gradients in both electron density and electron temperature were less significant with distance from the cathode. Therefore, the plasma became more uniform in the downstream direction. — Probe 5 (TH15) — Probe 1 (TH15) Saturated Trace Rp » d Not saturated due to sheath growth R „ ~ d < £ 0.8 0.6 3 o 0.4 o .a o 0.2 Q . 30 40 -10 -0.2 -0.4 V bias [V] Figure 5-3. Comparison of cylindrical probe IV characteristics. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 103 S ' a 2 3 2 a a E o 1 cm 2 cm 4 cm 6 cm -15 -10 -5 0 Radial D istance from Centerline [cm] Figure 5-4. Cylindrical Probe Electron Temperature Profiles at TH15. 1 cm 2 cm - * - 4 cm 43- 6 cm 2.51E+12 i 2.01E+12 - E . - S ' 1.51E+12 ( 0 c < D o 1.01E+12 c 2 4 - » o o 1 1 1 5.10E+11 1.00E+10 0 •5 -10 -15 Radial D istance from Centerline [cm] Figure 5-5. Cylindrical Probe Electron Number Density Profiles at TH15. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 104 b) Flat Disc Probe Data: A total of 6 flat disc probes were used in this study. The axial locations of the cylindrical probes were 1, 2, 3, 6, 10, and 14 cm downstream of the keeper electrode. Flat plate probes were used to eliminate the effect of radial sheath expansion that prevented electron saturation of the cylindrical probes in the low- density region of the discharge chamber. Although a sheath still forms around the flat disc probe, the expansion is perpendicular to the surface of the disc, and therefore does not increase the total probe collection area. As the aspect ratio (D/t) o f the disc is 100, end effects are assumed to be negligible. Figures 5-6 though 5-10 present radial variation in electron saturation current, electron number density, electron temperature, and plasma potential for each axial probe location at the TH15 operating point. TH15 operation is defined by the beam voltage, beam current and flow rates in the NSTAR throttle table (Table 4-2). Electron saturation current and number density data is shown from the anode wall to just past the centerline, to illustrate the symmetry and peaked nature of the plasma. However, electron temperature and plasma potential calculations were only made up to the thruster centerline, as passage of the alumina tubes in front of the cathode tended disturbed its operation. Figure 5-7 is the electron number density radial variation. Electron number density was R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 105 reduced from the electron temperature and electron saturation current measurements, both of which were obtained from the current voltage traces by the method described in chapter 2. In the conical region of the discharge chamber, electron number density was found to be peaked on the centerline at a maximum l e i 2 cm'3 1 cm downstream of the cathode and decreased rapidly in the radial direction to a minimum of 4el0 cm'3 near the anode wall consistent with other researchers in the field229,30. This structure is consistent with a high density cathode plume typical of a hollow cathode discharge plasma. In the cylindrical region of the discharge chamber, radial variation in density was not as peaked, and varied radially from 4 e ll cm'3 to 1 el 1 cm'3 at the anode wall. Density gradients in both the radial and axial direction decreased in magnitude with distance from the cathode. In figure 5-8, the radial variation, in electron temperature was similarly peaked. In the conical segment it spanned from a maximum of 5.5 eV on the centerline, to a minimum of 1.5 eV at the anode wall. Radial variation, in the cylindrical segment spanned 4.75 to 3 eV, with the maximum on the centerline, and minimum at the anode wall. Electron temperature measurements have an uncertainty band of +0.5eV, mainly a result of the Maxwellian exponential fitting process as the plasma was not purely Maxwellian. Figure 5-9 is the plasma potential variation, determined as the voltage corresponding to the maximum of the first derivative of the probe trace as discussed in reference 47. The uncertainty in the plasma potential R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 106 measurement is +2V due to the error induced from taking the derivative of a relatively noisy probe trace. Plasma potential was highly depressed on axis from 2 to 14cm downstream of the cathode. The depression is believed to be due to a high concentration o f primaries constrained to the centerline. The concentration of negative charge on the centerline then tends to depress the potential. Therefore, a higher density of primaries on axis will result in a deeper the depression in plasma potential. The on axis potential depression is consistent with the results of other researchers29,33. As you move axially from the cathode exit the primary density decreases and the plasma potential increases. Axial variation in this region was from 21 to 26.5 V, increasing in the downstream direction. The radial variation in plasma potential in the conical region at 1 cm downstream of the cathode exit exhibited a large increase from the centerline to 1 cm from the centerline, from 21 to 23. From 2 to 12 cm radially the potential increases monotonically to 24 V. A similar radial profile was measured for the 2 cm and 3 cm probes, with a centerline potential of 21 volts, increasing to 24V with radial distance from the centerline. There was little radial variation in the cylindrical segment, with the exception of the peak on the centerline. Similar to the electron temperature and density, the gradient in radial variation decreased in the downstream direction, consistent with a more uniform plasma with distance from the cathode. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 107 < E 2 cm 3 cm 6 cm 10 cm 14 cm * - » C 0 ) 3 o c o +3 3 0 .6 r e C O c o £ 0.4 o a > U J -0 .2 Radial Position from Centerline [cm] Figure 5-6. Electron Current Density Profiles at TH15 for VI Configuration. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 108 1.20E+12 1.00E+12 2 cm 3 cm 6 cm 10 cm 14 cm < ? 8.00E+11 6.00E+11 lu 4.00E+11 - 2.00E+11 O.OOE+OO 15 13 1 1 9 7 5 3 1 ■ 1 •3 ■ 5 Radial Position from Centerline [cm] Figure 5-7. Electron Number Density Profiles at TH15 for VI Configuration. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 109 r a 4 I E 10 cm 14 cm -5 1 3 5 7 9 Radial Position from Centerline [cm] 1 1 13 15 Figure 5-8. Electron Temperature Profiles at TH15 for VI Configuration. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 1 1 0 30 29 28 27 ! 26 0 > 0 25 0 . c o 1 24 23 2 2 2 1 2 0 1 cm 2 cm 3 cm 6 cm 10 cm 14 cm -3 1 3 5 7 9 Radial Position from Centerline [cm] 1 1 13 15 Figure 5-9. Plasma Potential Profiles at TH15 for VI Configuration. Figure 5-10 represents the variation in ion saturation current density throughout the discharge chamber. Ion saturation current measurements were made by biasing each probe 25V negative of cathode common potential, to repel all electrons and collect only ions. With the assumption that ions are collected by the probe at the Bohm velocity in order to form a stable sheath, the ion density was calculated using the method discussed in chapter 2. The ion density, like the electron density, was highly peaked on axis, in the conical section of the discharge chamber, confirming that most of the ionization in the nominal R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Ill configuration occurs within the cathode plume and in the vicinity of the cathode. With increasing distance from the cathode the ion density became more uniform (less peaked radially). It is also important to note that the ion density was within 10% of the measured electron density for all probe traces investigated, -5 0 5 10 15 R a d i a l D i s t a n c e F r o m T h r u s t e r C e n t e r l i n e [ c m ] confirming that ions are indeed electrostatically confined by the plasma Figure 5-10. Ion Saturation Current Density Profiles at TH15 for VI Configuration. In general, the plasma parameter measurements for the nominal configuration indicate that the plasma density and temperature is peaked on axis, consistent with a high degree of ionization within the cathode plume, resulting in a radially non-uniform plasma. Radial gradients in both electron density and electron R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 1 1 2 temperature were less significant in the cylindrical region o f the chamber, The beam profile, defined by the ion saturation probe trace at 14cm downstream of the cathode (2 cm upstream of the screen grid), was highly peaked on axis, consistent with faraday probe traces taken in reference 19. The plasma potential was depressed on axis (within the cathode plume) from 1 cm to 3 cm downstream of the cathode, but peaked on axis from 6 to 14 cm downstream. In general, outside of the cathode plume the radial potential variation was monotonic approaching the discharge voltage at the anode wall, in both the cylindrical and conical region of the chamber. c) Optical Probe Data: Relative Neutral Density Profiles: Relative neutral density profiles inside the discharge chamber were obtained with a spatially resolved fiber optic probe measuring photon flux at the 823.2 nm Xel transition. As discussed previously, the ion thruster discharge plasma is optically thin and collisional de-excitation is negligible compared to radiative de-excitation. Therefore all measured photon flux at the wavelength of interest is assumed to be from spontaneous de-excitation, which is by definition independent of the plasma parameters. Figure 5-11 is a plot of normalized 823.2nm photon flux radial profiles. The photon flux is proportional to the production of excited neutral xenon at the particular transition and will be R eproduced with perm ission o f the copyright owner. Further reproduction prohibited without perm ission. 113 referred to as such from this point onward. As an absolute value calibration was not possible, each trace was normalized with respect to the peak signal for each radial sweep to indicate the variation of peak to minimum excited neutral xenon production. All sweeps indicated a depression in the excited neutral production in the vicinity of the centerline. The depression was most severe near the cathode where the peak to minimum flux varied by up to 66%. The depressed region extended from the center out to 4 cm radially from the plume. The depth and radial expanse of the depression decreased with axial distance from the cathode exit. From 2 cm to 6 cm axially from the cathode exit, the centerline flux was 34% and 65% of the peak flux, respectively. From 10 to 14 cm axially from the cathode exit the centerline flux was 88% and 86% of the peak flux respectively. This variation in excited neutral production is consistent with the variation in ionization measured in the Langmuir probe sweeps. Figure 5-11 also indicates that the excited neutral production at the 2, 3 and 6 cm probe locations peaked just off of the centerline and then leveled off to a lower value out to the anode. Langmuir traces have shown the electron number density and temperature decreased sharply in this region. Therefore, an increase in excited neutral production outside of the plume is an indication of neutral depletion in the plume and an increase in neutral density outside of it. Radial variation in the 10 and 14 cm probe sweeps indicate a relatively constant excited neutral production from just outside the plume to the anode wall. This is consistent with R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 114 the electron density and electron temperature measurements in the cylindrical region. tun J 0 cm E c 2 cm 3 cm 6 cm 10 cm 14 cm CO CN 0 0 0 . 9 - ( 0 X D LL C o C L X D 0 . 7 - LL C o c 0 5 0.6 - C O D 0 ) z 0 . 5 - o X L U "8 0.4 - N r o E o z 0.3 -J 1 0 0 5 -5 Axial Distance From The Centerline (cm) Figure 5-11. Normalized Radial Profiles of Photon Flux at 823.2 nm. As mentioned previously, a calibration relating photon flux to the current recorded by the PMT was not made. Therefore, only relative neutral density profiles were obtained with the optical probe diagnostic. Figure 5-12 is a plot of relative neutral density radial profiles calculated from equation 2-23 and the measured electron density and temperature. Each profile was normalized to the peak signal of each probe to show radial variation of neutral density at the particular axial location in the discharge chamber. Figure 5-12 indicates that R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 115 neutral density was severely depleted on the thruster centerline and in the vicinity of the cathode for the 2, 3, and 6 cm probes. This is consistent with proximity to the cathode and a high degree of ionization in the cathode plume. The radial variation was less severe for the 10 and 14 cm probe location, however the neutral density increased sharply with proximity to the anode wall from 13 to 15 cm radially from the centerline. This increase in neutral density is consistent with the location of propellant plenum, which is the primary source of neutral xenon in the discharge chamber. This location is also consistent with the periphery of the NSTAR grid pattern, suggesting a significant loss of neutrals in the region due to a lack of ionization; a direct result of poor radial plasma uniformity in the near grid region. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 116 1 2 cm 3 cm 6 cm 10 cm 14 cm 0.9 0 .8 0.7 e 0 .6 0.5 0.4 0.3 0 .2 0 .1 0 9 1 1 13 15 3 5 •3 • 1 1 7 •5 Radial Position from Centerline [cm] Figure 5-12. Relative Neutral Density Profiles at TH15 for the VI Configuration. In general, the relative neutral density profiles indicate a large neutral density radial variation in the discharge chamber. The variation is consistent with a non- uniform plasma production, neutral depletion in the cathode plume, and the location of the propellant plenum. Another implication of neutral depletion on the centerline is the production of Xelll in this region. If the Xell density is comparable to the Xel density, the production of X elll will increase relative to the bulk of the discharge plasma. Measurements of double ion fraction with an ExB probe in the FT2 NSTAR engine confirm that the production of Xelll is R eproduced with perm ission o f the copyright owner. Further reproduction prohibited without perm ission. 117 restricted to the centerline1 9 . It is therefore likely that neutral depletion is responsible for this increase in doubly ionized xenon. 3) Sensitivity Testing: The FT2 NSTAR ion thruster was subjected to sensitivity testing in order to characterize the macroscopic dependence of discharge plasma production on operating conditions and component wear with runtime. The discharge chamber sensitivity to ±3% variation in main flow, cathode flow, and beam current, and to ±5% variation in beam and accelerator voltage, was determined for the minimum- (THO), half- (TH8), and full-power (TH15) throttle levels. For each power level investigated, 16 high/low operating conditions were chosen to vary the flows, beam current, and grid voltages in a matrix that mapped out the entire parameter space in accordance with the Taguchi theory of experiments64. The 16 x 5 matrix of data generated was used to determine the sensitivity of the dependent parameters— discharge voltage, discharge current, discharge loss, double-to-single-ion current ratio, and neutralizer-keeper voltage— to the variations in the independent parameters—main flow, cathode flow, beam current, and beam voltage. The sensitivities or partial derivatives of each dependent parameter with respect to each independent parameter were determined using a least-squares fit routine. Variation in these sensitivities with R eproduced with perm ission o f the copyright owner. Further reproduction prohibited without perm ission. 118 thruster wear / runtime was recorded over a 20,000 hour period, in order to determine if discharge performance changed with thruster wear. A sampling of calculated sensitivities is shown in Table 5-4. DISCHARGE PARAMETER SENSITIVITY TO MAIN FLOW SENSITIVITY TO CATHODE FLOW SENSITIVITY TO BEAM CURRENT Jd -0.19 A 1.48 A 10.94 — seem seem A v d V -0.54 V -2.08 V 8.31 — seem seem A £b W / W / W / -7.01 / A 3.71 /y4 107.0 seem seem A Table 5-4. BOL TH15 Engine Sensitivities to Flow and Beam Current at Full Power Figures 5-13 through 5-15 are plots of the discharge-loss, voltage, and current sensitivities at full power (TH15) versus runtime. The plots indicate that increasing main flow from the nominal set-point reduces discharge loss. This is because both the discharge voltage and discharge current are highly sensitive to changes in main flow. As the main flow is increased, the discharge voltage and discharge current decrease (Figure 5-13 and 5-14). Therefore, increasing main flow lowers the required cathode discharge power (J d V d ) for a given level of ionization, thus reducing the discharge loss for a given beam current set-point. Increasing cathode flow, however, increases discharge loss. Although increasing cathode flow also reduces discharge voltage, the cathode operates less R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 119 efficiently at cathode flow rates above the nominal set-point. As seen in figure 5-15, increasing cathode flow increases discharge current, to such an extent that the discharge power increases with increasing cathode flow. Therefore, for a fixed beam current, discharge loss increases for a high cathode flow rate set- point. Increasing the beam current also increases discharge loss. In order to create more ions, the discharge current and voltage must be increased. S E C O o c o a) C O 0 0 c t o . 2 c o o > _ _ l Q ) 25 2 0 15 1 0 5 0 -5 -1 0 A a A -A A • • • • □ □ □ □ □ □ □ □ Ch 0.0 5.0 10.0 15.0 R u n H ou r (khr) ~A r~ •- C a th o d e F lo w C t M ain F lo w A B e a m C u rren t □ 20.0 25.0 160.0 140.0 E 120.0 T O < D C O o 100.0 -£■< 80.0 > c ~ O C O ~ < = > aj a) C O 60.0 C O c O 2 40.0 = < D O o > 20.0 to sz o C O b 0.0 30.0 Figure 5-13. Discharge-Loss Sensitivity at Full Power (TH15). R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 1 2 0 u > E c o 0) o co ^2 ® S. O ) to ^ T O 0.0 -0.5 -1 .0 -1.5 -2 .0 -2.5 -3.0 -3.5 □ □ □ □ A A A • • • • • • • □ □ -A A C a t h o d e F lo w D M ain F lo w A B e a m C u r r e n t 9.0 8 .0 7.0 6 .0 5.0 4.0 3.0 2 .0 1 .0 0 .0 ( / ) ^ 5> C O a j O o > 0.0 5.0 10.0 15.0 R u n H o u r (k hr) 20.0 25.0 30.0 Figure 5-14. Discharge-Voltage Sensitivity at Full Power (TH15). c e 5 <D c o a ) o C O -2 C D o C D 16.0 3.0 2.5 12.0 2.0 10 .0 1.5 8.0 1 .0 6.0 • — C a t h o d e F lo w ; □ M ain F lo w -A — B e a m C u rren t 0.5 + 4.0 0.0 U2-D 0.0 -0.5 30.0 25.0 10 .0 15.0 20.0 0.0 5.0 C D ~ ~ C= < CD " W c ■ £ 2 ? 2 ? ^ o ° C D R u n H o u r (khr) Figure 5-15. Discharge-Current Sensitivity at Full Power (TH15). R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 121 Comparison of the sensitivity of discharge loss to runtime indicates that wear of the thruster components does affect discharge performance. Specifically, the sensitivity of required discharge power to changes in cathode flow increases with thruster wear. This is likely due to the enlargement of the keeper orifice, as well as increasing neutral loss from accelerator grid aperture enlargement. The net result, however, is that the discharge loss sensitivity to changes in flow and beam current increased with runtime. Figures 5-16 through 5-18 are plots of the discharge-loss, -voltage, and -current sensitivities at half power (TH8) versus runtime. As with TH15 operation, increasing main flow reduces the discharge power for a given beam current, and therefore reduces the discharge loss. However, unlike TH15 operation, increasing cathode flow reduces discharge loss. At TH8, the sensitivity and reduction in discharge voltage due to increasing cathode flow, outweighs the effect of increasing discharge current due to increasing cathode flow. Therefore, the product of current and voltage, the discharge power, decreases for increased cathode flow, as does the discharge loss. Similar to TH15, increasing beam current increased discharge loss, as more electrons (discharge current) are required to create the level of ionization necessary to support the increased beam current requirements. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 1 2 2 Comparison of TH8 sensitivity with runtime indicates that sensitivity of discharge current and voltage to beam current and flow rate was variable with runtime. In fact, after 25,000 hours of operation, the BOL and EOL discharge loss was roughly the same. 10 C D -o O sz c c o :! § 11 < D L C D T O S Z u -5 -10 -15 -20 C a th o d e Flow -E3- M ain Flow B eam C urrent k ~~O- "Q- tP 400.0 350.0 300.0 250.0 200.0 150.0 100.0 50.0 0.0 0.0 5.0 10.0 15.0 20.0 R un Flour (khr) 25.0 30.0 -&< ;> c f = t O c 5 ( ? ) ^ CO CO < D T O _ C O Figure 5-16. Discharge-Loss Sensitivity at Half Power (TH8) R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Discharge Current Sensitivity t o F lo w Discharge Voltage Sensitivity t o Flow 123 60.0 0.0 50.0 - 40.0 5 -3.0 30.0 20.0 -4.0 - C athod e Flow HU- Main Flow -A - B eam Current 10.0 -5.0 0.0 - 6.0 30.0 20.0 25.0 10.0 15.0 0.0 5.0 0 ro Q d Run Hour (khr) Figure 5-17. Discharge-Voltage Sensitivity at Half Power (TH8). 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 - 0.2 -0.4 C athode Flow □ Main Flow -A - B eam Current O -Q- - □ 1 9.0 8.8 8.6 8.4 8.2 8.0 7.8 - 7.6 0.0 5.0 10.0 15.0 20.0 25.0 30.0 Run Hour (khr) Figure 5-18. Discharge-Current Sensitivity at Half Power (TH8). R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Discharge Current Sensitivity t o B e a m Discharge Voltage Sensitivity t o Beam Current (V/A) Current (V/A) 124 Figures 5-19 through 5-21 are plots of the discharge-loss, -voltage, and -current sensitivities at minimum power (THO) versus runtime. As with TH15 and TH8 operation, discharge loss was reduced with increasing main flow, and increased with increasing beam current. Similar to TH8 operation, increasing cathode flow also reduced discharge loss. However, THO discharge current operation was not particularly sensitive to changes in cathode flow; therefore the reduction is discharge voltage decreased the required discharge power. In terms of sensitivity to thruster wear, the sensitivity of discharge current and voltage to flow rate and beam current, respectively, increased over time. As such, the discharge power and loss sensitivity also increased with thruster wear. 1400.0 1200.0 -20 1000.0 £ -40 - o o V ) ° -60 - > 0 ) 800.0 - 600.0 o £ -80 m * ■ * - 400.0 — — C a t h o d e F io w M ain F lo w — 4 — B e a m C u rren t -100 200.0 0.0 -120 30 20 25 10 15 0 5 ;> c . ■ * = : o c o ^ C > CD <D CO ^ C O c C O Q J O j— " T 1 = 3 a) o ™ T O O © < o C O R u n H o u r (khr) Figure 5-19. Discharge-Loss Sensitivity at Minimum Power (THO). R eproduced with perm ission o f the copyright owner. Further reproduction prohibited without perm ission. 125 60.0 0.0 50.0 u . - 2.0 f -3.0 I f -4.0 Q ) O w " cn < u > -5.0 O )'W ’ r a 0 3 | 5 '60 0 ) -7.0 CO I -8.0 40.0 30.0 20.0 — • - C a t h o d e F lo w — Q — M a in F lo w — A — B e a m C u r r e n t 10.0 -9.0 - 10.0 30 25 0 10 15 20 5 R u n H o u r (k h r) Figure 5-20. Discharge-Voltage Sensitivity at Minimum Power 35.0 0.4 03 " c o a : 5 o 30.0 p: 0.0 O S' -0.2 ’> 2 E -0.4 c o ( D o • e i. -°-6 Q ) - 0.8 25.0 20.0 15.0 C a t h o d e F lo w M ain F lo w B e a m C u r r e n t 10.0 C O sz o t o o 0.0 25 30 0 10 15 20 5 R u n H o u r (khr) Figure 5-21. Discharge-Current Sensitivity at Minimum Power (THO). R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. D i s c h a r g e - C u r e n t S e n s it iv it y t o Beam B D i s c h a r g e - V o l t a g e S e n s i t i v i t y to B e a m C u r r e n t (A /A ) S C u r r e n t ( V / A ) 126 The ±5% variation in accelerating voltage did not have a measurable effect on any discharge parameters for the three power levels investigated. Variation in beam voltage had a measurable effect only on discharge loss. Figure 5-22 shows the sensitivity of discharge loss to beam voltage versus runtime for the three power levels investigated. Increasing the beam voltage by 100 V tended to reduce discharge loss by 3-8 eV/ion, suggesting that a more focused beam improved the screen transparency : t l ~ o C O 'C *= > C D 0 ) (f) ^ * £ c o o > O T O " V o a> » I -§ 2 C O CD 0.00 - 0.01 - 0.02 -0.03 -0.04 -0.05 -0.06 -0.07 -0.08 -0.09 M in P o w e r H a lf P o w e r F u ll P o w e r 0.0 5.0 10.0 15.0 20.0 R u n H o u r (k h r) 25.0 30.0 Figure 5-22. Discharge-Loss Sensitivity to Beam Voltage at All Power Levels. Overall, the sensitivity data suggests that discharge operation is most sensitive to changes in cathode flow rate. This is because, as the Langmuir probe traces have shown, much of the ionization in the nominal NSTAR engine occurs along the R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 127 thruster centerline, in the cathode plume, with the neutral source being cathode flow rate, and not the main flow from the plenum. It is also clear that increasing main flow above the nominal set point reduces discharge voltage and discharge loss, however that effect must be traded with reduced propellant utilization, which reduces the total engine efficiency. Not surprisingly, plasma production and discharge voltage increases with beam current, as in order to increase ion production for a fixed neutral population, primary electron input must increase. Similarly, increasing the primary electron content, by increasing the discharge current for a fixed neutral input, increases the plasma’s resistivity, manifesting itself as an increase in the discharge voltage. Discharge plasma production was not highly sensitive to increasing the electric field strength between the grids, suggesting the current NSTAR grid configuration is sufficiently optimized in terms of the screen grid’s transparency to ions. B. Enhanced 4 Ring Cusp: Case V2 1) Overall Performance Case V2 is a 4-ring cusp modified NSTAR engine. In this configuration, a ring of magnets was added to the center of the conical section of NKOl, with the direction of magnetization pointing into to the discharge chamber, normal to the R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 128 surface of the magnet. To retain the alternating polarity cusp design, the cathode ring polarity was reversed, and the middle and front magnet rings were left unchanged. A thin steel shim was placed in the interior of the chamber to aid in the retention of magnets to the cone section. Although this aided in magnet insertion, the ferrous material resulted in a significant lowering of the cusp strength, reducing its effectiveness at confining electrons (Table 5-5). CUSP LOCATION CUSP STRENGTH [G] Cone 820 Middle 1230 Front 1100 Table 5-5. Cusp Strengths for Nominal Configuration Figure 5-23 and 5-24 are plots of the MAXWELL 2D predicted magnetic contour and field lines. Although this configuration closed the 30G contour throughout the chamber, it did not result in a noticeable performance change over the nominal configuration (Table 5-6). In fact the discharge current was 14.3A and discharge loss 201 eV/ion, essentially the same as the nominal configuration. This can be attributed to the weak cusp strength of the new conical magnet ring because of the steel shim used to retain the magnets. A ferrous material shunts magnetic field lines, and so the use of the shim reduced the surface magnetic field strength. Measurement of the cusp strength with a Gauss-meter revealed it was only 820G, insufficient to prevent measurable R eproduced with perm ission o f the copyright owner. Further reproduction prohibited without perm ission. 129 primary electron loss to the cusp. The shim was subsequently removed for case V3, and the cusp strength increased to 1800 G. V2 testing was made, however, with the shim in place. An analysis of the electron and ion confinement for all configurations will be discussed in chapter 6. 7 . 0 0 0 0 e - 0 0 3 6 . 0 0 0 0 e - 0 0 3 S . 0 0 0 0 e - 0 0 3 4 . 0 0 0 0 e - 0 0 3 3 . 0 0 0 0 e - 0 0 3 2 . 0 0 0 0 e - 0 0 3 1 . 0 0 0 0 e - 0 0 3 Figure 5-23. 4 Ring Cusp NSTAR (V2) Magnetic Contour Plot. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 130 Figure 5-24. 4 Ring Cusp NSTAR (V2) Magnetic Field Lines. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 131 DISCHARGE PARAMETER NKO (V2) TH15 TH8 TH0 Jb (A) 1.76 1.10 0.51 Jd (V) 14.3 8.5 5.3 Vd (V) 24.7 25.1 25.5 eb (V) 201.4 194.5 265.0 fitot 0.612 0.605 0.392 Table 5-6. Enhance 4-Ring Cusp NSTAR Performance. 2) Langmuir Probe Data Radial plasma parameter profiles for case V2 were made with six flat disk Langmuir probes located at 1cm, 3 cm, 4cm, 10cm, and 14cm axially with respect to the discharge cathode exit. Figures 5-25 to 5-27 present the radial variation in electron number density, electron temperature, and plasma potential, for each axial probe location at the TH15 operating point. As in the nominal case, TH15 operation is defined by the beam voltage, beam current, and flow rate set points in the NSTAR throttle table. Therefore changes in performance will be limited to changes in the discharge current and voltage required to produce and extract 1.76A of beam current through the optics. Figure 5-25 is a plot of the electron number density. In the conical region of the discharge chamber, the radial variation in electron density had a primary peak on the centerline, as well as a secondary peak off axis. The primary peak on the centerline was due to the cathode plasma plume and had a maximum value of R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 132 8.75ell cm-3, as measured 1cm downstream of the cathode. The secondary peak was caused by the addition of the conical magnet ring, causing electrons leave the centerline axis and to travel along the new field lines to the conical magnetic cusp. The maximum number density in the secondary peak was 1.5el 1 cm-3, as measured 9 cm radially from the centerline, by the probe 4cm axially downstream of the cathode. The radial variation of electron density in the cylindrical region o f the plasma was relatively flat, confirming that a field free volume is necessary for increased plasma uniformity. Electron density varied from a maximum of 2el 1 cm-3 on the centerline to 1.5el 1 cm-3 near the anode wall, in the cylindrical segment. Figure 5-26 is a plot of electron temperature radial profiles in the discharge chamber. The uncertainty in the electron temperature calculation is + 0.5 eV due to the Maxwellian fitting errors. The radial variation in electron temperature in the conical segment, was peaked on axis (5.2 eV), with an additional off axis peak (4.8 eV), corresponding to the electron density peaks described previously. The electron temperature reached a minimum of 2eV near the anode wall in the conical segment. Radial variation, in the cylindrical segment was less peaked, and spanned 4.5 to 3 eV, with the maximum on the centerline, and minimum at the anode wall. Figure 5-27 is the plasma potential variation. The plasma potential structure was varied in the conical region of the discharge chamber. In the region 1 to 3 cm downstream of the cathode, the plasma potential increased in the radial direction. The potential R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 133 also exhibited a depression in potential on axis and a large off axis peak in potential in the region of the conical magnetic cusp. At 4 cm downstream the plasma potential was peaked on axis, leveling off to about 26V, and then increasing in the radial direction in the region corresponding to the magnetic cusp. From 10 to 14 cm downstream, there was minimal radial variation in the plasma potential, but decreasing axially in value from 27.5 to 26.5V. '.00E+11 .00E+11 - 2 cm 3 cm 4 cm 10 cm 14 cm 7.00E+11 - E 6.00E+11 “ 5.00E+11 * D 4.00E+11 - 3.00E+11 2.00E+11 1.00E+11 O.OOE+OO 11 13 15 1 7 9 •3 • 1 3 5 -5 Radial Position from Centerline [cm] Figure 5-25. Electron Number Density Profiles at TH15 for V2 Configuration. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 134 5.5 5 - 4.5 4 > a > E 3,5 o U J 2.5 2 cm 3 cm 4 cm 10 cm 14 cm 1.5 1 -5 -1 1 3 5 7 9 Radial Position from Centerline [cm] 11 13 15 Figure 5-26. Electron Temperature Profiles at TH15 for V2 Configuration. R eproduced with perm ission o f the copyright owner. Further reproduction prohibited without perm ission. 135 30 29 .2 c a > E in r e “■ 26 25 - 24 J - - - - - - - - - - - - - - - - - - - -, - -- - -- - - -- - -- - -- - -- -, --------------------, - - - - - - - - - - - - - - - - - - - -, ---------------------, - -------------------r -------------------, - -------------------, - - - - - - - - - - - - - - - - - - - -, --------------------, -5 -3 -1 1 3 5 7 9 11 13 15 Radial Position from Centerline [cm] Figure 5-27. Plasma Potential Profiles at TH15 for V2 Configuration. Figure 5-28 represents the variation in ion saturation current density throughout the discharge chamber. In the conical section, ion density was highly peaked on axis, and also exhibited a secondary peak due to the new magnetic cusp. Ion density in the cylindrical segment was essentially flat from the centerline out to 13 cm radially. In fact, the 14cm probe trace which was used as the beam profile measurement for these studies, exhibited a flatness parameter of greater than 85%, largely due to the field free volume in the cylindrical segment near the grids. 2 cm 3 cm 4 cm 10 cm 14 cm 6 cm R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 136 The plasma parameter measurements for the VI 4-ring cusp configuration indicated that the electron density, ion density, and temperature had a primary peak on axis, as well as a secondary peak off axis, in the vicinity of the new magnetic cusp. The addition of the new cusp brought primary electrons and ions off the centerline and created a radially uniform plasma throughout the chamber. The V2 configuration also yielded a remarkably flat ion current density profile just upstream of the optics, which represents the optimum profile for an ion thruster in terms of minimizing grid wear and thrust vector losses. From the VI case alone, it is likely that the beam flattening effect was due to the migration of primary electrons off-axis and the fact that the addition of the conical magnet ring pulled the field lines closer to the anode, increasing the field free volume. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 137 -5 0 5 10 15 R adial D istan ce From T h ru ster C en terlin e [cm] Figure 5-28. Ion Saturation Current Density Profiles at TH15 for V2 Configuration. C. Enhanced 4 Ring Cusp: Case V3 1) Overall Performance Case V3 is a 4-ring cusp modified NSTAR engine. In this configuration (in addition to the conical ring added in case V2) the middle magnet ring was strengthened by adding a ring of magnets to the interior of the discharge chamber directly over the existing ring. The steel shim from case V2 was removed from the conical ring to reduce primary electron loss to this cusp R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. (Table 5-7). Figure 5-20 and 5-30 are plots of the MAXWELL 2D predicted magnetic contour and field lines. This configuration closed the 50G contour throughout the chamber at the expense of reducing the field free volume in the cylindrical segment of the discharge chamber, specifically just upstream of the optics. Equation 3-58 predicts a 30% improvement in ion confinement by going from the 20 to 50 G contour line closure. Primary electron loss is less than 10% in this configuration; therefore the gain in performance improvement can be attributed to enhanced ion confinement. CUSP LOCATION CUSP STRENGTH [G] Cone 1800 Middle 2000 Front 1100 Table 5-7. Cusp Strengths for V3 Configuration R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 139 B[T] 7 , 0 0 0 0 e ~ 0 0 3 / 6 . 0 0 0 0 C - 0 0 3 S.0000e-003 4. 0000e-003 / 3 , 0 0 0 0 6 - 0 0 3 2 . 0 0 0 0 e - 0 0 3 1 . 0 0 0 0 e - 0 0 3 Figure 5-29. Magnetic Contours for Case V3. R eproduced with perm ission o f the copyright owner. Further reproduction prohibited without perm ission. Figure 5-30. Magnetic Field Lines for Case V3. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 141 Table 5-8 is a performance summary of the V3 configuration. For TH15, the discharge current needed to produce 1.76A of beam current was only 11.5A, more than a 19% reduction from the nominal configuration. This resulted in a discharge loss o f 167.8 eV/ion, versus 207 eV/ion for the nominal NKOl performance. For TH8, the discharge current needed to produce 1.1 A of beam current was only 7.3 A, resulting in an 11% reduction in discharge loss from the nominal configuration. Similarly, for THO operation, the discharge loss was reduced 20% from the nominal configuration. This confirms that increasing the Gauss level of the closed magnetic contour closest to the anode serves to magnetically confine ions, and reduces their loss to the walls, lessening the discharge power requirement to extract the required beam current. More detail on this mechanism will be discussed in chapter 6. D I S C H A R G E P A R A M E T E R N K O ( V 3 J T H 1 5 T H 8 T H O J b ( A ) 1 . 7 6 1 . 1 0 0 . 5 1 J d ( V ) 1 1 . 5 7 . 3 4 . 3 V d ( V ) 2 5 . 6 2 6 . 5 2 5 £ b ( V ) 1 6 7 . 8 1 7 6 . 4 2 1 1 . 4 Plot 0 . 6 2 8 0 . 6 1 3 0 . 4 1 5 Table 5-8. 4-Ring Cusp V3 NSTAR Performance. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 2) Langmuir Probe Data 142 Radial plasma parameter profiles for case V3 were made with six probes located at 1cm, 2 cm, 3cm, 4cm, 10cm, and 14cm axially with respect to the discharge cathode exit for the TH15 operating point. Each probe traversed from the anode wall to just past the centerline. TH15 operation is defined by the beam voltage, beam current, and flow rate set-points in the NSTAR throttle table. Figure 5-31 is a plot of the electron number density. In the conical region of the discharge chamber, the radial variation in electron density had a primary peak on the centerline, with a secondary peak off axis. The primary peak, on the centerline had a maximum value of 4.5ell cm-3, as measured 1cm downstream of the cathode. The secondary peak was caused by the addition of the conical magnet ring, causing electrons to travel along the field lines to the new magnetic cusp. The maximum number density in the secondary peak was 1.75ell cm-3, 4cm radially from the centerline, as measured by the probe 4cm downstream of the cathode. The radial variation of electron density in the cylindrical region of the plasma decreased monotonically out to the anode wall. It varied from a maximum of 2 e ll cm-3 on the centerline to 5el0 cm-3 near the anode wall. Figure 5-32 is a plot of electron temperature profiles in the discharge chamber. The radial variation of electron temperature in the conical segment was peaked on axis (4.5 eV), with an additional off axis peak (3 eV), corresponding to the R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 143 electron density peaks described previously. The electron temperature near the anode wall reached a minimum of 2.5eV in the conical segment. The electron temperature reached a minimum of 2 eV in the conical section, just radially in from the secondary peak, as measured by the 1, 2, and 3 cm axial position probes, suggesting that both primary and secondary electrons were tightly confined to the field lines terminating at the magnetic cusps. Radial variation, in the cylindrical segment was less peaked, and spanned 4 to 2.5 eV, with the maximum on the centerline, and minimum at the anode wall. Figure 5-33 is the plasma potential variation. The plasma potential structure in both the conical and cylindrical region of the discharge chamber, exhibited a radial trend of increasing potential with proximity to the anode wall. In the conical section, the plasma potential was roughly 26V on axis, and increased up to 32 V near the anode wall. In the cylindrical region of the chamber, the radial variation was relatively flat from the centerline out to 11cm. From 11 cm to the anode wall, however, the potential increased by 2 to 3V. Figure 5-34 represents the variation in ion saturation current density throughout the discharge chamber. For case V3, saturation current measurements were only made with a 500 Ohm current shunt, resulting in off scale centerline data for the 1, 2, and 3cm radial profiles in the figure. In the conical section, ion current density was highly peaked on axis, with a secondary peak off axis due to the new magnetic cusp. This behavior is identical to the electron current density, confirming that the electrons R eproduced with perm ission o f the copyright owner. Further reproduction prohibited without perm ission. 144 electrostatically confine the ions, and quasineutrality is maintained throughout the plasma. In the near grid (cylindrical) region, ion density was peaked on the centerline, and exhibited a monotonically decreasing radial profile out to the anode. This behavior is markedly different than case V2, which had a uniform radial plasma profile. The increased magnetic field strength in this configuration reduced the field free region, which tends to make the plasma less uniform as it is more constrained. 5.00E+11 n 4.50E+11 - 4.00E+11 - ^ 3.50E+11 - E 3.00E+11 - §• £ 2.50E+11 - Q c 2 2.00E+11 - o a > U J 1.50E+11 - 1.00E+11 - 5.00E+10 - O.OOE+OO -5 -3 -1 1 3 5 7 9 11 13 15 Radial Position from Centerline [cm] Figure 5-31. Electron Number Density Profiles at TH15 for V3 Configuration. 1 c m 2 c m 3 c m 4 c m 6 c m 1 0 c m 1 4 c m R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 145 6 5 . 5 5 4 . 5 4 3 . 5 e o o 3 i » 4 -i o © IU 2 . 5 2 1 . 5 1 - 5 - 3 P rob el Probe2 Probe3 Probe4 Probe5 Probe6 Probe7 1 3 5 7 9 R a d i a l P o s i t i o n f r o m C e n t e r l i n e [ c m ] 11 1 3 1 5 Figure 5-32. Electron Temperature Profiles at TH15 for V3 Configuration. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 146 32 n 31 30 29 o 27 Q. J 2 C L 26 25 24 23 22 P r o b e l P r o b e 2 P r o b e 3 P r o b e 4 P r o b e 5 P r o b e 6 P r o b e 7 1 3 5 7 9 Radial Position from Centerline [cm] 11 13 15 Figure 5-33. Plasma Potential Profiles at TH15 for V3 Configuration. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 147 80 - 1 cm 2 cm ------ 3 cm 4 cm 6 cm 10 cm 14 cm 6 cm 10 cm 14 cm < / ) c 0 ) D 4 0 - 4 cm 3 o ° 2 0 - 3 cm 2 cm ” 1 cm o- 15 10 0 5 Radial Distance From Thruster Centerline [cm] Figure 5-34. Ion Saturation Current Density at TH15 for V3 Configuration. The plasma parameter measurements for the V3 4-ring cusp configuration indicated that the electron density, ion density, and temperature had a primary peak on axis, as well as a significant secondary peak off axis, in the vicinity of the conical segment magnetic cusp. The addition of the new cusp brought electrons and ions off of the centerline and created a more radially uniform plasma in the cylindrical section. The addition of the strengthened middle magnet ring, increased ion confinement by allowing closure of the 50G contour line, and as a result the discharge loss decreased by 20% versus the nominal configuration. The strengthening of the middle magnet ring, did however, reduce the magnetic field free region in the cylindrical section and this resulted in a peaked ion current density profile just upstream of the optics. Although the R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 148 beam profile was peaked, the magnitude of the current density peak was on the order of the nominal configuration; therefore V3 represents a dramatic improvement in performance and cathode life over the nominal configuration. D. Enhanced 3 Ring Cusp: Case V4 1) Overall Performance Case V4 is an enhanced 3-ring cusp engine. In this configuration, the conical ring from case V3 was removed, but the strengthened middle magnet ring was left in place. The cathode magnet ring polarity was reversed relative to case V2 and V3 to allow for alternating polarity magnetic cusps. Figures 35 and 36 are plots of the MAXWELL 2D predicted magnetic contour and field lines. This configuration also closed the 50G contour throughout the chamber and the removal of the conical ring pushed the 50G contour line closer to the anode wall. However, the total volume where the magnetic field is less than 10G was reduced for case V4, versus case V3. As magnetic plasma confinement has 1/B dependence, it is anticipated that increasing the volume relative to the 50G contour has more positive effect on plasma uniformity than increasing the volume that falls within the 10G contour. Therefore, case V4 did serve to increase the field free volume throughout the chamber. In addition, removal of R eproduced with perm ission o f the copyright owner. Further reproduction prohibited without perm ission. 149 the conical ring depressed the field line in the cylindrical segment, believed to be responsible for the peaked profile in case V3. This configuration separates the effects of increasing the closed contour line strength inside the chamber versus adding another cusp to drive primary electrons off axis. As long as the ions are adequately magnetically confined and the primary electron confinement length is sufficiently large to ensure an inelastic collision occurs prior to loss to the anode, the addition o f an additional cusp is not necessary for the 30cm engine. CUSP LOCATION CUSP STRENGTH [G] Cone N/A Middle 2000 Front 1100 Table 5-9. Cusp Strengths for V4 Configuration R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Figure 5-35. Magnetic Contours for Case V4. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 151 Figure 5-36. Magnetic Field Lines for Case V4. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 152 Table 5-10 is a performance summary of the V4 configuration. For TH15, the discharge current needed to produce 1.76A of beam current was 11.6A, as compared to 11.3A for case V2, and 14.5 for the nominal case VI. The discharge loss for V4 was 165 eV/ion, versus 167 for case V3, a 21% reduction from the nominal NSTAR configuration. The slight improvement in discharge loss for V4 versus V3 was due to lower discharge voltage operation. Similar gains in discharge loss and total thruster efficiency were achieved for the throttled conditions as well, with a 10% and 19% reduction in discharge loss at TH8 and THO operation respectively. An analysis of the systems engineering implications of this performance improvement will be discussed in chapter 7. D IS C H A R G E P A R A M E T E R N K O (V4) T H 15 TH 8 THO J b (A ) 1.76 1.1 0.51 J d (V ) 11.6 7.5 4.5 V d (V ) 25.1 26.2 24.65 Eb(V ) 166.3 179.1 218.1 Plot 0.629 0.612 0.396 Table 5-10. 4-Ring Cusp V3 NSTAR Performance. 2) Langmuir Probe Data Radial plasma parameter profiles for case V4 were made with six flat disk Langmuir probes located at 1 cm, 2 cm, 3 cm, 6 cm, 10 cm, and 14 cm axially R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 153 with respect to the discharge cathode exit. Figure 5-37 is a plot of the electron number density. In the conical region of the discharge chamber, the radial variation in electron density was highly peaked on the centerline. It reached a maximum value of 1.1 el 2 cm'3 , as measured 1cm downstream of the cathode on axis and a minimum of 3e9 cm'3 at the anode wall in the conical segment. It is important to note that this radial profile has the same axial peak value but a significantly lower density off the centerline. Therefore the radial averaged electron number density is proportionately lower for case V4, consistent with the discharge current set-point. The radial variation of electron density in the cylindrical region of the plasma was relatively flat, from the centerline out to 10 cm radially, at 2 e ll cm'3. From 10 to 15 cm radially, the electron density decreased monotonically from 2 e ll cm'3 to le9 cm'3, near the anode wall. Figure 5-38 is a plot of electron temperature profiles in the discharge chamber. The +0.5 eV error bars are not shown on the figure for clarity. The radial variation of electron temperature in the conical segment was peaked on axis (4.9 eV) and decreased monotonically to a minimum of 2.3 eV near the anode wall. Variation, in the cylindrical segment was less peaked, and spanned 4.0 to 3.3 eV from the centerline out to 11 cm radially. From 11 cm to the anode wall the electron temperature decreased monotonically to a minimum of 2.4 eV. Figure 5-39 is the plasma potential variation for case V4. The plasma potential structure in the conical region of the discharge chamber was depressed on axis with a R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 154 minimum of 20V on the centerline increasing to 23 V just outside of the cathode plume, similar to the nominal case. The potential on axis increased with axial distance from the cathode. As in case V3, the plasma potential increased with radial distance from the centerline, from 20V on the centerline to 26V near the anode wall. In the cylindrical region of the chamber, the plasma potential was peaked on axis, but exhibited little radial variation outside of the cathode plume region out to 12 cm radially. The plasma potential increase from 12cm to the anode wall was from 23.5 to 26.5 V respectively. 1.20E+12 1.00E+12 —a— 2 c m 3 c m « 8.01E+11 1 0 c m 1 4 c m 6.01E+11 E 4.01E+11 2.01 E+11 1.00E+09 20 10 15 ■ 5 0 5 Radial Position from Centerline [cm] Figure 5-37. Electron Number Density at TH15 for V4 Configuration. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 155 a > a. 3 E J p c o k - ® 2 h i 1 - - # 1 c m — ft— 2 c m - * — 3 c m —o — 6 c m — 1 0 c m — b — 1 4 c m 0 5 10 Radial Position from Centerline [cm] 15 20 Figure 5-38. Electron Temperature at TH15 for V4 Configuration. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 156 30 n 1 c m 2 c m 3 c m 6 c m 1 0 c m 1 4 c m 26 o 25 5 24 23 10 15 5 -5 0 Radial Position from Centerline [cm] Figure 5-39. Plasma Potential at TH15 for V4 Configuration. Figure 5-40 represents the variation in ion saturation current density, with the vertical scale expanded to show the ion density structure throughout the chamber. In the conical section, ion current density was highly peaked on axis, but became less peaked with axial distance from the cathode. In the near grid (cylindrical) region, ion density was flat from the centerline out to 11cm radially. From 11cm to 15cm the ion current density decreased monotonically to the anode wall. This behavior is different than case V3, which had a non- uniform beam profile from the centerline to the anode wall. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 157 - 5 0 5 1 0 1 5 R a d i a l D i s t a n c e F r o m T h r u s t e r C e n t e r l i n e [ c m ] Figure 5-40. Ion Current Density at TH15 for V4 Configuration. The plasma parameter measurements for the V4 3 ring cusp configuration indicated that the electron density, ion density and temperature had a large primary peak on axis and a non-uniform plasma in the conical region of the discharge chamber. However, in the cylindrical region, the plasma became more uniform as the primary and secondary electrons were brought off axis in their transit to the strengthened middle magnet ring. The ion current density profiles show a significant flattening out, suggesting that ions are electrostatically confined to the electrons. Case V4 also had excellent performance, i.e. reduced ion loss to the walls, indicating that the 50G contour line closure is all that is required to enhance ion confinement. The strengthening of the middle magnet R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 158 ring without the conical cusp increased the magnetic field free region in the cylindrical section and this resulted in a flat ion current density profile from the centerline out to 11cm, a dramatic improvement over case V3. In summary, V4 represents a dramatic improvement in performance and plasma uniformity, the implications of which will be discussed in chapter 7. E. Discharge Loss Versus Propellant Utilization Efficiency Measurement Discharge loss versus propellant utilization efficiency was measured for the V I, V2, V3, and V4 magnetic field configurations tested. Although a discharge loss curve was generated for V2, it was not made at a constant discharge voltage, therefore it is not directly comparable to V I, V3 and V4, and cannot be compared with the OD model. As such, it is not discussed in chapter 6 or below. The propellant utilization efficiency was measured from 95% to 80% in approximately 5% increments, whilst holding the discharge voltage and beam current fixed, allowing direct comparison of experimental data to the model developed in chapter 3. The propellant utilization efficiency was varied by changing the main flow rate, increasing main flow for reduced propellant utilization and decreasing main flow for increased propellant utilization. As shown in the sensitivity testing, the discharge voltage is highly dependent on cathode and main flow. Therefore, in order to hold the discharge voltage R eproduced with perm ission o f the copyright owner. Further reproduction prohibited without perm ission. 159 constant, the cathode flow rate was changed for each propellant utilization efficiency point investigated. The beam current was held at the nominal set point as defined by the NSTAR throttle table, by varying the discharge current. As all discharge parameters are dependent on flow rate it was an iterative process to find the cathode flow rate and discharge current to achieve the desired propellant utilization efficiency, beam current, and discharge voltage. Once this point was achieved the engine was allowed to equilibrate, then the discharge parameters were recorded. Figure 5-41 is a comparison of the TH15 discharge loss curve generated for cases V I, V3, and V4. It is interesting to note that the nominal and cases V3 and V4 have similar discharge loss curves. V4 is shifted essentially except they are shifted vertically from each other. Similarly, case V3 and VI have similar discharge loss curves, but they are shifted horizontally from each other. However, case V3, which closes the same contour line as case V4, has a different discharge loss shape because it has an additional cusp. What this suggests, is that from going to case VI to V4, the primary electron loss remains unchanged, and only ion and secondary electron loss is reduced. However, in case V3, primary electron loss is increased has a completely different shape although V3 and V4 close the same Gauss contour line, the shapes of the R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 160 discharge loss curves are different from 80 to 90% propellant utilization efficiency, but similar from 90 to 95%. A V 3 ( 4 R in g C u s p ) o V 4 ( 3 R i n g C u s p ) □ V 1 ( N o m i n a l) 0 . 8 0 . 8 5 0 . 9 P ropellant Utilziation Efficiency Figure 5-41. Discharge Loss Curves for Cases VI, V3, and V4. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 161 VI: DISCUSSION OF THEORY WITH EXPERIMENT A. Key Findings from Magnetic Confinement Studies The magnetic confinement studies yielded several important findings. First, it has been shown experimentally that improving ion confinement by improving secondary electron confinement, is necessary to improve the electrical efficiency (reducing the discharge loss) of the NSTAR thruster. This conclusion is drawn on the basis of comparing the ion density measurements between the nominal and enhanced cases. Figure 6-1 is a plot comparing the ion current density radial profiles between all cases investigated, 2 cm downstream of the cathode exit. The figure shows that the ion density is proportionately higher for the 3-ring cusp nominal case which operated at 14.5A o f discharge versus 11.6A for case V4, but both cases achieved 1.76A of beam current extracted from the thruster (Table 6-1). Similarly, comparison of the two 4-ring cusp cases indicates that V2, which operated at 14.3A, versus 11.5A for V3, had a proportionately higher ion density. The increased plasma density for the nominal and VI is consistent with the higher discharge current set point, thus increasing total ion production (ionization) in the discharge chamber. However, in VI and V2, more ions were created due to the higher discharge current operation (higher electron number R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. density), but more were also lost to recombination with the walls, as compared to V3 and V4. As a result, although the total ion production was higher for VI and V2, all cases had the same beam current. This is a key finding, as the plasma parameter mapping demonstrates that the inefficiency in the NSTAR discharge is ion loss to the walls. VI 40 V 1 ( N o m i n a l ) V 2 4 - R i n g C u s p V 3 4 - R i n g C u s p V 4 S t r e n g t h e n e d 3 R i n g C u s p V4 CN E o < B S t n e 0 ) o V2 □ o 4 - < < 0 ( O c o V3 9 5 7 3 1 ■ 5 •3 Radial Position from Centerline [cm] Figure 6-1. Ion Current Density Radial Profile Comparison 2cm Downstream of Cathode Exit. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 163 D IS C H A R G E P A R A M E T E R V I V 2 V 3 V 4 J b (A ) 1.76 1.76 1.76 1.76 J d (V ) 14.8 14.3 11.5 11.6 V D (V ) 24.65 24.7 25.6 25.1 eb (V ) 207.3 2 01.4 167.8 166.3 Tltot 0.609 0.612 0.628 0.629 fp 0.54 0.81 j 0.6 0.71 Table 6-1. Comparison of TH15 Performance for the 4 Configurations Investigated. The second critical finding is that ions are indeed electrostatically confined by the Maxwellian (secondary) electron population. Direct comparison of the measured electron and ion number density radial profiles for cases VI and V3 confirm that the ion distribution throughout the chamber is similar to that of the bulk electron population, in shape and magnitude. In figures 6-2 and 6-3, radial profiles taken 2 cm downstream of the cathode exit for case VI and V3 respectively, the electron density and ion density have the same radial distribution, with a similar magnitude. The difference in magnitude is within the error of the Langmuir probe method of determining electron density. As will be shown in section 6.2, the electron population is approximately 90% Maxwellian, and 10% primary electrons. Therefore, Langmuir probe traces of electron saturation current are indicating the movement of the bulk, Maxwellian population. The magnetic confinement of ions is essentially due to the requirement of quasineutrality in a plasma. As electrons are light, their motion is R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 164 governed by electron cyclotron gyration about the field lines as they drift towards the magnetic cusps. As electrons leave an area, the deficit of negative charge will set up an electric field that will attract ions. Therefore, ions will follow electrons in their magnetically constrained motion in order to shield out electric potentials that would otherwise exist due to electron magnetic confinement. Primary electrons that are at an energy of approximately the discharge voltage minus the cathode voltage, are well confined by the magnetic multi-cusp field, with 90% o f the primary population having an inelastic collision and only 10% being lost to the magnetic cusps even for the nominal configuration. These inelastic collisions form the Maxwellian or secondary electron population with a Gaussian energy distribution defined by the electron temperature. At only 4 to 5 eV, if not adequately magnetically constrained, secondary electrons can radially diffuse to the anode walls and/or diffuse rapidly to the magnetic cusps. As described in chapter 3, radial diffusion is represented by random walk of the electron with a diffusive path length equal to the ion- electron hybrid gyro-radius, in the direction opposite the density gradient (towards the anode wall)5 8 ,6 0 . For cases V3 and V4, where the goal was to substantially reduce or slow down Maxwellian electron diffusion, in the presence of strengthened magnetic field, substantial ion confinement was achieved, as demonstrated by the 20% reduction in discharge loss for cases V3 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. and V4 (Table 6-1). Therefore, minimizing electron diffusion by increasing the magnetic field strength did indeed confine the ion population. I o n N u m b e r D e n s i t y o E l e c t r o n N u m b e r D e n s i t y . 0 x 1 0 0 .8 - 0 .6 - 0 .4 - 0 .2 - 0 .0 - T 0 T 2 10 4 6 8 R a d i a l D i s t a n c e F r o m C e n t e r l i n e [ c m ] Figure 6-2. Ion and Electron Number Density Radial Profile Comparison 2 cm Downstream of Cathode Exit for case VI. The plasma potential profiles for the cases investigated also support the theory of electron-ion confinement by reducing diffusion to the anode walls. In the cases where ion confinement was enhanced, the plasma potential near the anode wall increased in value, suggesting electron loss to the walls was impeded, and R eproduced with perm ission o f the copyright owner. Further reproduction prohibited without perm ission. 166 therefore ion diffusion to the wall was also retarded due to the requirement of ambipolar diffusion in the plasma (Figures 5-34 and 5-41). Conversely, in the cases where ion confinement was poor, there was no radial gradient in potential in the anode wall region, allowing the ions to diffuse out radially, presumably, along with the bulk electron population (Figures 5-9 and 5-27). The measurements unfortunately do not provide quantitative insight into whether secondary electron diffusion in the presence of the ring cusp magnetic field is purely radial, or purely along the field lines to magnetic cusps. It is likely that primary electrons diffuse only along the magnetic field lines, due to their small larmor radius and high energy, however, as they comprise only 10% of the population, enhancing their confinement should not impact the confinement of ions. As the Maxwellian population is of a lower energy, and gyrates at the hybrid radius, radial diffusion across field lines is far more likely to occur, the reduction or slowing of which will also reduce and slow the diffusion of ions from the plasma as total diffusion in a plasma must be ambipolar60. Electron density measurements, do confirm that the bulk Maxwellian electron population is indeed constrained by the field lines on their way to the cusp, as demonstrated by the secondary peak in electron number density radial profiles, for cases V2 and V4, corresponding to the conical magnetic cusp region (Figure 5-25 and 5- 32). In either case, it has been shown that constraining the discharge plasma electrons to the field lines by reducing their larmor radius, whether diffusion is R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 167 radial, axial, or a combination of both, will also minimize ion diffusion to the wall, due to the requirement that the total diffusion must be ambipolar. The third key finding is that improving plasma uniformity in the conical region by driving primary electrons off axis to an additional cusp is not a requirement for improving the plasma uniformity in the near grid region. The flatness parameter, f p, for each case is shown in Table 6-1. The flatness parameter is traditionally used to quantify beam flatness for ion thrusters. Although there are several ways to calculate the flatness parameter, is it defined here as the average to peak beam current density ratio, averaged over the grid aperture region. For NSTAR, this corresponds to a beam diameter of 28.6 cm, or 14.3 cm radially from the center. f r = J±™_ (6 .,) J b, peak The nominal configuration, V I, had a flatness parameter of 0.54 as compared to 0.81 for case V2, 0.6 for case V3, and 0.78. In fact, case V3, which had the most uniform conical region plasma, due to the addition of the conical cusp, had the least radially uniform plasma profile in the near grid (cylindrical) region. The experimental results have shown that plasma uniformity in the near grid region is primarily a function of the magnetic field structure in this region. Therefore, increasing the field free volume in the cylindrical region is critical for producing R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 168 a flat beam profile. Figures 6-3 to 6-4 are comparative plots of ion current density for the four cases investigated. Figure 6-3 is representative of the beam profile, as this scan was taken 14cm downstream of the cathode (2cm upstream of the screen grid). The mirror image of the data is also plotted on the graph to show what the entire beam profile would look like, as an ion thruster plasma is cylindrically symmetric. Case V2 has a remarkably flat beam profile, versus V3 which is peaked on axis. Figure 6-4 is the ion current density taken at 6cm downstream of the cathode. Here V3 has the flattest beam profile, and V4 the most peaked. Therefore it is clear that the plasma distribution in the conical region did not affect the beam profile. This data suggests that depending on the size of the discharge chamber, conical cusps may need to be added to close a sufficiently high Gauss contour line throughout the chamber to enhance ion- electron confinement, however, the cusps should be situated so as to maximize the field free volume of the plasma and create a flat beam profile. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Io n Current Density (A/m2) 169 80 C ase v1: Nominal NSTAR C ase v2: Enhanced 4 Ring Cusp C ase v3: Enhance 4 Ring Cusp C ase v4: Enhanced 3 Ring Cusp VI 60 V3 V4 40 20 V2 0 10 15 5 0 -10 •5 -15 Radial Distance From Thruster Centerline (cm) Figure 6-3. Ion Current Density Comparison for 14cm downstream of cathode (near grid region) showing mirror image of data from 0 to -15cm. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 170 200 -1 VI 150 - - - C a s e v 1 : N o m i n a l N S T A R - C a s e v 2 : E n h a n c e d 4 R i n g C u s p - - C a s e v 3 : E n h a n c e 4 R i n g C u s p - C a s e v 4 : E n h a n c e d 3 R i n g C u s p < N E 5 < 7 > | 100 - 'c a > V4 V3 o C o 50 - V2 0 — I 15 10 0 5 ■ 5 R a d i a l D i s t a n c e F r o m T h r u s t e r C e n t e r l i n e ( c m ) Figure 6-4. Ion Current Density Comparison for 6 cm downstream of cathode (conical region). R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 171 B. Comparison of Model with Experiment D I S C H A R G E P A R A M E T E R V I V3 V 4 T e (eV ) 5 5 5 np/nm 0 . 0 9 0 . 0 9 0 . 0 9 Ti(eV ) 0 . 0 5 0 . 0 5 0 . 0 5 Jb(A) 1 . 7 6 1 . 7 6 1 . 7 6 Vd (V) 2 5 . 6 2 5 . 5 2 5 . 1 V c(V ) 8 8 8 Le (m) 1 7 . 2 1 2 . 8 2 1 . 1 fA 0.43 0 . 1 8 0 . 2 6 Bcontour,closed 2 0 5 0 5 0 d A n o d e (cm) 2 . 3 1 . 9 1 .5 Table 6-2. OD Model Input Parameters The OD analytical model discussed in chapter 3 was used to predict the performance of cases VI and V3, and V4. Specifically, discharge loss versus mass utilization curves were computed and compared to the measured test data presented in section 5.5. The input parameters for each case are shown in table 6-2. The primary electron confinement length was computed from equation 3-5, for each configuration based on the measured/predicted cusp strength magnetic field and the dimensions of each magnet ring. The ion loss fraction was calculated from equation 3-35, based on the Maxwell 2D simulations of the closed contour line to anode wall minimum gap and the hybrid larmor radius. The electron temperature and primary electron fraction were assumed to be 5eV and 9% respectively. Although an equation was developed to calculate the volume averaged electron temperature in chapter 3, it was not used in this model R eproduced with perm ission o f the copyright owner. Further reproduction prohibited without perm ission. 172 as much of the ionization occurs in the cathode plume, where an average value of 5eV was measured for all cases. The primary-electron-to-total-density ratio of 9% was computed from equation 3-65, based on an electron temperature of 5 eV. An ion temperature of 0.05 eV was used to calculate the ion velocity and larmor radius. As discussed in chapter 3, the ions are assumed to be lost to thruster surfaces (recombination) or are extracted as beam ions from the thruster and are assumed to not gain energy as they flow collisionlessly towards the grids or anode. A comparison of the predicted and measured discharge loss at TH15 is shown in figures 6-5 to 6-7 for cases V I, V3, and V4, respectively. All three predictions compare well to tests data over the propellant utilization range investigated. Figure 6-8 is a comparison of the predicted discharge loss curves. The nominal case and case V4 differed by a translation in the Y axis, but little change in the shape of the curve. Case V3 and VI differed in both shape and magnitude. The translation in Y is related to the ion loss which is independent of propellant utilization or neutral density, as the secondary electron diffusion is dependant on the hybrid larmor radius only. The change in shape of the curve from VI to V3 is due to the exponential dependence of primary electron confinement, on the magnetic field and neutral density (propellant utilization). This suggests that case V4 had similar primary electron confinement to case V I, and improved ion R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 173 confinement. Case V3 had reduced both primary electron confinement, but improved ion confinement, as compared to case V I. It is important to point out that the model was run assuming a fixed beam current (1.76A) and discharge voltage (see Table 6-2). Therefore, changes in discharge loss were due to changes in discharge current only. It is fair to say that the model adequately predicts the discharge loss over the measured propellant utilization range for all cases tested, suggesting the energy loss formulation used in the OD model is fundamentally accurate. 290 270 'c o § 250 to to o -I 230 E P r e o 210 5 u > f 190 170 - 150 \---------------------- , ---------------------- , ----------------------,---------------------- , -----------------------, ---------------------- , 0.7 0.75 0.8 0.85 0.9 0.95 1 Propellant Utllzlatlon Efficiency Figure 6-5. Comparison of Measured to Predicted Discharge Loss at TH15 for the Nominal Configuration VI. □ M e a s u r e d — C a l c u l a t e d R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 174 a M e a s u r e d — C a l c u l a t e d 240 - 220 200 i . 180 160 140 120 1 0 0 1 0.85 0.9 0.95 0.75 0.8 0.7 P ropellant Utilziation Efficiency Figure 6-6. Comparison of Measured to Predicted Discharge Loss at TH15 for Case 240 - □ M e a s u r e d C a lc u la t e d 220 - C 0 I , 200 < A ( A 1 180 o > k . ( 0 ■ g 160 » 5 ” 140 X h - 120 - 100 0.95 1 0.85 0.9 0.8 0.7 0.75 Propellant Utilziation Efficiency Figure 6-7. Comparison of Measured to Predicted Discharge Loss at THIS for Case V4. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 175 2 4 0 - 220 o « , 200 in in o V 3 V 4 - 1 1 8 0 o > 2 > r a ■g 1 6 0 in a ? 1 4 0 x H 120 - 1 0 0 1 0 . 9 0 . 9 5 0.8 0 .8 5 0 . 7 5 0 .7 P r o p e l l a n t U t i l z i a t i o n E f f i c i e n c y Figure 6-8. Comparison of Predicted Discharge Loss at TH15. There are four mechanisms for energy loss in the model. 1. Primary electron Utilization 2. Ion Loss to the Anode 3. Plasma Electron Loss to Anode 4. Hollow Cathode Operation The primary electron utilization was determined from the electron containment length which is a function of the total cusp length and cusp magnetic field strength. Figure 6-9 is a plot of primary electron utilization factor (percent of primary electrons that have an inelastic collision before being lost to the anode) R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 176 versus electron confinement length. The benefit of increasing confinement length begins to level off at about 14m, due to the exponential dependence of primary electron inelastic collision frequency. The experimental cases are also included on the graph for reference. Case V4 had the most efficient use of primary electrons, due to the strengthened middle magnet ring, and no net increase in cusp length versus the nominal case. At a propellant utilization efficiency o f 90%, 95% of primary electrons underwent an inelastic collision for V4. Case V3 had the least efficient use of primary electrons, due to the addition of the conical cusp (increase in the total cusp length), and the use of a stainless steel shim on the front magnet ring that reduced the cusp strength on the front ring from 1100 to 800G, in an attempt to increase the field free volume in the vicinity of the grids. In case V3, only 85% of primary electrons underwent an elastic collision, with 15% lost to the magnetic cusps. For the nominal case, with a primary electron containment length closer to that of case V4, 92% of primary electrons underwent an inelastic collision according to the model, at 90% propellant utilization. It is clear that the addition of magnet rings must be traded with the loss of primary electrons to the cusps. This issue could be mitigated by strengthening all the cusps to 2000 G, however, that must be traded with maintaining a relatively field free volume in the discharge chamber. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 177 In spite of the reduced primary electron confinement of case V3, the total discharge loss was 20% less than the nominal case, and equal to case V4. This is because the ion loss to the anode was lowest for case V3. Only 18% of the total ion production in the discharge chamber was lost to the anode, as compared to 43% for the nominal case, and 26% for case V4. The ion loss factor, f A, is both a function of the magnetic contour strength (the hybrid gyro radius) as well as the distance of the contour from the anode. Given the exponential dependence of ion loss fraction on this product, both decreasing the hybrid gyro radius and/or distance from the anode wall, will improve ion confinement. There is a tradeoff in that increasing the distance from the anode wall will reduce ion loss, but it will also reduce the magnetically field free volume reducing plasma uniformity. Similarly, if the strength of the magnets is increased, the higher Gauss contour lines will push further into the chamber, having a similar effect. Figure 6-10 is a plot of the ion loss fraction as a function the closed magnetic contour value at 1, 2, and 3 cm spacing from the anode wall. The closer the closed contour line is to the anode wall, the more dramatic effect increasing its value has on ion confinement. This was demonstrated by cases V3 and V4, which closed the 50G contour line. In case V3, the contour was located 1.9 cm from the anode wall as opposed to 1.5 cm for case V4. This resulted in the improved ion confinement for V3 versus V4. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. E l e c t r o n U t i l z a t i o n 178 1.0 0 . 9 0.8 0 .7 0.6 0 .5 0 . 4 ra 0 .3 E £ 0.2 0.1 0.0 — 2 4 V 2 5 V 2 6 V • V 1 ▲ C O > ■ V 4 10 1 5 20 Le (m) Figure 6-9. Primary Electron Utilization as a Function of the Magnetic Confinement Length for Different Discharge Voltages. 1 c m g a p ! 2 c m g a p 3 c m g a p 0 .9 0 0 . 8 0 • V 1 ▲ V 3 ■ V 4 0 . 7 0 0 . 6 0 0 .5 0 0 . 4 0 - 0 . 3 0 0.20 0.10 0.00 9 0 1 0 0 5 0 6 0 7 0 8 0 3 0 4 0 10 20 0 B closed (G ) Figure 6-10. Ion Loss Fraction as a Function of the Closed magnetic Contour Strength for Different Anode to Contour Spacing. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 179 Energy used to operate the hollow cathode is also a major loss mechanism for the NSTAR thruster. Eight volts was used to represent the plasma potential from which the electrons were supplied for all cases investigated. Reference 33 measured a plasma potential of 8 V in the cathode orifice region for simulated TH15 operation. It was also assumed to be constant over the propellant utilization range of 95 to 80%. The limit to this assumption is that the hollow cathode will begin to operate less efficiently and eventually go unstable as the cathode flow rate is reduced. As the propellant utilization efficiency is reduced, the main flow rate is increased, and the cathode flow rate decreased, to hold the discharge voltage constant. Therefore, it is likely, that at cathode flow rates below 2 seem, the hollow cathode losses increase dramatically, and thus discharge loss will also begin to increase, resulting in a parabolic discharge loss curve. A second order polynomial order curve fit is shown in figure 6-11, plotted along with the nominal case experimental test data for visual effect. The 0D model does not take hollow cathode efficiency as a function of propellant utilization into account; therefore it is only valid over a range where the cathode operation is stable. However, as ion engines are typically only operated in the vicinity o f 90% propellant utilization, far from the regime where the hollow cathode goes unstable, this effect does not need to be captured for a performance model to be representative. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 180 C. Plasma Parameter Predictions Although the plasma parameter equations of chapter 3 were not used in the calculation of ionization rate in section 6.2, due to the non-uniform or peaked nature of the plasma, it is still interesting to see how the volume averaged plasma parameters change as a function of propellant utilization and magnetic field. Figure 6-11 is a plot of TH15 electron temperature versus closed contour magnetic field strength, for 1, 2, and 3cm distance from the anode at 90% propellant utilization. As the magnetic field strength and therefore ion confinement is increased, the discharge loss decreases, and the discharge current is reduced for a fixed beam current. As a result, the energy of the primary electrons decreases and the Maxwellian electron temperature decreases, logarithmically, and levels off at about 3eV. Figure 6-12 is a plot of primary-to- total and Maxwellian-to-total density ratio as a function of magnetic field strength, assuming a fixed distance from the anode (2cm). As the magnetic field strength is increased, the fraction of primary electrons in the total electron population decreases, therefore the plasma becomes more Maxwellian.. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 181 9.00 i 8.00 - 7.00 - 6.00 - > 5.00 « ) , ^ 4.00 3.00 2.00 1.00 - 0.00 - 0 Figure 6-11. Volume Averaged Electron Temperature at TH15 as a Function of Closed Contour Strength. 1 c m G a p 2 c m G a p 3 c m G a p 10 20 30 40 50 60 70 80 Bclosed (G ) 0.98 0.12 0 . 9 7 0.10 0.96 0.95 n p / n o t n m / n t o t 0.08 0.94 0.93 •S 0.06 0.92 0.04 0.91 0.90 0.02 0.89 0.88 0.00 80 60 70 30 40 5 0 10 20 0 B closed (G ) Figure 6-12. Volume Averaged Primary to Total and Maxwellian to Total Electron Density Ratio at TH15 as a Function of Closed Contour Strength for a 2 cm Gap. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 182 Figure 6-13 is a plot of electron temperature as a function of propellant utilization, for fixed magnetic contour line closure values. For high utilization or low neutral number density, the temperature of the Maxwellian population increases to provide the required level of ionization. The sensitivity electron temperature to changes in neutral density is higher for low field strength or poor ion confinement. > < D 10.00 — 1 0 G — 2 0 G 9.00 — 3 0 G 8.00 — 4 0 G 7.00 — 5 0 G 6.00 5.00 4.00 3.00 2.00 n - - - - - - -- 1.00 0.00 7 J'h 0.2 0.3 0.4 0.5 0.6 0.7 Propellant Utilzation Efficiency 0.8 0.9 Figure 6-13. Volume Averaged Electron Temperature at TH15 as a Function of Propellant Utilization for Various Closed Contour Strengths. Figure 6-14 is a plot of primary to total electron density as a function of propellant utilization, for fixed magnetic contour line closure values. For high utilization, or low neutral density, the primary electron fraction increases, largely due to the increase in discharge current, to provide the required level of ionization. The plots show us plasma parameters are highly dependent on the R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 183 magnetic field configuration, and that their sensitivity to changes in neutral density is reduced with increasing magnetic strength 0 . 3 0 0 10 G 20 G 30 G 40 G 50 G 0 . 2 5 0 0.200 E ■ f 0 . 1 5 0 c 0.100 0 . 0 5 0 0 .0 0 0 0.6 0 . 9 1 0 . 3 0 . 4 0 .5 0 . 7 0.8 0.2 Propellant Utilzation Efficiency Figure 6-14. Volume Averaged Primary to Maxwellian Electron Number Density Ratio at TH15 as a Function of Propellant Utilization for Various Closed Contour Strengths. D. Ion Loss Locations The fractional ion loss, as discussed previously, was a function of the magnetic contour value and the location of that contour with respect to the anode. The 0D model only used the minimum distance, as it was assumed that most ions would flow to this region, essentially a field free anti-cusp region that attracted both secondary electrons and ions. The Maxwell 2D plots indicate that the conical region of the plasma actually closed the 60G contour line, with up to a 5cm gap R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 184 between that contour and the anode wall, as opposed to the cylindrical region, where the contour line was as close as 1 cm from the anode. This suggests that ion loss in the discharge chamber may have been concentrated in the cylindrical segment. Inspection of ion saturation profiles in both the conical and cylindrical segments does seem to support this theory (Figures 6-3 and 6-4). The experimental data does indicate that ion loss occurs primarily in the cylindrical region, and it is this loss that contributes to the peaked nature of the beam profile, in cases VI and V3. R eproduced with perm ission o f the copyright owner. Further reproduction prohibited without perm ission. 185 VII: LIFETIME AND SYSTEMS ENGINEERING IMPLICATIONS A. Im proving Perform ance PARAMETER NSTAR V2 V3 V4 Cathode Life (khr) 48 49 71 69 Throughput Based on Grid Life (kg) 235 426 255 360 Total Efficiency (at lkhr) 60 60 63 63 Table 7-1. Predicted NSTAR Performance Summary at TH15 Operation. Improving the performance of the nominal NSTAR configuration has lifetime, reliability, cost and systems engineering implications. For a given mission architecture, the total propellant throughput is used to characterize the total impulse needed to perform a given mission in terms of propulsive requirements. The throughput per NSTAR thruster is limited by thruster erosion mechanisms that are power level and plasma structure dependent. Reducing thruster wear increases the amount of propellant that can be processed per engine. Increasing propellant throughput per engine reduces the total number of engines needed to perform a given mission. The ion thruster is only one component of the ion propulsion system (IPS) that is needed to operate an engine. Each engine requires a separate power processing unit (PPU), flow controllers, digital control and interface unit (DCIU), gimbal, and associated cabling. A mass breakdown of R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. the NSTAR IPS is shown in Table 7-2. Although cases V2, V3, and V4, include a 1 to 1.5 kg mass addition to the thruster, for the new magnet rings and associated structure, the mass benefit of reducing the number of thrusters by increasing propellant throughput dwarfs the unit level mass change. The total IPS mass is N*36kg (+1 kg), with N being the number of thrusters needed to meet the propellant throughput requirements for the mission. Therefore, reducing the total number of thrusters needed reduces mass on the spacecraft, which amounts to a reduction in launch vehicle costs or increase in mass available to the scientific payload package. Reducing the total number of thrusters also eliminates the cost of fabricating, testing, and integrating each IPS, which amounts to tens of millions of dollars cost savings to a mission. For today’s cost-constrained missions, the IPS can be as much as 20% of the total spacecraft cost, and is the primary reason for its limited use on NASA science missions. Therefore, reducing the total cost of a multi-engine ion propulsion system by reducing N, can be enabling for science missions with large delta-V that require the high Isp that only electric propulsion provides. COMPONENT VI V2 V3 V4 Thruster (kg) 8.2 9.8 10.8 9.5 PPU (kg) 13.9 13.9 13.9 13.9 DCIU (kg) 5.7 5.7 5.7 5.7 Gimbal (kg 4.6 4.6 4.6 4.6 Other 3.3 3.3 3.3 3.3 Total Mass (kg) 35.7 37.3 38.3 37.0 Table 7-2. NSTAR and Enhanced NSTAR Mass Breakdown6 5 . R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 187 B. Thruster Wear Mechanisms There are several thruster component wear mechanisms that limit the NSTAR thruster’s life and propellant throughput capability. Wear mechanisms of the discharge hollow cathode assembly and ions optics are the primary sites of failure in the NSTAR thruster. These wear mechanisms were monitored and quantified during the course of the Extended Life Test and also during the post test destructive evaluation1 6 ,1 9 . In addition, several computational models have been developed and validated, at the Jet Propulsion Laboratory, to predict these wear mechanisms as a function of operating point and plasma properties61. Any design changes that can mitigate or reduce these component wear processes will increase the propellant throughput per engine, which is desirable for the reasons discussed previously. 1) Hollow Cathode Failure and Wear There are two primary wear mechanisms for the discharge hollow cathode assembly, cathode keeper erosion and failure of the insert to emit electrons. Severe ion bombardment of the cathode keeper electrode, which resulted in removal of the keeper cap and erosion of the cathode orifice plate, occurred during the ELT and several other precursor wear tests as part of the NSTAR program. The keeper’s primary function is to protect the cathode orifice plate, as R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 188 removal of the cathode orifice plate will result in cathode failure to operate. High energy ion bombardment and the resultant keeper erosion as measured by the ELT, is the subject of considerable research and its dependence on the plasma is still not understood. In order to mitigate this failure, a change in the keeper electrode material to a more sputter resistant material such as graphite, can be adopted with relative ease and with little violation of the heritage/flight qualified design. The second failure mode for the cathode assembly is inability of the low work function thermionic emitter to emit electrons. This can occur due to independent occurrence or combination of the following: depletion of the impregnate material, clogging of the tungsten matrix due to crystallite formation, or tungsten formation changing the chemical structure of the impregnate material. Physical depletion of the Barium-Calcium-Aluminate compound in the insert, (impregnate) is due to the temperature evaporation from the porous tungsten core. Barium depletion has an exponential dependence on insert temperature or current density. Palluel and Shroff investigated cathode life as a function of Ba evaporation rate, and validated their empirical models on an extensive vacuum cathode technology lifetime database41. They established the following empirical relationship between barium depletion depth, insert operating temperature, and cathode runtime. i d B a i m ) = A T in serl)t2 (7-1) R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 189 In equation 7-1, depletion depth, d Ba, is proportional to the square root of the runtime, t , and a proportionality constant dependent upon the operation temperature, A(Tjn sert) 4 '. This equation can be used to predict cathode (insert) life, by substituting the insert thickness for d Ba. dm sA v m) h ife ~ 2 (7-2) A (Tinsert) The cathode operating temperature can be computed from the Richardson equation. j s a t = 1 2 0 7 ^ exp k T V insert J (7-3) The current density is a function of the temperature of the insert and the cathode sheath potential. The current density at nominal TH15 operation is estimated from the NSTAR discharge cathode operation at 14.5 A. This is equivalent to a temperature of 1219°C 61. Palluel developed empirical relations for the constant A as a function of the insert temperature. Based on equation 7-2, the NSTAR cathode life due to cathode depletion can be computer. Figure 7-1 is a plot of insert life versus discharge current, with markers for the four cases investigated. At 14.5A of discharge current, the nominal NSTAR cathode has a total lifetime of 48khrs according to equation 7-2. At 11.5 A of discharge current, the enhanced NSTAR cases, V3 and V4, with have a cathode lifetime of 70khrs, a 45% improvement over the nominal case. This approach is further supported by R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 190 the ELT results. The extent of Ba depletion was measured as part of the destructive evaluation of the ELT discharge cathode insert. Discharge Current (A) Figure 7-1. Insert Life Plotted as A Function of Discharge Current. Figure 7-2 is a comparison of the inner diameter surface of the ELT insert, and an un-used insert. There are cavities in the ELT insert, corresponding to depleted impregnate. After 30,000 hours of operation, the insert had depleted by up to 52%, with increasing Ba content with depth from the ID surface. The measured depletion compares surprisingly well with the Palluel empirical model1 9 . R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 191 The other insert life limiting factors discussed previously are not reflected in equation (7-2). Clogging of the porous matrix with tungsten crystallite formation has the capacity to prevent the diffusion of BaO to the surface, changing the work-function of the insert. Although a computation model for this mechanism does not exist, results from the ELT post test analysis, indicate that crystallite formation is also current density or temperature dependent1 9 . Therefore, operation of an enhanced NSTAR thruster at 20% lower discharge current would also reduce the amount of crystallite formation and potential for clogging of the emitter surface. However, it should be stated, that post test analysis of the ELT insert did not reveal a significant reduction in surface area of the insert due to crystallite formation. Nor did the discharge cathode performance or ability to start change during its 30,000 Hrs of operation. Therefore, this particular insert degradation mechanism is not believed to be as important to cathode life as Ba depletion. The chemical unavailability of subsurface BaO due to tungstate formation within the matrix is also not directly quantifiable as a computational or empirical model does not exist. However, inspection of the ELT discharge cathode insert after 30,000 Hours of operation did not reveal any evidence of tungstate or poisoning layer formation in the cathode. Comparison of the ELT and Space Station Plasma Contact DPA results supports the theory that tungstate formation is dependent on feed system and propellant impurities66. As such, the requirements for the NSTAR engine and those that were followed during the R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 192 ELT prevented the cathode from being exposed to impurities such as oxygen, water, and chlorides that are believed to contribute to tungstate formation. These factors are more difficult to quantify than Ba depletion; however, after 30,000 hrs of operation as demonstrated by the ELT, there was no evidence that these surface factors were impeding the electron emission capacity of the ELT discharge-cathode insert 1 9 . Therefore, barium depletion is still viewed as the primary life limiter of the cathode and reducing the nominal discharge current set point provides significant lifetime and reliability improvement to NSTAR. Figure 7-2. Comparison of 30,000 Hr ELT insert surface (left) and an un-used insert surface (right)1 6 . R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 193 2) Engine Propellant Throughput Limitation Due To Accelerator Grid Erosion Wear of the ion optics assembly can be described by four primary mechanisms; erosion of the screen grid webbing, enlargement of the accelerator grid apertures, erosion of the intra-grid webbing of the accelerator grid, and reduction in the grid gap between the optics electrodes. Erosion of the screen grid is due to direct ion bombardment from the discharge plasma. Erosion of the accelerator grid apertures is due to charge exchange ion production in the aperture region, and is dependent on neutral density and beam current density. Erosion of the accelerator grid webbing occurs on the downstream (exit) side. It is due to charge exchange ion production in the beam plasma, and is dependent on the beam current density, neutral density, and accelerator grid voltage. The physical cause of reduction in grid gap is not fully understood, but it is related to stress relief in the grid material with time at temperature, general weakening of the accelerator grid electrode with sputter erosion (material removal), and material creep at temperature. If the optics were to come in such close proximity that they could no longer hold voltage, grid gap reduction would result in thruster failure. In general sputter erosion of either grid can lead to structural failure of the optics assembly, resulting in thruster failure. However performance of the optics assembly degrades during the course of these erosion processes that can result in thruster failure prior to actual structural failure. R eproduced with perm ission o f the copyright owner. Further reproduction prohibited without perm ission. 194 Namely, unpreventable electron backstreaming was found to be the first failure mode expressed by the NSTAR thruster during the ELT1 6 . Electron backstreaming occurs when electrons in the thruster beam plasma stream back into the discharge chamber. Each backstreaming electron consumes the same amount of energy as the acceleration of a thrust-producing beam ion. Because electrons are more mobile than ions, electron currents backstreaming into the discharge chamber results in overheating of the discharge chamber, and a reduction in actual beam current, and therefore thrust. A sufficiently negative voltage is applied to the accelerator grid to provide a potential barrier to the electrons preventing them from streaming into the discharge chamber. However, as the accelerator grid wears, and the apertures enlarge, an increasingly negative voltage must be applied to the accelerator grid to prevent backstreaming. Similarly, as the grid gap is reduced, the electric field between the grids increases, and an increasingly negative voltage most be applied to prevent backstreaming. For the DS1 PPU, a maximum of 250V negative of neutralizer common potential is available to prevent electron backstreaming. The electron backstreaming limit is defined as the voltage needed to prevent electrons from getting into the discharge chamber. When the electron backstreaming limit exceeds 250V, thruster failure has occurred, as backstreaming cannot be prevented. The electron backstreaming limit is also dependent on the beam current density, which is power level dependent. At lower power (throttle) levels R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 195 the beam current density is lower, and a lower voltage is needed to prevent backstreaming. During the ELT, unpreventable electron backstreaming at TH15 operation occurred after 30,000 hours of operation. This was defined as the first failure mode of the NSTAR engine, although the thruster was fully operational from THO to TH12, due to the lower current density set point. The propellant throughput of the NSTAR thruster was also defined as 235 kg as was demonstrated by the Extended Life Test at 30,000 Hours of operation. Inspection of the ELT accelerator grid, during and post-test, revealed that grid wear was most significant on axis, corresponding to the peaked beam current density profile. Figure 7-3 is a plot of accelerator grid aperture diameter as a function of radial distance from the thruster centerline measured during the ELT post test inspection. A faraday probe profile taken during the ELT is overlaid in the image to show the aperture size with respect to beam current density profile. It is clear that aperture erosion is directly related to accelerator grid aperture enlargement22. As accelerator grid erosion and electron backstreaming limit are a function of beam current density, reducing the peak current density by flattening out the beam profile, can significantly increase grid life and propellant throughput per thruster. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 196 A c c e l H o l e D i a m e t e r s T H 1 5 B e a m C u r r e n t D e n s i t y 0.95 0.8 - $ </) S 0.7 - Q 0.6 - 3 o E 0.5 - ( 0 0 ) C D ■ g 0.4 " jM r e P 0.3 - 0.85 \Q O z 0.2 - 0.7 -10 -15 •5 0 5 Radial Position from Centerline [cm] Figure 7-3. Comparison of Extended Life Test Accelerator Grid Aperture Enlargement to Normalized Beam Current Density Profile1 9 . The computational model developed in reference 3 provides predictions of molybdenum grid aperture enlargement as a function of the peak beamlet current (Figure 7-4). Applying a linear curve fit to the data, allows calculation of the aperture erosion rate for cases V I, V2, V3, and V4. The case V2 aperture erosion is 49% less than the nominal case. Similarly, case V4 is 38% lower than the nominal case, and V3, has an 8% lower erosion rate, than the nominal case, V I. As both aperture and grid webbing erosion is linearly dependent current density, and we assume that end of grid life is reaching the upper limit of the R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 197 PPU due to electron backstreaming, the reduction in beam current density increases propellant throughput per thruster to 426 kg for case V2, 360 kg for case V4, and 255 kg for V3, as shown in Figure 7-5. Although this is an over simplification of the thruster life model, the benefit to increasing grid life is remarkable. 1.3 1.2 QC 1 .1 C o 3 2 L < 0.9 ■ a a 0.8 0.7 A N o r m a l i z e d A p e r t u r e E r o s i o n R a t e — L i n e a r ( N o r m a l i z e d A p e r t u r e E r o s i o n R a t e ) y = 3.296x + 0.1037 0.6 0.15 0.25 Beamlet Current (mA) 0.35 Figure 7-4. Normalized Accelerator Grid Aperture Erosion Rate Versus Beamlet Current. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 198 450 400 _ 350 o > 250 200 150 V2 V 4 V 3 V 1 20 25 30 35 40 45 50 55 60 65 Peak Beam Current Density (A/m2 ) Figure 7-5. Predicted Propellant Throughput Versus Peak Beam Current Density. C. Systems Engineering Implications Increasing the propellant throughput per thruster can have an enormous impact on mission cost, mass and complexity. Reducing the IPS mass increases mass available to the science payload or can be used to lower the total spacecraft mass and resultant launch vehicle costs. Increasing throughput per engine also reduces risk to the mission, by both reducing system complexity and improving the reliability of the device. Reducing the number o f engines also eliminates the R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 199 non-recurring and recurring costs associated with engine build, fabrication, and test. In order to highlight the advantages of improving the performance o f the nominal NSTAR thruster, the throughput values calculated for grid wear in the previous section, were used to calculate the mass benefit of the enhanced cases versus the nominal case. Although case VI is estimated to fail due to insert depletion at 390 kg of throughput because of its higher discharge current operation, modification o f the VI configuration to reduce discharge loss by 7%, is all that is required return thruster failure due to unpreventable electron backstreaming as the primary life limiter for the modified engine. Using the analytical model, it is estimated that removing the magnetic shim on the VI configuration would have this effect, and therefore the propellant throughout calculated in Figure 7-4 is a valid throughput approximation for comparative purposes. Figure 7-5 is a plot of total number of thrusters versus propellant throughput, with markers for relevant Solar Electric Propulsion class mission throughput requirements6 5 ,6 7 . Figure 7-6 is a plot of total ion propulsion system mass versus propellant throughput, not including the high pressure side of the Xenon feed system as that is a recurring mass. The mass estimate was based on the assumption that each engine would require a PPU, DCIU, low pressure feed system, gimbal, and flight cable. If case V2 or V4 were used for the Dawn mission, with a mission requirement of 410 kg of throughput, the total number of thrusters required to process 410kg, would be 2 versus 3 for the nominal Reproduced with perm ission o f the copyright owner. Further reproduction prohibited without perm ission. 2 0 0 configuration, providing a mass savings of 46kg to the spacecraft, and cost savings of over $10M 67. For a mission requiring in excess of 800 kg throughput, using case V2 would result in a 100 kg mass savings and reduction in four thrusters. It is clear that the cost, system complexity, and mass savings benefit of adopting the V2 and V4 NSTAR engine configurations are significant. * 4 I E « V 1 a V 2 ■ V 4 Europa and Titan Missions JPOP Dawn * * Mission C o m e t Rendezvous DS1 f t a i i i i l a i i A L A A m m mil I R I I I I I I I I I A A A A A A 0 100 200 300 400 500 600 700 800 900 1000 Propellant Througput (kg) Figure 7-6. Total number of thrusters versus propellant throughput. R eproduced with perm ission o f the copyright owner. Further reproduction prohibited without perm ission. 2 0 1 250 200 £ c / > S: 100 50 - Europa and Titan Missions mV1 <3 V2 a V4 Dawn JPOP Mission Comet Rendezvous DS1 • • • • I# a ■ ■ ■ a i a a i i i A A A A A A 0 100 200 300 400 500 600 700 800 900 1000 Propellant Througput (kg) Figure 7-7. Total IPS mass versus propellant throughput. CASE DS1 COMET RENDEZVOUS DAWN TITAN AND EUROPA CLASS # of Thrusters IPS Mass # of Thrusters IPS Mass # of Thrusters IPS Mass # o f Thrusters IPS Mass VI 1 35.7 2 71.4 3 107 6 214.2 V2 1 37.3 1 74.6 2 74.6 3-4 111.9 V4 1 37.0 1 74.0 2 74 4 148 Table 7-3. IPS Mass Comparison for Typical SEP Missions. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. VIII: CONCLUSION 2 0 2 The objective of this research was to quantitatively understand and improve upon the confinement and production of the ion thruster discharge plasma. This was accomplished by theoretical development o f discharge plasma confinement theory and spatially resolved experimental measurements inside of an operating ion thruster. The experimental and analytical results have shown that the primary electrical inefficiency in the nominal NSTAR thruster is insufficient containment and the loss of ions and plasma electrons to the anode. The results have also demonstrated that ion confinement is entirely dependent on the magnetic confinement of the Maxwellian electron population. As diffusion in the discharge plasma is ambipolar, ions are electrostatically confined to the electrons. Increasing the magnetic strength of the chamber’s maximum closed contour line reduced the Larmor radius of the Maxwellian electrons and reduced cross field diffusion to the anode. As the fraction of ions that were lost to the anode was reduced, the discharge current to produce the same beam current was reduced for the enhanced NSTAR cases. R eproduced with perm ission o f the copyright owner. Further reproduction prohibited without perm ission. 203 The experimental results have shown the dependence of plasma uniformity on the magnetic field configuration. Plasma uniformity in the conical section was enhanced by the addition of a magnetic cusp on the cone of the discharge chamber. Primary electrons were driven off axis as they gyrated along the new magnetic field lines to the conical cusp. Inelastic primary electron collisions with neutrals in their path created more ionization outside of the cathode plume than the nominal case, as measured by radially translating Langmuir probes. Similarly, increasing the strength of the middle magnet ring drove primary electrons off axis, increasing ionization outside of the cathode plume in the cylindrical section of the chamber. Plasma uniformity in the near grid region is primarily a function of the magnetic field structure in this region. Increasing the field free volume in the cylindrical region was critical for producing a flat beam profile. Conversely, reducing the field free volume in this region resulted in a peaked beam profile. The addition of a conical cusp was not necessary to improve the performance of an NSTAR sized thruster; however conical cusps may need to be added to ensure adequate magnetic plasma confinement in larger engines to ensure adequate strength contour line closure. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 204 Therefore, the primary requirements for the magnetic design of any ion engine must be to minimize discharge loss and maximize the field free volume of the plasma, resulting in a flat beam profile. This is accomplished by the determination of the optimum number, strength, and location of magnetic cusps. Unfortunately, the state-of-the art engine was designed to minimize unit mass, and as a result the mass savings achieved by minimizing magnet weight resulted in a magnetic field that does not adequately confine or distribute the plasma, resulting in substantial performance and lifetime limitations. Although none of the cases investigated represent the optimum design solution for an enhanced NSTAR thruster, the experimental investigations have served to map out the plasma structure and its confinement as a function o f the magnetic field parameters. The end result of the research activity was to experimentally demonstrate new thruster designs that improved ionization efficiency by over 20% and plasma uniformity by 40%. These performance improvements directly impact thruster life by reducing the peak beam current density responsible for accelerator grid wear, and reducing the discharge power requirements, allowing the cathode to operate at a lower temperature. By reducing thruster component wear mechanisms, the propellant throughput per thruster is increased by almost a factor of two, as demonstrated by cases V2 and V4. Increasing thruster throughput reduces the number of thrusters required to perform a given mission, R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 205 which in turn reduces mission cost, mass, and complexity. These are the driving factors in the cost constrained environment of current NASA missions. The improvements demonstrated in this research program were accomplished via straightforward changes in the magnetic field, and should be made to ensure future and continued use of ion thrusters on NASA science missions. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 206 IX. REFERENCES [22] J.A. Anderson, et al., “An Overview of the Ion Optics 30,000 Hr Life Test of Deep Space 1 Flight Spare Ion Engine,” AIAA-2004-3610, presented at the 40th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, Ft. Lauderdale, FL, Jul. 2004. [24] J.R. Anderson, I. Katz, D. Goebel, “Numerical Simulation of Two-Grid Ion Optics Using a 3D Code,” AIAA-2004-3782, presented at the 40th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, Fort Lauderdale, FL, July 2004. [6] J.R. Brophy, J.E. Polk, and V.K. Rawlin, “Ion Engine Service Life Validation by Analysis and Testing,” AIAA-96-2715, presented at the 32nd AIAA/ASME/ASEE Joint Propulsion Conference, Lake Buena Vista, FL, Jul. 1996. [9] J.R. Brophy, et al., “Ion Propulsion System (NSTAR) DS1 Technology Validation Report,” JPL Publication 00-10, Oct. 2000. [15] J. R. Brophy, D.E. Brinza, J.E. Polk, M.D. Henry, and A. Sengupta, “The DS1 Hyper-Extended Mission,” AIAA-2002-3673, presented at the 38th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, Indianapolis, IN, Jul. 2002 . [18] J.R. Brophy, M. Marcucci, J. Gates, C. Gamer, B. Nakazono, and G. Ganapathi, “Status of the Dawn Ion Propulsion System,” AIAA-2004-3433, Jul. 2004. [23] J.R. Brophy, I. Katz, J.E. Polk, J.R. 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Christensen, et al., “Design and fabrication of a Flight Model 2.3 kW Ion Thruster for the Deep Space 1 Mission,” AIAA-98-3327, July 1998. [49] R.M. Clements, “Plasma Diagnostics With Electric Probes”, J. Vac. Sci. Technol., 15 (2), April 1978. [53] P.F. Feltsan, and I.P. Zapesochny, “Excitation of Inert Gases At Electron- Atom Collisions,” I.P., Ukr., Fiz. Zh., (13) 205, 1968. [45] R.B Godyak, et. al., “Probe Diagnostics o f Non-Maxwellian plasmas”, J. Applied Phys., 73 (8), 15 April 1998. [47] R.B Godyak, et. al., “Probe Diagnostics of Non-Maxwellian plasmas”, J. Applied Phys., 73 (8), 15 April 1998. [31] D.M. Goebel, et. al., “Hollow Cathode and Keeper-Region Plasma Measurements Using Ultra-Fast Miniature Scanning Probes”, AIAA-2004-3430, presented at the 40th Joint Propulsion Conference, Fort Lauderdale FL, July 2004. [34] Y. Hayakawa, et. al., “Measurements of Electron Energy Distributions in a 24cm Diameter Ring Cusp Ion thruster,”, AIAA 89-2715, July, 1989. [43] M. 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Hutchinson, Principles o f Plasma Diagnostics, Cambridge, New York: Cambridge University Press, 2002, pp. 191-213. [33] K. Jameson, D. Goebel, and R. Watkins, “Hollow Cathode and Keeper- Region Plasma Measurements”, AIAA 2005-3667, presented at the 41st AIAA/ASME/SAE/ASEE Joint Propulsion Conference, Tucson, Arizona, 2005. [61] I. Katz, I.G. Mikellides, R. Wirz, J.R. Anderson, D.M. Goebel, “Ion Thruster Life Models,” AIAA-2005-4256, 41st AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, Tucson, AZ, July 2005. [1] H.R. Kaufman, et. al., “Experimental Performance of Ion Rockets Employing Electron-Bombardment Ion Sources,” American Rocket Society Paper, 1374-60, 1960. [2] H.R. Kaufman, et. al., “An Ion Rocket with an Electron-Bombardment Ion Source,” NASA Tech. Note TN D -585, 1961. [59] C. Koch and G. Matthieussent, “Collisional Diffusion of a Plasma in a Multipolar and Picket Fence Devices,” Phys. Fluids 26 (2) February 1983. [27] R.D. Kolasinski and J.E. Polk, “Characterization O f Cathode Keeper Wear by Surface Layer Activation,” AIAA-2003-5144, presented at the 39th Joint Propulsion Conference, Huntsville, AL, July 2003. [57] J. Kune, AE520AB Molecular Gas Dynamics Class Notes, University of Southern California, Dept. Of Aerospace Engineering, May 2004. [50] J.G. Laframboise, “Theory of Spherical and Cylindrical Langmuir Probes in a Collionless, Maxwellian Plasma At Rest”, UTIAS Report No. 100, June 1966. [58] K.N. Leung, et.al, "Plasma confinement by localized cusps", Phys. Fluids 19(7), p. 1045 (1976). R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 209 [37] I.G. Mikellides, I. Katz, D.M. Goebel, and J.E. Polk, “Theoretical Model of a Hollow Cathode Plasma for the Assessment of Insert and Keeper Lifetimes,” AIAA Paper 05-4234, 41st AIAA/ASME/SAE/ASEE Joint Propulsion Conference, Tucson, Arizona, 2005. [38] NASA-Ion Propulsion, Retrieved July 15th 2005, from HTTP://www.nasa.gov/lb/centers/glenn/about/fs21grc.html. [65] D.Y. Oh, “Evaluation o f Solar Electric Propulsion Technologies for Discovery Class Missions,” AIAA-2005-4270, presented at the 41st AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, Tucson, AZ, July 2005. [39] S. Oleson, “Herakles: The Electric Propulsion Element of Prometheus 1,”AIAA Paper 2005-3888, 41st AIAA/ASME/SAE/ASEE Joint Propulsion Conference, Tucson, Arizona, 2005. [41] P. Palluel and A.M. Shroff, “Experimental Study of Impregnated Cathode Behavior, Emission, and Life,” J. Appl. Phys. 51(5), May 1980. [4] M.J. Patterson, V.K Rawlin, J.S. Sovey, M.J. Kussmaul, and J. Parkes, “2.3 kW Ion Thruster Wear Test,” CAIAAC-95-2516, presented at the 31st AIAA/ASME/SAE/ASEE Joint Propulsion Conference, San Diego, CA, Jul. 1995. [3] J.E. Polk, M.J. Patterson, J.R. Brophy, V.K. Rawlin, J.S. Sovey, R.M Myers, J.J Blandino, K.D. Goodfellow, and C.E. Gamer, “A 1000-Hour Wear Test of the NASA NSTAR Ion Thruster,” AIAA-96-27.17., presented at the 32nd AIAA/ASME/SAE/ASEE Joint Propulsion Conference, Lake Buena Vista, FL, Jul. 1996. [5] J.E. Polk, et al., “The Role of Analysis and Testing in the Service Life Assessment of Ion Engines,” IEPC-95-228, presented at the 24th International Electric Propulsion Conference, Moscow, Russia, Sept. 1995. [7] J.E. Polk, et al., “The Effect of Engine Wear on Performance in the NSTAR 8000 Hour Ion Engine Endurance Test,” AIAA-97-3387, presented at the 33rd AIAA/ASME/SAE/ASEE Joint Propulsion Conference, Seattle, WA, Jul. 1997. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 2 1 0 [8] J.E. Polk, J.R. Anderson, J.R Brophy, V.K. Rawlin, M. Patterson, J. Sovey, and J. Hamley, “An Overview of the Results from an 8200 Hour Wear Test of the NSTAR Ion Thruster,” AIAA-99-2446, presented at the 35th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, Los Angeles, CA, Jun. 1999. [12] J.E. Polk, et al, “Demonstration of the NSTAR Ion Propulsion System on the Deep Space One Mission,” 27th International Electric Propulsion Conference, October 2001. [13] J.E. Polk, et al., “Validation of NSTAR Propulsion system on the DS1 Mission,” AIAA-99-2246, June 1999. [14] J.E. Polk, et al., “In-Flight Performance of the NSTAR Ion Propulsion System on the Deep Space One Mission,” Z8_0304.PDF, IEEE Aerospace Conference Proceedings, March 2000. [20] J.E. Polk, J.R. Anderson, J.R. Brophy, V.K. Rawlin, M.J. Patterson, and J.S. Sovey, “In Situ, Time-Resolved Accelerator Grid Erosion Measurements in the NSTAR 8000 Hour Ion Engine Wear Test,” IEPC-97-047, presented at the 25th International Electric Propulsion Conference, Cleveland, OH, Aug. 1997. [21] J.E. Polk, J.R. Brophy, and J. Wang, “Spatial and Temporal Distribution of Ion Engine Accelerator Grid Erosion,” AIAA-95-2924, presented at the 31 st AIAA/ASME/SAE/ASEE Joint Propulsion Conference, San Diego, CA, Jul. 1995. [40] V.K. Rawlin, “Operation of the J-Series Thruster Using Inert Gas,” NASA TM-82977, Nov. 1982. [11] M.D. Rayman, P. Varghese, D.H. Lehman, L.L Livesay, “Results from the Deep Space 1 Technology Validation Mission,” Acta Astronautica 47, No. 2-9, pp. 475-487 (2000). [66] T.R. Sarver-Vehey and G.C. Soulas, “Destructive evaluation o f a xenon hollow cathode after a 28,000 hour life test,” AIAA-1998-3483, presented at the AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, 34th, Cleveland, OH, 1998 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 211 [16] A. Sengupta, et. al., “An Overview of the Results from the 30,000 Hr Life Test of Deep Space 1 Flight Spare Ion Engine,” AIAA-2004-C3608C, presented at the 40th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, Ft. Lauderdale, FL, Jul. 2004. [17] A. Sengupta, J.R. Brophy, and K.D. Goodfellow, “Status of the Extended Life Test of the Deep Space 1 Flight Spare Ion Engine after C30,352C Hours of Operation,” AIAA-2003-4558, presented at the 39th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, Huntsville, AL, Jul. 2003. [19] A. Sengupta, et al., “The 30,000-Hour Extended-Life Test of the Deep Space 1 Flight Spare Ion Thruster, Final Report,” NASA TP 2004-213391, Nov. 2004. [55] A. Sengupta, et. al., “Experimentally Determined Neutral Density and Plasma Parameters in a 30cm Ion Engine”, AIAA-2004-3613, presented at the 40th Joint Propulsion Conference, Fort Lauderdale, FL, July 2004. [25] J.S. Snyder and J.R. Brophy, “Performance Characterization and Vibration Testing of 30-cm Carbon-Carbon Ion Optics,” AIAA-2004-3782, presented at the 40l AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, Fort Lauderdale, FL, July 2004. [26] J.S. Snyder, J. Brophy and J. Anderson, “Results of a 1000-Hour Wear Test of 30-cm-Diameter Carbon-Carbon Ion Optics,” presented at the 41st AIAA/ASME/SAE/ASEE Joint Propulsion Conference, Tucson, Arizona, 2005. [48] I.D. Sudit, R.C. Wood., “A study of the Accuracy of Various Langmuir Probe Theories”, J.Appl. Phys. 76 (8) 1995. [64] G. Taguchi, S. Chowdhury, and Y.Wu, Taguchi’ s Quality Engineering Handbook, John Wiley & Sons, Inc., New Jersey, 2005. [44] H. Tawara and T. Kato, “Total and Partial Ionization Cross Sections of Atoms and Ions by Electron Impact,” Atomic Data and Nuclear Tables, Vol. 36, No. 2, March 1987. [28] G.J. Williams, et al., “Characterization of FMT-2 Discharge Cathode Plume,” IEPC-99-104, Oct. 1999. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 2 1 2 [32] G.J. Williams, “The Use of Laser-Induced Fluorescence to Characterize Discharge Cathode Erosion in a 30 cm Ring-Cusp Ion Thruster”, Ph.D. Dissertation, Dept, of Aerospace Engineering, University of Michigan, Ann Arbor, MI, 2000. [36] R. Wirz, “2D Discharge Chamber Model for Ion Thrusters,” AIAA-2004- 4107, 40th Joint Propulsion Conference, Fort Lauderdale, FL, July 2004. [67] K.E. Witzberger, et. al., “NASA’s 2004 In-Space Propulsion Refocus Studies for New Frontiers Class Missions”, AIAA-2005-4271, presented at the 41st AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, Tucson, AZ, July 2005. [51] S.Yun, et. al., “Neutral Uniformity and Transport mechanisms for Plasma Etching”, Physics of Plasmas, (8) 6, June 2001. [52] S. Yun, et. al., “Measurement of Radial Neutral Pressure and Plasma Density Profiles in Various Plasma Conditions in Large-Area High-Density Plasma Sources”, Physics of Plasma, (7) 8, August 2000. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 213 APPENDIX A: Xenon Cross Section Data Xenon cross section data obtained from references 43 and 44 was used to calculate the probability of both primary and Maxwellian electron ionization and excitation collisions. Excitation cross section data is plotted as a function of primary energy in figure A -l. This cross section data represents the integration over all possible transitions for Xel. The peak cross section or probability for excitation occurs at 10.1 eV. Ionization cross section data is plotted as a function of primary energy in figure A-2. The first ionization potential for Xel is 12.1 eV. Figures A3 to A6 represent the excitation and ionization cross sections and reaction rates averaged over a Maxwellian electron energy distribution function. The reaction rates are defined in equations A-l and A-2. ^excitation ^ excite^ max wellian ^ ) ^ionization ^ io n iz e ^m ax wellian The cross section data for the 823.2 nm excited Xel transition was obtained from reference 53. Figure A-7 is the excitation cross section as a function of the primary electron energy. Figure A-8 is the maxwellian averaged excitation cross section as a function of the electron temperature. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 214 4.5E-20 4.0E-20 T e ~ 3.5E-20 o '■ g 3.0E-20 0 ) ® 2.5E-20 S 2.0E-20 1.5E-20 g 1.0E-20 x m 5.0E-21 0 .0 E + 0 0 o c o 20 40 60 S p(V ) 80 100 Figure A-l. Excitation Cross Section as a Function of the Primary Electron Energy. 7.0E-20 rf- 6.0E-20 E, o 5.0E-20 ' • M O w 4.0E-20 ( / ) ( 0 o O 3.0E-20 c 5 2.0E-20 n .N O 1.0E-20 O.OEt-OO 20 40 60 B p (V) 80 1 0 0 Figure A-2. Ionization Cross Section as a Function of the Primary Electron Energy. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 215 V > W o L . o c o 1.4E-20 1.2E-20 1.0E-20 > < ^ !£ .iL8.0E-21 & § S 0 6 .O E-21 ® a > < W c 4.0E-21 m | 2.0E-21 x r a S 0.0E+00 10 Te (eV) 15 20 Figure A-3. Maxwellian Averaged Ionization Cross Section as a Function of Te . ( 0 in o 3.5E-20 0 3.0E-20 c o ( Q N 2.5E-20 ■ o 0 ) O ) n a > > < c ( 0 J 2 .0E -20 c o O1.5E-20 o > W 1.0E-20 - § 5.0E-21 0.0E+00 10 Te (eV) 15 20 Figure A-4. Maxwellian Averaged Excitation Cross Section as a Function of Te R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Maxwelllian Averaged Ionization Rate [m3 /s] Maxwelllian Averaged Excitation Rate [nf/s] 216 4.0E-14 3.5E-14 3.0E-14 2.5E-14 - I 2.0E-14 1.5E-14 1.0E-14 5.0E-15 ).0EK)0 0 10 Te (eV) 15 20 Figure A-5. Maxwellian Averaged Ionization Rate as a Function of Te . 1.4E-13 1.2E-13 1.0E-13 8.0E-14 6.0E-14 4.0E-14 2.0E-14 O .O E + O O 10 Te (eV) 15 20 Figure A-6. Maxwellian Averaged Excitation Rate as a Function of T „. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 217 E 7.0E-23 c C N J S 6.0E-23 00 o C “ 5.0E-23 O a > W c 4.0E-23 m — 8 % <5 g 3.0E-23 | * = 3 2.0E-23 o X L U 1.0E-23 10 20 30 sp (eV) 40 50 60 Figure A-7 Excitation Cross Section (823.2 nm) as a Function of the Primary Electron Energy. w ( 0 o L _ O c o 3.5E-23 « 3.0E-23 O ' c S - 2.5E-23 - W c 2 2.0E-23 o x in * D V o > re L _ V > < c n E c 1.5E-23 c v i C O « 1.0E-23 g 5 . 0 E - 2 4 $ O .O E + O O 10 20 3 0 s p ( e V ) 40 50 60 Figure A-8. Maxwellian Averaged Excitation (823.2 nm) Cross Section as; Function of Te . R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 218 APPENDIX B: Publications List Several technical meeting papers and a NASA Technical Report were written for data obtained in this research project. Notably, the paper entitled “An Overview of the Results from the 30,000 Hr Life Test of Deep Space 1 Flight Spare Ion Engine” was selected for the AIAA Best Paper Award in 2004 due to its technical significance to NASA solar electric propulsion missions. 1. A. Sengupta, “Experimental Investigation of Discharge Plasma Magnetic Confinement in an NSTAR Ion Thruster,” AIAA-2005-4069, presented at the 41st Joint Propulsion Conference, Tucson, Arizona, July 2005. 2. A. Sengupta, et. al., “An Overview of the Results from the 30,000 Hr Life Test of Deep Space 1 Flight Spare Ion Engine,” AIAA-2004-3608, presented at the 40th Joint Propulsion Conference, Ft. Lauderdale, FL, Jul. 2004. 3. A. Sengupta, et al., “The 30,000-Hour Extended-Life Test of the Deep Space 1 Flight Spare Ion Thruster, Final Report,” NASA TP 2004- 213391,2004. 4. A. Sengupta, et. al., “Experimentally Determined Neutral Density and Plasma Parameters in a 30cm Ion Engine”, AIAA-2004-3613, presented at the 40th Joint Propulsion Conference, Fort Lauderdale, FL, July 2004. 5. A. Sengupta et. al, “Status of the Extended Life Test of the Deep Space 1 Flight Spare Ion Engine after 30,352 Hours of Operation,” AIAA- 2003-4558, presented at the 39th Joint Propulsion Conference, Huntsville, AL, July 2003. 6. A. Sengupta et. al, “Wear Characteristics from the Extended Life Test of the DS1 Flight Spare Ion Thruster,” 28th International Electric Propulsion Conference, Toulouse, France, March 2003. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 7. A. Sengupta et. al., “Performance Characteristics of the Deep Space 1 Flight Spare Ion Thruster Long Duration Test after 21,300 Hours of Operation,” AIAA-2002-3959, presented at the 38th Joint Propulsion Conference, Indianapolis, IN, July 2002. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission.

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Creator Sengupta, Anita (author)

Core Title Experimental and analytical investigation of a ring cusp ion thruster: Discharge chamber physics and performance

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Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag engineering, aerospace,OAI-PMH Harvest,Physics, Fluid and Plasma

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Advisor Erwin, Dan (committee chair), Gruntman, Mike (committee member), Katsouleas, Thomas (committee member), Kunc, Joseph (committee member), Muntz, E. Phillip (committee member)

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