Wear Testing of a Magnetically Shielded Hall Thruster at 2000 s Specific Impulse

Transcription

1 Wear Testing of a Magnetically Shielded Hall Thruster at 2000 s Specific Impulse IEPC Presented at Joint Conference of 30 th International Symposium on Space Technology and Science, 34 th International Electric Propulsion Conference and 6 th Nano-satellite Symposium Hyogo-Kobe, Japan Michael J. Sekerak Richard R. Hofer James E. Polk Benjamin A. Jorns Ioannis G. Mikellides Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA Magnetically shielded Hall effect thrusters (HET) have specially contoured magnetic fields that minimize ion bombardment and, consequently, erosion of the acceleration channel. A full life test of a magnetically shielded (MS) HET has not yet been conducted, but two tests of approximately 150 h operating at 300 V discharge voltage and 2000 s specific impulse were conducted to characterize the performance, stability, thermal, and wear of a 6 kw MS HET called the H6MS. Based on uniform backsputtered carbon deposition on the discharge channel erosion rings, it was assessed that magnetic shielding was sustained for more than 300 h of thruster operation. After the first wear test, surface roughening likely from ion sputtering was noted on the inner front pole, while the outer pole primarily showed net carbon deposition. The thruster maintained over 60% efficiency and stable operation for both tests. In an attempt to quantify and mitigate the inner front pole erosion observed in the first test, the second wear test incorporated carbon graphite covers over the inner and outer front poles as well as material samples to measure erosion. At the end of 153 h of operation, net erosion was observed on the inner front pole carbon and molybdenum samples using an optical profilometer to measure the height difference between masked and unmasked regions. The calculated erosion rates varied from 0.12 to 0.27 μm/h for molybdenum and to μm/h for carbon, which is still one or more orders of magnitude lower than channel erosion rates observed in the unshielded version of this thruster. Assuming the erosion is caused by a single ion population impacting at normal incidence angle, an approximate ion energy of 156 ev is calculated from the erosion rate ratio with a bound of ev due to uncertainty in sputter yields for carbon and molybdenum. These results suggest that techniques are required to mitigate pole erosion. Protective pole covers are one approach, where a 3.5 mm thick carbon cover would prevent pole erosion during 50 kh of H6MS operation at this operating condition assuming a constant erosion rate. Engineer, Electric Propulsion Group, 4800 Oak Grove Dr., MS , Pasadena, CA, 91109, michael.j.sekerak@jpl.nasa.gov Senior Engineer, Electric Propulsion Group, 4800 Oak Grove Dr., MS , Pasadena, CA, 91109, richard.r.hofer@jpl.nasa.gov Principal Engineer; Propulsion and Materials Engineering Section, 4800 Oak Grove Dr., MS , Pasadena, CA, 91109, james.e.polk@jpl.nasa.gov Engineer, Electric Propulsion Group, 4800 Oak Grove Dr., MS , Pasadena, CA, 91109, benjamin.a.jorns@jpl.nasa.gov Principal Engineer, Electric Propulsion Group, 4800 Oak Grove Dr., MS , Pasadena, CA, 91109, ioannis.g.mikellides@jpl.nasa.gov 1

2 Nomenclature a L E E th E e I D I sp J j k e M x m x n e P PSD q R ch r s KrC n s TF n T T e V cg V D Z Z x α β Γ γ ɛ ε ε η λ μ ρ Φ i φ = Lindhard screening length, Å = ion energy, ev = threshold energy and fit parameter, ev = electric field parallel to magnetic field line, V m 1 = elementary charge, C = discharge current, A = specific impulse, s = ion current, A = ion current density, ma cm 2 = Lindhard electronic stopping coefficient(yamamura) = mass of particle x, amu = mass of particle x, kg =electronnumberdensity,m 3 = pressure, Torr = power spectral density, arb. units Hz 1 = fit parameter (Eckstein) = mean discharge channel radius, m = radial location, m = Kr-C potential nuclear stopping cross section = Thomas-Fermi nuclear stopping cross section = thrust, mn = electron temperature, ev = cathode to ground potential, V = discharge potential, V = charge state = atomic number of particle x = energy-independent function (Bohdansky) = fit parameter (Sekerak) = contribution of internal reflection sputtering (Yamamura) = sputter yield, atoms ion 1 = reduced energy = erosion rate, μm h 1 = erosion rate ratio = fit parameter (Sekerak) = fit parameter (Eckstein) = fit parameter (Eckstein) = density, kg m 3 = ion flux, ion m 2 s 1 = plastma potential, V I. Introduction Magnetic shielding in Hall thrusters is a technique that reduces discharge chamber erosion rates by orders of magnitude, effectively eliminating wall erosion as a failure mode. The physics of magnetic shielding were first derived at JPL 1 after numerical simulations of Aerojet-Rocketdynes BPT-4000 explained why the thruster reached a low-erosion state 5.6 kh in to a 10.4 kh wear test. 2 Subsequently, magnetic shielding was shown to reduce erosion rates by three orders of magnitude in a series of simulations and 2

3 experiments designed to validate the physics of magnetic shielding through modification of the H6 Hall thruster. 3 6 Through nearly 5 kh of wear testing in a low-erosion configuration with the BPT-4000 and detailed simulations and experiments with the H6MS, the physics of magnetic shielding have been established for thrusters operating at 2000 s specific impulse and kw discharge power. Magnetic shielding of Hall thrusters has effectively eliminated discharge channel erosion as the lifelimiting factor for thruster life, so other mechanisms such as pole or cathode erosion may become the life-limiting factors. Characterizing and understanding these potential failure mechanisms are critical to building predictive models, because a 100 kh life test would be cost prohibitive and/or impractical. During operation of magnetically shielded thrusters, roughening of the inner front pole has been observed and was first reported during a 100 h test at 3000 s. 7 The identification of pole roughening for a 150 h, 2000 s specific impulse test was noted in Ref. 8 as the motivation for plasma measurements near the pole and Ref. 9 as the motivation for simulations of pole erosion. The plasma measurements in Ref. 8 showed significant electron temperatures exist where the magnetic field lines from the channel terminate on the surface of the pole pieces near the discharge channel, which could contribute to pole surface sputtering. Figure 13 of Ref. 9 predicts the erosion rate of magnetic poles made from carbon would be less than the facility backsputter rate. However, it was also argued that the absence of the precise geometry of the pole covers and/or sheath effects in the vicinity of the downstream channel corner could have led to the under-prediction by, in part, altering the true trajectories of high-energy ions. These previous works and results presented here motivated the follow-on simulations in Ref. 10. The objectives of these experiments are to demonstrate H6MS performance at 2000 s specific impulse over 150 h of operation and to measure erosion of the pole pieces. These objectives were achieved during two separate wear tests where the thruster was operated in excess of 150 h at 300 V discharge voltage, 2000 s specific impulse, and 6 kw discharge power for each test. Test 1 was the initial wear characterization test where magnetic shielding of the discharge channel was demonstrated, but roughening was noted on the inner front pole. This test did not control for pole erosion and the pole erosion appeared to be greater than what was qualitatively observed during the 100 h test at 3000 s. 7 Test 2 incorporated graphite covers on the magnetic poles with wear strips to measure erosion rates. The thruster showed stable operation and magnetic shielding during both tests. Test 2 measured a carbon erosion rate of μm/h on the inner front pole and a molybdenum erosion rate of μm/h. The calculated ion energy is 156 ev with a bound of ev based on the uncertainty in sputter yields for carbon and molybdenum. A companion paper is presented by Lopez-Ortega, 10 which explores pole erosion using numerical simulations and compares with the results presented here. The paper is organized as follows. Sect. II describes the experimental setup for Test 1 with bare magnetic poles and additional temperature diagnostics, and Test 2 with carbon pole covers and sample materials for erosion measurements. Sect. III shows the results from each 150 h wear test including performance characteristics as well as the erosion measurements from Test 2 for carbon and molybdenum. Sect. IV calculates an estimated ion energy and ion current density causing the erosion and discusses the implications of the measured erosion rates for thruster life. The Appendix describes the techniques used to measure erosion from the samples. II. Experimental Setup A. H6MS Information All experiments were conducted using the magnetically shielded (MS) version of the H6 Hall thruster, the H6MS. The original, unshielded (US) version of this laboratory thruster, the H6US, was a joint development between JPL, the University of Michigan, and the Air Force Research Laboratory. 11 High performance is achieved through the use of a plasma lens magnetic field topography, a centrally mounted lanthanum hexaboride (LaB 6 ) cathode, 15 and a high-uniformity gas distributor/anode assembly. 16 The H6MS incorporates magnetic shielding that experiments show decreases wall erosion by three orders of magnitude relative to the US variant, effectively eliminating channel erosion as a failure mode. 3 5 The throttling range of the H6MS is approximately kw discharge power, s specific impulse, and mn thrust. At the nominal 300 V, 6 kw condition, thrust, total specific impulse, and total efficiency of the H6MS are 384 mn, 2000 s, and 62.4%, respectively. 17 During the experiments, power and propellant were delivered to the H6 with commercially available power supplies and flow controllers. The plasma discharge was sustained by a pair of power supplies wired 3

4 in parallel capable of up to 500 V, 40 A operation. The discharge filter consisted of an 80 μf capacitor in parallel with the discharge power supply outputs. Additional power supplies were used to power the magnet coils and the cathode heater and keeper. The cathode heater and keeper were used only during the thruster ignition sequence. Research-grade xenon ( % pure) was supplied through stainless steel feed lines with 50 and 500 sccm mass flow controllers. The controllers were digitally controlled with an accuracy of ±1% of the set point. The cathode flow rate was always set to 7% of the anode flow rate. The H6MS has detachable boron nitride erosion rings that fit onto the end of the discharge channel. New rings were used for Test 1 and were bright white. After testing the rings were blackened from carbon deposition and the same rings were used unaltered for Test 2. The thruster body was grounded to the vacuum chamber for Test 1 and 2. B. Facilities 1. Vacuum Chamber This experiment was conducted in the Owens Chamber at NASA JPL, which is a 3 m diameter by 10 m long cryogenically pumped vacuum chamber. The pressure during testing was typically Torr, as measured by a xenon calibrated ion gauge mounted below the thrust stand for Test 1 and next to the thrust stand for Test 2. Section II.B of Ref. 7 and Section IV of Ref. 17 contain additional details about the facility. 2. Data Acquisition A 20 MHz current probe and an 8-bit, 2 GHz Tektronix DPO-3054 digital oscilloscope were used to measure discharge current oscillations during steady-state thruster operation with an accuracy of ±3%. 17 The current probe was located on the anode side of the power input between the thruster and discharge filter described in Sect. II.A. Oscillations were characterized by calculating the root-mean-square (RMS), peak-to-peak (P2P), and the power spectral density. 3. Thrust Stand Thrust measurements were acquired using a water-cooled, inverted-pendulum thrust stand with closed loop inclination control and active damping Thermal drift and inclination of the thrust stand were accounted for during post-processing. Pressures of less than Torr are sufficient to reliably obtain performance measurements without needing to correct for neutral gas ingestion. 20 This criterion was met in these experiments and no attempts to correct for neutral ingestion were made. Calibrations were performed by deploying a series of known weights ten times each. 18 When inclination and thermal drift were accounted for, the response of the thrust stand was repeatable and linear to the applied force. Analysis of thrust stand uncertainty indicated a range of ±0.5%. Given the uncertainty of the thrust, mass flow rate, current, and voltage, the uncertainty for specific impulse was previously calculated as ±1.4% and ±2.3% for efficiency Quartz Crystal Microbalance (QCM) A Quartz Crystal Microbalance (QCM) was used to measure the backsputter rate of carbon from the surfaces of the vacuum chamber subject to high-energy ion bombardment. The readout of the QCM was used in total deposition mode with the instrument parameters set for carbon deposition. A witness plate mounted next to the QCM (see Figure 1 from Ref. 7) made from boron nitride disks was used to validate the QCM settings by providing the average deposition rate over the entire wear test. The QCM was water-cooled and the temperature was monitored with a thermocouple. Radiation barriers and thermal insulation were used to thermally isolate the QCM from the thruster such that the temperature of the QCM was maintained to less than 1 C. The QCM was axially positioned at the exit plane of the thruster discharge chamber and radially positioned within 3 cm of the thruster outer front pole. The uncertainty of the backsputter rate from the QCM measurements was estimated to be ± μm/h. C. Test 1-Initial Wear Test 1. Thermocouples and Thermal Camera The temperature of various thruster components was measured using several different diagnostics. Type K thermocouples were mounted on the inner diameter of the inner front pole, the outer diameter of the outer 4

5 front pole, the upstream end of the inner screen, and the downstream end of the outer screen. These signals were monitored continuously during the wear test using a data acquisition system that converts the thermoelectric potentials to temperature and corrects for cold junction temperatures. The uncertainty in the thermocouple reading is 2.2 C. 7 The temperature of external thruster components was measured periodically throughout the test with a FLIR SC655 infrared imaging camera. This camera measures the thermal radiation emitted by a surface between wavelengths of 7.5 and 14 μm with a microbolometer detector and calculates a temperature based on inputs for the surface emittance and the transmission of any optical components. The uncertainty is dominated by uncertainty in the emittance for the components, which results in an uncertainty in the camera data of ±12 C. Further details are provided in Ref. 7. The average temperature of the magnet coils was inferred from the measured coil resistance and the temperature dependence of copper resistivity. The resistance inferred from measured coil current and voltage is corrected for the resistance of the coil leads, which was measured separately. The estimated uncertainty of these temperatures is 3% below 500 K (227 C) and 5% above 500 K, based on uncertainties in the electrical measurements and the uncertainty in the model for resistivity as a function of temperature Coordinate Measuring Machine (CMM) A Coordinate Measuring Machine (CMM) was used to measure the geometry of the insulator rings before and after the first test. Wall profiles were obtained at four equally spaced locations around the circumference of a ring. Analysis of the various data sets taken during the experiments in Ref. 17 yielded an uncertainty of ±30 μm. Expressed as an erosion rate for a reference 10 h run time, the noise floor of the CMM is estimated to be ±1 μm/h. D. Test2-WearTestwithPoleCovers 1. Carbon Pole Covers The graphite pole covers had the same inner and outer radius as the H6MS inner and outer front poles so they were completely covered as shown in Fig. 1(a). The material was G540 graphite and the covers were 3.2 mm thick. The inner pole cover was polished with a diamond grinding wheel to a mirror finish as shown in Fig. 1(b). The outer pole cover did not fit on the polishing wheel, so it was not polished and showed evidence of the machining markings. The pole covers were held in place by stainless steel clips spot welded to the outer radius of the inner and outer H6MS magnetic poles with three clips per cover at the 2, 6 and 10 o clock positions, which are circled in Fig. 1(a). 2. Molybdenum Foil Pure molybdenum foil was placed over the pole covers at the 8 o clock position as shown in Fig. 1(a). The strip was wrapped over the pole cover and spot-welded to the edge of the H6MS magnetic iron poles. The 8 μm thick foil was meant to provide a simple indication of erosion. If a foil strip eroded through during 150 hours of testing, then the erosion rate at some radial location on the pole was ε>0.05 μm/h. This simple erosion metric was implemented because it was uncertain whether enough erosion would occur on the carbon cover or molybdenum to be measured by the profilometer. 3. Molybdenum Strips Pure molybdenum sheets 394 μm thick were used to create masks for the carbon pole covers. A strip was placed across the inner and outer pole at 12 o clock as shown in Fig. 1(a) with bent edges and spot-welded to the edge of the iron poles. Another strip was polished on a diamond grinding wheel to a mirror finish. Unfortunately, the strips were not adequately flat and the surface finish was not uniform, but this was accounted for in post-test analysis discussed in the Appendix. Tantalum foil 58 μm thick was spot welded to the molybdenum strip that had alternating masked and unmasked regions along the radius of each pole cover as shown in Fig. 1(a) and (b). These strips were placed at 4 o clock on the inner and outer pole covers and spot welded to the edges of the magnetic poles. 5

6 (a) H6MS with pole covers installed by 3 clips at 2, 6 and 10 o clock. The Mo foil is at 8 o clock and the Mo masks are at 4 and 12 o clock. (b) Close up of inner front pole cover showing mirrored finish, foil, masks, and clips. The Ta foil on the 4 o clock Mo strip is spot-welded on the edge closer to 6 o clock. Figure 1. H6MS with pole covers and masks for Test Nanovea Profilometer The uncertainty in profile measurement for Test 1 motivated acquisition of a new tool for measuring ring profiles. The Nanovea custom ST400 Optical Profilometer uses the Chromatic Confocal technique to measure height without contact. It is a 3-axis (x y θ) profilometer with a resolution of less than 1 μm, depth of field of greater than 20 mm, and can accommodate sample sizes of mm. This resolution is 60 greater than the CMM used in Test 1. The automated sample acquisition was used to make surface plots consisting of points to increase the statistical significance for measuring small step heights as discussed in the Appendix. Additional advanced analysis software called Expert 3D was used for smoothing and leveling of surface scans before further analysis. Originally purchased for ring erosion measurements, the Nanovea ST400 and Expert 3D software enabled measurements of small step sizes for pole erosion testing in Test 2. III. Results A. Test 1-Initial Wear Test 1. Performance and Operating Characteristics The H6MS was operated for 150 h during Test 1 and is shown in Fig. 2. Fig. 3 shows the thruster before and after the testing where differences in their appearance including blackening of the discharge channel erosion rings and texturing of the inner pole are discussed in Sect. III.A.4 and Sect. III.A.5, respectively. The discharge was maintained continuously except for chamber venting to repair a leaking o-ring and thrust stand zeros. The times shown in the following figures are cumulative run time and not absolute run time. Chamber pressure measured by the xenon calibrated ionization gauge below the thrust stand is shown in Fig. 4. The higher than expected pressure shown in the first 5 hours of operation was caused by a leaking o-ring. The chamber was vented and the seal repaired. The chamber outgassed over the first approximately 20 h of operation, after which the pressure remained stable throughout the remainder of the test at Torr. Fig. 5 shows the discharge voltage and current for the entirety of Test 1. Except during warmup periods, the discharge voltage and current were maintained at 300 V and 20.0 A, respectively. The mass flow rate to the thruster was manually controlled by adjusting the flow until the discharge current reached 20.0 A. 6

7 (a) Nearly straight on view. (b) Oblique view. Figure 2. H6MS operating at 150 h during Test 1. (a) Before. (b) After. Figure 3. H6MS before and after Test 1, the first 150 h wear test. 7

8 Figure 4. Tank pressure measured by the xenon calibrated ionization gauge mounted below the thrust stand during Test 1. The thruster outgassed in the first few hours, but a higher than expected pressure indicated an o-ring leak that was repaired. The chamber finished outgassing at 20 h. During the final 96 h of uninterrupted operation, during which time the mass flow rate was constant, the discharge current was stable at ± 0.06 A or within 0.3%. Figure 5. Discharge voltage and current during Test 1. Mass flow rate was held constant over many hours while the discharge current was open loop. Over the final 96 h of operation, the discharge current variation was ±0.06 A or 0.3%. Fig. 6 shows the cathode floating potential with respect to facility ground during Test 1. After the first 30 h of operation, the variations in cathode potential decreased to less than 1 V. During the final 96 h of uninterrupted operation, the cathode potential remained at V to within +0.17/-0.33 V or +2/-4%. These observed cathode potential variations are typical for this thruster. Performance during Test 1 is shown in Fig. 7 and Table 1, which have been power corrected to exactly 6.00 kw. The highest measurements were taken at the beginning of the test and decreased with time after the first 10 h for all parameters. The thrust at the beginning of the test was 380 mn and decreased to 376 mn by the end of the test. The thruster efficiency remained over 60% during the test. Table 1 shows thrust decreased by 3.6 mn (< 1%), specific impulse decreased by 14 s (0.7%) and efficiency decreased by 1%, however, these are within the uncertainty of the calculations. These small changes in thrust are possibly 8

9 Figure 6. Cathode potential with respect to facility ground during the Test 1. Variations during in the final 96 h of operation were only +0.17/-0.33 V or +2/-4%. related to the formation of a carbon layer on the erosion rings, which could make them perform similar to the graphite-walled version of the H6MS. 21 In Test 2 discussed later in Sect. III.B.1, performance was constant within the uncertainty of the measurements, which supports the argument that the wall properties were approaching those of a graphite-wall as the deposition layer increased in thickness. Figure 7. Thruster performance during Test 1 including thrust, specific impulse and efficiency. The power spectral density (PSD) of the discharge current oscillations at the beginning and end of Test 1 are shown in Fig. 8, which did not change significantly. Table 2 compares the root-mean-square (RMS), peak-to-peak (P2P) and primary frequencies of the spectra in Figure 8. The RMS and P2P increased by 0.6% and 4%, respectively, during Test 1. The peak frequencies increased by 1 khz (low frequency) and decreased by 10 khz (high-frequency), but the shape of the PSDs in Fig. 8 were unchanged. Unlike the 3000 s wear test where a 68 khz oscillation dominated over any low frequency breathing modes, 7 the 8-9 khz breathing mode dominated over the khz cathode related oscillations. Similar broadband noise above 2 MHz is noted as the 3000 s wear test, 7 but it is 5-6 orders of magnitude lower than other oscillations. 9

10 Time Thrust Isp Efficiency h mn s Table 1. Thruster performance during Test 1. Figure 8. Power spectral density of the discharge current oscillations during Test 1. Time RMS P2P Freq h % mean % mean khz , , 72 Table 2. Discharge current oscillatory properties during Test 1. 10

11 2. Temperature The thruster thermal behavior for Test 1 is shown in Fig. 9, where the temperatures were generally very stable over the test. The thruster reached thermal steady state with all component temperatures less than 450 C. The pole, screen and coil temperatures in Fig. 9(a) reached steady state by 20 h and remained relatively constant throughout the remainder of the test. This differs from the 3000 s wear test that observed a decrease in outer front pole and outer coil temperature, which was likely due to an increase in effective emissivity from carbon deposition. 7 The cathode keeper temperature in Fig. 9(a) dropped 65 C over the course of the test. The ring temperatures in Fig. 9(b) were consistent with earlier thermal characterization tests, but the other temperatures were approximately 30 C lower. The inner ring temperature distribution became less symmetric as the 9 o clock position where it cooled by 46 C drop over the last 100 hours. These effects could be due to loss of thermal contact between thruster components. (a) Temperatures measured with thermocouples and thermal camera during Test 1. Calculated coil temperatures from resistance measurements are also shown. (b) Temperatures from thermal camera measurements. Figure 9. Temperatures for Test 1. 11

12 3. Backsputter Rate The carbon back sputter measurements from the QCM and witness plates are in good agreement. The QCM measured carbon backsputter rate was ± μm/h. The witness plates shown in Fig. 10 had a film thickness equivalent to a carbon backsputter rate of ± μm/h. Figure 10. Witness plates used to calculate the carbon back sputter rate for Test Ring Erosion (a) Before. (b) After. Figure 11. H6MS before and after Test 1. The inner and outer erosion rings are clean at the beginning of the test and uniformly coated with carbon at the end. The inner pole shows sputtering across the entire surface. The outer pole shows sputtering near the discharge channel to a less degree than the inner pole and deposition at the outer radii. Figs. 3 and 11 show the thruster before and after Test 1, and have been previously presented in Refs. 8,9. Fig. 11(a) shows the erosion rings before Test 1 were bright white and free of carbon deposition from backsputtered carbon within the facility. The rest of the discharge channel is black from carbon deposition from previous testing. Fig. 11(b) after the wear test shows the erosion rings to be completely coated in carbon similar to the rest of the discharge channel. The rings are removed and shown separately in Fig. 12 where the carbon coating on the exposed surfaces is apparent. The white surfaces visible in Fig. 12 are mating surfaces to the discharge channel and not exposed to the plasma or facility. The inset in Fig. 12 is a close up of the inner erosion ring where the uniform black coating is indicative of carbon deposition. Unlike the 3000 s wear test where magnetic shielding of the inner ring was not perfect due to limitations of the magnetic circuit at this operating condition, 7 the magnetic field for the present test at 2000 s does completely shield the inner ring as evidenced by the uniform carbon deposition. These observations are consistent with previous H6MS testing at 300 V, 6 kw. 5 Therefore, it is concluded that the H6MS was magnetically shielded during Test 1. The average erosion rate measured by the CMM profilometry is plotted in Fig. 13 for various trials of the H6 in the unshielded (US) and magnetically shielded (MS) configurations. Data from previous 2000 s specific impulse testing from Ref. 5 and 3000 s specific impulse testing from Ref. 7 are shown for comparison. 12

13 Figure 12. H6MS erosion rings after the initial wear test showing the carbon coating from backsputter. The inset is a closeup of the inner ring. The inner channel data closely matches the 3000 s (800 V) results and also agrees with the previous MS result for 2000 s (300 V) test. The data for the outer channel from the present testing was corrupted by an alignment error and should be disregarded in Fig. 13. The CMM noise threshold has been estimated to be approximately 1 μm/h and all MS cases are below this noise threshold. 5. Pole Wear Close-up photographs of the poles are shown in Fig. 14. The outer front pole in Fig. 14(a) shows a deposition pattern that varies radially across the face. Near the inner radius by the discharge channel there is a crystalline appearance, while towards the outer radius a uniform coating is observed. This same pattern can be seen in Fig. 11(b), which may indicate different plasma interactions with the outer pole near the discharge channel. The inner front pole in Fig. 14(b) shows surface texturing suggesting sputtering. This observation generated further analysis and measurements of plasma interactions with the inner pole. 8, 9 The inner pole surface appears pitted and rough, indicative of sputtering. This same pattern can be seen in Fig. 11(b), where the roughening is present on the entire surface of the inner pole. These observations of pole roughening motivated the subsequent investigation of Test 2 in Sect. III.B in order to measure the erosion rates on the front poles of this magnetically shielded thruster and to consider mitigation techniques through material coatings or covers. B. Test2-WearTestwithPoleCovers 1. Performance and Operating Characteristics The H6MS was operated at 300 V discharge voltage and 20 A discharge current for 6 kw of discharge power as shown in Fig. 15 for Test 2 with the pole covers. The anode flow rate was varied from mg/s to maintain the 20.0 A discharge current. The cathode mass flow rate was varied with anode flow rate to maintain a 7 % cathode flow fraction. The magnetic field shape and magnitude were held constant with an 13

14 Figure 13. Average erosion rate measured by CMM for the unshielded (US) and magnetically shielded (MS) configurations of the H6. Data from previous 2000 s specific impulse (V D = 300 V) testing from Ref. 5 and 3000 s specific impulse (V D = 800 V) from Ref. 7 are shown for comparison. The data from the present test is denoted as MS, 300 V, 150 h. The data for the outer channel from the present testing was corrupted by an alignment error and should be disregarded. inner coil current of 4.00 A and and outer coil current of 3.31 A. Chamber pressure measured by the xenon calibrated ionization gauge next to the thrust stand 20 is shown in Fig. 16. The thruster was turned off and the chamber was vented at 11 h and 46.5 h to remove the remnants of the outer and inner molybdenum foil, respectively, which are described in Sections III.B.7 and III.B.8. An over-current limit triggered the thruster to turn off at 63.7 h, but the cause was not determined and the chamber was not vented. The thruster was turned off briefly at other times to record thrust stand zero points. Outgassing appears to continue through h at the inner pole foil failure and could be caused by the carbon pole covers outgassing or the chamber. After the over-current event, the pressure remained constant at Torr, which is in good agreement with Test 1 in Fig. 4. The thruster was operated on high purity xenon for the cathode and anode with a total throughput of kg. Fig. 17 shows the discharge voltage and current for the entirety of Test 2. The only time the thruster was operated below 6 kw was during warm-up periods after the thruster was turned off or the chamber had been vented. The total run time across all operating conditions was h with a total energy of kw-h, for an equivalent operation time at 6 kw of h. Fig. 18 shows the cathode floating potential with respect to facility ground during Test 2. After the the second foil strip was removed at 46.5 h, the cathode to ground potential remained at 7.9 ± 0.1 V except when the thruster was turned off. This is in good agreement with Test 1 in Fig. 6. Performance during Test 2 is shown in Fig. 19 and Table 3, which have been power corrected to exactly 6.00 kw. The same erosion rings from Test 1 were used during Test 2, so they were already coated with backsputtered carbon. Thrust remained within the measurement uncertainty at /-1 mn over the entire Test 2 window. This suggests that the carbon layer was thick enough that the wall acted essentially as a carbon wall. Definitive evidence of this effect will require still longer testing windows. Further investigation is planned during a longer wear test as discussed in Sect. IV.I. 2. Backsputter Rate The QCM measured a back sputter rate of 4 ± μm/h, which is in agreement with Test 1 and the previously measured value. 5 During the 153 h test, 0.6 μm of carbon would be deposited, which is below the 1 μm detection threshold of the Nanovea profilometer. The QCM crystal was analyzed to determine materials depositing from testing. Molecular Raman analysis shows the deposited material to be primarily amorphous carbon. This is expected due to the carbon panels downstream from the thruster protecting the vacuum chamber as well as from the eroding carbon pole covers. An elemental analysis of the non-carbon components was performed on the center of the QCM using a Horiba Model XGT-5000 X-Ray Fluorescence 14

15 (a) Outer Pole. (b) Inner Pole. Figure 14. Close-up pictures of the (a) outer pole and (b) inner pole after Test 1. The outer pole picture is a composite of two different pictures to show the entire radius and emphasize the different patterns from the inner to outer radius. Time Thrust Isp Efficiency h mn s Table 3. Thruster performance during Test 2. 15

16 Figure 15. H6MS operating at 6 kw at 153 h. 25x Outer Pole Foil Failure Inner Pole Foil Failure Overcurrent Limit Tank Pressure (Torr) Time (h) Figure 16. Tank pressure measured by the xenon calibrated ionization gauge mounted next to the thrust stand during Test 2. The chamber was vented at 11 h and 46.5 h to remove broken foil strips. 16

17 Discharge Voltage (V) Voltage Current Discharge Current (A) Time (h) Figure 17. Discharge voltage and current for Test Cathode-to-Ground Voltage (V) Time (h) Figure 18. Cathode potential with respect to facility ground during the Test 2. 17

18 Thrust [mn] Thrust Isp Eff Specific Impulse [s] Efficiency [-] Time [h] Figure 19. Thruster performance during Test 2 including thrust, specific impulse and efficiency. Microscope (μxrf) with the results shown in Table 4. This technique non-destructively excites the sample with high energy X-Rays and measures the energies and intensities of Fluorescence X-Rays emitted by the sample. Table 4 shows the expected gold (QCM coating) and silicon dioxide (from quartz) from the microbalance sensor surface. The iron and chromium are likely from steel or stainless steel surfaces in the chamber and similarly for copper. The molybdenum and tantalum are likely from the pole cover masks. The source of the palladium is unknown. Si Cr Fe Cu Mo Pd Ta Au Table 4. Elemental analysis of the center of the QCM crystal using μxrf showing relative mass in percent. 3. Carbon Cover - Inner Pole The polished carbon cover on the inner pole showed roughening similar to the magnetic pole in Test 1. Fig. 20 shows the masked region at 12 o clock still has a mirror finish, while the unmasked regions of the pole cover have a satin finish. The same observation is made for the mask at the molybdenum strip at 4 o clock and the three clips holding the pole cover in place at 2, 6 and 10 o clock. 4. Carbon Cover - Outer Pole The outer carbon pole cover in Fig. 21 shows a small band of significant discoloration and possible sputtering within a few millimeters of the inner radius by the discharge channel. Fig. 21 shows a coloration difference between the masked and unmasked region, but unlike the inner pole there is no noticeable difference in the surface texture. The outer pole was not polished, which made it difficult to identify differences. Profilometry scans before testing showed the machine marks were deeper than the erosion measured on the inner pole after testing. Profilometry measurements of the outer pole after testing are inconclusive because of the rough, machined surface. 5. Molybdenum Strip - Inner Pole The tantalum masked molybdenum samples on the inner pole at 4 o clock show noticeable roughening after the test. The polished molybdenum samples exhibit a satin finish for unmasked regions, while the mirror 18

19 Figure 20. Inner pole carbon cover 12 o clock with mask removed showing texture difference between masked and unmasked region after Test 2. Figure 21. Outer pole carbon cover 12 o clock with mask removed showing color difference, but no texture difference between masked and unmasked region after Test 2. The pole cover was not polished and machining marks are visible running continuously through the masked region. 19

20 finish is unchanged for masked regions. Profilometry later discussed in Sect. III.B.9 will show a very clear erosion pattern for unmasked areas. The tantalum shields spot welded onto the molybdenum are observed to have completely eroded through at points near the pole cover inner and outer radius, or near the cathode and discharge channel, respectively. Note that due to a gap between the pole edge and the discharge channel inner radius (where the downstream edge of the inner magnetic screen is visible), the outer edge of the inner pole is directly exposed to the plasma. Fig. 22(a) shows the corner by the outer radius at the discharge channel where the tantalum is completely eroded at a location. (a) Inner pole discharge channel edge. (b) Outer pole discharge channel edge. Figure 22. Polished molybdenum samples with tantalum shields for the inner and outer pole cover after Test 2. The tantalum shields are eroded through at the edges by the discharge channel. 6. Molybdenum Strip - Outer Pole The polished molybdenum sample on the outer pole did not show clear erosion or deposition except at the inner radius near the discharge channel as shown in Fig. 22(b). Note that due to a gap between the discharge channel outer radius and the pole edge (where the downstream edge of the outer magnetic screen is visible), the inner edge of the outer pole is directly exposed to the plasma. Fig. 22(b) shows the corner by the inner radius at the discharge channel where the tantalum is completely eroded at the inner radius edge that faces radially inward. Profilometry measurements of the outer pole molybdenum sample did not yield measurable step-height differences between the shielded and unshielded areas. Therefore, if any erosion or carbon deposition did occur, it was less than approximately 1 μm. This is in agreement with the qualitative observations of the outer pole after Test 1 where net deposition was observed in Fig. 14(a). The estimated net deposition was 0.6 μm from the QCM, which is below the profilometer detection threshold. 7. Molybdenum Foil - Outer Pole The molybdenum foil on the outer pole was observed to fail at 11 h. The failure occurred at the inner radius by the discharge channel as shown in Fig. 23(a). After the failure the foil bent back from the pole and was observed to be flapping at the edge of the plume with an amplitude of approximately a few centimeters and a period of approximately a few Hz. If the failure was due to erosion, this would correspond to an erosion rate of ɛ Mo 0.73 μm/h on the inner radius corner of the outer pole. It should be noted that the failure could have been caused or enhanced by mechanical means. The foil was wrapped over the carbon pole cover and spot welded to the iron pole. The coefficient of thermal expansion (CTE) of iron is 2-6 times that of carbon graphite, so the failure could be mechanical due to a CTE mismatch as discussed in Sect. IV.G. 20

21 8. Molybdenum Foil - Inner Pole The molybdenum foil on the inner pole failed sometime before 46.5 h, at which point the thruster was shut down automatically due to an over-current limit. Upon investigation the foil on the inner pole was mostly destroyed as shown in Fig. 23(b) with some fragments or drops adhered to the carbon pole cover. The foil remains were removed and the test was resumed. Based on the foil remains in Fig. 23(b), it is suspected that the foil failed on the outer radius near the discharge channel and peeled back similar to the foil on the outer pole. The foil was exposed to higher density and higher temperature plasma near the inner pole a that destroyed the foil. If the failure was due to erosion, this would correspond to an erosion rate of ɛ Mo 0.17 μm/h. As with the outer pole, the possibility of failure or increased stress hastening failure due to mechanical forces from the CTE mismatch between carbon and iron cannot be ruled out as discussed in Sect. IV.G. (a) Failure of outer pole Mo foil at 11 h near discharge channel radius on the corner. The foil strip can be seen to bend away from the pole cover face and it reflects light onto the pole cover. (b) Remains of the inner pole Mo foil before 46.5 h after the thruster was shut off and the chamber vented. Figure 23. Failure of the Mo foil on the inner and outer poles. 9. Erosion Measurements Measured erosion as a function of normalized radius is shown in Fig. 24. The location is normalized to mean channel radius, R ch. The measurement and calculations are discussed in detail in the Appendix. The zero value is the height of the masked surface, so the height difference is the step height measured from a masked to an unmasked surface using the techniques described in the Appendix. The measured carbon erosion varied from 4.0 μm atr/r ch =0.30 to 10.8 μm atr/r ch =0.62. The measured molybdenum erosion varied from 17.9 μm atr/r ch =0.46 to 41.3 μm atr/r ch =0.61. The maximum erosion occurred at the outer radius near the discharge channel. The erosion rates, ε, can be calculated from the erosion measurements in Fig. 24 and dividing by the 153 h run time with the results shown in Fig. 25. This approach yields an averaged erosion rate and assumes the erosion rate is constant during the run time. The carbon erosion is ε C = μm/h for r/r ch = , which is 71% of the inner pole radius. The worst case erosion is μm/h on the outer radius near the discharge channel. The inner radius near the cathode also shows high erosion at μm/h. The molybdenum erosion is high as expected because of the higher sputter yield. The erosion is ε Mo = μm/h for r/r ch = , which is 73% a The higher density and temperature plasma is due to the discharge channel geometry where the plasma converges on thruster centerline and the presence of an internally mounted cathode. 21

22 Height Difference [μm] Inner Pole Cover Inner Radius Increased Erosion at Inner Radius by Cathode Carbon Molybdenum Inner/Outer Radius Uncertainty Carbon Uncertainty Molybdenum 0.30 Inner Front Pole Cover Increased Erosion at Outer Radius by Discharge Channel Inner Pole Cover Outer Radius Normalized Thruster Radius [r/r ch ] Figure 24. Measured erosion on the inner front pole cover as a function of normalized thruster radius for carbon and molybdenum. The ordinate origin is the masked surface so negative height difference values are a step down (i.e. erosion) from the reference surface. R ch is the mean discharge channel radius. An estimated uncertainty of ±1.5 μm is shown for carbon and ±5 μm for molybdenum. Measurement and calculation details are in the Appendix Erosion Rate, ε [μm/h] Carbon Molybdenum Inner/Outer Radius Normalized Thruster Radius [r/r ch ] Figure 25. Calculated erosion rates on the inner front pole cover as a function of normalized thruster radius for carbon and molybdenum. R ch is the mean discharge channel radius. Estimated erosion rate uncertainties are ±0.010 μm/h for carbon and ±0.03 μm/h for molybdenum. 22

23 of the inner pole radius. The worst case erosion is 0.27 μm/h on the outer radius near the discharge channel. The inner radius near the cathode also shows high erosion at 0.24 μm/h. The conservatively estimated erosion uncertainty of ±1.5 μm for carbon and ±5 μm for molybdenum yields erosion rate uncertainties of ±0.010 μm/h for carbon and ±0.03 μm/h for molybdenum. The effects of backsputtered carbon from the facility depositing at μm/h and subsequently being eroded has not been accounted for in the calculated erosion rates. C. Summary of Test 1 and Test 2 A summary of the testing is provided in Table 5. Based on uniform backsputtered carbon deposition on the discharge channel erosion rings after both tests, it was assessed that magnetic shielding was sustained for more than 300 h of thruster operation. Parameter Units 1 2 Anode propellant throughput kg Cathode propellant throughput kg Total expended energy kw-h Total thruster operating time h Equivalent run time at 6 kw h Longest continuous firing time h Table 5. Summary of operation for Test 1 and 2 at 300 V, 2000 s and 6 kw. IV. Discussion A. Pole Roughening The pole roughening observed during the 3000 s, 100 h wear test 7 was qualitatively much less severe than the 2000 s 150 h wear test in Test 1. In that test, carbon deposition was noted on the inner and outer poles except in the regions near the discharge channel where the field lines with high electron temperatures intercept the poles. It was estimated that the sputtering rate was close to the carbon backsputter rate from the facility, but this test did not control for pole erosion so this estimate is order of magnitude at best. However, the inner front pole in Figs. 11(b) and 14(b) for Test 1 clearly show erosion, indicating sputtering at a discharge voltage of 300 V and discharge current of 20 A yields higher inner pole erosion than 800 V and A, which could be due to higher plasma density with the 20 A discharge. B. Pole Cover Erosion at the Corners The highest erosion rates were measured near the discharge channel edges of the inner pole and both poles showed evidence of high erosion on the edge by the discharge channel in Fig. 22 where the tantalum shields were eroded through. Plasma simulations of the H6MS 6 in Fig. 26 predict that magnetic field lines with high temperature plasma will intercept the inner pole outer radius and outer pole inner radius (i.e. the corners near the discharge channel). The principles of magnetic shielding capitalize on the isothermality of magnetic field lines of force. The electron temperature along a line of force is nearly constant, T e 0, so the electron momentum equation simplifies to E T e ln(n e ) where T e is electron temperature, E is the electric field parallel to the magnetic field line, and n e is the electron number density. 4 This yields the well known thermalized potential φ φ 0 + T e0 ln(n e /n e0 ) (1) where T e T e0,andt e0, φ 0 and n e0 are constants of integration. 22 This shows that lines of force are nearly isothermal, but not necessarily equipotential. Eq. 1 shows that high electron temperatures and large changes in plasma density can generate significant potential differences along a field line that can accelerate ions. For example, an order of magnitude decrease in plasma density will yield a potential drop of Δφ = φ 0 φ = 12 V for a cold field line of T e = 5 ev or a potential drop of Δφ = 92 V for a hot field line of T e = 40 ev such as 23

24 Figure 26. Discharge plasma simulations from Hall2De showing the carbon pole cover corners intercepting high temperature plasma. the field lines intercepting the cover corners in Fig. 26. In magnetically shielded thrusters, the magnetic field lines are shaped to extend deep into the channel towards cold electron populations (T e < 5 ev) minimizing the potential drop and maintaining nearly the discharge potential at the walls. In addition, the cold electrons near the walls minimize the sheath potential, which is a function of electron temperature. These factors reduce the kinetic energy ions can obtain from these potential differences before striking the wall, thus reducing discharge channel sputtering. However, the high electron temperature field lines intersect the corners of the pole covers near the discharge channel in Test 2 as shown in Fig. 26, which are grounded so they are only 8 V above cathode potential. This inherent feature of magnetically shielded thrusters, where high-temperature magnetic field lines converge onto the poles (as shown in Fig. 26), was recognized early in the derivation of the magnetic shielding first-principles 3, 4, 6 as a potential region of higher erosion. However, it was also argued that by the time the plasma reaches these regions of the thruster it has already expanded significantly such that the ion flux that could strike the surface is also reduced compared to the amount striking the channel walls. Indeed, compared to erosion rates of the channel in the unshielded version of this thruster, at locations where the high-temperature lines converge, the rates at these regions in the magnetically shielded thruster are at least an order of magnitude lower. Nevertheless, our measurements suggest they may be high enough to be the cause of the higher sputtering observed in these areas of the pole covers. C. Sputter Rates 1. General Sputter Rate Relation In order to calculate the ion energy from the erosion rate measurements, a functional form for the erosion rate of molybdenum and carbon must be determined from literature values. Bohdansky gives a relation for sputter yield of monatomic solids at normal incidence for the threshold regime as 23 [ γ(e) αs T n F (E) 1 ( Eth E ) ] 2/3 [ 1 E ] 2 th (2) E where E is the energy of the primary particle, E th is the threshold energy, α is an energy-independent function of the mass ratio between the target (M 2 ) and projectile (M 1 ) from Sigmund s original derivation, 24 and Sn TF is the Thomas-Fermi nuclear stopping cross section. The mass ratio function α is interpreted as a fitting parameter by others García-Rosales suggested modifying the Bohdansky model of Eq. 2 by 24

25 replacing the Thomas-Fermi nuclear stopping cross section with the Kr-C potential, which is appropriate for low energies 25 s KrC 0.5 ln( ɛ) n (ɛ) = ɛ (3) ɛ ɛ The reduced energy, ɛ, is M 2 a L ɛ = E M 1 + M 2 Z 1 Z 2 e 2 (4) where Z 1 and Z 2 are the atomic numbers of the projectile and target, respectively, e 2 = 14.4 ev Å, and the Lindhard screening length, a L,isgivenby 25 Eckstein derived a new fitting formula 26 ( ) 1/2 a L = Z 2/3 1 + Z 2/3 2 Å (5) γ(e) =qs KrC n ( E ) μ E th 1 (ɛ) ( ) μ (6) E λ + E th 1 where q, μ and λ are fit parameters. Yamamura derived a new empirical formula for sputter energy 27 γ(e) =0.042 Q(Z 2)α (M 2 /M 1 ) U s [ S n (E) 1+Γk e ɛ Eth E ] s (7) where k e is the Lindhard electronic stopping coefficient, and Γ is the contribution of the internal reflection sputtering mechanism. The nuclear stopping cross section S n, reduced energy ɛ, Q, U s,andα used in Eq. 7 are given in Ref Carbon Sputter Rate Literature values for carbon sputter yield from xenon bombardment at normal incidence angle are shown in Fig. 27(a) obtained from Doerner 28 (weight loss measurements only), Kolasinksi, 29 Deltschew, 30 Gruber, 31 Williams, 32 Rosenberg, 33 and Gopel. 30 In some cases, the data is copied from tables and others it is electronically extracted from plots. The data from Deltschew, Gruber, and Williams are not peer-reviewed and Gopel s data is extracted from Deltschew. For the carbon pole cover sputtering, M 1 = M Xe = 131.3, M 2 = M C =12.0, Z 1 = Z Xe =54and Z 2 = Z C = 6. Using these values in Eq. 5 yields a L = Å and Eq. 4 yields ɛ = E. Eq. 2 with the modifications suggested by García-Rosales is shown in Fig. 27(a) with E th =40eVandα =2.2. Eq. 6 is shown in Fig. 27(a) with E th =30eV,λ = 50, μ =1.9, and q = 4. Note these values are not close to the q μ λ 3 shown in Figure 3(b) of Ref 26 for a projectile mass of 131 AMU impacting carbon. Eq. 7 is also shown in Fig. 27(a) as presented in Figure 24 of Ref. 27. For +1 xenon ions impacting carbon, s =2.50, Q =1.70, and U s = 7.37, and the threshold energy is calculated to be E th = ev. While the Eckstein fit of Eq. 6 is the best of the three presented, none of these equations are an adequate fit for the carbon sputter data to calculate ion energy based on sputter rate ratio so a better fit is needed. Both Eqs. 2 and 6 have the sputter energy linearly related to the nuclear stopping cross section and a function of the particle energy to the threshold energy γ s KrC n (ɛ)f (E/E th ). Eq. 7 is similar except for the Γ term. The f (E/E th ) term describes sputtering behavior at low energy near the threshold of sputtering. Using these previous derivations as a guide we select an empirical fit of the form γ(e) =s KrC n exp where β, η and E th are all fit parameters. The data in Fig. 27(a) is used to manually determine β, η and E th in Eq. 8 with the results shown in Table 6. These fit parameters and bounds plotted in Fig. 27(a) were selected to encompass a majority of the experimental results and to provide a reasonable estimate of uncertainty in sputter yield. Note the threshold energy of over 700 ev is not representative of a true, physical threshold sputtering value, which is also the case with the threshold energy of the Yamamura fit. [ β ( Eth E ) η ] (8) 25

26 (a) Carbon. (b) Molybdenum. Figure 27. Sputter yield from xenon bombardment data and curve fits. 26

27 Fit Parameter Fit to Data Upper Bound Lower Bound E th [ev] η β Table 6. Carbon sputtering fit parameters for Eq. 8 with upper and lower bounds plotted in Fig. 27(a). 3. Molybdenum Sputter Rate Literature values for molybdenum sputter yield from xenon bombardment at normal incidence angle are shown in Fig. 27(b) obtained from Doerner 28 (weight loss and spectroscopic measurements), Gruber, 31 and Rosenberg. 33 The peer-reviewed data from Doerner is considered more reliable, but the other data is shown for completeness. For the molybdenum sample sputtering, M 2 = M Mo =96.0 andz 2 = Z Mo = 42. Using these values in Eq. 5 yields a L = Å and Eq. 4 yields ɛ = E. The data in Fig. 27(b) is used to manually determine β, η and E th in Eq. 8 with the results shown in Table 7. The fit parameters and bounds plotted in Fig. 27(b) are selected based on the Doerner data with the bounds encompassing the measurement uncertainty. A fit to the Gruber and Rosenberg data is also shown in Fig. 27(b) and Table 7. Fit Fit to Data Upper Lower Fit to Data Parameter Doerner Bound Bound Gruber-Rosenberg E th [ev] η β Table 7. Molybdenum sputtering fit parameters for Eq. 8 with upper and lower bounds plotted in Fig. 27(b). 4. Sputter Rate Ratio The erosion rate of a target material, ε t,inμm/h is calculated from ε t = γ Φ i m t /ρ t (9) where m t is the mass of the target particle (Mo or C here) in kg, ρ t is the density of the target material in kg/m 3 and Φ i is the ion flux density to the target surface in ion/m 2 /s. The ion current density to the target surface is j t = ZqΦ i where Z is the charge state and e is the fundamental charge. The required ion current to the target in ma/cm 2 for a measured erosion rate and sputter yield can be calculated from Eq. 9 as j =( ε(e)) ρ t Ze γ(e) m t (10) where E is the ion energy in ev. The erosion rate ratio, ε, for molybdenum to carbon erosion under the same ion flux is ε (E) = ρ C m Mo γ Mo (E) ρ Mo m C γ C (E) =1.762γ Mo(E) γ C (E) where γ Mo (E) andγ C (E) are sputter yields from Eq. 8 with values from Tables 7 and 6, respectively. The erosion rate ratio as a function of energy is shown in Fig. 28 as well as the upper and lower bounds based on the bounds in Tables 7 and 6. Fig. 28 shows there is considerable uncertainty in calculating the ion energy from the erosion rate ratio without accounting for the ion angle. Therefore, these calculations are only for normal ion incidence angle and variable ion angles will be considered in future experiments and analyses. Additionally, Eq. 11 implies the erosion is caused by one primary ion energy population. If erosion is caused by ions with a large spread in energy or with multiple peaks in ion energy, then empirical measurements of erosion rates will yield misleading results for ion energy. For example, a population of Xe + and Xe ++ ions accelerated through the same potential will impact with different energies and different sputter rates making the interpretation of erosion rate ratio data difficult. (11) 27

28 30 25 Ratio from Fits Upper/Lower Bounds Erosion Rate Ratio, ε Ion Energy [ev] Figure 28. Erosion rate ratio from Eq. 11 with upper and lower bounds at normal incidence. D. Ion Energy Calculation The erosion rate ratio from the inner pole erosion measurements is the ratio of the rates shown in Fig. 25 with the results shown in Fig. 29(a). The mean erosion rate ratio is ε =4.89 with a standard deviation of 0.73 across the inner pole radius. The maximum and minimum values are 6.32 and The inner half of the inner pole by the cathode generally has a higher ratio than the outer half. Fig. 28 shows that higher ε corresponds to lower ion energy and conversely lower ε is higher ion energy. Erosion Rate Ratio, ε Ratio Data Mean Ratio Data Min/Max Ratio +/- Stand Dev Ratio Inner/Outer Radius Erosion Rate Ratio, ε Ratio from Fits Upper/Lower Bounds Mean Ratio Data +/- Stand Dev Ratio Min/Max Ratio Normalized Thruster Radius [r/r ch ] (a) Inner pole erosion rate ratio from measured average erosion rates of Mo and C. The mean value, minimum, maximum and standard deviations are shown for reference Ion Energy [ev] (b) Erosion rate ratio of Mo to C as a function of ion energy. Upper and lower limits are shown based on the bounds in Fig. 27. The ion energy is estimated at the intersection marked by a green circle Figure 29. Erosion rate ratio (a) on the inner pole and (b) Mo/C erosion rate ratio as a function of ion energy at normal incidence. The vertical axes are the same scale with the experimental mean, minimum, maximum, and standard deviation shown on both plots. The mean ion energy from the mean erosion rate ratio is calculated to be 156 ev in Fig 29(b). The bounds using the standard deviation are ev. The discharge voltage is 300 V so no singly charged ions are expected to be higher than 300 V, but multiply charged ions could impact the poles with higher energies than the discharge voltage. The lower bound of 51 ev is realistic and shows that the erosion is not 28

29 done by low energy (< 20 ev) ions. This means the ions causing the erosion are accelerated by at least 51 V potential for singly charged ions and 25 V for doubly charged ions. An independent ion energy calculation was performed for the pole erosion simulations 10 that yielded 130 ev ions, based on the measured erosion rates presented in Fig. 25. This value was then used for comparisons with the simulation results. Figs. 28 and 29(b) show that ε must be greater than 8 for low energy ions (< 20 ev) to be the primary ion population causing erosion assuming a normal incidence angle, and Fig. 29(a) clearly shows this is not the case. Therefore, it is believed that the ion energy is greater than 50 ev if the erosion is caused by a single, normal incidence ion population. The fit with the Gruber-Rosenberg data shown in Fig. 27(b) was used to calculate ion energy yielding a value of 1067 ev, which is not realistic. Therefore, only the fit to Doerner s molybdenum sputter yield data was used. E. Current Density to Inner Pole The ion current density to the carbon and molybdenum samples on the inner pole can be calculated from Eq. 10 for the range of ion energies. The current density to the carbon samples must equal that of the molybdenum, j C = j Mo = j, which provides a unique solution for ion energy from a given erosion rate and erosion rate ratio determined from the measurements in Figs. 25 and 29(a), respectively. The predicted ion current density to the inner pole for the range of ion energies discussed in Sect. IV.D is shown in Table 8. An intermediary ion energy of 80 ev is also shown from the lower bound erosion rate ratio, which provides a value between 51 and 156 ev. The lower energy ions require more current to achieve the same amount of erosion as higher energy ions because of the sputter yield dependence on ion energy in Eq. 8. Energy E i ε j Xe + j Xe ++ Bound ev ma/cm 2 ma/cm 2 Lower Lower-Int Expected Upper Table 8. Calculated ion current density, j, to the inner pole from erosion measurements and different ion energy calculations, E i. A carbon erosion rate of ε C =0.035 μm/h from Fig. 25 is used and the upper energy bound is the discharge potential. F. Comparison with Simulation An important collaboration between modeling and experimentation is guiding future numerical and laboratory experiments in order to understand the source(s) of the inner pole erosion. The erosion rate estimations from simulations with the Hall2De code 34 currently under-predict the measurements by factors of 3 to Efforts are underway to determine the cause of additional erosion and to take new experimental data to assist modeling as discussed in Section IV.I. The results presented here suggest the presence of ions with energy higher than that associated with the local plasma potential, which could be either beam ions or doubly or triply charge ions in the plume. To explain the observed pole erosion as the result of beam ion bombardment, the simulations show that the plasma must be at an unreasonable downstream location or it would require discharge oscillations of much higher amplitudes than those observed. For plume (low-energy) ions to cause erosion, the plasma potential in the pole region has to be large ( 80 V) or large plasma oscillations would have to exist. 10 Other mechanisms for enhanced erosion in the near-pole region are being investigated with the Hall2De code. G. Foil Failure and Coefficient of Thermal Expansion This section addresses the possibility that the 8 μm thick molybdenum foil failures were caused by or enhanced by mechanical stress due to CTE mismatches. The CTE of molybdenum is m/m/k and the CTE for graphite can range from m/m/k. The CTE of iron is m/m/k and the stainless steel clips are m/m/k. The pole covers and foil strips were installed at room temperature and from Fig. 9 the inner front pole temperature for Test 1 is 310 C and the outer front pole is 220 C, which 29

30 can be assumed for Test 2. The inner pole may have expanded μm more than the carbon pole cover at the outer radius and the outer pole μm more than the carbon pole cover at the outer radius. The stainless steel clips may have expanded more than the carbon pole covers by up to 26 μm for the inner pole and 18 μm for the outer pole. This slight loosening of the pole covers or shifting at operational temperatures may have put mechanical strain on the foil causing them to break or hastening the time to failure. In light of the above discussion, the inner pole erosion rate from the foil of ɛ Mo 0.17 μm/h is within the bounds of the molybdenum erosion rate on the inner pole of μm/h. The erosion rate of ɛ Mo 0.73 μm/h for the outer pole molybdenum foil is over 2 higher than the highest molybdenum erosion rate on the face of the inner pole. However, in Fig. 22 both the inner and outer pole radii by the discharge channel (outer and inner radius, respectively) qualitatively exhibited more erosion than the faces, which were not measurable. In addition, it is confirmed the outer strip failed at the discharge channel corner and it is suspected the inner strip did as well. Therefore, we cannot exclude the possibility that the foil strips failed primarily due to erosion. H. Implications for Pole Cover Design 1. Erosion Rate Comparison Comparison of discharge channel erosion between magnetically shielded thrusters and a range of unshielded thrusters is provided in Ref. 5. This has been summarized in Fig. 30 where the range of carbon pole cover erosion rates observed here are more than an order of magnitude lower than even the best case for unshielded thrusters. The carbon backsputter rate is also shown for comparison in Fig. 30. Being significantly smaller than channel erosion in unshielded thrusters, pole erosion in this magnetically shielded thruster is easier to mitigate even at the present state of our understanding on the source(s) that cause it. Mitigation strategies include using low sputter yield material to design mechanical pole covers or applying coatings to the pole surfaces. Optimization of the magnetic shielding topology in a manner that minimizes both channel and pole erosion is also a longer-term solution. Such an approach will benefit significantly from the near-term investigations on the possible sources of pole erosion. Figure 30. Order of magnitude comparison between the discharge channel walls of unshielded thrusters, the carbon pole covers, and the carbon back sputter rate. 2. Pole Cover Thickness Based on the erosion rates shown in Figs. 25 and 30, an estimate is made for the required pole cover thickness for a given mission duration. The Hall Effect Rocket with Magnetic Shielding (HERMeS) is being developed for the Space Technology Mission Directorate (STMD) Solar Electric Propulsion Technology Demonstration Mission (SEP TDM) project. 35 A mission concept for the SEP TDM is the proposed Asteroid Redirect Robotic Mission (ARRM), which will require up to 50 kh of operation. If HERMeS were to exhibit similar pole erosion, then using the worst case measured values for the H6MS and a 50 kh lifetime, Table 9 shows 30

31 graphite pole covers greater than 3.5 mm thick (unmargined) would be required. The pole covers do not impact performance, they only protect the magnetic poles from erosion. The magnetic poles will begin to erode at locations where the pole covers have eroded through, which may eventually degrade thruster performance as the magnetic circuit is slowly altered. This process will likely take significant time before any appreciable change is observed in the magnetic field as the poles are eroded. Therefore, it is expected complete erosion of the pole covers only marks the beginning of a slow and graceful degradation of thruster performance at worst. Erosion Rate Mission Duration μm/h 10 kh 50 kh Table 9. operation. Required thickness in millimeters for carbon pole covers to survive 10 kh and 50 kh of thruster It is important to note that further work is required to determine if the values presented here represent the worst case. With only a single operating condition with quantified erosion rates, it is uncertain how erosion varies with thruster operational time and operating condition. In addition, it is uncertain how erosion rate varies with thruster operating condition. I. Future Experimental Work A set of experiments are currently underway to measure the plasma properties near the poles in order to understand the mechanism for the observed erosion. These measurements will include Faraday probes to measure ion current density, a retarding potential analyzer to measure ion energy, emissive probes to measure plasma potential and LASER induced fluorescence to measure ion velocity. Time-resolved measurements will be included to investigate plasma oscillations near the pole. In addition, the thruster body will be floated or grounded and different operating conditions (discharge voltage and current) will be investigated in an attempt to ascertain the worst case operating condition. Candidate pole cover materials will be placed in the plume to assess their effectiveness. The results of the plasma measurements will be coordinated with the modeling and simulation efforts to determine the physical mechanisms for pole erosion. Finally, a h test is planned to determine the longer term performance and wear characteristics. V. Conclusions Magnetically shielded HETs have specially contoured magnetic fields that minimize ion bombardment and, consequently, erosion of the acceleration channel. Two tests of approximately 150 h operating at 300 V discharge voltage, 2000 s specific impulse were conducted in order to characterize the performance, stability, thermal, and wear of the H6MS. After the first wear test at 2000 s the rings were coated with carbon, surface roughening likely from ion sputtering was noted on the inner front pole, the outer front pole inner radius near the discharge channel had a crystalline patterned appearance, and the outer front pole outer radius showed net carbon deposition. The thrust at the beginning of the first test was 380 mn and decreased to 376 mn, but remained constant at 380 mn +2/-1 mn during the second. Based on uniform backsputtered carbon deposition on the discharge channel erosion rings, it was assessed that magnetic shielding was sustained through 150 h of thruster operation. The thruster efficiency remained over 60% during both tests. The power spectral density of the discharge current at 10 h and 150 h of operation both showed similar peaks near 10 and 80 khz indicating the oscillation characteristics of the thruster did not change during the test. The thruster reached thermal steady state with all component temperatures less than 450 C. For all testing at 2000 s, the back sputter rate of carbon was measured to be μm/h. The second wear test at 2000 s employed carbon covers over the inner and outer front poles as well as material samples to measure erosion. The samples on both the inner and outer pole covers included masking of the carbon pole covers, polished molybdenum samples with tantalum masking, and 8 μm thick molybdenum foil. At the end of 153 h of operation, net erosion was observed on the inner front pole carbon and molybdenum samples and both molybdenum foil samples were worn through during the testing. The 31

32 erosion rates varied from to μm/h for carbon and 0.12 to 0.27 μm/h for molybdenum. This erosion rate is still one or more orders of magnitude lower than channel erosion rates observed in the unshielded version of this thruster. Assuming the erosion is caused by a single ion population impacting at normal incidence angle, an approximate ion energy is 156 ev with a bound of ev based on the uncertainty in sputter yields for carbon and molybdenum. The calculated ion current density to the poles to generate the measured erosion rates for 156 ev ions are 0.8 or 1.6 ma/cm 2 for a population consisting of only Xe + or Xe ++, respectively, and for 51 ev ions are 24 or 48 ma/cm 2 for Xe + or Xe ++, respectively. For the worst case erosion rate, 3.5 mm thick carbon pole covers would be required for 50 kh of thruster operation. However, with only one experiment at a single operating point, it is uncertain if the erosion rate is constant or if the 2000 s and 6 kw operating condition represents the worst case erosion. Since some inner front pole erosion has been observed (albeit at least one order of magnitude lower than channel erosion in unshielded thrusters), the results of the wear test presented here suggest that further optimization of the magnetic shielding topology is possible and may in fact be necessary for missions requiring several years of thruster operation. Acknowledgments The research described in this paper was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. The support of NASA s Space Technology Mission Directorate through the Solar Electric Propulsion Technology Demonstration Mission (SEP TDM) project is gratefully acknowledged. The authors thank Mark Anderson for the QCM chemical analysis. The authors are indebted to Ray Swindlehurst and Nowell Niblett for their assistance throughput the test campaign constructing and implementing the test apparatus and maintaining the vacuum facility. The collaboration and discussions with Alejandro Lopez-Ortega regarding simulations were very helpful. Finally, the efforts of Jose Uribe to polish the samples is greatly appreciated. References 1 Mikellides, I. G., Katz, I., Hofer, R. R., Goebel, D. M., de Grys, K., and Mathers, A., Magnetic Shielding of the Acceleration Channel Walls in a Long-Life Hall Thruster, AIAA , 46th AIAA Joint Propulsion Conference & Exhibit, Nashville, TN, July Grys, K. d., Mathers, A., Welander, B., and Khayms, V., Demonstration of 10,400 Hours of Operation on 4.5 kw Qualification Model Hall Thruster, 46th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, AIAA , 46th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, Nashville, TN, July Mikellides, I. G., Katz, I., Hofer, R. R., Goebel, D. M., de Grys, K., and Mathers, A., Magnetic shielding of the channel walls in a Hall plasma accelerator, Physics of Plasmas, Vol. 18, No. 3, 2011, pp Mikellides, I. G., Katz, I., Hofer, R. R., and Goebel, D. M., Magnetic shielding of walls from the unmagnetized ion beam in a Hall thruster, Applied Physics Letters, Vol. 102, No. 2, 2013, pp Hofer, R. R., Goebel, D. M., Mikellides, I. G., and Katz, I., Magnetic shielding of a laboratory Hall thruster. II. Experiments, Journal of Applied Physics, Vol. 115, No. 4, Jan. 2014, pp Mikellides, I. G., Katz, I., Hofer, R. R., and Goebel, D. M., Magnetic shielding of a laboratory Hall thruster. I. Theory and validation, Journal of Applied Physics, Vol. 115, No. 4, Jan. 2014, pp Hofer, R. R., Jorns, B. A., Polk, J. E., Mikellides, I. G., and Snyder, Wear test of a magnetically shielded Hall thruster at 3000 seconds specific impulse, IEPC , 33rd International Electric Propulsion Conference, Washington, D.C., Oct Goebel, D. M., Jorns, B., Hofer, R. R., Mikellides, I. G., and Katz, I., Pole-piece Interactions with the Plasma in a Magnetically Shielded Hall Thruster, AIAA , 50th AIAA Joint Propulsion Conference, American Institute of Aeronautics and Astronautics, Cleveland, OH, July Mikellides, I. G., Lopez Ortega, A., and Jorns, B., Assessment of Pole Erosion in a Magnetically Shielded Hall Thruster, AIAA , 50th AIAA Joint Propulsion Conference, American Institute of Aeronautics and Astronautics, Cleveland, OH, July Lopez-Ortega, A., Mikellides, I. G., and Katz, I., Hall2De numerical simulations for the assessment of pole erosion in a magnetically shielded Hall thruster, IEPC , 34th International Electric Propulsion Conference, Hyogo-Kobe, Japan, July Haas, J. M., Hofer, R. R., Brown, D. L., Reid, B. M., and Gallimore, A. D., Design of the H6 Hall Thruster for High Thrust/Power Investigation, 54th JANNAF Propulsion Meeting, Denver, CO, May Hofer, R. R., Jankovsky, R. S., and Gallimore, A. D., High-Specific Impulse Hall Thrusters, Part 1: Influence of Current Density and Magnetic Field, Journal of Propulsion and Power, Vol. 22, No. 4, July 2006, pp Hofer, R. R. and Gallimore, A. D., High-Specific Impulse Hall Thrusters, Part 2: Efficiency Analysis, Journal of Propulsion and Power, Vol. 22, No. 4, July 2006, pp

33 14 Hofer, R. R., Development and characterization of high-efficiency, high-specific impulse xenon Hall thrusters., Ph.d. dissertation, University of Michigan, Ann Arbor, MI, Hofer, R., Johnson, L., Goebel, D., and Wirz, R., Effects of Internally Mounted Cathodes on Hall Thruster Plume Properties, IEEE Transactions on Plasma Science, Vol. 36, No. 5, Oct. 2008, pp Reid, B. M., Gallimore, A. D., Hofer, R. R., Li, Y., and Haas, J. M., Anode Design and Verification for a 6-kW Hall Thruster, JANNAF Journal of Propulsion and Energetics, Vol. 3, No. 1, 2010, pp Hofer, R., Goebel, D., Mikellides, I., and Katz, I., Design of a Laboratory Hall Thruster with Magnetically Shielded Channel Walls, Phase II: Experiments, AIAA , 48th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, Atlanta, GA, Aug Hofer, R. R., Goebel, D. M., Snyder, J. S., and Sandler, I., BPT-4000 Hall Thruster Extended Power Throttling Range Characterization for NASA Science Missions, IEPC , 31st International Electric Propulsion Conference, Ann Arbor, MI, Sept Hofer, R., High-Specific Impulse Operation of the BPT-4000 Hall Thruster for NASA Science Missions, AIAA , 46th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, Nashville, TN, July Hofer, R. R. and Anderson, J. R., Finite Pressure Effects in Magnetically Shielded Hall Thrusters, AIAA , 50th AIAA Joint Propulsion Conference, American Institute of Aeronautics and Astronautics, Cleveland, OH, July Goebel, D. M., Hofer, R. R., Mikellides, I. G., Katz, I., Polk, J. E., and Dotson, B. N., Conducting Wall Hall Thrusters, IEEE Transactions on Plasma Science, Vol. 43, No. 1, Jan. 2015, pp Morozov, A. I. and Savelyev, V. V., Fundamentals of Stationary Plasma Thruster Theory, Reviews of Plasma Physics, edited by B. B. Kadomtsev and V. D. Shafranov, Vol. 21, Springer US, Boston, MA, 2000, pp Bohdansky, J., A universal relation for the sputtering yield of monatomic solids at normal ion incidence, Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, Vol. 2, No. 1-3, March 1984, pp Sigmund, P., Theory of Sputtering. I. Sputtering Yield of Amorphous and Polycrystalline Targets, Physical Review, Vol. 184, No. 2, Aug. 1969, pp Garcia-Rosales, C., Eckstein, W., and Roth, J., Revised formulae for sputtering data, Journal of Nuclear Materials, Vol. 218, No. 1, Jan. 1995, pp Eckstein, W. and Preuss, R., New fit formulae for the sputtering yield, Journal of Nuclear Materials, Vol. 320, No. 3, Aug. 2003, pp Yamamura, Y. and Tawara, H., Energy Dependence of Ion-Induced Sputtering Yields from Monatomic Solids at Normal Incidence, Atomic Data and Nuclear Data Tables, Vol. 62, No. 2, March 1996, pp Doerner, R. P., Whyte, D. G., and Goebel, D. M., Sputtering yield measurements during low energy xenon plasma bombardment, Journal of Applied Physics, Vol. 93, No. 9, 2003, pp Kolasinski, R. D., Polk, J. E., Goebel, D., and Johnson, L. K., Carbon sputtering yield measurements at grazing incidence, Applied Surface Science, Vol. 254, No. 8, Feb. 2008, pp Deltschew, R., Tartz, M., Plicht, V., Hartmann, E., Neumann, H., Leiter, H. J., and Esch, J., Sputter Characteristics of Carbon-Carbon Compound Material, IEPC , 27th International Electric Propulsion Conference, Pasadena, CA, Oct Gruber, J. R., Low-Energy Sputter Erosion of Various Materials in a T5 Ion Thruster, IEPC , 27th International Electric Propulsion Conference, Pasadena, CA, Oct Williams, J. D., Johnson, M. L., and Williams, D. D., Differential Sputtering Behavior of Pyrolytic Graphite and Carbon-Carbon Composite Under Xenon Bombardment, AIAA , 40th AIAA Joint Propulsion Conference, Fort Lauderdale, FL, July Rosenberg, D. and Wehner, G. K., Sputtering Yields for Low Energy He+-, Kr+-, and Xe+-Ion Bombardment, Journal of Applied Physics, Vol. 33, No. 5, 1962, pp Mikellides, I. G. and Katz, I., Numerical simulations of Hall-effect plasma accelerators on a magnetic-field-aligned mesh, Physical Review E, Vol. 86, No. 4, Oct Hofer, R. R., Herman, D. A., Polk, J. E., Kamhawi, H., and Mikellides, I. G., Development Approach and Status of the 12.5 kw HERMeS Hall Thruster for the Solar Electric Propulsion Technology Demonstration Mission, IEPC , 34th International Electric Propulsion Conference, Hyogo-Kobe, Japan, July Appendix This section describes the step height measurements and calculations. Areas including the masked and unmasked regions are scanned with the profilometer creating data sets consisting of points. These large data sets are analyzed to calculate the height difference between the masked (reference) and unmasked surfaces three ways yielding similar results: 1) profile calculations with Nanovea Expert 3D software, 2) area calculations with Nanovea Expert 3D software and 3) least-squares fits to profiles with MathWorks MatLab. Measuring erosion over such a short duration test is difficult and requires a sensitive instrument and large sample sizes for statistical significance. The surface roughness of the polished surfaces was estimated to be 6 μm and the Nanovea ST400 discussed in Sect. II.D.4 has a resolution of < 1 μm. Erosion is measured as the step-height between masked and unmasked surfaces at the end of the test. Dividing by the 153 h test duration yields an average erosion rate during the test, but does not determine whether the erosion rate is steady state during the test. Carbon erosion on the inner pole is measured across the entire radius by the 33

34 molybdenum masks at 4 and 12 o clock shown in Fig. 1(b). The carbon erosion at the outer radius near the discharge channel is also measured at the three clips holding the inner pole cover at 2, 6, and 10 o clock also shown in Fig. 1(b), which also acted as masks. The molybdenum erosion is measured on the polished sample at 4 o clock that has a tantalum shield. The shield consists of two strips of tantalum spot welded to the molybdenum sample shown in Fig. 1(b). (a) 12 o clock carbon cover surface scan after molybdenum mask removal. (b) 4 o clock carbon cover surface scan after molybdenum mask removal. (c) 4 o clock molybdenum sample surface scan after tantalum mask removal. Figure 31. Oblique views of carbon pole cover and molybdenum surface scans using the Nanovea ST400 profilometer. All scans are leveled, a Gaussian filter applied, and non-measured points are removed with the Nanovea Expert 3D Analysis Software. After the mask is removed, the 12 o clock location on the inner pole cover is scanned with 1 μm azimuthal steps and 150 μm radial steps yielding points as shown in Fig. 31(a). The 4 o clock erosion strip location is scanned with 0.5 μm azimuthal steps and 150 μm radial steps yielding points as shown in Fig. 31(b). Both surface scans are leveled, a mm Gaussian filter applied, and non-measured points are removed and approximated using the nearest neighbors with the Nanovea Expert 3D Analysis Software. Fig. 32 shows examples of calculating the step height on the azimuthal profiles extracted from the smoothed surface using the Nanovea Expert 3D software. An example of an azimuthal scan before filtering is shown in Fig. 33(a). However, this manual method is inefficient for calculating step heights at hundreds of radial locations, so the smoothed surface scans are imported into MatLab. For each radial step, the masked region is least-squares fit to a linear equation and the unmasked region is least-squares fit to a second order polynomial as shown in Fig. 33(b). The molybdenum masks on the carbon pole cover were strips, which presents two edges to measure step heights from the masked to unmasked regions. The height differences between the fits at the two boundary locations are averaged to calculate the height difference for that step. The uncertainties in the fits at the boundary locations are used to calculate the uncertainty in the mean, which is the uncertainty in height difference for that step. The radial erosion measurements for the 4 and 34

35 Figure 32. Azimuthal profile at the 12 o clock position near inner pole outer radius by the discharge channel. The step height of 9.3 μm agrees with Fig. 24 for r/r ch o clock are then averaged together and the uncertainty in the mean between those measurements is the uncertainty for that radial location. Additional surface scans are made of the clips and different scans are made of the pole cover at the inner radius. The inner radius near the cathode, r/r ch < 0.31, is an averaged result of azimuthal sweeps with a rotational stage and azimuthal sweeps with the linear stages. The outer radius near the discharge channel, r/r ch > 0.57, is an averaged result of the azimuthal sweeps of the 4 and 12 o clock mask and the 2, 6 and 10 o clock clips. The net result for carbon erosion measurements as a function of inner pole radius are shown in Fig. 24, which has been smoothed by a moving average filter. Combining the uncertainty measurements across the inner pole radius yields an estimated ±1.5 μm uncertainty on the carbon erosion, which is shown bounding the erosion in Fig. 24. After the tantalum mask is removed, the molybdenum sample from the 4 o clock location on the outer pole cover is scanned with 0.5 μm azimuthal steps and 50 μm radial steps yielding points as shown in Fig. 31(c). The surface scan is leveled, filtered with a 0.35 mm Gaussian filter and non-measured points are removed with the Nanovea Expert 3D Analysis Software. An example of an azimuthal scan before filtering is shown in Fig. 34(a). In MatLab, the masked and unmasked regions are least-squares fit to second order polynomials as shown in Fig. 34(b). For most of the radius, except for r/r c < 0.19 near the cathode, there are three edges to measure step heights from the masked to unmasked regions. The height differences between the fits at the three boundary locations are averaged to calculate the height difference for that step. The uncertainties in the fits at the boundary locations are used to calculate the uncertainty in the mean, which is the uncertainty in height difference for that radial location. The net result for molybdenum erosion measurements as a function of inner pole radius are shown in Fig. 24, which has been smoothed by a moving average filter. Combining the uncertainty measurements across the inner pole radius yields an estimated ±5 μm uncertainty on the molybdenum erosion, which is shown bounding the erosion in Fig. 24. The fact that different calculation techniques with different software packages yields the same step height measurements within the uncertainty for both carbon and molybdenum is validation of the analysis techniques. However, a second set of measurements on the samples with a different measurement tool would be required to validate the measurements. 35

36 (a) Raw scan (without leveling or Gaussian filter). The calculated height difference is 6.1 μm. This is not used in later analysis and is only shown to demonstrate the effect of surface smoothing, which did not alter the results. (b) Scan profile of filtered surface showing 2nd order fit to unmasked region and linear fit to masked region. The calculated height difference is 6.3 μm. Figure 33. Example azimuthal scan for the carbon pole cover 12 o clock strip at r/r ch = The height difference is 6.6 μm in Fig. 24, which is a combination of the 4 and 12 o clock measurements. 36

37 (a) Raw scan (without leveling or Gaussian filter). The calculated height difference is 41.9 μm. This is not used in later analysis and is only shown to demonstrate the effect of surface smoothing, which did not alter the results. (b) Scan profile of filtered surface showing 2nd order fit to unmasked and masked regions. The calculated height difference is 40.4 μm and is within 1 μm of the value calculated using Nanovea Expert 3D. Figure 34. Example azimuthal scan for the molybdenum sample at r/r ch = The height difference is 40.8 μm infig