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Performance and plume characteristics of an 85 W class Hall thruster
Journal Pre-proof Performance and Plume Characteristics of an 85 W Class Hall Thruster Hiroki Watanabe, Shinatora Cho, Kenichi Kubota PII:
S0094-5765(19)31344-X
DOI:
https://doi.org/10.1016/j.actaastro.2019.07.042
Reference:
AA 7723
To appear in:
Acta Astronautica
Received Date: 11 March 2019 Revised Date:
28 May 2019
Accepted Date: 15 July 2019
Please cite this article as: H. Watanabe, S. Cho, K. Kubota, Performance and Plume Characteristics of an 85 W Class Hall Thruster, Acta Astronautica, https://doi.org/10.1016/j.actaastro.2019.07.042. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 IAA. Published by Elsevier Ltd. All rights reserved.
Title: Performance and Plume Characteristics of an 85 W Class Hall Thruster
Authors: Hiroki Watanabe1, Shinatora Cho2, and Kenichi Kubota3
Affiliations: 1
Department of Aeronautics and Astronautics, Faculty of System Design, Tokyo Metropolitan University
6-6 Asahigaoka, Hino City, Tokyo, 191-0065, Japan 2
Research and Development Directorate, Japan Aerospace Exploration Agency
3-1-1 Yoshinodai, Chuo-ku, Sagamihara City, Kanagawa, 525-5210, Japan 3
Aeronautical Technology Directorate, Japan Aerospace Exploration Agency
7-44-1 Jindaiji Higashi-machi, Chofu City, Tokyo, 182-8522, Japan
Corresponding Author: Hiroki Watanabe Department of Aeronautics and Astronautics Faculty of System Design Tokyo Metropolitan University 6-6 Asaghigaoka, Hino City, Tokyo, 191-0065, Japan Tel: +81-42-585-8671 E-mail: [email protected]
Abstract: An 85 W class Hall thruster with inner and outer electromagnetic coils was developed, and its thrust performance and plume characteristics were experimentally evaluated. The 85-W Hall thruster required a maximum magnetic flux density along the channel centerline above 24.3 mT to achieve stable and efficient operation above a discharge voltage of 225 V. A specific impulse of 1,050 s, thrust-to-power ratio of 59.5 mN/kW, and anode efficiency of 0.306 were achieved at a discharge voltage of 225 V and a discharge power of 88.9 W under a background pressure of 7.9 × 10-4 Pa. Moreover, the thruster achieved throttling at a discharge power of 47.6 to 118.5 W with stable operation. The low anode efficiency of the 85-W Hall thruster was due to low propellant utilization and a large beam divergence. The short effective length for the propellant ionization owing to the narrow channel is deduced to be the cause for the low anode efficiency in low-power Hall thrusters. The mass utilization efficiency of the 85-W Hall thruster improved as the anode mass flow density increased. Therefore, an increase in the anode mass flow density is required to improve the performance of the 85-W Hall thruster.
Keywords: Electric rocket propulsion; Hall thruster; Low-power discharge; Plasma diagnostic
Highlight: A 85-W Hall thruster with inner and outer coils was developed and evaluated. The thruster required > 24.3 mT to achieve efficient operation above 225 V. Anode efficiency was low because of low mass utilization and beam efficiencies.
1.
Introduction
Miniature Hall thrusters whose input power is several hundred watts [1–14] have received great attention as the primary thrusters for micro and small satellites. The BHT-200 [1] Hall thruster successfully achieved an anode efficiency of 0.46 and on-orbit operations at a discharge power of 200 W. However, Hall thrusters with a nominal discharge power of 100 W or less [10-12] have exhibited low anode efficiency (≤ 0.37). Hall thrusters are downsized as the discharge power decreases in order to maintain the propellant flow density in the discharge channel. The downsizing induces an increase in the surface-to-volume ratio, which leads to high energy loss to the discharge channel wall. In addition, the small inner channel diameter in miniature Hall thrusters makes it difficult to design an optimal magnetic field topology [15]. Cylindrical Hall thrusters [13, 14] have been developed as a unique idea to avoid the surface-to-volume ratio increase; however, their anode efficiency is still 0.35 or less. Thus, the high surface-to-volume ratio and difficulty in magnetic circuit design are challenging issues when attempting to achieve efficient operation in Hall thrusters with a nominal discharge power of 100 W or less. Kim [15] showed that the magnetic field strength is inversely proportional to the discharge channel width at a constant discharge voltage under the optimized operating conditions. Dannenmayer and Mazouffre [16] showed that the magnetic field strength is also inversely proportional to the discharge channel length in order to maintain the ratio of the electron Larmor radius to the channel length. From the experimental scaling law and discharge similarity criteria, Shagayda [17] indicated that the channel length and ionization length depend on the channel width. As a consequence of the discussion about Hall-thruster scaling, low-power Hall thrusters require a higher magnetic field strength than middle- and high-power Hall thrusters. Hence, the magnetic field requirement for low-power Hall thrusters with a stable and efficient operation should be evaluated. Based on the above consideration, the discharge characteristics and performance of a low-power Hall thruster have been extensively studied [1-12]. Lev et al. [4] researched and developed a low-power Hall thruster with a lowcurrent heater-less hollow cathode. Conversano et al. [5,6] evaluated the performance and plume characteristics of a magnetically shielded Hall thruster with discharge powers ranging from 160 to 750 W. In addition, they evaluated the ionization fraction as a function of the axial position in the discharge channel by using the numerical simulation [7]. Szabo et al. [10] demonstrated the operation of a 100 W class Hall thruster with xenon and iodine propellants. Mazouffre and Grimaud [12] evaluated the performance and plume characteristics of a 100 W class Hall thruster for two magnetic field strengths and two channel widths.
In the present study, we developed an 85 W class Hall thruster to clarify the magnetic field requirement for Hall thrusters with a nominal discharge power of 100 W or less. The thrust performance during 85-W operation was evaluated as a function of the magnetic field strength while maintaining the magnetic field topology. The power throttling capability was evaluated by changing the propellant mass flow rate. Moreover, the plume plasma property was obtained to evaluate the loss mechanism of the 85-W Hall thruster. In this paper, the thrust performance and plume characteristics of the 85-W Hall thruster are described, and the magnetic field requirement and performance improvement of low-power Hall thrusters are discussed.
2.
Experimental Apparatus
2.1. 85-W Hall Thruster To construct a Hall thruster system with a total input power of 100 W, the power consumption for the main discharge should be approximately 85 W because of the power consumption required for the keeper discharge and magnetic field induction. Figures 1 and 2 show a cross-section diagram and the magnetic field profile of the 85-W Hall thruster head. The discharge channel and anode are composed of boron nitride and molybdenum, respectively. A database analyzed by Shagayda [17] showed that the channel mean diameter was approximately proportional to the discharge power square root at a constant discharge voltage. Using the scaling law, the discharge channel of the 85-W Hall thruster was fabricated with a mean diameter of 20 mm. From the balance between the maximum magnetic field strength and the surface-to-volume ratio, the channel width was 6 mm. The distance from the anode downstream surface to the channel exit plane was 8 mm. A commercial plasma bridge cathode with tungsten wire [18] was
Fig. 1. Cross-section diagram of the 85-W Hall thruster head.
Fig. 2. Magnetic field profile of the 85-W Hall thruster: magnetic field topology at (a) Br,max = 18.8 mT and (b) Br,max = 24.3 mT, and (c) radial magnetic flux density along channel centerline at two magnetic field strengths. The profile was obtained by using the magnetic simulation tool “FEMM.”
externally mounted. Figure 3 shows the photographs of the Hall thruster with the cathode and the thruster firing. The thruster was composed of inner and outer concentric coils that were responsible for inducing the magnetic field. The channel exit plane was near the magnetic flux density peak along the channel centerline. The magnetic flux density near the anode was kept significantly low by using inner and outer screen yokes. The maximum radial magnetic flux density along the channel centerline was measured using a Gaussmeter (Model 421, LakeShore). The uncertainty in the Gaussmeter was ± 0.20%. The probe-to-thruster alignment was performed with an accuracy of
±0.1 mm. Because of the thermal limit of the coil wire, the magnetic circuit could induce a maximum radial magnetic flux density along the channel centerline of up to 24.3 mT.
Fig. 3. Photographs of (a) the 85-W Hall thruster head with the cathode and (b) the thruster firing.
2.2. Vacuum Facility and Electrical Configuration A performance test was conducted in the Large Space Science Chamber located at the Institute of Space and Astronautical Science (ISAS). The vacuum facility and measuring apparatus are schematically shown in Fig. 4. The chamber diameter and length were 2.5 m and 5.0 m, respectively. Two cryogenic pumps and one turbomolecular pump were installed in the chamber to provide a 24 kL/s pumping speed of xenon. The background pressure was measured by an ionization gauge (M-336MX, Canon-Anelva) attached to the vacuum chamber wall near the thruster. DC power supplies for thruster operation were connected to the thruster from outside the chamber. The electrical circuit diagram of the thruster operation is shown in Fig. 5. The output terminals of the power supplies were galvanically isolated from the ground potential. The vacuum chamber and beam dumper were grounded. The inner and outer electromagnetic coils were connected to each power supply in order to change the magnetic field strength
Fig. 4. Schematic of vacuum facility and measuring apparatus (not on scale).
Fig. 5. Electrical circuit diagram of the Hall thruster operation. “PS” is “power supply.”
while maintaining the magnetic field topology. The thruster body and the negative terminal of the coil power supplies were tied to cathode common.
2.3. Instrumentation Xenon propellant was fed to the anode and cathode via mass flow controllers (SEC-N112, HORIBA STEC). The uncertainty in the mass flow controllers regarding the anode and cathode was ± 1.0%. The cathode flow rate was maintained at 10% of the anode mass flow rate. To evaluate the thrust performance at a constant discharge power, the anode mass flow rate for various discharge voltages was selected to have a discharge power of approximately 85 W under the magnetic field strength at which the anode efficiency is maximum. Table 1 lists the anode mass flow rates and background pressures for various discharge voltages during 85-W operation.
Table 1. Anode mass flow rate and background pressure for various discharge voltages during 85-W operation. Background pressure was corrected for xenon. Discharge voltage, V 150 175 200 225 250 275 300
Anode mass flow rate, mg/s 0.655 0.616 0.547 0.513 0.454 0.410 0.376
Background pressure, ×10-4 Pa 9.8 9.3 8.4 7.9 7.1 5.9 5.4
The thrust was measured using an in-house pendulum-type thrust stand with an optical displacement sensor. The stand was calibrated using measured masses on a pulley system connected to a stepping motor stage. To minimize the measurement error owing to thermal drift, the thrust stand’s zero (the displacement sensor output corresponding to a no-load condition) was measured for each thrust measurement. Based on the calibration curve obtained by 32 paired calibration points, a 95% confidence interval [19] was achieved below 0.20 mN for thrust ranging from 2.0 to 7.0 mN. For example, under the same operation conditions, the thrust for the beginning, middle, and end of the performance test was 5.3 mN, 5.2 mN, and 5.3 mN, respectively. The variations of the three thrusts were within the abovementioned confidence interval. Thus, the thrust measurement uncertainty was measured as ± 0.20 mN. The discharge current and its oscillation were measured using a current probe (CT6700, HIOKI). The uncertainty in the current measurement was ± 1.0%. To evaluate the discharge current oscillation, the amplitude of the discharge current oscillation, ∆, is defined as follows [20]: τ 1 0 Id -Id 2 dt ∆= τ Id
(1)
τ where Id is the discharge current, τ is the measurement time, and Id is the average discharge current (Id = 0 Id dt⁄τ).
The amplitude is the ratio of the standard deviation of the discharge current to the average discharge current. Given that a strong oscillation induces an increase in mass of a filter circuit mounted between the thruster and the power processing unit, it is preferable for a Hall thruster system to maintain a low level of discharge current oscillation. Thus, the threshold between “stable operation” and “unstable operation” was defined as an amplitude of discharge current oscillation of 0.20 in this study.
The plasma plume exhausted from the thruster was measured using a nude-type Faraday probe, Langmuir probe, E×B probe, and retarding potential analyzer (RPA). Figure 6 shows the schematic illustration and electrical configuration of each probe. The E×B probe was located 1,000 mm downstream of the channel exit plane to measure the ion species current fractions. The Faraday probe, Langmuir probe, and RPA were placed on an X-Y-Z motion control system. Using the Faraday probe, the radial distribution of the ion beam current density was obtained at 300 mm downstream of the exit plane. Using the Langmuir probe and RPA, the plasma potential of the plume and the most probable ion potential were obtained at 500 mm downstream of the exit plane. The center of the Langmuir probe, RPA, and E×B probe was positioned on the channel centerline.
Fig. 6. Schematic illustration and electrical configuration of (a) RPA, (b) Langmuir probe, (c) E×B probe, and (d) Faraday probe.
Figure 7 shows a typical trace of the plasma probes and the analysis techniques. The most probable ion potential, Vmp, was determined by dI/dV in the RPA trace. The plasma potential of the plume, Vp, was determined by curve fitting to the “knee” in the Langmuir probe trace. The method of Gaussian fitting [21] was applied to the analysis of the E×B probe trace to obtain the current fractions of the ith ion species, Ωi. The total ion beam current, Ib, and the axial ion
Fig. 7. Typical trace and analysis technique of (a) RPA, (b) Langmuir probe, (c) E×B probe, and (d) Faraday probe: Vd = 225 V, m a = 0.513 mg/s, and Br, max = 24.3 mT. beam current, Ia, were calculated for an axisymmetric plume about the thruster centerline in Eqs. (2) and (3). Ib =2π
rJb rdr
(2)
rJb rcosθdr
(3)
450
0
Ia =2π
450
0
where r, Jb(r), and θ are the radial distance from the thruster centerline, radial distribution of the ion current density, and the probe angle (θ = r/300), respectively. A correction for secondary electron emission at the molybdenum collector surface [22] was applied to the ion current density measurement. In Eqs. (2) and (3), the measured current densities from each side of the plume (0 mm to 450 mm and 0 mm to -450 mm) are integrated, and the calculated beam currents are the average of the two sides. Based on a comparison between an RPA and an electrostatic energy analyzer reported by Beal and Gallimore [23], the uncertainty in the most probable ion potential was estimated as ± 50% of the half width at half maximum of
dI/dV. The uncertainty in the plasma potential was measured as ± 3 V owing to the error in curve fitting. An error analysis conducted by Shastry et al. [21] recommended that the product of p and z be kept below 2.7 to keep the amount of charge exchange within reasonable limits; p is the facility background pressure in units of 10-3 Pa, and z is the distance from the thruster exit to the probe in meters. In this paper, p was below 8.4 × 10-4 Pa, and z was 1 m for all E×B probe measurements; thus, pz was below 0.84. Hence, as a consequence of the error analysis, the uncertainty in the E×B probe measurement was estimated as 3% in the Xe+ current fraction and 20% in the Xe2+ and Xe3+ current fractions. From the ion beam distribution obtained as a function of the axial distance from the thruster exit, the uncertainties in the total ion beam current and the ratio of the axial ion beam current to the total ion beam current were ± 7% and ± 4%, respectively.
2.4. Hall Thruster Performance Architecture To evaluate the performance of the thruster head, the specific impulse, Isp, thrust-to-power ratio, F/P, and anode efficiency, ηa, are defined as follows: Isp =
F gm a
F⁄P = ηa =
(4)
F Id Vd
(5)
F2 =η η η η η η 2m a Id Vd v c q m n b
(6)
where F, g, Vd, and m a are the thrust, acceleration of gravity, discharge voltage, and anode mass flow rate, respectively. Based on the methodology of a Hall thruster efficiency analysis developed by Brown et al. [24], as shown in Eq. (6), the anode efficiency is the product of six Hall thruster efficiencies: voltage utilization, ηv, current utilization, ηc, charge utilization, ηq, mass utilization, ηm, neutral-gain utilization, ηn, and beam, ηb. The efficiencies are defined as follows: ηv =
Vmp -Vp Vd
(7)
Ib Id
(8)
ηc =
∑ Ωi⁄ Zi ηq = ∑Ωi⁄Zi
2
(9)
ηm = ηn =1+2y0
mxe Ib Ωi em a Zi
(10)
1-ηm
ηm ηq ⁄∑Ωi ⁄Zi
Ia 2 ηb = Ib
(11)
(12)
where Zi, mxe, e, and y0 are the charge state of the ith ion species, mass of a xenon atom, elementary charge, and ratio of the neutral speed to the singly charged ion speed, respectively. The neutral-gain utilization efficiency shows the contribution of non-ionized propellant to thrust generation. From the measured ion [25] and neutral [26] velocity at discharge voltages ranging from 150 to 250 V, the value of y0 was assumed to be 0.02. In addition, an effective plume divergence half-angle, ψ, is calculated as shown in Eq. (13). This angle is significantly less than typically reported 95% plume divergence half-angle [24]: Ia ψ= cos-1 Ib
3.
(13)
Experimental Results
3.1. Thrust Performance Figure 8 shows the amplitude of the discharge current oscillation as a function of the magnetic flux density for various discharge voltages. For discharge voltages ranging from 150 to 200 V, a discharge current oscillation was suppressed at higher magnetic field strengths. On the other hand, above a discharge voltage of 200 V, a discharge current oscillation was induced at magnetic flux densities ranging from 14.8 to 20.8 mT. The primary frequency of the discharge current oscillations was approximately 20 kHz. Hence, the discharge current oscillations at higher discharge voltages were induced by the breathing-mode ionization instability. The discharge current oscillation was suppressed at 24.3 mT except 300 V. In addition, the magnetic field strength required to suppress the oscillation increased as the discharge voltage increased. Figures 9 and 10 show the average discharge current, thrust, and anode efficiency as a function of the magnetic flux density at discharge voltages of 200, 225, and 275 V, as typical characteristics of the 85-W Hall thruster. In Fig. 10, gray square and red circle symbols indicate the anode efficiency calculated using Eq. (6) by the plasma plume property and by the thrust and discharge current, respectively. The discharge current decreased as the magnetic field increased, and remained constant at higher magnetic field strengths. At 200 V, the thrust increased as the magnetic
field was strengthened. At 225 and 275 V, the thrust decreased when the discharge current oscillation was induced, and then increased as the oscillation became weak. Consequently, the discharge current oscillation degraded the thrust performance of the 85-W Hall thruster. At 200 and 225 V, the anode efficiency saturated at over 22.6 mT. However, at 275 V, the anode efficiency did not saturate at 24.3 mT.
Fig. 8. Amplitude of discharge current oscillation as a function of magnetic flux density for various discharge voltages.
Fig. 9. Average discharge current and thrust as a function of magnetic flux density for various discharge voltages. Error bars of average discharge current appear within symbols.
Fig. 10. Anode efficiency as a function of magnetic flux density for various discharge voltages.
Figure 11 shows the thrust performance for various discharge voltages during 85-W operation under the magnetic field strength at which the anode efficiency is maximum. For discharge voltages ranging from 150 to 250 V, the anode efficiency improved as the discharge voltage increased. Above 250 V, the anode efficiency degraded because the specific impulse remained constant in spite of the increase in discharge voltage. As with 275-V operation, the anode efficiency at 250 V did not saturate at 24.3 mT. The results show that the magnetic field was not sufficiently high to achieve efficient operation above 225 V. Hence, as typical thrust performance, a specific impulse of 1,050 s, thrust-to-power ratio of 59.5 mN/kW, and anode efficiency of 0.306 were achieved at a discharge voltage of 225 V and a discharge power of 88.9 W. However, the power consumptions for the magnetic field induction and cathode operation were 19.2 W and 64.7 W, respectively. These power consumptions were comparable with the discharge power. Therefore, the power reduction for the magnetic field induction and cathode operation is one of the critical issues when constructing a Hall thruster system with a total input power of 100 W.
Fig. 11. Thrust performance for various discharge voltages during 85-W operation under magnetic field strength at which anode efficiency is maximum.
Fig. 12. Discharge power, amplitude of discharge current oscillation, and anode efficiency as a function of anode mass flow rate: Vd = 225 V and Br, max = 22.6 mT. For the power throttling capability of the 85-W thruster, the effects of the anode mass flow rate on the performance at a discharge voltage of 225 V are shown in Fig. 12. A discharge current oscillation was suppressed at anode mass flow rates ranging from 0.318 to 0.611 mg/s. Thus, the thruster achieved throttling at a discharge power of 47.6 to 118.5 W with stable operation. The anode efficiency remained constant at anode mass flow rates ranging from 0.415 to 0.611 mg/s.
3.2. Plume Characteristics Figure 13 shows the Hall thruster efficiencies as a function of the magnetic flux density at discharge voltages of 200, 225, and 275 V. Regardless of the discharge voltage, the effect of the magnetic field strength on the charge
Fig. 13. Hall thruster efficiencies as a function of magnetic flux density for various discharge voltages. Error bars of charge and neutral-gain utilization efficiency appear within symbols.
efficiency was minimal, and the neutral-gain utilization efficiency decreased slightly as the magnetic field strength increased. At 200 V, the current utilization, mass utilization, and beam efficiencies improved as the magnetic field strength increased and then saturated at higher magnetic field strengths, whereas the voltage utilization decreased slightly as the magnetic field strength increased. The efficiency characteristics were roughly the same at 225 and 275 V. However, the current utilization, mass utilization, and beam efficiencies at 225 V decreased when the discharge current oscillation was induced at 20.8 mT and increased as the oscillation became weak. At 275 V, the current utilization, mass utilization, and beam efficiencies increased sharply when the oscillation was suppressed at 24.3 mT. In addition, the voltage utilization at 225 and 275 V sharply decreased when the discharge current oscillation was induced. Figure 14 shows the Hall thruster efficiencies as a function of the anode mass flow rate at a discharge voltage of 225 V and magnetic flux density of 22.6 mT. The mass utilization efficiency improved as the anode mass flow rate increased. The charge and neutral-gain utilization efficiencies did not depend on the anode mass flow rate. The data shown in Fig. 14 suggested that the current utilization and beam efficiency degraded slightly as the anode mass flow rate increased from 0.415 to 0.611 mg/s. However, note that the error bars are too large to evaluate the effect of the flow rate on the voltage, current, and beam efficiencies. The increase rate of the mass utilization efficiency was higher than the change rate of the charge utilization and beam efficiency.
Fig. 14. Hall thruster efficiencies as a function of anode mass flow rate: Vd = 225 V and Br, max = 22.6 mT.
4.
Discussion
4.1. Magnetic Field Strength Requirement To suppress the breathing-mode oscillation, Yamamoto et al. [20] demonstrated that the electron flow to the ionization region should be restricted. However, the axial electron velocity increases as the discharge voltage increases owing to the increase in the electric field. When the discharge voltage increases, the magnetic field strength increases to restrict the inflow. The relationship between the magnetic field strength and the discharge voltage resulted in an increase in the magnetic field strength, as shown in Fig. 8. Hence, the magnetic field strength was not sufficiently high to achieve stable operation of the 85-W Hall thruster at 300 V. The SPT-100 Hall thruster requires maximum magnetic flux densities along the channel centerline ranging from 15 to 20 mT to achieve efficient operation at discharge voltages ranging from 200 to 300 V [15]. On the other hand, the data presented in Fig. 11 show that the 85-W Hall thruster required a magnetic flux density above 24.3 mT to achieve efficient operation above a discharge voltage of 225 V. The results demonstrated that the magnetic field strength for stable and efficient operation increases with the downsizing of the Hall thruster. The downsizing effect corresponded to the scaling law suggested by Kim [15]. The magnetic field strength strongly affected the propellant ionization, ion beam divergence, and electron current flowing to the anode, as shown in Fig. 13. Additionally, the electron current determined by the cross-field electron transport should be restricted to achieve efficient operation. The electron-wall interaction, which is one of the determinants of cross-field transport, becomes stronger as the channel width decreases. As a result, channel narrowing requires an increase in the magnetic field strength in order to restrict the increase in the cross-field electron transport at a constant discharge voltage.
4.2. Loss Evaluation The data presented in Figs. 10 and 12 show that the anode efficiency predicted by the thrust and discharge current corresponded to that predicted by the plume profile. In addition, the degradation of the anode efficiency at 225 V and 20.8 mT and the great improvement in the anode efficiency at 275 V and 24.3 mT were detected by using the plume profile. The degradation and improvement were caused by the thrust changes, as shown in Fig. 9. The plume profile presented in Fig. 13 indicates that thrust changes were caused by changes in propellant utilization, electron confinement by the magnetic field, and beam divergence. These results demonstrated that the measured plume profile and predicted efficiencies were validated and represented losses in the performance of the 85-W Hall thruster.
Table 2. Performance comparison between fabricated 85-W Hall thruster and H6 Hall thruster. Discharge voltage, V Discharge power, W Anode efficiency (thrust), Voltage utilization efficiency, Current utilization efficiency, Energy efficiency, Mass utilization efficiency, Charge utilization efficiency, Neutral-gain utilization efficiency, Beam efficiency, Effective plume divergence half-angle, deg
85-W Hall thruster 200 225 86.6 88.9 0.28 0.31 0.88 0.88 0.69 0.71 0.61 0.63 0.70 0.69 0.99 0.99 1.02 1.02 0.69 0.72 34 32
H6 Hall thruster 150 300 3,230 6,170 0.53 0.68 0.82 0.89 0.72 0.80 0.59 0.71 0.97 0.98 0.99 0.98 1.00 1.00 0.86 0.93 22 16
Table 2 shows a performance comparison between the 85-W Hall thruster and the H6 Hall thruster. The H6 is a state-of-the-art Hall thruster with high power and high efficiency. The H6 data shown in Table 2 were calculated using Eqs. (7) – (12) by the thrust performance shown in [24]. The voltage, charge, and neutral-gain utilization efficiencies were independent of the thruster size. The energy efficiency listed in Table 2 is the product of the voltage utilization efficiency and the current utilization efficiency. The energy efficiency is defined as the ratio of the jet power to the input power. In other words, the energy efficiency shows an energy loss for ion production. Typically, the ratio of the jet power to input power increases as the discharge voltage increases [27]. Considering the discharge voltage effect, the energy efficiency of the 85-W Hall thruster was compared to that of the H6 Hall thruster. Therefore, the low anode efficiency of the 85-W Hall thruster was mainly due to the degradation in the mass utilization and beam efficiencies. The low mass utilization efficiency and large beam divergence were confirmed in another 100-W Hall thruster as evaluated by Mazouffre and Grimaud [12]. Hence, low propellant utilization and a large beam divergence are critical issues for achieving efficient operation in Hall thrusters with a nominal discharge power of 100 W or less. The ionization mean free path in the discharge channel, λi, is given by λi =
vn 〈σive 〉ne
(14)
where vn, 〈σi ve 〉, and ne are the neutral velocity, ionization reaction rate, and electron number density, respectively. Because of the quasi-neutrality in the Hall thruster discharge, the following relationship is assumed in the discharge channel [15]:
ne ≈ni ≅
1 m a mxe vi πdh
(15)
Fig. 15. Ionization mean free path in discharge channel as a function of anode mass flow density for various neutral velocities and electron temperatures.
where ni, vi, d, and h are the ion number density, ion velocity, channel mean diameter, and channel width, respectively. Figure 15 shows the ionization mean free path estimated by Eqs. (14) and (15) as a function of the anode mass flow density, m a ⁄πdh, for various neutral velocities and electron temperatures. The ionization reaction rate was calculated by a database [28] for various electron temperatures. The range of the neutral velocity was obtained from laser-induced fluorescence velocimetry measurements conducted by Huang et al. [26]. The range of the electron temperature was assumed based on Langmuir probe measurements conducted by Reid and Gallimore [29]. The ion velocity in the ionization region lies between the neutral velocity and fully accelerated ion velocity. If the ion velocity is assumed to be equal to the neutral velocity, the estimated ionization mean free path represents the minimum value. The data shown in Fig. 15 were obtained under the situation that the ion velocity in the ionization region is equal to the neutral velocity. Thus, Fig. 15 represents the lower limits of the ionization mean free path for various neutral velocities and electron temperatures. The threshold of the anode mass flow density for efficient operation of the SPT-100 [30] and SPT-140 [31] is approximately 0.1 mg/(s·cm2). In addition, the anode mass flow density of the 85-W Hall thruster was varied from 0.08 to 0.16 mg/(s·cm2) during the performance test. The ionization mean free path ranges from 0.1 to 2.0 mm at a flow density of 0.1 mg/(s·cm2), as shown in Fig. 15. To achieve sufficient propellant utilization, the effective length
for the ionization should be much longer than the ionization mean free path. Raitses et al. [32] demonstrated that long channel length degraded the mass utilization and anode efficiencies in higher anode mass flow rates because of the increase in ion and electron losses. The result shows that an excessive increase in the channel length is not fruitful solution for increasing the effective length for the ionization. Shagayda [17] indicated that the effective length for the ionization depends on the channel width, because the probability that the ions produced at the channel upstream impinge on the channel wall increases as the channel width decreases. Therefore, we deduce that the short effective length owing to the narrow channel is the cause for the low anode efficiency in low-power Hall thrusters. Indeed, the mass utilization efficiency improved as the anode mass flow density (which affected the ionization mean free path) increased, as shown in Fig. 14. An increase in the flow density is required to improve the performance of the 85-W Hall thruster. However, the anode efficiency remained constant above an anode mass flow rate of 0.415 mg/s as shown in Fig. 12. Dannenmayer and Mazouffre [16] showed that the magnetic field strength depends on the flow density at a constant discharge voltage in order to maintain the electron confinement. Thus, for performance improvement, an increase in the magnetic field strength is required to maintain the charge utilization efficiency in parallel with the increase in flow density. For a typical ion beam source, there is a trade-off between the energy loss for ion production and the gas utilization [28]. Additionally, strong energy loss owing to the increase in the surface-to-volume ratio was not confirmed at the 85-W Hall thruster. Hence, maintaining the energy efficiency at a high flow density and a high magnetic field strength in low-power Hall thrusters should be experimentally confirmed by redesigning the 85-W Hall thruster and improving the accuracy in the current utilization and beam efficiencies as a future work. Two possible causes of the beam efficiency degradation were investigated. One was a shortfall in the plasma lens effect. The other was a radial acceleration owing to the plasma sheath created on the channel wall. Hofer et al. [33] demonstrated that changing the plasma lens design affected the anode efficiency by 4%. The magnetic field lines of the 85-W Hall thruster were slightly asymmetric about the channel centerline and insufficiently concave, as shown in Fig. 2. Thus, we deduce that the shortfall in the plasma lens topology induced the low ion beam focusing. A plasma simulation using the particle-in-cell method conducted by Taccogna et al. [34] indicated that the thickness and potential drop of the plasma sheath with the presheath were approximately 4 mm and 60 V, respectively, in the acceleration region at a discharge voltage of 300 V. Because the sheath thickness has an order of magnitude similar to the channel width, the effect of the radial electric field induced by the plasma sheath on the ion vector of the 85-
W Hall thruster is deduced to be stronger than those of middle- and high-power Hall thrusters. Therefore, to clarify the mechanism of the large ion beam divergence in the 85-W Hall thruster, the potential distribution in the acceleration region should be evaluated by using probe measurements and plasma simulations.
5.
Conclusion
An 85 W class Hall thruster with inner and outer electromagnetic coils was developed, and its thrust performance and plume characteristics were experimentally evaluated. For discharge voltages ranging from 225 to 300 V, a discharge current oscillation was detected at maximum magnetic flux densities along the channel centerline ranging from 14.8 to 20.8 mT. The discharge current oscillation was suppressed at 24.3 mT except 300 V. Hence, the magnetic field strength was not sufficiently high to achieve stable operation of the 85-W Hall thruster at 300 V. In addition, the performance and plume characteristics showed that the magnetic field strength of the 85-W Hall thruster was not sufficiently high to achieve efficient operation above 225 V. As a result, the 85-W Hall thruster required a magnetic flux density above 24.3 mT to achieve stable and efficient operation above a discharge voltage of 225 V. A comparison between the 85-W Hall thruster and the SPT-100 demonstrated that the magnetic field strength for stable and efficient operation increases with Hall-thruster downsizing. At a constant discharge voltage, narrowing the channel requires an increase in the magnetic field strength to restrict the increase in cross-field electron transport owing to the electron-wall interaction. As a typical thrust performance of the 85-W Hall thruster, a specific impulse of 1,050 s, thrust-to-power ratio of 59.5 mN/kW, and anode efficiency of 0.306 were achieved at a discharge voltage of 225 V and a discharge power of 88.9 W under a background pressure of 7.9 × 10-4 Pa. Moreover, the thruster achieved throttling at a discharge power of 47.6 to 118.5 W with stable operation. A performance comparison between the 85-W Hall thruster and the H6 showed that the low anode efficiency of the 85-W Hall thruster was caused by low propellant utilization and large beam divergence. The short effective length for the propellant ionization owing to the narrow channel was deduced to be the cause of the low anode efficiency in low-power Hall thrusters. Indeed, the mass utilization efficiency improved as the anode mass flow density increased. Therefore, an increase in the anode mass flow density is required to improve the performance of the 85-W Hall thruster. However, the anode efficiency remained constant at anode mass flow rates ranging from 0.415 to 0.611 mg/s because of the decreased current utilization efficiency.
Hence, for a performance improvement, an increase in the magnetic field strength is required to maintain the electron confinement in parallel with an increase in the flow density.
Acknowledgments This research results were obtained using Space Chamber Laboratory of ISAS, JAXA. This study was supported by JSPS KAKENHI Grand Number 17H04972. The author would like to thank Editage (www.editage.jp) for English language editing.
Nomenclature B
=
magnetic flux density, mT
Br,max =
maximum radial magnetic flux density on discharge channel centerline, mT
d
=
discharge channel mean diameter, m
e
=
elementary charge, C
F
=
thrust, mN
F/P
=
thrust-to-power ratio, mN/kW
g
=
acceleration of gravity, m/s2
h
=
discharge channel width, m
Ia
=
axial ion beam current, A
Ib
=
total ion beam current, A
Id
Id
=
discharge current, A
=
average discharge current, A
Isp
=
specific impulse, s
Jb
=
ion beam current density, A/m2
m a
=
anode mass flow rate, mg/s
mxe
=
mass of a xenon atom, kg
ne
=
electron number density, /m3
ni
=
ion number density, /m3
p
=
background pressure, Pa
r
=
radial distance from thruster centerline, mm
Te
=
electron temperature, eV
Vd
=
discharge voltage, V
Vmp
=
most probable ion potential, V
Vp
=
plasma potential, V
vn
=
ion velocity, m/s
vn
=
neutral velocity, m/s
y0
=
ratio of neutral speed to singly-charged ion speed, -
Zi
=
charge-state of the ith ion species, -
z
=
distance from thruster exit to E×B probe, m
∆
=
amplitude of discharge current oscillation, -
ηa
=
anode efficiency, -
ηb
=
beam efficiency, -
ηc
=
current utilization efficiency, -
ηm
=
mass utilization efficiency, -
ηn
=
neutral-gain utilization efficiency, -
ηq
=
charge utilization efficiency, -
ηv
=
voltage utilization efficiency, -
λi
=
ionization mean free path, m
Ωi
=
current fractions of the ith ion species, -
τ
=
measurement time, s
ψ
=
effective plume divergence half-angle, deg
〈σi ve 〉 =
ionization reaction rate, m3/s
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Vitae:
Hiorki Watanabe received the B.E. degree from the Department of Aerospace Engineering, National Defense Academy, Kanagawa, Japan, in 2006 and the M.E. and Ph. D degrees from the Department of Aerospace Engineering, Tokyo Metropolitan University, Tokyo, Japan, in 2009 and 2012, respectively. From 2012 to 2014, he was a Postdoctoral Research Fellow with Japan Aerospace Exploration Agency, Kanagawa, Japan. Since 2014, he has been an Assistant Professor with Tokyo Metropolitan University. His research interests include spacecraft propulsion and plasma application.
Shinatora Cho obtained his Ph.D. at the University of Tokyo, Japan in 2013. Since 2013, He has been working at Japan Aerospace Exploration Agency (JAXA) as a researcher. He has been devoting to the research and development of the 6-kW Hall thruster for JAXA Engineering Test Satellite-9 (ETS-9) all-electric satellite. His research interests include electric propulsion, Hall thruster, plasma dynamics, and especially fully kinetic particle simulation.
Kenichi Kubota received the B.S. degree from Department of Physics, Tokyo Institute of Technology, Tokyo, Japan in 2004, and M.E. and Ph. D. degrees from the Department of Energy Sciences, Tokyo Institute of Technology, Kanagawa, Japan, in 2006 and 2009, respectively. In 2009, he worked for Japan Aerospace Exploration Agency (JAXA) as a research fellow of Japan Society for the Promotion of Science, and since 2010, he has been working for Aeronautical Technology Directorate, JAXA as a researcher. His research interests include numerical simulation of plasma in electric propulsion devices.
Title: Performance and Plume Characteristics of an 85 W Class Hall Thruster
Highlight: An 85-W Hall thruster with inner and outer coils was developed and evaluated. The thruster required > 24.3 mT to achieve efficient operation above 225 V. Anode efficiency was low because of low mass utilization and beam efficiencies.
S0094-5765(19)31344-X
DOI:
https://doi.org/10.1016/j.actaastro.2019.07.042
Reference:
AA 7723
To appear in:
Acta Astronautica
Received Date: 11 March 2019 Revised Date:
28 May 2019
Accepted Date: 15 July 2019
Please cite this article as: H. Watanabe, S. Cho, K. Kubota, Performance and Plume Characteristics of an 85 W Class Hall Thruster, Acta Astronautica, https://doi.org/10.1016/j.actaastro.2019.07.042. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 IAA. Published by Elsevier Ltd. All rights reserved.
Title: Performance and Plume Characteristics of an 85 W Class Hall Thruster
Authors: Hiroki Watanabe1, Shinatora Cho2, and Kenichi Kubota3
Affiliations: 1
Department of Aeronautics and Astronautics, Faculty of System Design, Tokyo Metropolitan University
6-6 Asahigaoka, Hino City, Tokyo, 191-0065, Japan 2
Research and Development Directorate, Japan Aerospace Exploration Agency
3-1-1 Yoshinodai, Chuo-ku, Sagamihara City, Kanagawa, 525-5210, Japan 3
Aeronautical Technology Directorate, Japan Aerospace Exploration Agency
7-44-1 Jindaiji Higashi-machi, Chofu City, Tokyo, 182-8522, Japan
Corresponding Author: Hiroki Watanabe Department of Aeronautics and Astronautics Faculty of System Design Tokyo Metropolitan University 6-6 Asaghigaoka, Hino City, Tokyo, 191-0065, Japan Tel: +81-42-585-8671 E-mail: [email protected]
Abstract: An 85 W class Hall thruster with inner and outer electromagnetic coils was developed, and its thrust performance and plume characteristics were experimentally evaluated. The 85-W Hall thruster required a maximum magnetic flux density along the channel centerline above 24.3 mT to achieve stable and efficient operation above a discharge voltage of 225 V. A specific impulse of 1,050 s, thrust-to-power ratio of 59.5 mN/kW, and anode efficiency of 0.306 were achieved at a discharge voltage of 225 V and a discharge power of 88.9 W under a background pressure of 7.9 × 10-4 Pa. Moreover, the thruster achieved throttling at a discharge power of 47.6 to 118.5 W with stable operation. The low anode efficiency of the 85-W Hall thruster was due to low propellant utilization and a large beam divergence. The short effective length for the propellant ionization owing to the narrow channel is deduced to be the cause for the low anode efficiency in low-power Hall thrusters. The mass utilization efficiency of the 85-W Hall thruster improved as the anode mass flow density increased. Therefore, an increase in the anode mass flow density is required to improve the performance of the 85-W Hall thruster.
Keywords: Electric rocket propulsion; Hall thruster; Low-power discharge; Plasma diagnostic
Highlight: A 85-W Hall thruster with inner and outer coils was developed and evaluated. The thruster required > 24.3 mT to achieve efficient operation above 225 V. Anode efficiency was low because of low mass utilization and beam efficiencies.
1.
Introduction
Miniature Hall thrusters whose input power is several hundred watts [1–14] have received great attention as the primary thrusters for micro and small satellites. The BHT-200 [1] Hall thruster successfully achieved an anode efficiency of 0.46 and on-orbit operations at a discharge power of 200 W. However, Hall thrusters with a nominal discharge power of 100 W or less [10-12] have exhibited low anode efficiency (≤ 0.37). Hall thrusters are downsized as the discharge power decreases in order to maintain the propellant flow density in the discharge channel. The downsizing induces an increase in the surface-to-volume ratio, which leads to high energy loss to the discharge channel wall. In addition, the small inner channel diameter in miniature Hall thrusters makes it difficult to design an optimal magnetic field topology [15]. Cylindrical Hall thrusters [13, 14] have been developed as a unique idea to avoid the surface-to-volume ratio increase; however, their anode efficiency is still 0.35 or less. Thus, the high surface-to-volume ratio and difficulty in magnetic circuit design are challenging issues when attempting to achieve efficient operation in Hall thrusters with a nominal discharge power of 100 W or less. Kim [15] showed that the magnetic field strength is inversely proportional to the discharge channel width at a constant discharge voltage under the optimized operating conditions. Dannenmayer and Mazouffre [16] showed that the magnetic field strength is also inversely proportional to the discharge channel length in order to maintain the ratio of the electron Larmor radius to the channel length. From the experimental scaling law and discharge similarity criteria, Shagayda [17] indicated that the channel length and ionization length depend on the channel width. As a consequence of the discussion about Hall-thruster scaling, low-power Hall thrusters require a higher magnetic field strength than middle- and high-power Hall thrusters. Hence, the magnetic field requirement for low-power Hall thrusters with a stable and efficient operation should be evaluated. Based on the above consideration, the discharge characteristics and performance of a low-power Hall thruster have been extensively studied [1-12]. Lev et al. [4] researched and developed a low-power Hall thruster with a lowcurrent heater-less hollow cathode. Conversano et al. [5,6] evaluated the performance and plume characteristics of a magnetically shielded Hall thruster with discharge powers ranging from 160 to 750 W. In addition, they evaluated the ionization fraction as a function of the axial position in the discharge channel by using the numerical simulation [7]. Szabo et al. [10] demonstrated the operation of a 100 W class Hall thruster with xenon and iodine propellants. Mazouffre and Grimaud [12] evaluated the performance and plume characteristics of a 100 W class Hall thruster for two magnetic field strengths and two channel widths.
In the present study, we developed an 85 W class Hall thruster to clarify the magnetic field requirement for Hall thrusters with a nominal discharge power of 100 W or less. The thrust performance during 85-W operation was evaluated as a function of the magnetic field strength while maintaining the magnetic field topology. The power throttling capability was evaluated by changing the propellant mass flow rate. Moreover, the plume plasma property was obtained to evaluate the loss mechanism of the 85-W Hall thruster. In this paper, the thrust performance and plume characteristics of the 85-W Hall thruster are described, and the magnetic field requirement and performance improvement of low-power Hall thrusters are discussed.
2.
Experimental Apparatus
2.1. 85-W Hall Thruster To construct a Hall thruster system with a total input power of 100 W, the power consumption for the main discharge should be approximately 85 W because of the power consumption required for the keeper discharge and magnetic field induction. Figures 1 and 2 show a cross-section diagram and the magnetic field profile of the 85-W Hall thruster head. The discharge channel and anode are composed of boron nitride and molybdenum, respectively. A database analyzed by Shagayda [17] showed that the channel mean diameter was approximately proportional to the discharge power square root at a constant discharge voltage. Using the scaling law, the discharge channel of the 85-W Hall thruster was fabricated with a mean diameter of 20 mm. From the balance between the maximum magnetic field strength and the surface-to-volume ratio, the channel width was 6 mm. The distance from the anode downstream surface to the channel exit plane was 8 mm. A commercial plasma bridge cathode with tungsten wire [18] was
Fig. 1. Cross-section diagram of the 85-W Hall thruster head.
Fig. 2. Magnetic field profile of the 85-W Hall thruster: magnetic field topology at (a) Br,max = 18.8 mT and (b) Br,max = 24.3 mT, and (c) radial magnetic flux density along channel centerline at two magnetic field strengths. The profile was obtained by using the magnetic simulation tool “FEMM.”
externally mounted. Figure 3 shows the photographs of the Hall thruster with the cathode and the thruster firing. The thruster was composed of inner and outer concentric coils that were responsible for inducing the magnetic field. The channel exit plane was near the magnetic flux density peak along the channel centerline. The magnetic flux density near the anode was kept significantly low by using inner and outer screen yokes. The maximum radial magnetic flux density along the channel centerline was measured using a Gaussmeter (Model 421, LakeShore). The uncertainty in the Gaussmeter was ± 0.20%. The probe-to-thruster alignment was performed with an accuracy of
±0.1 mm. Because of the thermal limit of the coil wire, the magnetic circuit could induce a maximum radial magnetic flux density along the channel centerline of up to 24.3 mT.
Fig. 3. Photographs of (a) the 85-W Hall thruster head with the cathode and (b) the thruster firing.
2.2. Vacuum Facility and Electrical Configuration A performance test was conducted in the Large Space Science Chamber located at the Institute of Space and Astronautical Science (ISAS). The vacuum facility and measuring apparatus are schematically shown in Fig. 4. The chamber diameter and length were 2.5 m and 5.0 m, respectively. Two cryogenic pumps and one turbomolecular pump were installed in the chamber to provide a 24 kL/s pumping speed of xenon. The background pressure was measured by an ionization gauge (M-336MX, Canon-Anelva) attached to the vacuum chamber wall near the thruster. DC power supplies for thruster operation were connected to the thruster from outside the chamber. The electrical circuit diagram of the thruster operation is shown in Fig. 5. The output terminals of the power supplies were galvanically isolated from the ground potential. The vacuum chamber and beam dumper were grounded. The inner and outer electromagnetic coils were connected to each power supply in order to change the magnetic field strength
Fig. 4. Schematic of vacuum facility and measuring apparatus (not on scale).
Fig. 5. Electrical circuit diagram of the Hall thruster operation. “PS” is “power supply.”
while maintaining the magnetic field topology. The thruster body and the negative terminal of the coil power supplies were tied to cathode common.
2.3. Instrumentation Xenon propellant was fed to the anode and cathode via mass flow controllers (SEC-N112, HORIBA STEC). The uncertainty in the mass flow controllers regarding the anode and cathode was ± 1.0%. The cathode flow rate was maintained at 10% of the anode mass flow rate. To evaluate the thrust performance at a constant discharge power, the anode mass flow rate for various discharge voltages was selected to have a discharge power of approximately 85 W under the magnetic field strength at which the anode efficiency is maximum. Table 1 lists the anode mass flow rates and background pressures for various discharge voltages during 85-W operation.
Table 1. Anode mass flow rate and background pressure for various discharge voltages during 85-W operation. Background pressure was corrected for xenon. Discharge voltage, V 150 175 200 225 250 275 300
Anode mass flow rate, mg/s 0.655 0.616 0.547 0.513 0.454 0.410 0.376
Background pressure, ×10-4 Pa 9.8 9.3 8.4 7.9 7.1 5.9 5.4
The thrust was measured using an in-house pendulum-type thrust stand with an optical displacement sensor. The stand was calibrated using measured masses on a pulley system connected to a stepping motor stage. To minimize the measurement error owing to thermal drift, the thrust stand’s zero (the displacement sensor output corresponding to a no-load condition) was measured for each thrust measurement. Based on the calibration curve obtained by 32 paired calibration points, a 95% confidence interval [19] was achieved below 0.20 mN for thrust ranging from 2.0 to 7.0 mN. For example, under the same operation conditions, the thrust for the beginning, middle, and end of the performance test was 5.3 mN, 5.2 mN, and 5.3 mN, respectively. The variations of the three thrusts were within the abovementioned confidence interval. Thus, the thrust measurement uncertainty was measured as ± 0.20 mN. The discharge current and its oscillation were measured using a current probe (CT6700, HIOKI). The uncertainty in the current measurement was ± 1.0%. To evaluate the discharge current oscillation, the amplitude of the discharge current oscillation, ∆, is defined as follows [20]: τ 1 0 Id -Id 2 dt ∆= τ Id
(1)
τ where Id is the discharge current, τ is the measurement time, and Id is the average discharge current (Id = 0 Id dt⁄τ).
The amplitude is the ratio of the standard deviation of the discharge current to the average discharge current. Given that a strong oscillation induces an increase in mass of a filter circuit mounted between the thruster and the power processing unit, it is preferable for a Hall thruster system to maintain a low level of discharge current oscillation. Thus, the threshold between “stable operation” and “unstable operation” was defined as an amplitude of discharge current oscillation of 0.20 in this study.
The plasma plume exhausted from the thruster was measured using a nude-type Faraday probe, Langmuir probe, E×B probe, and retarding potential analyzer (RPA). Figure 6 shows the schematic illustration and electrical configuration of each probe. The E×B probe was located 1,000 mm downstream of the channel exit plane to measure the ion species current fractions. The Faraday probe, Langmuir probe, and RPA were placed on an X-Y-Z motion control system. Using the Faraday probe, the radial distribution of the ion beam current density was obtained at 300 mm downstream of the exit plane. Using the Langmuir probe and RPA, the plasma potential of the plume and the most probable ion potential were obtained at 500 mm downstream of the exit plane. The center of the Langmuir probe, RPA, and E×B probe was positioned on the channel centerline.
Fig. 6. Schematic illustration and electrical configuration of (a) RPA, (b) Langmuir probe, (c) E×B probe, and (d) Faraday probe.
Figure 7 shows a typical trace of the plasma probes and the analysis techniques. The most probable ion potential, Vmp, was determined by dI/dV in the RPA trace. The plasma potential of the plume, Vp, was determined by curve fitting to the “knee” in the Langmuir probe trace. The method of Gaussian fitting [21] was applied to the analysis of the E×B probe trace to obtain the current fractions of the ith ion species, Ωi. The total ion beam current, Ib, and the axial ion
Fig. 7. Typical trace and analysis technique of (a) RPA, (b) Langmuir probe, (c) E×B probe, and (d) Faraday probe: Vd = 225 V, m a = 0.513 mg/s, and Br, max = 24.3 mT. beam current, Ia, were calculated for an axisymmetric plume about the thruster centerline in Eqs. (2) and (3). Ib =2π
rJb rdr
(2)
rJb rcosθdr
(3)
450
0
Ia =2π
450
0
where r, Jb(r), and θ are the radial distance from the thruster centerline, radial distribution of the ion current density, and the probe angle (θ = r/300), respectively. A correction for secondary electron emission at the molybdenum collector surface [22] was applied to the ion current density measurement. In Eqs. (2) and (3), the measured current densities from each side of the plume (0 mm to 450 mm and 0 mm to -450 mm) are integrated, and the calculated beam currents are the average of the two sides. Based on a comparison between an RPA and an electrostatic energy analyzer reported by Beal and Gallimore [23], the uncertainty in the most probable ion potential was estimated as ± 50% of the half width at half maximum of
dI/dV. The uncertainty in the plasma potential was measured as ± 3 V owing to the error in curve fitting. An error analysis conducted by Shastry et al. [21] recommended that the product of p and z be kept below 2.7 to keep the amount of charge exchange within reasonable limits; p is the facility background pressure in units of 10-3 Pa, and z is the distance from the thruster exit to the probe in meters. In this paper, p was below 8.4 × 10-4 Pa, and z was 1 m for all E×B probe measurements; thus, pz was below 0.84. Hence, as a consequence of the error analysis, the uncertainty in the E×B probe measurement was estimated as 3% in the Xe+ current fraction and 20% in the Xe2+ and Xe3+ current fractions. From the ion beam distribution obtained as a function of the axial distance from the thruster exit, the uncertainties in the total ion beam current and the ratio of the axial ion beam current to the total ion beam current were ± 7% and ± 4%, respectively.
2.4. Hall Thruster Performance Architecture To evaluate the performance of the thruster head, the specific impulse, Isp, thrust-to-power ratio, F/P, and anode efficiency, ηa, are defined as follows: Isp =
F gm a
F⁄P = ηa =
(4)
F Id Vd
(5)
F2 =η η η η η η 2m a Id Vd v c q m n b
(6)
where F, g, Vd, and m a are the thrust, acceleration of gravity, discharge voltage, and anode mass flow rate, respectively. Based on the methodology of a Hall thruster efficiency analysis developed by Brown et al. [24], as shown in Eq. (6), the anode efficiency is the product of six Hall thruster efficiencies: voltage utilization, ηv, current utilization, ηc, charge utilization, ηq, mass utilization, ηm, neutral-gain utilization, ηn, and beam, ηb. The efficiencies are defined as follows: ηv =
Vmp -Vp Vd
(7)
Ib Id
(8)
ηc =
∑ Ωi⁄ Zi ηq = ∑Ωi⁄Zi
2
(9)
ηm = ηn =1+2y0
mxe Ib Ωi em a Zi
(10)
1-ηm
ηm ηq ⁄∑Ωi ⁄Zi
Ia 2 ηb = Ib
(11)
(12)
where Zi, mxe, e, and y0 are the charge state of the ith ion species, mass of a xenon atom, elementary charge, and ratio of the neutral speed to the singly charged ion speed, respectively. The neutral-gain utilization efficiency shows the contribution of non-ionized propellant to thrust generation. From the measured ion [25] and neutral [26] velocity at discharge voltages ranging from 150 to 250 V, the value of y0 was assumed to be 0.02. In addition, an effective plume divergence half-angle, ψ, is calculated as shown in Eq. (13). This angle is significantly less than typically reported 95% plume divergence half-angle [24]: Ia ψ= cos-1 Ib
3.
(13)
Experimental Results
3.1. Thrust Performance Figure 8 shows the amplitude of the discharge current oscillation as a function of the magnetic flux density for various discharge voltages. For discharge voltages ranging from 150 to 200 V, a discharge current oscillation was suppressed at higher magnetic field strengths. On the other hand, above a discharge voltage of 200 V, a discharge current oscillation was induced at magnetic flux densities ranging from 14.8 to 20.8 mT. The primary frequency of the discharge current oscillations was approximately 20 kHz. Hence, the discharge current oscillations at higher discharge voltages were induced by the breathing-mode ionization instability. The discharge current oscillation was suppressed at 24.3 mT except 300 V. In addition, the magnetic field strength required to suppress the oscillation increased as the discharge voltage increased. Figures 9 and 10 show the average discharge current, thrust, and anode efficiency as a function of the magnetic flux density at discharge voltages of 200, 225, and 275 V, as typical characteristics of the 85-W Hall thruster. In Fig. 10, gray square and red circle symbols indicate the anode efficiency calculated using Eq. (6) by the plasma plume property and by the thrust and discharge current, respectively. The discharge current decreased as the magnetic field increased, and remained constant at higher magnetic field strengths. At 200 V, the thrust increased as the magnetic
field was strengthened. At 225 and 275 V, the thrust decreased when the discharge current oscillation was induced, and then increased as the oscillation became weak. Consequently, the discharge current oscillation degraded the thrust performance of the 85-W Hall thruster. At 200 and 225 V, the anode efficiency saturated at over 22.6 mT. However, at 275 V, the anode efficiency did not saturate at 24.3 mT.
Fig. 8. Amplitude of discharge current oscillation as a function of magnetic flux density for various discharge voltages.
Fig. 9. Average discharge current and thrust as a function of magnetic flux density for various discharge voltages. Error bars of average discharge current appear within symbols.
Fig. 10. Anode efficiency as a function of magnetic flux density for various discharge voltages.
Figure 11 shows the thrust performance for various discharge voltages during 85-W operation under the magnetic field strength at which the anode efficiency is maximum. For discharge voltages ranging from 150 to 250 V, the anode efficiency improved as the discharge voltage increased. Above 250 V, the anode efficiency degraded because the specific impulse remained constant in spite of the increase in discharge voltage. As with 275-V operation, the anode efficiency at 250 V did not saturate at 24.3 mT. The results show that the magnetic field was not sufficiently high to achieve efficient operation above 225 V. Hence, as typical thrust performance, a specific impulse of 1,050 s, thrust-to-power ratio of 59.5 mN/kW, and anode efficiency of 0.306 were achieved at a discharge voltage of 225 V and a discharge power of 88.9 W. However, the power consumptions for the magnetic field induction and cathode operation were 19.2 W and 64.7 W, respectively. These power consumptions were comparable with the discharge power. Therefore, the power reduction for the magnetic field induction and cathode operation is one of the critical issues when constructing a Hall thruster system with a total input power of 100 W.
Fig. 11. Thrust performance for various discharge voltages during 85-W operation under magnetic field strength at which anode efficiency is maximum.
Fig. 12. Discharge power, amplitude of discharge current oscillation, and anode efficiency as a function of anode mass flow rate: Vd = 225 V and Br, max = 22.6 mT. For the power throttling capability of the 85-W thruster, the effects of the anode mass flow rate on the performance at a discharge voltage of 225 V are shown in Fig. 12. A discharge current oscillation was suppressed at anode mass flow rates ranging from 0.318 to 0.611 mg/s. Thus, the thruster achieved throttling at a discharge power of 47.6 to 118.5 W with stable operation. The anode efficiency remained constant at anode mass flow rates ranging from 0.415 to 0.611 mg/s.
3.2. Plume Characteristics Figure 13 shows the Hall thruster efficiencies as a function of the magnetic flux density at discharge voltages of 200, 225, and 275 V. Regardless of the discharge voltage, the effect of the magnetic field strength on the charge
Fig. 13. Hall thruster efficiencies as a function of magnetic flux density for various discharge voltages. Error bars of charge and neutral-gain utilization efficiency appear within symbols.
efficiency was minimal, and the neutral-gain utilization efficiency decreased slightly as the magnetic field strength increased. At 200 V, the current utilization, mass utilization, and beam efficiencies improved as the magnetic field strength increased and then saturated at higher magnetic field strengths, whereas the voltage utilization decreased slightly as the magnetic field strength increased. The efficiency characteristics were roughly the same at 225 and 275 V. However, the current utilization, mass utilization, and beam efficiencies at 225 V decreased when the discharge current oscillation was induced at 20.8 mT and increased as the oscillation became weak. At 275 V, the current utilization, mass utilization, and beam efficiencies increased sharply when the oscillation was suppressed at 24.3 mT. In addition, the voltage utilization at 225 and 275 V sharply decreased when the discharge current oscillation was induced. Figure 14 shows the Hall thruster efficiencies as a function of the anode mass flow rate at a discharge voltage of 225 V and magnetic flux density of 22.6 mT. The mass utilization efficiency improved as the anode mass flow rate increased. The charge and neutral-gain utilization efficiencies did not depend on the anode mass flow rate. The data shown in Fig. 14 suggested that the current utilization and beam efficiency degraded slightly as the anode mass flow rate increased from 0.415 to 0.611 mg/s. However, note that the error bars are too large to evaluate the effect of the flow rate on the voltage, current, and beam efficiencies. The increase rate of the mass utilization efficiency was higher than the change rate of the charge utilization and beam efficiency.
Fig. 14. Hall thruster efficiencies as a function of anode mass flow rate: Vd = 225 V and Br, max = 22.6 mT.
4.
Discussion
4.1. Magnetic Field Strength Requirement To suppress the breathing-mode oscillation, Yamamoto et al. [20] demonstrated that the electron flow to the ionization region should be restricted. However, the axial electron velocity increases as the discharge voltage increases owing to the increase in the electric field. When the discharge voltage increases, the magnetic field strength increases to restrict the inflow. The relationship between the magnetic field strength and the discharge voltage resulted in an increase in the magnetic field strength, as shown in Fig. 8. Hence, the magnetic field strength was not sufficiently high to achieve stable operation of the 85-W Hall thruster at 300 V. The SPT-100 Hall thruster requires maximum magnetic flux densities along the channel centerline ranging from 15 to 20 mT to achieve efficient operation at discharge voltages ranging from 200 to 300 V [15]. On the other hand, the data presented in Fig. 11 show that the 85-W Hall thruster required a magnetic flux density above 24.3 mT to achieve efficient operation above a discharge voltage of 225 V. The results demonstrated that the magnetic field strength for stable and efficient operation increases with the downsizing of the Hall thruster. The downsizing effect corresponded to the scaling law suggested by Kim [15]. The magnetic field strength strongly affected the propellant ionization, ion beam divergence, and electron current flowing to the anode, as shown in Fig. 13. Additionally, the electron current determined by the cross-field electron transport should be restricted to achieve efficient operation. The electron-wall interaction, which is one of the determinants of cross-field transport, becomes stronger as the channel width decreases. As a result, channel narrowing requires an increase in the magnetic field strength in order to restrict the increase in the cross-field electron transport at a constant discharge voltage.
4.2. Loss Evaluation The data presented in Figs. 10 and 12 show that the anode efficiency predicted by the thrust and discharge current corresponded to that predicted by the plume profile. In addition, the degradation of the anode efficiency at 225 V and 20.8 mT and the great improvement in the anode efficiency at 275 V and 24.3 mT were detected by using the plume profile. The degradation and improvement were caused by the thrust changes, as shown in Fig. 9. The plume profile presented in Fig. 13 indicates that thrust changes were caused by changes in propellant utilization, electron confinement by the magnetic field, and beam divergence. These results demonstrated that the measured plume profile and predicted efficiencies were validated and represented losses in the performance of the 85-W Hall thruster.
Table 2. Performance comparison between fabricated 85-W Hall thruster and H6 Hall thruster. Discharge voltage, V Discharge power, W Anode efficiency (thrust), Voltage utilization efficiency, Current utilization efficiency, Energy efficiency, Mass utilization efficiency, Charge utilization efficiency, Neutral-gain utilization efficiency, Beam efficiency, Effective plume divergence half-angle, deg
85-W Hall thruster 200 225 86.6 88.9 0.28 0.31 0.88 0.88 0.69 0.71 0.61 0.63 0.70 0.69 0.99 0.99 1.02 1.02 0.69 0.72 34 32
H6 Hall thruster 150 300 3,230 6,170 0.53 0.68 0.82 0.89 0.72 0.80 0.59 0.71 0.97 0.98 0.99 0.98 1.00 1.00 0.86 0.93 22 16
Table 2 shows a performance comparison between the 85-W Hall thruster and the H6 Hall thruster. The H6 is a state-of-the-art Hall thruster with high power and high efficiency. The H6 data shown in Table 2 were calculated using Eqs. (7) – (12) by the thrust performance shown in [24]. The voltage, charge, and neutral-gain utilization efficiencies were independent of the thruster size. The energy efficiency listed in Table 2 is the product of the voltage utilization efficiency and the current utilization efficiency. The energy efficiency is defined as the ratio of the jet power to the input power. In other words, the energy efficiency shows an energy loss for ion production. Typically, the ratio of the jet power to input power increases as the discharge voltage increases [27]. Considering the discharge voltage effect, the energy efficiency of the 85-W Hall thruster was compared to that of the H6 Hall thruster. Therefore, the low anode efficiency of the 85-W Hall thruster was mainly due to the degradation in the mass utilization and beam efficiencies. The low mass utilization efficiency and large beam divergence were confirmed in another 100-W Hall thruster as evaluated by Mazouffre and Grimaud [12]. Hence, low propellant utilization and a large beam divergence are critical issues for achieving efficient operation in Hall thrusters with a nominal discharge power of 100 W or less. The ionization mean free path in the discharge channel, λi, is given by λi =
vn 〈σive 〉ne
(14)
where vn, 〈σi ve 〉, and ne are the neutral velocity, ionization reaction rate, and electron number density, respectively. Because of the quasi-neutrality in the Hall thruster discharge, the following relationship is assumed in the discharge channel [15]:
ne ≈ni ≅
1 m a mxe vi πdh
(15)
Fig. 15. Ionization mean free path in discharge channel as a function of anode mass flow density for various neutral velocities and electron temperatures.
where ni, vi, d, and h are the ion number density, ion velocity, channel mean diameter, and channel width, respectively. Figure 15 shows the ionization mean free path estimated by Eqs. (14) and (15) as a function of the anode mass flow density, m a ⁄πdh, for various neutral velocities and electron temperatures. The ionization reaction rate was calculated by a database [28] for various electron temperatures. The range of the neutral velocity was obtained from laser-induced fluorescence velocimetry measurements conducted by Huang et al. [26]. The range of the electron temperature was assumed based on Langmuir probe measurements conducted by Reid and Gallimore [29]. The ion velocity in the ionization region lies between the neutral velocity and fully accelerated ion velocity. If the ion velocity is assumed to be equal to the neutral velocity, the estimated ionization mean free path represents the minimum value. The data shown in Fig. 15 were obtained under the situation that the ion velocity in the ionization region is equal to the neutral velocity. Thus, Fig. 15 represents the lower limits of the ionization mean free path for various neutral velocities and electron temperatures. The threshold of the anode mass flow density for efficient operation of the SPT-100 [30] and SPT-140 [31] is approximately 0.1 mg/(s·cm2). In addition, the anode mass flow density of the 85-W Hall thruster was varied from 0.08 to 0.16 mg/(s·cm2) during the performance test. The ionization mean free path ranges from 0.1 to 2.0 mm at a flow density of 0.1 mg/(s·cm2), as shown in Fig. 15. To achieve sufficient propellant utilization, the effective length
for the ionization should be much longer than the ionization mean free path. Raitses et al. [32] demonstrated that long channel length degraded the mass utilization and anode efficiencies in higher anode mass flow rates because of the increase in ion and electron losses. The result shows that an excessive increase in the channel length is not fruitful solution for increasing the effective length for the ionization. Shagayda [17] indicated that the effective length for the ionization depends on the channel width, because the probability that the ions produced at the channel upstream impinge on the channel wall increases as the channel width decreases. Therefore, we deduce that the short effective length owing to the narrow channel is the cause for the low anode efficiency in low-power Hall thrusters. Indeed, the mass utilization efficiency improved as the anode mass flow density (which affected the ionization mean free path) increased, as shown in Fig. 14. An increase in the flow density is required to improve the performance of the 85-W Hall thruster. However, the anode efficiency remained constant above an anode mass flow rate of 0.415 mg/s as shown in Fig. 12. Dannenmayer and Mazouffre [16] showed that the magnetic field strength depends on the flow density at a constant discharge voltage in order to maintain the electron confinement. Thus, for performance improvement, an increase in the magnetic field strength is required to maintain the charge utilization efficiency in parallel with the increase in flow density. For a typical ion beam source, there is a trade-off between the energy loss for ion production and the gas utilization [28]. Additionally, strong energy loss owing to the increase in the surface-to-volume ratio was not confirmed at the 85-W Hall thruster. Hence, maintaining the energy efficiency at a high flow density and a high magnetic field strength in low-power Hall thrusters should be experimentally confirmed by redesigning the 85-W Hall thruster and improving the accuracy in the current utilization and beam efficiencies as a future work. Two possible causes of the beam efficiency degradation were investigated. One was a shortfall in the plasma lens effect. The other was a radial acceleration owing to the plasma sheath created on the channel wall. Hofer et al. [33] demonstrated that changing the plasma lens design affected the anode efficiency by 4%. The magnetic field lines of the 85-W Hall thruster were slightly asymmetric about the channel centerline and insufficiently concave, as shown in Fig. 2. Thus, we deduce that the shortfall in the plasma lens topology induced the low ion beam focusing. A plasma simulation using the particle-in-cell method conducted by Taccogna et al. [34] indicated that the thickness and potential drop of the plasma sheath with the presheath were approximately 4 mm and 60 V, respectively, in the acceleration region at a discharge voltage of 300 V. Because the sheath thickness has an order of magnitude similar to the channel width, the effect of the radial electric field induced by the plasma sheath on the ion vector of the 85-
W Hall thruster is deduced to be stronger than those of middle- and high-power Hall thrusters. Therefore, to clarify the mechanism of the large ion beam divergence in the 85-W Hall thruster, the potential distribution in the acceleration region should be evaluated by using probe measurements and plasma simulations.
5.
Conclusion
An 85 W class Hall thruster with inner and outer electromagnetic coils was developed, and its thrust performance and plume characteristics were experimentally evaluated. For discharge voltages ranging from 225 to 300 V, a discharge current oscillation was detected at maximum magnetic flux densities along the channel centerline ranging from 14.8 to 20.8 mT. The discharge current oscillation was suppressed at 24.3 mT except 300 V. Hence, the magnetic field strength was not sufficiently high to achieve stable operation of the 85-W Hall thruster at 300 V. In addition, the performance and plume characteristics showed that the magnetic field strength of the 85-W Hall thruster was not sufficiently high to achieve efficient operation above 225 V. As a result, the 85-W Hall thruster required a magnetic flux density above 24.3 mT to achieve stable and efficient operation above a discharge voltage of 225 V. A comparison between the 85-W Hall thruster and the SPT-100 demonstrated that the magnetic field strength for stable and efficient operation increases with Hall-thruster downsizing. At a constant discharge voltage, narrowing the channel requires an increase in the magnetic field strength to restrict the increase in cross-field electron transport owing to the electron-wall interaction. As a typical thrust performance of the 85-W Hall thruster, a specific impulse of 1,050 s, thrust-to-power ratio of 59.5 mN/kW, and anode efficiency of 0.306 were achieved at a discharge voltage of 225 V and a discharge power of 88.9 W under a background pressure of 7.9 × 10-4 Pa. Moreover, the thruster achieved throttling at a discharge power of 47.6 to 118.5 W with stable operation. A performance comparison between the 85-W Hall thruster and the H6 showed that the low anode efficiency of the 85-W Hall thruster was caused by low propellant utilization and large beam divergence. The short effective length for the propellant ionization owing to the narrow channel was deduced to be the cause of the low anode efficiency in low-power Hall thrusters. Indeed, the mass utilization efficiency improved as the anode mass flow density increased. Therefore, an increase in the anode mass flow density is required to improve the performance of the 85-W Hall thruster. However, the anode efficiency remained constant at anode mass flow rates ranging from 0.415 to 0.611 mg/s because of the decreased current utilization efficiency.
Hence, for a performance improvement, an increase in the magnetic field strength is required to maintain the electron confinement in parallel with an increase in the flow density.
Acknowledgments This research results were obtained using Space Chamber Laboratory of ISAS, JAXA. This study was supported by JSPS KAKENHI Grand Number 17H04972. The author would like to thank Editage (www.editage.jp) for English language editing.
Nomenclature B
=
magnetic flux density, mT
Br,max =
maximum radial magnetic flux density on discharge channel centerline, mT
d
=
discharge channel mean diameter, m
e
=
elementary charge, C
F
=
thrust, mN
F/P
=
thrust-to-power ratio, mN/kW
g
=
acceleration of gravity, m/s2
h
=
discharge channel width, m
Ia
=
axial ion beam current, A
Ib
=
total ion beam current, A
Id
Id
=
discharge current, A
=
average discharge current, A
Isp
=
specific impulse, s
Jb
=
ion beam current density, A/m2
m a
=
anode mass flow rate, mg/s
mxe
=
mass of a xenon atom, kg
ne
=
electron number density, /m3
ni
=
ion number density, /m3
p
=
background pressure, Pa
r
=
radial distance from thruster centerline, mm
Te
=
electron temperature, eV
Vd
=
discharge voltage, V
Vmp
=
most probable ion potential, V
Vp
=
plasma potential, V
vn
=
ion velocity, m/s
vn
=
neutral velocity, m/s
y0
=
ratio of neutral speed to singly-charged ion speed, -
Zi
=
charge-state of the ith ion species, -
z
=
distance from thruster exit to E×B probe, m
∆
=
amplitude of discharge current oscillation, -
ηa
=
anode efficiency, -
ηb
=
beam efficiency, -
ηc
=
current utilization efficiency, -
ηm
=
mass utilization efficiency, -
ηn
=
neutral-gain utilization efficiency, -
ηq
=
charge utilization efficiency, -
ηv
=
voltage utilization efficiency, -
λi
=
ionization mean free path, m
Ωi
=
current fractions of the ith ion species, -
τ
=
measurement time, s
ψ
=
effective plume divergence half-angle, deg
〈σi ve 〉 =
ionization reaction rate, m3/s
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Vitae:
Hiorki Watanabe received the B.E. degree from the Department of Aerospace Engineering, National Defense Academy, Kanagawa, Japan, in 2006 and the M.E. and Ph. D degrees from the Department of Aerospace Engineering, Tokyo Metropolitan University, Tokyo, Japan, in 2009 and 2012, respectively. From 2012 to 2014, he was a Postdoctoral Research Fellow with Japan Aerospace Exploration Agency, Kanagawa, Japan. Since 2014, he has been an Assistant Professor with Tokyo Metropolitan University. His research interests include spacecraft propulsion and plasma application.
Shinatora Cho obtained his Ph.D. at the University of Tokyo, Japan in 2013. Since 2013, He has been working at Japan Aerospace Exploration Agency (JAXA) as a researcher. He has been devoting to the research and development of the 6-kW Hall thruster for JAXA Engineering Test Satellite-9 (ETS-9) all-electric satellite. His research interests include electric propulsion, Hall thruster, plasma dynamics, and especially fully kinetic particle simulation.
Kenichi Kubota received the B.S. degree from Department of Physics, Tokyo Institute of Technology, Tokyo, Japan in 2004, and M.E. and Ph. D. degrees from the Department of Energy Sciences, Tokyo Institute of Technology, Kanagawa, Japan, in 2006 and 2009, respectively. In 2009, he worked for Japan Aerospace Exploration Agency (JAXA) as a research fellow of Japan Society for the Promotion of Science, and since 2010, he has been working for Aeronautical Technology Directorate, JAXA as a researcher. His research interests include numerical simulation of plasma in electric propulsion devices.
Title: Performance and Plume Characteristics of an 85 W Class Hall Thruster
Highlight: An 85-W Hall thruster with inner and outer coils was developed and evaluated. The thruster required > 24.3 mT to achieve efficient operation above 225 V. Anode efficiency was low because of low mass utilization and beam efficiencies.