Performance and plume evolutions during the lifetime test of a Hall-effect thruster

Journal Pre-proof Performance and plume evolutions during the lifetime test of a Hall-effect thruster Shuai Cao, Xuan Wang, Junxue Ren, Ning Ouyang, Guangchuan Zhang, Zhe Zhang, Haibin Tang PII:

S0094-5765(19)31469-9

DOI:

https://doi.org/10.1016/j.actaastro.2019.12.036

Reference:

AA 7819

To appear in:

Acta Astronautica

Received Date: 26 September 2019 Revised Date:

25 December 2019

Accepted Date: 29 December 2019

Please cite this article as: S. Cao, X. Wang, J. Ren, N. Ouyang, G. Zhang, Z. Zhang, H. Tang, Performance and plume evolutions during the lifetime test of a Hall-effect thruster, Acta Astronautica, https://doi.org/10.1016/j.actaastro.2019.12.036. 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. © 2020 IAA. Published by Elsevier Ltd. All rights reserved.

1

Performance and plume evolutions during the lifetime test of a

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Hall-effect thruster

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Shuai Caoa,b, Xuan Wangc, Junxue Rena,b, Ning Ouyangc, Guangchuan Zhangb,d, Zhe Zhange, Haibin Tangb,d,* a

School of Astronautics, Beihang University, Beijing 100083, China

b

Key Laboratory of Spacecraft Design Optimization & Dynamic Simulation Technologies, Ministry of Education, Beijing

100083, China c

Shanghai Institute of Space Propulsion, Shanghai 201112, China

d

School of Space and Environment, Beihang University, Beijing 100083, China

e

School of Instrumentation and Optoelectronic Engineering, Beihang University, Beijing 100083, China

*

Corresponding author. E-mail address: [email protected].

Abstract: To demonstrate the qualifications of the thruster lifetime, performance and reliability design, an 8000-hour ground test of a Hall-effect thruster was conducted. Except for the ignition stage, the thruster operated at the nominal condition with a gas flow rate of 53.7 sccm and a discharge current of 4.2 A. In this paper, the research focuses on the evolutions of the thruster performance parameters and plume plasma properties during the long-duration (about 8240 hours) test. An optical imaging system was developed to observe the erosion configuration of the insulator rings. The far-field diagnostic instruments consisted of a Langmuir probe, a Faraday probe and a Retarding Potential Analyzer. These probes were configured to measure the local plasma potential, plasma density, ion current density and ion energy. The results show that the thrust value first increases and then decreases during the first 2000 hours. At the stage ranging from 2000 to 8240 hours, the thrust value shows a slowly rising trend on the whole and stabilizes at the end. The thruster plume exhibits the phenomena of beam expansion and beam contraction at the early-to-mid lifetime stage and the midto-late lifetime stage, respectively. During these two periods, the relevant variations of the plume plasma parameters are related to the erosion configuration of the insulator ceramic walls. It also suggests that the evolutions of the thruster performance are largely determined by the properties of the plume plasma, especially the behaviours of the beam ions. Keywords: Hall-effect thruster; lifetime test; performance evolution; plasma diagnostics; erosion configuration

Nomenclature EP g GEO HC HET HET-80 Id Isp ݉ሶ Mn NA P Pa Pin Pex ‫ݍ‬ሶ RPA sccm SPT T Ud Vm ߟ

= = = = = = = = = = = = = = = = = = = = = = =

electric propulsion 9.8 m/s2, gravitational acceleration Geostationary Earth Orbit hollow cathode Hall-effect thruster a Hall-effect thruster with a nominal thrust of 80 mN discharge current specific impulse xenon mass flow rate 2.18×10-25 kg, xenon atom mass 6.022×1023 mol-1, Avogadro constant total input power anode power power of inner magnetic coil power of outer magnetic coil volume flow rate Retarding Potential Analyzer standard cubic centimeter per minute stationary plasma thruster thrust value discharge voltage 22.4 L/mol, molar volume of gas total efficiency

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1. Introduction Based on the advantages of high specific impulse (Isp) and propellant efficiency, electric propulsion (EP) system becomes an attractive option for the missions of spacecraft attitude control and deep-space exploration [1]. A Hall-effect thruster (HET) is a popular EP thruster that has been widely applied for the orbit transfer and station keeping of the Geostationary Earth Orbit (GEO) satellites [2][3][4]. HET-80 is a modified Hall-effect thruster, which has been developed in Shanghai Institute of Space Propulsion. It will be used for various space tasks proposed in China. Other medium-power devices with a similar configuration include SPT-100 and PPS1350 series. Several institutions have conducted the qualification demonstrations of HETs for space application. The thruster performance parameters such as the thrust, specific impulse, efficiency and lifetime have been demonstrated. As an important issue of integrating HETs in the spacecraft, the plumes of HETs have a wider expansion divergence compared to those of other EP thrusters [5]. This would raise some critical problems on the plume-spacecraft interactions, involving the surface charging interaction, solar array interaction and communication interaction. Hence, the plume characteristics of HETs have also been diagnosed during the lifetime test. This can help to evaluate the plume-spacecraft interactions and quantify the performance loss mechanisms associated with plume divergence [6]. Extensive plume measurements have been performed for HETs, including SPT-100 [7][8][9], PPS1350 [10][11], BPT-4000 [12][13] and BHT-1500 [5]. There have been some previous researches concerning the HET lifetime verification and the relevant experimental measurements. To increase confidence in the propulsion subsystem for application on large longlived western spacecraft, the on-ground qualification programs for the stationary plasma thruster (SPT) were executed at Fakel Experimental Design Bureau and at the Jet Propulsion Laboratory (JPL) [14][15]. Arkhipov et al. at Fakel Bureau investigated the performance variations during the qualification life testing of a SPT-100 module [16]. The thruster operated at a discharge voltage of 300 V and a discharge current of 4.5 A. The xenon propellant flow rate was 5.3 mg/s. In this case, the nominal thrust and specific impulse were 83 mN and 1600 s, respectively. The parameter measurements and ignition cycles of SPT-100 were conducted in the Fakel life test chamber (with a diameter of 2.5 m and a length of 5 m). The vacuum pumps of this facility were capable of maintaining the chamber environment below 5×10-6 torr static pressure and 5×10-5 torr (for xenon) during firing operation. The vacuum chamber was equipped with a thrust stand, which served to determine the thrust value. During the first 1000 hours, an initial period of performance degradation occurred. Following this period, the thruster performance rose slowly until the firing time reached 4000 hours. It indicated that the thruster performance returned to a higher performance level. During the last 1000 hours, the thruster performance parameters became stable. The thrust value, specific impulse and total efficiency reached the stabilized values of approximately 82 mN, 1500 s and 44%, respectively. In addition, the insulator rings had a relatively high rate of erosion during the initial 600 hours period. After 1000 hours of firing operation, the erosion rate decreased by a factor of 5. It suggested that the erosion phenomenon mainly appeared at the initial stage of the test. PPS1350 is an another HET designed for North/South station keeping of the GEO satellites [17] and the lunar detector mission [18]. Its dimensions and performance parameters are similar to SPT-100 and HET-80. This thruster was improved to produce a nominal thrust of 88 mN with an input electrical power of 1.5 kW. During the lifetime testing program of PPS1350 [10][19], Marchandise et al. investigated the thruster performance in terms of the thrust stability, thermal behaviour and efficiency. A pendulum balance system was employed to perform the thrust measurement, which helped to precisely determine the thruster efficiency and specific impulse. An arm equipped with the Faraday probes and Retarding Potential Analyzer (RPA) probes was used to characterize the thruster plume. These two kinds of probes measured the distributions of the plume plasma parameters, including the beam divergence angle, ion current density and ion energy. The experimental data measured along the lifetime test showed that the thrust evolution of PPS1350 versus lifetime was similar to the thrust variations of other HETs. The thrust showed a decrease of about 6 mN from the beginning to 200 hours. Then the thrust value increased to 92 mN after 400 hours lifetime. Between 400 hours and 2500 hours, the thrust fluctuated obviously with the firing duration. Following this phase, the thrust increased gradually and then reached a stabilized value of 90 mN after 3500 hours of operation. After 3500 hours of firing, the specific impulse and efficiency stabilized at about 1650 s and 50%, respectively. The erosion configuration of the insulator rings was obtained by measuring the remaining thickness of the ceramic walls. It indicated that the wall erosion mainly occurred in the first half of the life test. The probe measurements showed that the ion mean energy remained quasi-constant (approximately 270 eV) for the whole lifetime. The beam divergence half-angle exhibited a variation tendency of growing first (from 40° to 43.3°) and then going down (from 43.3° to 38°). The BPT-4000 thruster is developed for the low-cost planetary missions [20] and NASA science missions [21]. To assess the performance and plasma properties of the BPT-4000 thruster, a long-duration lifetime test and the relevant measurements were performed [22]. An inverted-pendulum thrust stand was used to determine the performance parameters. In the far-field plume, an assembly of the emissive probe, RPA and E×B probe served for the measurements of the plasma potential, ion energy and ion species’ fractions. Compared to SPT100 and PPS1350 thrusters, the BPT-4000 operated at a higher discharge power of 4.5 kW. Its functioning 2

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points were chosen to span 500-800 V discharge voltage and 2.5-5.5 kW discharge power. Based on these functioning points, the BPT-4000 thrust value, specific impulse and efficiency ranged from 134 to 288 mN, 1980 to 2720 s and 0.50 to 0.59, respectively. The testing results showed that the thrust measured at all conditions exhibited a decrease of 3% after the first 500 hours [23]. Then the thrust value increased slowly or remained constant for the remainder of the lifetime test. At the stage of the first 500 hours, the specific impulse showed a similar evolution trend. Following this period, the specific impulse also increased gradually throughout the remainder of the test. It was concluded that no obvious degradation occurred in the thruster performance during long-duration test. The probe measurements showed that both the ion loss voltage and the full-width at high-maximum increased with the discharge voltage. Additionally, no measurable erosion of the ceramic walls was obtained after 5600 hours of firing. It indicated that the thruster insulator rings had the nearzero erosion rates and reached a “zero” erosion configuration. The studies noted above give a detailed insight into the HET lifetime test, accompanied with the relevant performance measurements. The long-duration tests of other EP thrusters such as ion engines [24][25], arcjet thruster [26] and pulsed plasma thrusters [27][28], were also performed to demonstrate the qualifications of the thruster performance, availability and reliability. However, there are still some plume plasma characteristics that have not been examined in the longtime ground tests. The relationships and interactions between the evolutions of the performance parameters and the plume plasma properties, were not fully understood. The experimental work presented in this paper focuses on the evolution mechanisms of the thruster performance and plume plasma involved in the HET lifetime test. The investigated plasma parameters regarding the plume characteristics include the plasma potential, beam divergence angle, ion density, ion energy and ion current density. Through the entire lifetime test of HET-80, these plume parameters were obtained using the assembly of a Langmuir probe, a Faraday probe and a RPA. An interesting phenomenon named “beam contraction” is presented and discussed. The innovative experimental effort proposed in this paper is aimed to explain the underlying physical mechanisms of HET long-duration operation and provide useful conclusions for the community.

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2. Experimental setup The spacecraft rely on the HETs to provide the required micro-thrust control with long operational lifetime [29][30]. The cross-section geometry of a typical Hall thruster and its main components are presented in figure 1. This axisymmetric device consists mainly of an annular discharge channel, an external cathode, several magnetic poles and an anode capped at the upstream end. The bulk plasma is generated and then accelerated in the discharge chamber, which is shaped as an annular channel. The discharge potential (about 300 V) between the external hollow cathode (HC) and the internal anode establishes an axial accelerating electric field for the dense ions. The inner and outer magnetic poles surrounding the discharge chamber create a radial magnetic field. Under the influence of the strong magnetic field and electric field, the primary electrons provided by the HC will be trapped in an azimuthal Hall drift around the annular discharge chamber. The propellant (xenon) is injected at the anode side. The neutral gas is then ionized by the trapped electrons. In addition, a large number of electrons generated in the HC are also extracted into the plume region. These electrons are aimed at neutralizing the accelerated beam ions and avoiding charging of the satellite.

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Fig. 1. Schematic view of a HET. 2.1 HET-80 Hall-effect thruster

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HET-80 thruster is an electromagnetic propulsion device capable of high efficiency operation (about 47.3%). During the lifetime test, the HET-80 thruster operated at a discharge voltage of 310 V and a discharge current of around 4.2 A. Taking into account the power consumption of the inner and outer magnetic coils, the total electrical power of the thruster reaches 1350 W. The thruster propellant is the 99.9995% high-purity xenon gas. The gas flow rate for the anode and the HC is around 51 sccm and 3 sccm, respectively. The corresponding thrust level is approximately 80 mN. The discharge voltage and gas flow rate were constant over the entire course of the firing test. Figure 2 depicts the operation state of HET-80 during the longtime firing test. The thruster plume is blue in color. A long narrow spike appears in the middle of the thruster plume. This spike stretches from the exit plane and extends to about 25 cm downstream from the exit plane. It indicates that the thruster discharge plume is in a “jet mode” [5].

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Fig. 2. Long-firing operation state of HET-80 at 310 V, 1.35 kW.

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2.2 Vacuum facility

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For the whole lifetime test, the measurements associated with the thruster performance and plume plasma were performed in a vacuum tank with four cryogenic pumps. This vacuum chamber is 2.5 m in diameter and 5.5 m in length. The vacuum system consists of an Edwards GXS 750/2000 rotary pump, 16 sets of Sumitomo F-70H compressors, two conventional cryogenic pumps and two xenon cryogenic pumps. For each cryogenic pump, there are 4 sets of Sumitomo CH104 cold heads. The actual pumping speed for xenon is around 47480 L/s. The vacuum pumps are capable of maintaining the chamber at or below 2×10-5 Pa ultimate pressure and 3×10-3 Pa firing vacuum degree. The chamber is equipped with a displacement device, a micro-thrust stand and an optical apparatus. The probes used for the plume diagnostics are mounted on a translation platform. By adjusting the position of the translation platform, the diagnostic probes are moved between the plume measurement points. The HET-80 thruster is assembled on the thrust stand. It is worth mentioning that the thruster exhausted towards the chamber door during the long-duration firing. As suggested in reference [6], it is reasonable to direct the thruster's exhaust towards the door for determining the beam current density and divergence angle. Before the formal lifetime testing, a preliminary experiment [6] and the relevant investigations of HET-80 principle prototype were successfully conducted in this vacuum facility.

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2.3 Measuring apparatuses for the thruster performance and plume plasma

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The measuring apparatuses for the thrust value and plume plasma parameters are depicted in figure 3. The measurement of the thrust was performed on a micro-thrust stand, which was equipped with a torsional balance system [31][32][33]. This stand is mainly composed of a torsional arm, two flexural pivots, a stationary structure, a displacement sensor and a feedback control system with the position follow-up mechanism. Based on the swing signal detected by a displacement sensor, the PID feedback control circuit outputs a compensating current signal. This current signal is strengthened through a power amplifier and then transferred to an electromagnetic coil. The electromagnetic feedback force derived from this coil and the compensator magnets balances the thrust of HET-80. As a consequence, the swing arm will return back to the pre-set equilibrium position. In order to obtain the real-time static characteristics and accurate thrust results, the thrust stand is also equipped with an on-line calibration and locking system. The thrust measurement range is 0-200 mN with an accuracy not worse than ±0.5 mN and a static error not large than 1.5%. To insure that reliable thrust data could be obtained, additional work was performed to minimize the effects of the electromagnetic environment and heat conduction. In addition, the measured thrust is then used to precisely determine the thruster efficiency and specific impulse.

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Fig. 3. Micro-thrust measuring apparatus and the plume diagnostic probes. The specific impulse ‫ܫ‬௦௣ of the thruster is defined as follows

I sp =

T & mg

(1)

Where ܶ represents the measured thrust value. The variable ݉ሶ refers to the xenon flow rate. The constant ݃ is equal to 9.8 m/s2. The total efficiency ߟ of the thruster is given by

η=

T2 & 2 mP

(2)

The total input power P can be written as follows

P = Pa + Pin + Pex , Pa =Ud Id

(3)

The total power of the thruster includes the anode power (Pa), the power of the inner magnetic coil (Pin) and the power of the outer magnetic coil (Pex). The discharge voltage and the discharge current are denoted by Ud and Id, respectively. HET-80 can be characterized as a plasma discharge device. Thus, further investigations regarding the plasma properties and parameter distributions are needed to gain a deeper insight into the thruster performance evolutions. Throughout the entire life test, the plume plasma parameters were determined using the diagnostic probes. As shown in figure 3, the plume measuring facility consists of a Langmuir probe, a Faraday probe and a RPA. The Langmuir probe is a well-established and widely-used plasma diagnostic technique that measures the plasma potential, electron density and ion density [34][35][36][37]. The ringed Faraday probe (with a resolution of 1 µA and a repeatability error of less than 2%) allows the determination of the beam divergence half-angle, based on the measured distribution of the ion current density [38][39]. The 3-grids RPA (with a resolution of 1 eV and a measuring range of 0-1000 eV) is usually used to determine the ion energy distributions [40][41]. These three kinds of probes are assembled into three new designed stands, which are fixed on a translation platform.

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2.4 Measuring apparatus for the erosion configuration

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During the lifetime test, an innovative measuring method was applied to determine the erosion depths of the ceramic walls. As described in figure 4, the erosion measuring equipment mainly consists of an optical imaging system, a swing arm, two protecting covers and a three-dimensional (3D) reconstruction software system (outside of the vacuum chamber). The optical imaging system includes two charge-coupled-device (CCD) cameras and an optical grating projector. The covers serve to protect the cameras. The swing arm and relevant rotating structure are used to move the CCD cameras between the measurement points.

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Fig. 4. Optical measuring apparatus used for the erosion determination of the discharge chamber walls. The 3D position coordinates of the points on the ceramic wall surfaces are collected through the optical imaging system. Then the image-based modeling software reestablishes the surface of the thruster walls, according to the output signal of the optical system. Based on the self-developed digital-image-processing techniques, the 3D surface appearance of the HET-80 annular channel and insulator rings can be restored to its real shape. The non-contact 3D optical system could depict accurately the wall surface shape covering the azimuthal range of 0-360°. By measuring the distance difference between the erosion appearance and the original wall shape, one can obtain the precise erosion data of the ceramic chamber walls.

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3. Experimental results and discussion

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3.1 Long-running test results

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As drawn in figure 5, the steady-state operation power of HET-80 anode was almost constant (approximately 1310 W) during the test. The average total power, including the power consumption of the inner and outer magnetic coils, was around 1350 W. Thus, the performance measurements, along with the plume plasma diagnostics were all performed at the same operating conditions. Figure 6 illustrates the relationship between the steady-state anode power and the gas flow rate. The anode power can be specified as a linear function of the gas flow rate. The steady-state anode power increases gradually with the rising gas flow rate.

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Fig. 5. Evolution profile of the steady-state anode power with respect to the thruster lifetime.

Except for the ignition stage, the operation conditions of HET-80 were maintained at the nominal point with a discharge voltage of 310 V and a gas flow rate of 53.7 sccm. In order to improve the veracity of the measured thrust values, the thrust measurements, combined with the thrust-stand calibrations, were performed at both the ignition stage and the shut-down stage. The actual static characteristics of the micro-thrust stand were obtained in real time. As a consequence, the thrust values were determined precisely for the entire lifetime test. The total firing duration of HET-80 lifetime test reached nearly 8240 hours.

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Fig. 6. Linear fitting of the steady-state anode power versus the xenon flow rate. 3.2 Measured results of the thrust value

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Figure 7 exhibits the evolution trend of the measured thrust versus the thruster lifetime. During the first 2000 hours, the unstable thrust value increases at first and then decreases quickly. From 400 to 1500 hours, the thrust decreases by 9 mN. This initial performance degradation is associated with the relatively high erosion rates of the chamber insulator rings and the discharge oscillations, as suggested in [16][10]. Following this stage, the increasing trend and the stabilization of the thrust are clearly visible. At the stage of 1500-7000 hours, the thrust rises gradually from 77.5 mN to 82.5 mN. After 7000 hours of firing duration, the thrust reaches a stabilized value of approximately 83 mN. The phenomenon of performance stability appeared at the final lifetime stage, since the erosion rates and depths of the ceramic walls remained almost unchanged during this period. The slightly decreasing trend of the start-up thrust measured at the test stage of 7000-8000 hours is mainly due to the variations of the thruster operating conditions. Figure 8(a) illustrates the thrust variations measured with different anode power values. The evolution of the thrust with respect to the anode power could be characterized by a linear function. As depicted in figure 8(b), the averaged thrust also has a linear rising trend as the gas flow rate increases. The linearity error, hysteresis error and repeatability error of the employed thrust stand are 0.37%, 0.56% and 0.61%, respectively. Thus, the integrated static error of the employed thrust stand is less than 1%. Relevant repeated experiments suggest that the uncertainty in the measured thrust value is estimated to be ±1.8% (corresponding to ±1.44 mN). The error bars, which represent one standard deviation of uncertainty, serve to indicate the vertical interval of possible measuring deviation.

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Fig. 7. Evolution trend of the thrust value versus the thruster lifetime.

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Fig. 8. Linear fitting of the thrust value versus the anode power (a) and the xenon flow rate (b). For the gas propellant of xenon, the conversion relationship between the mass flow rate ݉ሶ (in mg/s) and the volume flow rate ‫ݍ‬ሶ (in sccm) is expressed as

m& =

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103 × N A M n q& 60 × Vm

(4)

Where ܰ஺ represents the Avogadro constant. The mass of xenon atom is denoted by ‫ܯ‬௡ . The constant ܸ௠ refers to the molar volume of gas. During the lifetime test of HET-80, the power values of the inner and outer magnetic coils are both equal to Pin = Pex = 20 W (5) Based on the relevant linear-fitting relationships (see figure 6, figure 8(a) and figure 8(b)) and equations (see equations 1-3), the semi-empirical functions for HET-80 performance parameters are obtained, as listed in table 1. These semi-empirical formulas can help to predict the evolutions of the HET-80 performance parameters versus the operation conditions. Table 1. Semi-empirical formulas for the performance parameters of HET-80, with respect to various operating conditions of the anode power and xenon flow rate. Performance parameters

Anode power (W)

Xenon flow rate (sccm)

Thrust value (mN)

ܶ = 0.06397ܲ௔ − 3.99755

ܶ = 1.68228‫ݍ‬ሶ − 9.61725

10ଷ × (0.06397ܲ௔ − 3.99755) ‫ܫ‬௦௣ = (0.00396ܲ௔ + 0.24881)݃ (0.06397ܲ௔ − 3.99755)ଶ ߟ= (0.00792ܲ௔ + 0.49762)(ܲ௔ + 40)

10ଷ × (1.68228‫ݍ‬ሶ − 9.61725) 0.09737‫ݍ‬ሶ ݃ (1.68228‫ݍ‬ሶ − 9.61725)ଶ ߟ= (0.19474‫ݍ‬ሶ )(24.55869‫ݍ‬ሶ − 22.75435)

Specific impulse (s) Total efficiency

‫ܫ‬௦௣ =

16

3.3 Thruster efficiency and specific impulse

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The evolution profiles of the specific impulse and total efficiency are displayed in figure 9. The average values of the specific impulse and total efficiency are around 1617 s and 47.3%, respectively. The evolution trends of the specific impulse and thruster efficiency are similar to the thrust variation tendency during the lifetime test, since both the efficiency and the specific impulse are calculated on the basis of the measured thrust values. The function relationships between these performance parameters are indicated in equation (1) and equation (2). At the final stage (after 7000 hours of firing), the specific impulse and total efficiency stabilize at about 1600 s and 47.5%, respectively. The uncertainty in the specific impulse is estimated to be ±2%. The uncertainty of the thruster efficiency is dominated by uncertainty in the thrust (±1.44 mN), xenon flow rate (±0.04 mg/s) and total power (±5 W), resulting in a combined standard uncertainty of ±1.9%.

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Fig. 9. Evolution profiles of the specific impulse and total efficiency versus the thruster lifetime.

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3.4 Plume diagnostic results

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The evolution of the beam divergence angle during the lifetime test is presented in figure 10. This angle corresponds to the cone angle containing 90% of the whole ion current. Before 4000 hours of the firing time, the divergence angle of the thruster beam is relatively stable (around 83°). However, the beam divergence angle exhibits an obvious decline after this period. It indicates that the phenomenon named “beam contraction” appears in the mid-to-late stage of the long-duration test. Finally, the beam divergence angle drops to 68°. The uncertainty in the beam divergence angle is estimated to be ±4%.

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Fig. 10. Evolution trend of the beam divergence angle with respect to the firing time. Figure 11(a) shows the profiles of the far-field plasma potential along the symmetry axis. At different stages of thruster lifetime, the corresponding values of the plume plasma potential have a similar variation trend as the axial distance relative to the thruster exit plane varies. The far-field plasma potential decreases slightly with the axial coordinate increasing from 500 to 800 mm. However, the exact values of the plume plasma potential measured at different lifetime stages change a lot. During the test stage of 12-1127 hours, the plume plasma potential shows an overall decline of about 1.5 V. After this period, the far-field plasma potential almost keeps constant (around 13.2 V) until the lifetime of 4530 hours. From the firing duration of 4530 hours to the end of lifetime (8100 hours), the plume plasma potential increases clearly by approximately 2.5 V. The variations of the far-field plasma potential along the radial direction are described in figure 11(b). On the whole, the plume plasma potential decreases gradually with an increase in the radial coordinate. The plasma potential curves measured at different lifetime stages exhibit the same evolution trend. Additionally, the overall plasma potential also changes with the lifetime stages, especially in the regions adjacent to the symmetry axis. At the radial location of 50 mm, the plume plasma potential shows a decrease of 3.5 V and an increase of nearly 6 V during the test stage of 12-1127 hours and 4530-8100 hours, respectively. The repeated measurements indicate that the uncertainty in the plume plasma potential of HET-80 is estimated to be ±4.2%. 9

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For the test stage of 1127-4530 hours, the values of the far-field plasma potential change slightly. It indicates that the potential distribution of the far-field plume is relatively stable during this period. Compared to the values of the plasma potential measured at 4530 hours lifetime, the far-field plasma potential of 8100 hours lifetime performs an overall increase in the radial direction. In addition, the corresponding potential increase of the plume regions close to the symmetry axis is much larger than that of the plume zones located at the beam edge. It is mainly due to the plume plasma behaviours involved in the beam contraction phenomenon. The plume ions migrated to the beam center (equivalent to the symmetry axis) at the mid-to-late stages of lifetime test. This would result in the appearance of a higher ion number density or current density in the regions around the beam center. Hence, according to the Poisson equation law [42][43], the plasma potential of these areas is markedly enlarged.

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Fig. 11. Evolution profiles of the plume plasma potential measured at different lifetime stages. (a) Along the symmetry axis; (b) Along the radial direction (The axial distance relative to the thruster exit plane is 600 mm). As depicted in figure 12, the ion current density of the far-field plume reduces gradually as the axial distance or radial coordinate increases. The two-dimensional distributions of the ion current density investigated at different lifetime stages are similar. In the regions near the symmetry axis and the thruster exit plane, the ion current density is relatively high (around 3-12 mA/cm2). It indicates that the far-field plume ions mainly concentrate in these regions. Although the beam divergence angle in figure 10 changes slightly for the first half of the thruster lifetime, the detailed values of the plume ion current density with respect to different test stages vary considerably. During the firing duration of 12-1856 hours, the dense ion region close to the symmetry axis (corresponding to the red and yellow zones in figure 12) extends gradually to the external zones of thruster plume. It suggests that at the initial stage a “beam expansion” phenomenon arises in the far-field plume region of HET-80. For the lifetime stage of 2850-4000 hours, the dense ion region expands slightly. Following this period, the dense ion region of thruster plume gets closer to the beam center during the long-duration test of 4000-8100 hours. It demonstrates that the “beam contraction” phenomenon occurred at this stage. For the lifetime of 8100 hours, the far-field ion current density located at the beam center rises dramatically. At that time, the peak value of the far-field ion current density approaches 12 mA/cm2. 10

1

2

3

11

1

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Fig. 12. Two-dimensional distribution of the far-field ion current density versus the thruster lifetime. The variation trends of the normalized ion current density along the radial direction are presented in figure 13. Although the actual values of the ion current density observed at different lifetime stages vary greatly, the curves in figure 13 have the same evolution trend. It shows that the far-field ion current density decreases quickly as the radial coordinate rises from 0 to 400 mm. For the remaining radial distance of 400-1000 mm, the ion current density declines slowly. In these regions (radial coordinate greater than 400 mm) of far-field plume, the values of the ion current density are relatively small (nearly equal to 0). Thus, it is concluded that in the farfield plume the beam ions mainly concentrate in the radial range of 0-400 mm.

11 12

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Fig. 13. Evolution curves of the normalized ion current density versus the radial location (at different lifetime stages). The axial distance relative to the thruster exit plane is 600 mm. As revealed by figure 14, the far-field plume of HET-80 exhibits different evolution behaviours as the lifetime stage changes, especially in the radial range of 0-300 mm. During the test stage of 12-1856 hours, the dense ion beam expands gradually to the exterior zones of far-field plume in the radial direction. As the thruster lifetime increases, the normalized ion current density is enlarged obviously at the same radial location. Following this stage, the radial distribution shape of the ion beam shows a smaller expansion phenomenon during the firing duration of 2850-4000 hours. In this period, the values of the normalized ion current density change slightly, except for the areas close to the symmetry axis. For the second half of the test (implying the lifetime range of 4000-8100 hours), the normalized ion current density is lowered clearly at the same radial coordinate. It implies that during this stage the far-field beam ions gather to the beam center along the radial direction. The phenomenon called “beam contraction” arises at the mid-to-late stages of thruster lifetime.

13

14

13

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37

Fig. 14. Variation trends of the normalized ion current density versus the radial location. (a) At the lifetime stage of 12-1856 hours; (b) At the lifetime stage of 2850-4000 hours; (c) At the lifetime stage of 4000-8100 hours. The axial distance relative to the thruster exit plane is 600 mm. Figure 15(a) plots the radial variations of the far-field ion current density at both the initial stage and the final stage of the long-duration firing. Compared to the experimental data measured at 144 hours lifetime, the ion current density tested at 8100 hours lifetime is raised significantly at the far-field radial locations ranging from 0 to 300 mm. At the axial position of 500 mm, the highest ion current density of 8100 hours lifetime reaches 7 mA/cm2 while the corresponding value of 144 hours lifetime is only 3.5 mA/cm2. In the regions far away from the beam center line, the values of the far-field ion current density measured at the initial and final stages are relatively small (approximately equal to 0). It indicates that the beam ions located in the far-field plume are sparse at the radial coordinate exceeding 400 mm. More details can be found in figure 15(b) and figure 15(c), which reveal the evolution trends of the ion current density along the radial coordinate of 0-400 mm and 400-1000 mm, respectively. In the radial range of 0-400 mm, the values of the ion current density of 8100 hours lifetime are visibly larger than those of 144 hours lifetime at the same axial coordinate. However, in the remaining radial range of 400-1000 mm, the far-field ion current density measured at the final stage is always smaller than that obtained at the initial stage. At 8100 hours lifetime, the values of the far-field ion current density are reduced to a lower level in the areas adjacent to the beam edge and in the regions outside of the thruster beam. As mentioned in literature [10], the energy of the beam ions varied slightly during HET lifetime test. It indicated that the velocity of the beam ions almost kept constant as the thruster lifetime extended. Thus, the evolutions of the ion current density during the long-duration test could equivalently reveal the variation trends of the ion number density versus the thruster lifetime. It suggests that abundant ions, which were derived from the discharge chamber and the exterior plume zones with larger radial coordinates, were transferred to the beam center line at the late stages of lifetime. This may help to lower the divergence and expansion of thruster beam. Hence, the beam divergence angle determined in the far-field plume becomes smaller at the final stage, as also introduced in figure 10. Owing to the contraction behaviour of the ion beam, the radial component of beam ion velocity, combined with the beam divergence angle, is reduced accordingly. Since the kinetic energy of the beam ions is almost constant during the lifetime test of a HET, the axial component of beam ion velocity is enlarged correspondingly. As a consequence, a higher proportion of beam ion energy is used to generate the thrust. In the regions adjacent to the symmetry axis, the current density and number density of the far-field ions increase obviously due to the phenomenon of beam contraction. A larger quantity of the beam ions located in these zones would contribute to the formation of the thrust, with the total velocity nearly parallel to the thruster center line. It is concluded that the macroscopically lowered beam divergence angle may account for the thruster performance improvements appearing at the mid-to-late lifetime stages. As demonstrated in figure 7 and figure 9, the thrust, accompanied with the specific impulse and total efficiency rises distinctly during the thruster lifetime of 4000-8100 hours.

14

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3 4 5 6 7 8 9 10 11

Fig. 15. Evolution profiles of the ion current density versus the radial location. (a) From 0 mm to 1000 mm; (b) From 0 mm to 400 mm; (c) From 400 mm to 1000 mm. The comparisons of these curves are conducted at the initial stage (144 hours lifetime) and the final stage (8100 hours lifetime). Figure 16 shows the typical RPA I-V characteristic drawn from the far-field plume measurements. The differential current-voltage (dI/dV-V) curve is also depicted in figure 16. The energy of the beam ions was measured in the plume region located 500 millimetres downstream of the thruster exit. The most-probable energy of the beam ions is determined using the peak value of the differentiated I-V curve. At the axial location of 500 mm, the corresponding value of the most-probable ion energy is around 267 eV. The beam ion energy of

15

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HET-80 is distributed in the range of 207-300 eV. Hence, the most-probable velocity of the beam ions is approximately 19810 m/s. The uncertainty in the most-probable ion energy is calculated to be ±5%.

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Fig. 16. RPA current-voltage (I-V) and differentiated I-V (dI/dV-V) curves derived from the plume measurements at axial 500 mm downstream from the centre of the thruster exit plane. By combining the measured results of the ion current density and the most-probable ion energy, the evolution profiles of the ion number density along the radial direction and the symmetry axis are provided in figure 17(a) and figure 17(b), respectively. Since the energy of the beam ions changes slightly during HET lifetime test [10], the variation trends of the plume ion density are similar to those of the ion current density in the far-field plume regions. On the whole, the ion number density of the far-field plume zones decreases quickly at first and then slowly declines with increasing the radial coordinate. Compared to the experimental data measured at 4000 hours lifetime, the ion number density determined at the final lifetime stage (8100 hours lifetime) increases a lot in the regions (radial coordinate of 0-300 mm) close to the symmetry axis. At the axial coordinate of 500 mm, the highest value of the ion number density is enlarged from 1.07×1016 m-3 to 2.18×1016 m-3 with the firing duration ranging from 4000 to 8100 hours. However, in the regions (radial coordinate of 3001000 mm) far away from the symmetry axis, the plume ion density derived from the measurements at 4000 hours lifetime is larger than that measured at 8100 hours lifetime. These evolutions of the plume ion density verify the existence of the beam contraction behaviour, which occurred at the mid-to-late stages of HET-80 lifetime test. The plume ion density decreases gradually with the axial distance relative to the thruster exit plane extending from 500 to 800 mm. Along the centre line of thruster beam, the ion number density of the far-field plume exhibits an overall increase as the thruster lifetime varies from 4000 to 8100 hours. It is consistent with the evolutions of the plasma potential depicted in figure 11(a). The uncertainty in the ion number density of the thruster plume is estimated to be ±6%.

24

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Fig. 17. Evolutions of the plume ion density. (a) Along the radial direction; (b) Along the symmetry axis. The relevant experimental measurements were performed at the mid-to-late stages of the lifetime test. 3.5 Wall erosion of the discharge chamber

5 6 7 8 9 10

During the lifetime test, the erosion configuration of the ceramic walls has been determined using an optical imaging apparatus. By comparing the remaining thickness of the insulator rings with the original geometry sizes, one can obtain the erosion depths of the chamber walls. The erosion shapes of the ceramic insulator wall and the cathode keeper are shown in figure 18. After approximately 8240 hours of long-duration firing, both the ceramic walls and the keeper plate exhibit visible external erosions. The insulator rings of HET-80 were eroded to a visibly diverging annulus from the initial cylindrical shape.

11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

Fig. 18. Erosion profiles of the ceramic chamber walls and the cathode keeper plate. The evolution trends of the erosion depths with respect to the thruster lifetime are drawn in figure 19(a) (in the radial direction) and figure 19(b) (in the axial direction). On the whole, the erosion depths of the ceramic rings rise gradually as the thruster lifetime increases. It is noticed that the erosions of the internal insulator and external insulator mainly occurred at the lifetime stages of 0-6500 hours and 0-4500 hours, respectively. During these periods, the insulator walls exhibited higher erosion rates. The evolutions of the axial erosion depths and rates with respect to the thruster lifetime are similar to the variation trends of the radial erosion properties. The erosion rates of the insulator rings decrease gradually with an increase in the firing time. After about 5500 hours and 7000 hours of firing operation, the erosion configuration of both the ceramic outer ring and inner ring becomes stable. In the radial direction, the largest erosion depths of the inside wall and the outside wall stabilize at approximately 11.8 mm and 7.6 mm, respectively. In the axial direction, both the inner insulator and the outer insulator have an initial erosion configuration after the first ignition (about 125 hours duration). This phenomenon agrees well with the published model predictions and experimental results in [23]. The initial axial erosion depths of the inner ring and the outer ring are about 5.0 mm and 3.9 mm, respectively. Compared to the radial erosion rates and the largest radial erosion depths of the insulator rings, the corresponding axial erosion parameters are relatively small at the remaining lifetime stages. The largest axial erosion depths of the ceramic inside wall and outside wall are approximately 6.8 mm and 5.4 mm, respectively. The static measuring error of the optical imaging apparatus is less than 1% (about 0.7%). Relevant repeated experiments indicate that the 17

1 2

vacuum environment and the control error of the transmission device may lead to an uncertainty of ±3% in the erosion depth measurements.

3

4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

Fig. 19. Erosion depths of the insulator rings versus the firing time. (a) In the radial direction; (b) In the axial direction. At the early-to-mid stages of lifetime test, the larger erosion rates of the ceramic rings resulted in the rapidly increasing erosion depths. The actual geometry boundaries of the ceramic walls, along with the corresponding erosion shapes, extended accordingly. In the discharge chamber, some ions would move toward the plume along the gradually expanding surface of the insulator outer ring. It implied that more ions generated from the ionization reactions could enter into the plume with a larger divergence angle. In the thruster plume, more ions would be transported to the external plume regions which were far away from the central axis of the thruster. This may lead to the expansion of the ion beam. As also revealed by figure 14(a) and figure 14(b), the phenomenon of beam expansion occurred at the test stages of 12-1856 hours and 2850-4000 hours. Additionally, the beam expansion extent depicted in figure 14(a) is more serious than that shown in figure 14(b), on account of the gradually decreasing erosion rate with respect to the thruster lifetime. In other words, the radial expansion velocity drawn from the current density distributions of far-field beam ions was mainly determined by the erosion rate of the insulator outer ring at the early-to-mid lifetime stages. At the mid-to-late stages of HET-80 lifetime test, the erosion rate of the outer ceramic ring declined to a lower level. The erosion depth of the outer ring increased slowly after 4000 hours of firing operation. Thus, the expansion phenomenon of the ion beam disappeared gradually. However, the erosion rate of the inner ceramic ring still kept the relatively high level. The erosion depth of the inner ring also rose obviously at the lifetime stage of 4000-7000 hours. The evolutions of the ion transport process were mainly determined by the erosion configuration of the inner insulator ring at this stage. In the discharge chamber, more ions could move toward the plume centre line along the gradually contracting surface of the inner ceramic ring. As a consequence, more ions extracted from the discharge chamber would be transported to the plume central zones, which were adjacent to the centre line of thruster beam. This behaviour may lead to the contraction phenomenon of the ion beam. For this period, the evolutions of the far-field plume plasma were mainly reflected in the contraction behaviour of the beam ions. After 7000 18

1 2 3 4

hours of firing, the erosion rates of both the inner ring and the outer ring were nearly equal to 0. At that time, the erosion depths and shapes of the ceramic walls remained almost unchanged with respect to the thruster lifetime. Thus, at the final test stage, the measured performance parameters of HET-80 also became stable, as illustrated in figure 7 and figure 9.

5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

4. Conclusion

26 27

Acknowledgments

28

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In this paper, the experimental work examined the performance and the far-field plume plasma of a Halleffect thruster. Various steady-state parameters including the thrust value, specific impulse, total efficiency, beam divergence angle, beam current density and plume plasma potential were evaluated for a Hall-effect thruster operating at the nominal condition (a discharge current of 4.2 A and a xenon flow rate of 53.7 sccm). The evolutions of the thruster performance parameters and plume plasma characteristics with respect to the firing lifetime are investigated. In addition, the underlying physical mechanisms of these evolutions are also clarified by observing the variations of the thruster configuration and the plume plasma properties. The experimental results show that the performance parameters including the thrust, specific impulse and total efficiency exhibit the similar evolution trend during the long-duration firing. The performance parameters are unstable at the initial lifetime stage ranging from 0 to approximately 2000 hours. Following this period, the performance parameters rise gradually as the thruster lifetime increases. It may result from the gradually reduced divergence angle of the thruster beam. The ion beam of the thruster expands gradually at the lifetime stage of 0-4000 hours. It may occur as a result of the larger erosion rate and the gradually extending erosion depth of the outer ceramic ring during this period. The phenomenon “beam contraction” appearing at the mid-tolate stages suggests that the beam ions derived from the discharge chamber or the external plume regions are transported to the zones close to the beam central axis. For the second half of the long-duration test, it leads to a gradually decreasing divergence angle with respect to the thruster lifetime. During the thruster lifetime of 40007000 hours, the improvements of the performance parameters also arise from this beam behaviour. After about 7000 hours of firing, the erosion shapes of both the insulator inner wall and outer wall become stable. As a consequence, the performance parameters also stabilize at the final test stage.

This work was supported by the National Natural Science Foundation of China (Grant No. 11872093).

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Highlights 1. Actual parameter evolutions during a Hall thruster’s lifetime were investigated. 2. An optical imaging system was used to measure the wall erosions precisely. 3. Variations of thruster performance, plume plasma and erosions are coherent. 4. Phenomena of beam expansion and contraction arise from the erosion evolutions. 5. Behaviors of plume ions largely determine the performance of a Hall thruster.

Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: