Matching characteristics of magnetic field configuration and chamfered channel wall in a magnetically shielded Hall thruster

Zhaoyu WANG (王昭宇), Hong LI (李鸿),2, Chao ZHONG (钟超),Yanlin HU (扈延林), Yongjie DING (丁永杰),2, Liqiu WEI (魏立秋),2 and Daren YU (于达仁),2

1 Lab of Plasma Propulsion, Harbin Institute of Technology, Harbin 150001, People’s Republic of China

2 Key Laboratory of Aerospace Plasma Propulsion, Ministry of Industry and Information Technology,Harbin 150001, People’s Republic of China

3 Beijing Institute of Control Engineering, Beijing 100190, People’s Republic of China

Abstract To date,the selection of the magnetic field line used to match the chamfered inner and outer channel walls in a magnetically shielded Hall thruster has not been quantitatively studied.Hence, an experimental study was conducted on a 1.35 kW magnetically shielded Hall thruster with a xenon propellant.Different magnetic field lines were chosen, and corresponding tangentially matched channel walls were manufactured and utilized.The results demonstrate that high performance and a qualified anti-sputtering effect cannot be achieved simultaneously.When the magnetic field lines that match the chamfered wall have a strength at the channel centerline of less than 12% of the maximum field strength, the channel wall can be adequately protected from ion sputtering.When the magnetic field lines have a strength ratio of 12%–20%,the thruster performance is high.These findings provide the first significant quantitative design reference for the match between the magnetic field line and chamfered channel wall in magnetically shielded Hall thrusters.

Keywords: magnetically shielded Hall thruster, magnetic field line, chamfered channel wall,tangent matching

1.Introduction

With the rapid development of space science and technology in recent years [1], space missions and research have shown significant changes in their long-term characteristics.Commercial aerospace is rapidly developing and has attracted significant attention.Commercial and civil-oriented low-orbit communications constellations, Internet of Things constellations, and other space missions require long-term operations in orbit[2].Excellent development opportunities and adverse application-related challenges both contribute to demanding requirements for the working life of Hall thrusters [3–5], which are expected to achieve a cumulative working time of over 150 000 h [6].Therefore,developing long-life Hall thrusters will be imperative in the future.

The most critical factor that influences the lifespan of a Hall thruster is the sputtering erosion of the discharge channel wall caused by high-energy ions[7–9].In addition to maintaining and participating in the discharge process in the Hall thruster[10–14],another important role of the channel is to protect the magnetic circuit.When the channel wall is eroded through, high-energy ions in the acceleration zone bombard and erode the magnetic circuit.Once the components of the magnetic circuit are eroded and damaged,further degradation or overheating may occur,and the magnetic field distribution may deviate from the designed configuration and may not be able to maintain a stable discharge.This would ultimately lead to thruster failure.

NASA’s Jet Propulsion Laboratory (JPL) conducted life tests for BPT-4000 in 2012[15,16].They found that the wall of BPT-4000 remained unchanged from 5600 to 10 400 h.Since then, the magnetic shielding theory of anti-sputtering has been refined based on simulations and experiments.The magnetic field lines of the magnetically shielded field have been made concave toward the anode and almost parallel to the channel wall.In this magnetic field configuration,the high potential and low electron temperature near the anode can be maintained at the wall by isothermal and equipotential magnetic field lines [17–19].The electric field parallel to the direction of the magnetic fieldE‖is negligible,and the electric field is almost perpendicular to the magnetic field.The potential near the wall is as high as the potential of the channel center.Moreover, the wall has a low electron temperature and low potential drop of the sheath, and the electric field along the wall being directed to the channel center effectively reduces the probability of ion bombardment on the wall [20].Compared with those of an unshielded magnetic field,the position of the maximum magnetic field strength and the ionization zone constrained by the magnetic field both move downstream, moving the acceleration zone further outside the channel.Because high-energy ions are produced outside the channel owing to the outward shift of the acceleration zone,wall erosion caused by high-energy ions can be avoided.It has been found that in a magnetically shielded Hall thruster, a wall profile that is parallel to the magnetic field lines can protect the wall from ion bombardment[21, 22].A chamfered wall in a 50 kW high-power magnetically shielded Hall thruster reduced the interaction intensity between the plasma and wall [23, 24], and the wall was protected from ion bombardment.The chamfered wall in a 1.35 kW magnetically shielded Hall thruster underwent almost no changes after an experiment [25].However, there are no institutional quantitative design references, and the knowledge regarding magnetic field line selection is insufficient.In this study, the matching characteristics of the magnetic field and wall chamfer were investigated by choosing different magnetic field lines, and the first quantitative design reference for the wall chamfer was obtained.

To ensure that the thruster can prevent the wall from sputtering, the electron temperature at the wall must be low and the wall cannot hinder the magnetic field lines.By studying the discharge characteristics of the thruster considering different matched walls, the change regularity in performance and the anti-sputtering effect with the change in magnetic field lines can be determined.Finally, a design reference for magnetic field line selection for wall profiles in magnetically shielded thrusters with high performance can be established.This will serve as a basis for the wall design of magnetically shielded Hall thrusters.

The remainder of this paper is organized as follows.Section 2 introduces the experimental methodology, and section 3 analyzes the change in the anti-sputtering effect and discharge characteristics under the wall profiles matching different magnetic field lines and the mechanism.The final section summarizes the paper.

2.Research methodology and schemes

2.1.Experimental design of matched wall profiles for antisputtering effect

For a magnetically shielded Hall thruster, when the magnetic field and the wall are matched, the wall does not hinder the magnetic field lines and is equipotential.The magnetic field lines graze the wall, and the intersection points of the magnetic field lines and wall are the start and end positions of the chamfer, as shown in figure 1.In this study, different matched wall profiles were designed according to the magnetic field lines.

A 1.35 kW magnetically shielded Hall thruster with inner and outer diameters of 70 mm and 100 mm,respectively,was independently developed by the Harbin Institute of Technology, as shown in figure 2.One inner and one outer magnetic coil were used for the magnetic field, providing satisfactory circumferential symmetry.The operation flow rate range of the thruster is 50–56 sccm,and the power ranges from 1.3 to 1.5 kW.The characteristics of the magnetic field can be expressed in detail using the FEMM two-dimensional axisymmetric finite element analysis software program.

To quantitatively and conveniently designate and distinguish the magnetic field line used to match the chamfered channel wall, the characteristic parameteris defined as

whereBcis the magnetic field strength at the intersection of the magnetic field line and the channel centerline,andBc,maxis the maximum magnetic field strength on the channel centerline.is dimensionless and describes the ratio of the magnetic field strength.Magnetic field lines withvalues of 36%, 28%, 20%, 12%, and 5% were selected using FEMM,as shown in figures 3(a) and (b), and the corresponding tangent wall profiles were designed and referred to as Cases 1,2,3,4,and 5,respectively.A straight channel,denoted as Case 0,was designed for comparison.A wall matched with a smallerhas a larger flow area and a larger chamfer.Table 1 lists the details of the chamfer size;the radial length represents the radial distance between the exit of the channel and the start of the chamfer, and θ is the angle between the chamfered wall and axial axis.

Table 1.Chamfer size specifications.

Table 2.Energy spectrum analysis results.

The discharge characteristics of the thruster were analyzed using different magnetic field lines under constant flow rate and constant power conditions.The wall states were observed, and the wall profiles were measured after approximately 17 h of ignition.The relationship between the deposition and erosion rates can be determined by comparing the wall colors before and after the experiment.Before the experiment, the inner and outer walls were the original white of the boron nitride ceramic.When the walls were black after the experiment,the erosion rate of the ions on the wall was negligible during discharge.These black deposits consist of various different products formed by discharging, including sputtering of the thruster shell and vacuum chamber, as well as evaporation of the insulation layer of the magnetic coil due to the high temperature.If the thruster discharges normally when the wall has black depositions, the life of the thruster can be significantly extended.When the wall was white after the experiment,the sputtering rate was non-negligible, and the white area was the sputtering zone.The existence of a sputtering zone indicates that the life of the thruster is threatened.

2.2.Experimental equipment

The experiments were performed at the Plasma Propulsion Laboratory of the Harbin Institute of Technology.The vacuum chamber has a size of ∅1.5 m×4 m and is evacuated by two oil-diffusion pumps, three mechanical booster pumps, and one rotary pump.The ultimate vacuum pressure reached 5×10−3Pa.When the thruster operated at a volume flow rate of 50 sccm,the vacuum pressure was below 5×10−3Pa.The uncertainty of the facility pressure was below 10%[26,27].The uncertainty of the gas flow controller was approximately 1%,and the purity of the propellant was 99.9995%.

The thrust (T) was measured using a three-wire torsion pendulum device [28], which was a spring–mass–damper system [29].The thruster was placed on a suspended pallet,and the mass of the counterweight was adjusted to level the pallet.The generated thrust rotated the pallet, causing the angle of the laser incident on the mirror to change.After the laser was reflected, the position on the scale moved.The propulsion produced by the thruster can be calibrated based on the laser displacement produced by the weight of the known mass as a reference.Based on the discharge current(Id), thrust (T), discharge voltage (Ud), and anode flow (ma.),the thruster anode efficiency (ηa) can be calculated as follows [30]:

A Faraday probe was used to measure the change in the ion beam current.The probe was mounted on a circular arc scanning rail, and the center of rotation coincided with the center of the thruster exit plane.The distance between the Faraday collector and center of rotation was 300 mm,the diameter of the collector was 9.5 mm, and the gap between the collector and the guard ring was 0.5 mm,which was less than 10 times the Debye length[31,32].Figure 4 shows the structure of the Faraday probe.Parallel capacitor and resistor connections were adopted to eliminate noise (R=1 kΩ,C=3 μF).

Figure 1.Matching of the magnetic field lines and wall.

Figure 2.1.35 kW magnetically shielded Hall thruster.

Figure 3.Selected magnetic field lines with different in (a) axial distribution and (b) planar distribution .

Figure 4.Structure of the Faraday probe.

Figure 5.Measurement of wall profile using CMM.

Figure 6.Diagram of the placement of tantalum sheet.

Figure 7.Inner channel walls after the experiments.

During the measurements, both collector and shield electrodes were provided with a bias voltage of −24 V.The total ion current (Ii) was calculated as

wherelis the distance between the probe and thruster center.

The plume divergence angle was obtained by determining the ion current density distribution (θj( )) in the plume area.With the center of the thruster as the center, the plume divergence half-angle (α) was calculated as follows:

The thruster wall profile measurement was commissioned by Harbin Ultra Precision Equipment Engineering and Technology Center Co., Ltd.The measurements were performed using a coordinate measuring machine (CMM) (Leitz, Germany), as shown in figure 5.The CMM model was a PMMCUtra12107.The contours of the four circumferential positions,i.e.0°, 90°, 180°, and 270°, at both the inner and outer walls were measured before and after the experiment (the circumferential azimuth of the cathode was defined as 0°).Then, the change in wall profile was determined by calculating the average difference between the values before and after the experiment.Unshielded Hall thrusters, such as the SPT-100, PPS1350, and H6US, have a minimum prophase erosion rate of 10 μm h−1[33], while those of magnetically shielded thrusters are 2–3 orders of magnitude lower; the H6MS and MSHT-600 have maximum erosion rates of 0.1 and 0.08 μm h−1, respectively[34].The measurement accuracy of the CMM is of the submicron order.To accurately determine the change in wall profile,the thruster was ignited for approximately 17 h in each case.

A tantalum sheet was used to collect the deposits during the experiment.The sheet was placed at the thruster exit plane,located outside the outer pole and radially from the channel centerline, as shown in figure 6.The deposition spectrum was analyzed using a high-resolution fully automatic field-emission scanning electron microscope (FE-SEMSU5000).

3.Experimental results and analysis

3.1.Anti-sputtering effects

By observing the wall color after a long ignition time under standard conditions (300 V, 50 sccm) in figure 7, we analyzed the thruster’s ability to protect the wall against ion sputtering.For Cases 4 and 5,it can be seen that when the walls match the magnetic field lines withvalues of 12% and 5%, black depositions appear on the chamfered walls, and the thruster is qualified with the anti-sputtering effect.With a reduction in chamfer area,part of the chamfer in Case 3 appears gray,and the anti-sputtering effect is poor.Prominent sputtering bands are observed on the straight section in the channels for Cases 1 and 2;this indicates that erosion could not be prevented.In addition,a 2–3 mm white sputtering band was observed in Case 0.

The energy spectrum analysis results for the depositions are presented in table 2.The weight percentage of C in the deposition was 62.81%.The main composition of the depositions indicates that the depositions are conductive.

The differences in the wall profile after the experiments were determined using the CMM, as shown in figure 8.For Cases 1 and 3,the relative change in the outer wall is only 1/3 of that in the inner wall,indicating that the outer wall has a better anti-sputtering effect; moreover, the outer wall in Case 5 is thickened after the experiment.The wall profile changes the most in Case 0;the erosion of the inner wall significantly decreases with increasing chamfer area.The prophase erosion rate for Case 0 reached 2.5 μm h−1.For the unshielded thruster, the erosion rate in the straight channel was greater than 10 μm h−1, which indicates that the application of the magnetically shielded magnetic field significantly reduced the wall erosion.The erosion of the inner wall in Case 5 was too small to be measured, the average difference in the profile near the exit was approximately 1.8 μm, and the prophase erosion rate was estimated to be 0.106 μm h−1, which is the same as the value determined by JPL.Figure 8 shows that the erosion in Case 0 continuously varied along the axial direction and that there was a dramatic change in erosion rate when the matched wall chamfer could not maintain the anode potential and low electron temperature.For the inner wall,drastic drops occurred near the beginning of the chamfer,indicating that the erosion was severe downstream at the beginning of the chamfer, as shown in figure 8.For Cases 1 and 3, substantial changes were observed at 23.6 mm and 22.8 mm, respectively.

Figure 8.Changes in profiles of (a) inner and (b) outer channel walls after the experiments.

Figure 9.Sketch of electron motion in the matching area of magnetic field and chamfered wall.

Figure 10.Atom density along the channel centerline.

When the chamfer area is reduced,although the matching magnetic field line strength is sufficient to restrain electrons(as indicated by the green line in figure 9), there exist magnetic field lines with lowervalues that can also restrain electrons, causing the field line with the lowerto be hindered by the wall(as indicated by the yellow line in figure 9).Electrons restrained by yellow lines tend to hit the chamfer directly.In this case, the wall potential is reduced, and the electron temperature increases with theof the line.The decrease in chamfer potential increases the energy that ion gained through acceleration from the anode to the chamfer.The wall potential with a reduced chamfer failed to repel high-energy ion bombardment at the wall.In addition,because the electrons confined by the magnetic field line hit the wall, an electronic current parallel to the magnetic direction was generated, which further led to ion movement toward the wall and weakened the anti-sputtering effect.From the foregoing analysis,we found that reducingenhances the anti-sputtering effect.In this experiment, the thruster met the requirement for protection against ion sputtering when the wall matched the magnetic field lines withvalues under 12%.

3.2.Discharge characteristics

The channel is the boundary of the discharge chamber, and the chamfer area has a significant effect on the gas flow and density distribution.In addition, the channel material affects electron conduction.High-energy ions are ejected from the channel exit, which develop the force.Furthermore, the chamfer significantly affects the strong interaction between the plasma and wall and determines the energy loss.For different matching cases,the potential distribution of the wall and its vicinity determines the beam utilization.In this study,the influences of the chamfer on the neutral gas distribution,electron conduction, interaction between ions and walls, and spatial potential were analyzed to elucidate the relationship between the chamfer and discharge characteristics.

The ratio of the mean free path of the xenon atom to the channel characteristic length in the Hall thruster is greater than 10, which satisfies the condition that the Knudsen coefficient exceeds 10.Therefore, the free molecular flow model can be used to simulate anode distribution [35].The atom density distributions of the channel centerline in the steady-state for the different cases are shown in figure 10.These distributions demonstrate that the area of the matched chamfer wall increases and that the atom density in the channel decreases with decreasingof the field line.The atomic density in Case 0 was much higher than that in the other cases.

The ionization process of atoms in the channel can be expressed as

wherenais the anode density,neis the electron density,σiis the ionization cross-section,veis the velocity of the electrons,and〈σive〉 is the mean ionization rate.Because the maximum magnetic field strength exists outside the channel in the magnetically shielded thruster, the ionization zone is at the channel exit,and the acceleration zone is outside the channel.As theof the field line decreases, a low atom density can reduce the ionization intensity.

3.2.1.Results under the constant power condition.Figure 11 shows the performance characteristics of the thruster under a constant power of 1.5 kW (300 V).In all cases apart from Case 0,the anode flow rate decreases with a decrease in theBˆ of the field line.Case 3 exhibits a clear advantage in terms of performance.

Figure 11.(a)Volume flow rate and thrust and(b)anode efficiency and specific impulse under different chamfered wall cases at a constant discharge power of 1.5 kW.

Figure 12.(a)Discharge current and thrust and(b)anode efficiency and specific impulse under different chamfered wall cases at a constant anode flow rate of 50 sccm.

Figure 13.Ion current density distribution under different chamfered wall cases.

Figure 14.Normalized plume divergence angle.

The flow rates in Cases 3 and 5 were 54 sccm and 52.5 sccm,respectively.Compared with that in Case 3,the flow rate in Case 5 decreased by approximately 2.8%;however, the thrust dropped from 97.2 to 91.4 mN,i.e.a reduction of 6.0%.The decrease in thrust is not proportional to the decrease in flow rate,and it can be inferred that the ionization intensity decreased from Case 3 to Case 5.Importantly, although the ionization intensity decreased, the flow rate declined continuously from Case 3 to Case 5 as well.This represents the deposition that accelerates the electron conduction to the anode and increases the electron current in the anode current in Case 5, which further contributes to the low current efficiency,low efficiency,and low specific impulse in Case 5.

The energy loss at the wall is another important factor affecting the performance of the thruster.Case 0 is a straight channel, which has the highest atom density in the channel but stops the ions from scattering at the channel exit and causes energy loss.Therefore, the thrust and efficiency in Case 0 are 2.5% and 3.6% less than those in Case 1,respectively.

The flow rate decreased by 2.7% from Case 1 to Case 3,whereas the thrust increased by 5.4%.The reduction in energy loss significantly improves performance and increases propellant utilization, contributing to the improvement in performance in Case 3.

3.2.2.Results under the constant flow rate condition.Further experiments were performed at a constant flow rate of 50 sccm.The discharge voltage was 300 V.As shown in figure 12,the current increased gradually with decreasingof the field line (except for Case 0), while the thrust first increased and subsequently decreased.Case 4 had a high specific impulse, and Case 3 exhibited a high efficiency.Therefore, high performance is achieved when the wall matches the magnetic field lines with aof 12%–20%.

Compared with those in Case 1, the discharge current in Case 0 was 4.8%higher,while the thrust was approximately 1%lower.Because many ions are lost at the wall,the low propellant utilization contributes to the low thrust in Case 0;this is because the energy loss at the wall is relative to the anti-sputtering effect,and Case 0 cannot prevent ions from sputtering.From Case 1 to Case 3, the discharge current changed from 4.15 to 4.32 A,an increase of 4%; however, the thrust increased from 80.4 to 87.53 mN, i.e.by 8.9%, indicating that the ions lost at the wall in Case 1 form the thrust in Cases 2 and 3.As theBˆof the magnetic field lines decreases from Case 0 to Case 5,the energy loss gradually decreases.Therefore, the wall can protect itself from ion sputtering when it matches the magnetic field lines with a lowB,ˆ which is consistent with the results in section 3.1.

The discharge current continues to increase from Case 1 to Case 5.Since the depositions are conductive,the electrons accelerated by the depositions maintain a high discharge current.The discharge current increases by 2.9%from Case 3 to Case 4, whereas the thrust in Case 4 is only 0.3% higher than that in Case 3;we can infer from the experimental results that the increase in the electron current contributes to the increase in the discharge current and that the decrease in energy loss contributes to the increase in thrust.The rising gradient in the discharge current from Case 4 to Case 5 is lower than that from Case 3 to Case 4.Because the depositions in Case 4 are sufficiently firm to reduce the surface resistance, the increased deposition in Case 5 cannot significantly increase the discharge current, and the electron loss at the wall reduces the ionization intensity in Case 5;this causes the thrust to decrease in Case 5.

A Faraday probe can be used to obtain the ion current and beam profile in different cases under constant flow rate conditions,as shown in figure 13.Case 3 has the highest peak ion current density, and the ion current obtained using the integral along the curve is 4.3 A.The ion current in Case 5 decreased by 2.33% compared with that in Case 3, which is consistent with the regularity of the thrust shown in figure 12.The thrust decreased by 2.58% from Case 3 to Case 5.The decrease in the ion current from Case 3 to Case 5 is attributed to the decrease in atom density (approximately 5%, as seen from figure 10) and the shortened electron resident time(approximately 10%, represented by the increase in electron current).The decrease in the current efficiency explains the decrease in performance.The ion current increased by 10.2%from Case 0 to Case 3, while the thrust increased by 9.8%;this is attributed to the reduced ion loss at the wall as the high potential wall repels the ion bombardment.

After further calculation, the divergence angle of the plume was obtained, as shown in figure 14.The divergence angle first exhibits a steep drop and then a slight rise.Because of the outward shifts of the magnetic field, the acceleration zone is located outside the channel, and the flow area of the channel exit determines the plume divergence.When the wall chamfer is large,as in Cases 4 and 5,it is difficult for the wall to restrain the beam from diverging, and the ions accelerate outward at the large flow area; thus, the plume is divergent.With a decrease in chamfer area,the radial divergence of ions is hindered by the high potential wall, and the plume divergence is slightly reduced, as in Case 3.However, when the chamfer area is further reduced, the magnetic field lines are interrupted by the wall, and the wall can no longer maintain a high potential and low electron temperature.The electric field is parallel to the local magnetic field, and the ions acquire radial acceleration near the wall and significantly diverge along the radial direction in Cases 0, 1, and 2.Thus,the large loss of energy and large plume divergence result in poor performance, as shown in figure 12.Accordingly, the thrust and efficiency are low in Cases 0, 1, and 2.

4.Conclusion

An experimental study was performed to quantitatively select the magnetic field line to match the chamfered channel wall tangentially in a magnetically shielded Hall thruster.For this purpose, a dimensionless characteristic parameterwas defined,i.e.the ratio of the field strength at the intersection of the selected magnetic field line and channel centerline to the maximum magnetic field strength along the centerline.

A reduction inbrings the selected magnetic field line closer to the anode; consequently, the channel wall is better protected from ion sputtering.However, more deposition accumulates on the wall surface, degrading the wall insulation; thus, electron cross-field transport is enhanced through the wall,and the current efficiency deteriorates.In addition,asdecreases,the chamfered area of the channel wall increases.On one hand,the atom density in the channel decreases, and the ionization intensity declines;conversely,the wall energy loss caused by the ion bombardment is reduced.Considering these effects, it is inferred that asdecreases in the range of 20%–36%, the reduction in the wall energy loss is the primary factor controlling the change in thruster performance.Asdecreases further below 12%, the decline in both the current efficiency and ionization intensity governs the change in thruster performance.As a result, the thruster performance first increases and then decreases asdecreases.

To quantitatively achieve high performance, the selected magnetic field line should have aof 12%–20%.Moreover,to ensure a satisfactory anti-sputtering effect at the wall, the selected magnetic field line should have aof less than 12%.

Acknowledgments

This work was funded by National Natural Science Foundation of China (Nos.52076054 and 51736003), Civil Aerospace Technology Pre-research Project (No.D03015), and Defense Industrial Technology Development Program (No.JCKY2019603B005).