Hall effect thrusters operating at power levels in excess of several hundreds of kilowatts have been identified as enabling technologies for applications such as lunar tugs, large satellite orbital transfer vehicles, and solar system exploration. These large thrusters introduce significant testing challenges due to the propellant flow rate exceeding the pumping speed available in most laboratories. Even with proposed upgrades in mind, the likelihood that multiple vacuum facilities will exist in the near future to allow long duration testing of high-power Hall thrusters operating at power levels in excess of 100 kW remains extremely low. In this article, we numerically explore the feasibility of testing Hall thrusters in a quasi-steady mode defined by pulsing the mass flow rate between a nominal and a low value. Our simulations indicate that sub-second durations available before the chamber reaches critical pressure are sufficiently long to achieve the steady-state current and flow field distributions, allowing us to characterize thruster performance and the near plume region.
Hall effect thrusters (HETs) are spacecraft electric propulsion (EP) devices routinely used for orbit raising, repositioning, and solar system exploration applications. To date, the highest power Hall thruster flown is the 4.5 kW BPT-4000 launched in 2010 aboard the Advanced EHF satellite1 (which the HET helped to deliver to the correct orbit after a failure of the primary chemical booster), although a 13 kW system is being readied for near-term flight operation as part of the Lunar Gateway,2 and thrusters at 503,4–100 kWs power levels have been demonstrated in the laboratory. Solar cell advancements and a renewed interest in nuclear power has led the aerospace community to consider the use of Hall thrusters operating at even higher power levels. Multi-hundred kW EP systems would offer an economical solution for LEO to GEO orbit raising or for deployment of a Earth-to-Moon delivery tug, and power levels in excess of 600 kW could be utilized for crewed transport to Mars.5–9 While such power levels could be delivered using existing devices, a single large thruster requires less system mass and has a reduced footprint than a cluster of smaller devices.10
At these high power levels, it becomes difficult, if not outright impossible, for vacuum chamber pumps to keep up with the propellant mass injection rates. Numerous experiments have found Hall thruster performance to be influenced by the ground facility effects. While the vacuum chamber also introduces new electrical current pathways,11,12 the primary contributing factor is the chamber pressure. Thrust is observed to vary almost linearly with increasing background pressure, suggesting that a return flux of wall-neutralized beam ions acts as an additional propellant source.13 For the NASA 173M thruster (operating in the power range of 1.5–4.0 kW), thrust was observed to vary by about 3% over the typical pressure ranges encountered in ground testing,14 while for other models, variations approaching 10% have been reported. The background pressure also affects beam divergence15 and cathode coupling, especially with non-centrally mounted cathodes,16 leading to the acceleration zone moving upstream,7 and thus altering the voltage drop through which the propellant is accelerated. The frequency of discharge oscillations is also affected, although this response does not seem to be universal. In the Princeton cylindrical HET (operating in the range of 50–300 W), breathing mode frequency and amplitude remained mainly constant until about Torr after which they disappeared.17 Note that we utilize the non-SI unit of Torr (1 Torr 133.32 Pa; Torr Pa) due to its prevalence in the field of electric propulsion vacuum testing. The rotating spoke increased in frequency until this pressure after which it also disappeared. Matlock et al.18 considered pressure effects in a different 1 kW PPPL thruster and found it to exhibit a strong frequency dependence on background pressure for both the anode current or cathode potential waveforms. Overall, these varied ground facility impacts, including sometimes conflicting results, call into question whether ground testing properly simulates in-space operation and highlight the fact that the challenge will become much harder as thruster power increases.
The early work on pressure effects of Randolph et al. has suggested that HETs should be tested below Torr.19 However, even this level may not be sufficiently conservative, given that thrust is observed to continue decreasing further as the pressure is lowered without an apparent asymptotic plateau.20 In fact, the SPT-100 thruster was found to be the most sensitive to variations at Torr.21 Yet, a recent survey of international facilities found that the vast majority of existing chambers are simply unable to maintain pressures in the Torr range when used with 100 kW devices.10,22 To the best of our knowledge, there are no facilities anywhere that can maintain this pressure with a 1 MW Hall thruster. Some facilities may be able to run a pod of 100 kW thrusters, but the thrusters must be in a close proximity leading to a large number of unknowns in the plume-to-plume interaction. Clearly, such a limited testing capacity drastically limits the development of high-power devices by placing research well beyond the capabilities of university and small business programs. In fact, testing of the 100 kW Nested Hall thruster (NHT) at University of Michigan had to be reduced to only a partial operation at 30 kW due to facility limitations,7 despite access to one of the largest academic electric propulsion testing facilities in the United States. The full scale testing had to be delayed until Vacuum Facility 5 (VF-5) at the NASA Glenn Research Center became available. This chamber, measuring 15 ft in diameter and 60 ft in length, recently underwent an extensive simulation-driven retrofit23,24 to help achieve its theoretical maximum pumping speed of l/s on air thanks to 6 cryopumps and 20 oil diffusion pumps. The facility at the Aerospace Corporation also recently underwent a redesign to increase pumping capabilities in support of anticipated future high-power EP testing campaign.25 Yet even this second high-power facility is not expected to be sufficient given the rapid increase in the use of EP. The facilities can be envisioned to be occupied by months-long wear testing campaigns,26 adversely affecting the development of new devices.
To address the pressure effect issues, some researchers have considered the use of metal or liquid propellants that condense on the facility walls.27 Such propellants pose contamination risk to spacecraft and thus may be of limited practical use. In this article, we carry out a numerical study to assess the feasibility of an alternate scheme based on a quasi-steady pulsed operation. In order to reduce start-up transients, we assume that all thruster operating conditions, including the magnet current and cathode–anode coupling potential, remain in the nominal configuration. The only variation is the reduction in the anode propellant flow rate by two orders of magnitude to allow the chamber pressure to decay. The reduced mass flow is utilized in order to maintain a low density discharge to aid with reignition. It should be noted that this is not a completely novel idea. The quasi-steady pulsed approach has been utilized for decades at Princeton University28,29 and at NASA Glenn VF-1 and VF-5 facilities,30 as an economical option for VASIMR and MW-class MPD thruster research and testing. Pulsed mode has also been suggested for on-orbit operation to deliver fine propulsive bits.31,32 We utilize the industry standard HET simulation code HPHall33 to perform a series of simulations based on the 1.35 kW SPT-100 thruster placed in a scaled down chamber with a limited pumping capacity. This route was selected after an initial effort of scaling up the SPT-100 simulation to a MW class proved challenging. We begin the article by reviewing a 0D model for estimating chamber pressure variation. Subsequently, we describing the modifications made to HPHall and present results from the numerical study.
II. CYCLED OPERATION
From mass conservation, the temporal evolution of chamber pressure is governed by the balance between the injected and the removed mass, with the latter typically specified in terms of pumping speed. This volumetric quantity is related to the mass flow through the gas mass density. Here we neglect transient effects such as the flash-off of surface-adhered water on initial activation or the decay in composite outgassing rates and simply assume a constant baseline pressure. We also ignore the transit time associated with the finite molecular speed (which for xenon is approximately 220 m/s at room temperature) and treat the pumping speed as a constant with respect to chamber pressure. We also ignore finite conductance reduction introduced by the geometrical configuration of the chamber. From the ideal gas law at constant temperature, we have
Considering the entire vacuum chamber as a single control volume, mass conservation yields
The rate of mass removal is given by , where is the pumping speed. Power of an EP device can be related to the mass flow rate with
where is the efficiency, is the discharge voltage, is the injected mass flow rate, is the mean ion ionization state, is the elementary charge, and is the working gas atomic mass. Numerical integration of Eq. (1) with dimensions of the University of Michigan Large Vacuum Facility and pumping speed of 240 000 l/s on xenons leads to the plot in Fig. 1. This facility was chosen as an example of a large chamber that may be available at university settings. Here we used , V, and . We also considered four different power levels ranging from 1 kW to 1 MW and set the baseline pressure to Torr. The thruster was assumed to operate for 30 s in the nominal mode. The injection flow rate is then reduced by a factor of 100. This low-flow mode is envisioned to help maintain a low-density plasma population to aid with reignition. The mass flow rate is subsequently returned to the nominal level to demonstrate repeatability.
In all configurations, we observe the chamber pressure first rising rapidly but then stabilizing within approximately 15 s. Next, we also observe a decrease in pressure once the flow rate is reduced, with the chamber stabilizing at a new baseline within 30 s. It should be noted that in the real chamber, both of these time periods would be extended by the molecular transit time and non-constant pumping speeds, which are here ignored. Switching back to the nominal flow rate returns the pressure to the level observed on the first cycle. This sequence can be repeated for as long as needed, with occasional breaks for cryopanel regeneration.
For the 1 and 10 kW thrusters, the pressure remains below Torr level at all times, thus confirming the experimental heritage of using similar facilities for testing at these power levels. At 100 kW and 1 MW, this threshold is breached after 1.08 and 0.050 s, respectively. The initial pressure rise, before the Torr level is reached, may thus be used to obtain performance data free from facility pressure effects. While these time periods may appear short, they are sufficiently long in the frame of reference of Hall thruster dynamics. Even the 50 ms interval corresponds to 750 breathing mode cycles at a 15 kHz frequency. As demonstrated by Sekerak and Lobbia, modern high speed plasma probes can resolve plume properties at 5 s intervals,34,35 offering us 10 000 unique measurements within this window. The actuation of probes to the next sampling location would be done during the low-flow cycle, and thus, the cycled operation should have a minimal impact on the total duration of a plume mapping campaign. Fast electromagnetic valves with delay times shorter than 40 s and a 160 s pulse full width at half maximum have been developed in support of pulsed inductive plasma thrusters as reported by Guo.36 These valves were demonstrated to deliver up to 2.5 mg of argon gas per pulse, which translates to mass flow rates in excess of those required even for a 1 MW class Hall thruster.
A significant unknown is a quantification of the start-up behavior during a pulsed operation. Hall thrusters are known to exhibit a current spike when they are first operated after a chamber pump down. Despite the limited available literature, it does not appear that this spike is present on subsequent restarts. For example, while Hargus37 found the initial anode current transient to last for 300–500 s, this behavior was not observed on subsequent restarts after the thruster had been conditioned. The current transient would reappear after the chamber has been opened to the atmosphere or after cryopanels have been regenerated, which exposed the thruster to a “dirty” vacuum, characterized by the presence of water vapor and volatile gases. A typical regeneration cycle involves valving off the cryopump from the chamber and utilizing a downstream rough vacuum pump to remove the material evaporated from the warmed up panels. An oil-based pump could introduce volatile contaminant gases into the pump cavity, which can subsequently diffuse into the main chamber upon the completion of the regen cycle. It is also well known that a thin film of water forms on surfaces (and inside porous materials) exposed to atmosphere and boils off upon exposure to vacuum. Surface water concentration is also increased by the ambient air reaching dew point during pump down as the temperature decreases with the pressure. A subsequent study utilized a residual gas analyzer (RGA) and indeed found that hydrogen emission profiles follow the anode spike closely, further reinforcing the hypothesis that the excess anode current during the start transient is due to water vapor release38 and, as such, should not reappear during pulsing. Another experimental study by Santos39 looked at the startup process using a Princeton thruster and found that the transitional regime is characterized by a 20% increase in the discharge current for 15–30 min. This study correlated the presence of gas impurities such as water, hydrogen, or nitrogen with the increase in discharge current. The porous boron nitride used to line channel walls was identified as one possible source of the contaminants.
Therefore, once the thruster is conditioned and contaminants have been depleted, we can expect the ignition to be governed by the fluid and electrodynamic transient times. Fast camera imaging has demonstrated that Hall thrusters settle into steady-state operation with about 50 s.40,41 This is further evidenced by ignition videos that demonstrate an essentially instantaneous steady plume formation.42,43 Busek analytical and experimental study demonstrated that for the BHT-200 thruster, the startup electrical transients decay within 0.06 ms and the peak discharge current is reached within 0.2 ms. The time required to fill the discharge channel with neutrals was around 10 ms. The longest identified transient effect was associated with the diffusion of the magnetic field throughout the discharge, which was observed to take about 20 ms. This effect may not be relevant to our proposed quasi-steady testing approach given that the discharge is never completely shut off. Based on this analysis and experimental observations, the authors estimated the minimum pulse required to achieve 80% of the steady-state performance to be between 30 and 50 ms.31 This is comparable to the pressure rise time for the 1 MW thruster as seen in Fig. 1.
III. NUMERICAL SIMULATIONS
We next used the popular Hall thruster modeling tool HPHall to simulate a thruster operating in the quasi-steady mode. This code was originally developed by Fife at MIT33 and has since been upgraded by a number of other researchers.44–47 HPHall uses simulation particles to represent the heavy neutral and ion species using the Particle-in-Cell (PIC) method. The electron population is treated as a fluid with motion decoupled into the direction parallel and perpendicular to the magnetic field lines. Electrons are free to move along a field line, allowing one to write a relationship relating the local potential to a reference “thermalized” potential and the local density, . In the perpendicular direction, current balance is used to derive an expression for the variation of with the magnetic field line temperature, . HPHall is thus predominantly an electron temperature solver for the following form of the energy equation:
where and are energy sources due to Ohmic heating and inelastic losses associated with ionization and the is the velocity term obtained from Ohm’s law. The computed temperature is used to set and the corresponding 2D potential that is then used in the PIC method to set the electric field that accelerates the ions. Electron temperature is also used to compute the ionization rate. HPHall has been applied to numerous thrusters; however, the Russian-developed SPT-100 is regularly used for benchmarking due to a ready availability of the magnetic field. In this work, we have utilized the same simulation inputs as in a prior work focusing on electrical coupling.48 The nominal mass flow rate was set to kg/s. Simulation time step was set to s, with the code run for up to time steps. The cathode line serves as a Dirichlet boundary for the electron energy solver and was set to eV throughout the simulation. We also assumed that the power supply maintains a 300 V discharge voltage with cathode to ground coupling potential held at . It is feasible that cathode properties will be affected by the variation in plume density during the low-flow mode, but this quantification remains as future work.
A. Chamber neutral injection model
Fife’s legacy HPHall allowed setting a scalar background density that was added to the spatially varying value computed from the particles. Parra subsequently introduced the ability to use the downstream boundary as an injection source of constant flux neutral particles. This kinetic approach allowed approximating the backstreaming found in a vacuum facility. The flux for each “panel” (a radially revolved cell edge) is computed from
The code loops over the downstream panels and on each generates a user-specified number of neutral macroparticles with simulation weight set according to the injection flux and the revolved panel area. The neutral velocity is set to and an isotropic velocity is sampled such that , where is the panel normal vector pointing into the computational domain.
This algorithm was modified to dynamically update the chamber pressure used in Eq. (5) according to the provided chamber volume and pumping speed. Pump mass collection rate is first computed per , where assumes uniform pressure distribution and is the molecular mass of the ion species. The pressure rate of change is then computed per Eq. (1), with obtained from
We also add the option to include a fixed term to model the constant rate of pressure increase effects. The chamber pressure is updated with the Forward Euler method, . The relevant facility properties are specified in the input parm.in file.
B. Quasi-steady simulations
HPHall was also modified to support a quasi-steady mode operation. The injection mass flow rate is one of the many parameters listed in the input file. In addition to this value, we now also load values for , and and . These intervals, if specified, turn on the quasi-steady operation in which the thruster alternates between the nominal and the low mass flow rate modes. The transition was assumed to be instantaneous.
IV. SIMULATION RESULTS
A. Nominal operation
Figure 2 plots the temporal evolution of the simulated discharge current, thrust, and power () from a nominal operation with constant background pressure and time-invariant propellant flow rate. The simulation was started by first running in a neutrals-only mode to fill the discharge channel with the neutral propellant. The code was then restarted in the normal mode, which would be analogous to turning on the power supply to force ignition. The plot shows data only from this “normal” mode run. Despite not directly modeling outgassing or magnetic field ramp up, it is interesting to observe that the numerical simulation predicts a current spike similar to experimental observations. The discharge stabilizes within 0.05 ms, in agreement with the electrical transient measurements reported in Ref. 31 and fast camera imaging in Ref. 39. The magnetic field is applied externally, and as such, this simulation would not capture any transient effects associated with energization of the magnetic circuits. The thruster subsequently establishes the oscillatory steady state with total power averaging around the expected 1.35 kW level.
The time evolution of the discharge current can be further analyzed by plotting spectrogram of the power spectrum, as shown in Fig. 3. These plots were created with a Python script that parses the HPHall output log file and uses the built-in FFT routines to compute the spectrum along a sliding window covering 5000 time steps. The contour values correspond to . Time increases from the bottom to the top. The initial current spike can be seen along the bottom edge as higher power across a wideband of frequencies. The thruster quickly achieves an oscillatory steady state with dominant modes at 15 and 90 kHz.
B. Uniform pressure increase
Next, we considered the response of the simulated thruster to a variation in chamber pressure. The goal of this study was to verify that the background neutral injection model described in Sec. III A does indeed affect the thruster behavior. Here we utilized the constant model, with pressure increasing linearly from Torr. We ran several simulations with the pressure rate of increase ranging from Torr/s to upward of Torr/s. The plot in Fig. 4 corresponds to this latter rate, while the inset illustrates the increase at a slower Torr/s. The slower rate of increase allowed us to capture additional detail in the numerical results, since data are exported at a fixed time step frequency. The plot shown in the inset thus effectively increases the detail in the main figure over the selected pressure range.
A pressure response is clearly visible in the inset plot of Fig. 4. High-frequency modes become quenched as the pressure grows, and at approximately Torr, only the primary breathing mode remains, along with a broad signal extending to 200 kHz. The amplitude of the breathing mode grows with an increase in pressure, along with a new 100 kHz mode that appears at approximately Torr. These modes continue growing in amplitude as the ambient neutrals provide the thruster with an additional source of propellant. In a real device, this growth in discharge oscillations would likely lead to testing difficulties and an eventual thruster failure.
Figure 5(a) zooms further on the power spectrum variation at the start of the simulation by considering a run with Torr/s. We can clearly observe a nearly linear drift of the dominant frequencies as the pressure increases, with the drift rate increasing at higher frequencies. Interestingly, a similar drift in the frequency space was observed experimentally by Hargus et al.37 utilizing a different thruster, Fig. 5(b). It was speculated to correspond to a pressure increase from outgassing. Since the outgassing rate is proportional to surface temperature, it is reasonable to expect the contaminant pressure to increase as the thruster warms up. Our forced pressure increase can be expected to have a similar effect on the thruster behavior.
C. Quasi-steady operation
The original goal of this work was to scale the SPT-100 thruster simulation to the >100 kW range following the scaling model of Misuri.49 However, challenges were encountered along the way, possibly involving a need to increase the computational mesh refinement while no longer having access to the mesh generator. Instead, we simulate the baseline 1.35 kW SPT-100 operating in a small chamber of a reduced pumping speed. Equation (6) indicates that pumping speed and chamber volume can be scaled by the factor to retain the pressure increase of a thruster operating at kW power. Using this ratio, the pressure increase of the 1.35 kW device can be made comparable to a high-power thruster operating in a larger chamber. The simulation was scaled to approximate a 1 MW class device operating in the same facility used in Fig. 1. Flow control was adjusted to consist of a 40 ms nominal operation followed by a 20 ms low flow case, in which the mass flow rate was reduced by a factor of 10. Given that HPHall is not parallelized, it takes the code almost a day to simulate just 0.01 s of real time, and the pulse sequence described here required almost 3 weeks of run time. In the experimental testing, the pulse duration would be selected based on the rate of pressure increase for a given chamber and pump configuration. For the conditions described in Fig. 1, the pulse duration could be extended to over 1 s for a 100 kW class device.
Figure 6 plots the frequency spectrum from the quasi-steady operation. Good agreement can be seen by comparison with Fig. 3. We do not observe any noticeable impact of the background pressure on the power spectrum. This finding is expected, since each pulse terminated before the facility pressure had a chance to increase above Torr. The corresponding thrust, discharge current, power, and chamber pressure are shown in Fig. 7. We can observe an excellent repeatability between cycles and with the steady-state nominal operation in Fig. 2. The gaps can be easily removed in post-processing, leaving us with a continuous trace of discharge current. Near-plume plasma potential and current density measurements can be used to estimate thrust if a thrust stand settling time proves to be incompatible with the pulse duration.50 Characterization of repeatability in the laboratory setting is planned as future work.
The variation in the mesh-averaged simulation results computed by HPHall for the nominal and low flow cycles is shown in Fig. 8. We can see that in the low flow mode phase, the potential profile corresponds to an almost linearly decaying drop from the anode to the cathode potential. In the nominal mode, Fig. 8(a), the acceleration zone is pushed outward. Plots 8(c) and 8(d) compare the neutral density. While the density in the channel decreases in the low flow mode, as expected, the neutral density downstream of the exit plane is actually increased in this mode due to the reduced loss of neutrals to ionization. The final set of plots compares the electron density, which per quasineutrality balances the total ion charge density. It is reduced by almost 3 orders of magnitude.
V. LIFETIME TESTING AND SECONDARY EFFECTS
While quasi-steady operation appears to be an attractive method for characterizing performance and plume characteristics of high-power Hall thrusters using facilities with limited pumping. However, the major challenge remains in lifetime testing. Utilizing the simple model visualized in Fig. 1, the chamber requires approximately 40 s to reduce the pressure to the baseline following each pulse. Assuming a 1 s measurement time available at 100 kW, this difference between testing and pump down times implies a 40 increase in lifetime testing time line. This time line could be decreased by delegating aspects of lifetime characterization to the numerical analysis and using acceleration techniques such as a careful removal of the discharge channel material following the predicted erosion pattern.
Furthermore, there is some evidence of second-order hardware temperature effects influencing HET performance and lifetime. One way to incorporate these effects is to operate a high-power thruster for a period of hours at a poor facility pressure until the hardware temperature reaches the steady state. The thruster performance and lifetime measurements would be uncertain for this phase, but the hardware temperature distribution should not be strongly affected by the background pressure if the desired power level is maintained.
The anode flow would then be reduced to reduce the chamber pressure, while maintaining the cathode flow to keep the cathode hot. If the thruster cools slowly and nearly maintains its steady-state temperature distribution, this approach will allow us to reproduce a near-steady-state temperature profile, a good space-like vacuum, and critical thruster and plume measurements with correct distributions.
While having been identified as enabling technologies for a range of new space missions, the development of high-power Hall thruster remains hindered by the low number of facilities available for testing in the 100 kW range and no facilities for testing at MW power levels. In this article, we identified a testing approach for high power Hall thrusters based on quasi-steady pulsed operation. We propose to run the device in a series of pulses during which the propellant flow rate is cycled between the nominal and a reduced value to allow the chamber pressure to recover. The thruster remains powered in the low flow mode to reduce electrical transient effects encountered with restarts. We utilize a numerical simulation to demonstrate that the pulsed operation is able to reproduce characteristic properties such as the discharge current spectrum in the time interval until the chamber pressure exceeds a critical background pressure. We also visualized the predicted near plume plasma profiles for the nominal and low configuration and discussed implications for lifetime testing.
This research was partially funded through AFOSR Grant No. FA9550-19-1-0166.
The data that support the findings of this study are available from the corresponding author on request. Scripts used for generation of plots of pressure evolution (Fig. 1), HPHall performance metrics (Fig. 2), and frequency spectrum (Fig. 3 and similar) are available in Quasi Steady-State Testing Approach for Hall Thrusters at https://www.particleincell.com/2021/qs-het, Ref. 51.
VII. AUTHOR DECLARATIONS
A. Conflict of Interest
The authors have no conflicts to disclose.