Hall Thruster Research Articles

Generation of multiply charged ions in accordance with geometry and magnetic field in Hall thruster plasmas

The production of multiply charged ions in Hall effect plasmas has been investigated. The factors that significantly affect plasma characteristics, such as geometry, magnetic field configuration, and magnetic mirror ratio, were analyzed. Among the co-current and counter-current configurations of a cylindrical Hall thruster (CHT) and an annular Hall thruster (AHT), the co-current configuration of the CHT shows the largest fractions of multiply charged ions. In particular, for the CHT, the region with high magnetic flux density had a significant influence on the fraction of multiply charged ions, but the fraction of multiply charged ions was not significantly different depending on magnetic mirror ratios. In addition, the configuration having a similar magnetic field in the CHT demonstrated comparable fractions of multiply charged ions and thrust even with different channel lengths. Hence, the broad region with the high magnetic flux density could enhance the probability of further ionization inside the discharge channel.

Experimental and numerical studies of low power Hall thruster performance

The low power Hall thruster has the potential to be applied in multiple apace missions. In order to study the performance of the low power Hall thruster, a 200W-class Hall thruster is designed and manufactured. The plasma properties in the discharge channel are investigated via numerical simulation. The ionic composition and ion current density are respectively measured by a Wien filter and a Faraday probe. The generated thrust is measured by a thrust target. The simulation results show that the maximal ion number density is more than 1×1018 m-3. The ionization and acceleration regions are located in the midstream and downstream of the discharge channel. The experimental results reveal that thrust, anode specific impulse and anode efficiency are 12.13 mN, 1380 s, and 41% at 200 W. The ion current density decreases along the radial direction. According to the results of simulation and experiment, the thruster is reasonable and feasible. Our research provides a reference for the design of low power Hall thruster. Structural optimization and performance improvement will be carried out further.

Challenges with the self-consistent implementation of closure models for anomalous electron transport in fluid simulations of Hall thrusters

The performance of closure models for the anomalous electron transport when self-consistently implemented in a fluid model for a Hall effect thruster is investigated. This cross-field transport, which is orders of magnitude higher than classical collisional transport, is represented as an effective collision frequency. The proposed closure models relate this transport coefficient to local fluid properties of the plasma. Before implementation, the models are calibrated against values of the collision frequency inferred empirically from a 9 kW Hall thruster at 300 V and 15 A. It is found that even though closure models match the empirical collision frequency values, they diverge from these values when implemented self-consistently in a Hall thruster code. Possible drivers of this behavior are examined, including the role of non-linearity in the governing equations of the Hall thruster fluid model, artifacts from using time-averaged calibration data, and the non-uniqueness of the empirically-inferred collision frequencies. These results are discussed in the context of their implications for discovering and validating new closures necessary for enabling fully-predictive Hall thruster models.

Influence of the axial oscillations on the electron cyclotron drift instability and electron transport in Hall thrusters

A 2D-3V finite-element particle-in-cell model, which is applied to simulate the radial-azimuthal plane near the exit of Hall thrusters, has been presented to investigate the influence of axial oscillation on electron cyclotron drift instability (ECDI) and anomalous cross field electron transports. The simplified theoretical analysis about the ECDI and the anomalous electron transport has been introduced. The uniform and harmonic axial electric fields, which are based on the typical axial oscillations in Hall thrusters, have been considered in the simulations. It is concluded that different constant axial electric fields can influence the properties of instability but cannot significantly change the cross field electron mobility. However, the axial oscillation plays a significant role in the instability, and the electron transports provided that appropriate amplitudes and frequencies are achieved. The equilibrium of the instability is destroyed and reformed with the axial oscillation. The cross field electron transports are enhanced in the range of low amplitudes and frequencies and are suppressed when they are in a high value. In addition, it is observed that the variation of the electron mobility and electron–ion friction force show high consistency with the trend of electron temperature. It is further confirmed that the increase in electron temperature takes responsibility for the enhanced cross field electron transport due to the axial oscillation.

Specific Features of Transient Processes in Stationary Plasma Thrusters and a Device for Their Simulation

Specific Features of Transient Processes in Stationary Plasma Thrusters and a Device for Their Simulation

Collisionless dissipation at the boundary sheath of magnetized low temperature plasmas

In partially magnetized technological plasmas like magnetron discharges or Hall-effect thrusters, the interaction of gyrating electrons with the plasma boundary sheath plays an important role. This study shows that the interaction can be described as a dissipative process. It is assumed that the Debye length is much smaller than the electron gyroradius , and in turn much smaller than the mean free path λ and the field gradient length l. Focusing on the scale of the gyroradius, the sheath is assumed as thin (), collisions are neglected (), the magnetic field is taken as homogeneous, and electric fields (= potential gradients) in the bulk are neglected (). The interaction of an electron with the electric field of the plasma boundary sheath is represented by specular reflection, , where v is the electron velocity and n is the sheath normal. A previous study showed that this set-up leads to a scattering process where gyrophase invariant incoming velocity distributions are scattered into outgoing distributions with fractal dependence on the gyrophase (Krüger and Brinkmann 2017 Plasma Sources Sci. Technol. 26 115009). The present research focuses on the subsequent evolution. It is shown that the gyromotion results in fast phase mixing with respect to the gyrophase which quickly restores the gyrophase invariance. In combination, the two phases of the sheath interaction constitute a mapping within the space of gyrophase invariant distributions. This combined process is dissipative and leads to isotropization. As an explicit comparison shows, it acts similarly to elastic electron-neutral collisions and can even dominate the latter in low pressure plasmas. A simplified version of the operator that applies for weakly anisotropic distributions is suited for practical simulation work.

On inward deflection of excitation magnetic field in a Hall thruster operating at high discharge voltage

The inward deflection of the excitation magnetic field was found in a Hall thruster voltage-varying experiment. The influence of Hall current magnitude and radial distribution on the total magnetic field was analyzed through magnetic field simulations. The probable reason why the excitation magnetic field deflected inward evidently at high discharge voltages (＞600 V) was obtained by combining the simulation results and theoretical analysis. This study provides qualitative guidance on the design of the excitation magnetic field in high-specific-impulse Hall thrusters.

A theoretical thrust density limit for Hall thrusters

Hall Thrusters typically operate at thrust densities on the order of 10 N/m^2, which appear to be orders of magnitude below the thrust density limits suggested in previous literature. These limits have been considered here and each component of thrust density is analyzed to demonstrate the relative contribution to the total thrust density. Dependencies of the thrust density limits upon the thruster geometry, electron mobility, and the applied magnetic field are revealed and compared with experimental measurements of thrust density. This analysis reveals that with conventional applied magnetic field strengths, Hall thruster thrust density appears to be on the order of 1000 N/m^2. It is shown that this limit can be further increased through higher applied magnetic fields, applied voltage, and suppression of anomalous electron transport. This suggests Hall thrusters can be made much more compact and operated at higher power densities, given improvements to the thermal management and materials.

Parametric investigation of azimuthal instabilities and electron transport in a radial-azimuthal E × B plasma configuration

Partially magnetized low-temperature plasmas (LTP) in an E × B configuration, where the applied magnetic field is perpendicular to the self-consistent electric field, have become increasingly relevant in industrial applications. Hall thrusters, a type of electrostatic plasma propulsion, are one of the main LTP technologies whose advancement is hindered by the not-fully-understood underlying physics of operation, particularly, with respect to the plasma instabilities and the associated electron cross field transport. The development of Hall thrusters with unconventional magnetic field topologies has imposed further questions regarding the instabilities' characteristics and the electrons' dynamics in these modern cross field configurations. Accordingly, we present in this effort a detailed parametric study of the influence of three factors on the plasma processes in the radial-azimuthal coordinates of a Hall thruster, namely, the magnetic field gradient, secondary electron emission, and plasma number density. The studies are carried out using the reduced-order particle-in-cell code developed by the authors. The setup of the radial-azimuthal simulations largely follows a well-defined benchmark case from the literature in which the magnetic field is oriented along the radius, and a constant axial electric field is applied perpendicular to the simulation plane. The salient finding from our investigations is that, in the studied cases corresponding to elevated plasma densities, a long-wavelength azimuthal mode with the frequency of about 1 MHz is developed. Moreover, in the presence of strong magnetic field gradients, this mode results from an inverse energy cascade and induces a significant electron cross field transport as well as a notable heating of the ions.

Demonstration and experimental characteristics of a water-vapor Hall thruster

Water is an attractive candidate for condensable propellants owing to its availability, handleability, and sustainability. This study proposes the use of water vapor as a propellant for a low-power Hall thruster, and experimentally demonstrates the feasibility of this proposal. Based on the performance estimation from the plume diagnostics, a thrust-to-power ratio of 19 mN/kW, specific impulse of 550–860 s, and anode efficiency of 5–8 % were obtained at an anode power of 233–358 W. From further efficiency analysis, the mass utilization efficiency of water was found to be the most deteriorated among the internal efficiencies compared to the conventional xenon propellant, which was consistent with the expectations from a small discharge current oscillation, large beam divergence, and increase in low-energy ions. Moreover, additional power loss via reactions unique to polyatomic molecules was indicated by evaluation of the ionization cost. In this experiment, the mass utilization efficiency was improved with an increase in the anode voltage from 200 to 240 V without degradation of the power utilization. This suggests that operating at a higher voltage is more suitable for a water-vapor Hall thruster.

Study on the influence of magnetic field on the performance of a 5 kW hall thruster

Hall thruster is a kind of plasma optics device, which is used mainly in space propulsion. To study the influence of magnetic field on the performance of a 5 kW hall thruster, a two-dimensional PIC-MCC model was built. The Bohm diffusion was modeled by using a Brownian motion instead of the Bohm collision method and the near-wall conduction was modeled by a secondary electron emission model. When the mass flow rate is 5 mg/s, the thruster performance like thrust, efficiency and discharge current was simulated under a discharge voltage from 300 to 1,000 voltage. At first, the performance under constant magnetic field was simulated. The results showed that the magnetic field could not restrain the electrons as the discharge voltage increased. Later, the performance under varied magnetic field was simulated. The results showed that increasing the magnetic field strength with the increasing discharge voltage could restrain the electrons more efficiently, which proved that increasing the magnetic field strength is necessary for high specific impulse operation of hall thruster. At last, the performance measurement experiment of the thruster was carried out, and the experimental results verified the accuracy of the simulation results.

Concept of the generalized reduced-order particle-in-cell scheme and verification in an axial-azimuthal Hall thruster configuration

The reduced-order particle-in-cell (PIC) scheme is a novel modeling approach that enables computationally efficient electrostatic kinetic simulations of plasma. In our previous publications, we demonstrated that a proof-of-concept implementation of this novel PIC scheme resolves the multi-dimensional plasma processes and their interactions in a Hall thruster in a manner close to traditional electrostatic PIC codes. In this work, we extend our efforts on this topic and present a mathematically mature formulation for the dimensionality reduction of Poisson’s equation in the Vlasov–Poisson system, which enables the generalized reduced-order ‘quasi-multi-dimensional’ PIC scheme. The applicability of the dimensionality-reduction approach to solve general 2D Poisson problems is numerically verified. Next, we present several reduced-order quasi-2D (Q2D) simulations of a well-defined axial-azimuthal simulation case from the literature using approximation orders of the 2D problem whose computational costs are 2%–15% of a full-2D simulation. It is shown that these reduced-order simulations allow us to recover the same characteristics, behaviors and effects reported in the literature regarding the azimuthal instabilities in Hall thrusters. Moreover, in terms of the time-averaged plasma properties, it was found that, when increasing the approximation order, the error associated with the Q2D simulations’ predictions decreases from 15% to 4% for the electric field and from 20% to 2% for the ion number density. We have additionally discussed a series of sensitivity analysis results, including the influence of the initial number of macroparticles per cell on the predictions of the Q2D simulations. According to the detailed results and analyses presented, we conclude that the generalized reduced-order PIC scheme serves as a rigorous foundation for eventual cost-effective and comprehensive three-dimensional kinetic studies of the physics in Hall thrusters and similar electrostatic plasma technologies.

The Influence of the Magnetic Field Line Curvature on Wall Erosion near the Hall Thruster Exit Plane

One of the main factors that limit the lifetime of the Hall effect Thrusters (HETs) is the erosion of the acceleration channel caused by the flux of energetic ions. The magnetic field that is curved and convex towards the anode has been widely used in HETs because of its role in reducing the divergence angle of the ion beam and the channel wall erosion. However, the mechanism of the influence of the magnetic field line curvature on the wall erosion is not clear. Therefore, in this paper, a 2D3V numerical model based on the immersed-finite-element and particle-in-cell (IFE-PIC) method is established to simulate the radial-azimuthal plane near the exit of the Hall thruster. The effect of the tilt angle of the magnetic field line on the wall sputtering erosion rate is analyzed. The results show that compared to the case with the electric field E perpendicular to the magnetic field B, the energy of the ions hitting the channel wall is smaller and the wall erosion is weaker when the magnetic field lines are convex to the anode. As the tilt angle of the magnetic field lines increases from 0° to 60°, the erosion rate is reduced by 90%. Conversely, when the magnetic field lines are convex to the exit plane of the channel, the wall erosion is much more serious compared to the case with the orthogonal electric field E and the magnetic field B. As the tilt angle of the magnetic field line changes from 0° to 60°, the erosion rate is enhanced by 171%. The results in this paper are instructive for the design and optimization of the magnetic field of the HETs.

Facility Effects on the Ion Characteristics of a 12.5-Kilowatt Hall Thruster

During a laser-induced fluorescence test of a 12.5 kW magnetically shielded Hall thruster, ion characteristics in the discharge channel and near the poles were measured as the background pressure and electrical configuration were varied. The acceleration zone of the thruster moved upstream by 2 and 10% of the channel length when the background pressure was raised to 1.8 times and seven times the lowest achievable pressure, respectively. Examination of the characteristics of the ions near the pole covers suggested that as the background pressure decreased, the pole covers might be experiencing more erosion. When operating at a discharge voltage of 300 V, the acceleration zone was observed to be at the same location for all electrical configurations. When operating at a discharge voltage of 600 V, the acceleration zone was observed to move 3% of the channel length upstream when the thruster body was floated instead of tied to the cathode or grounded to the facility. Characteristics of the ions bombarding the pole covers did not vary across the tested electrical configurations. This observation combined with thruster body voltage measurements suggested that varying the electrical configuration only affected the thruster body sheath voltage and did not affect the plasma potential beyond the sheath.

Scaling of Magnetic Circuit for Magnetically Shielded Hall Effect Thrusters

Scaling of Magnetic Circuit for Magnetically Shielded Hall Effect Thrusters

Practical analysis of different neutral algorithms for particle simulation of Hall thruster

The modeling of neutral atoms is important for the full-particle simulations of Hall thrusters. In previous studies, researchers have developed various algorithms to model the neutral kinetics. The choice of those algorithms can influence significantly the computational speed, simulation convergence, and physical results. In this work, we perform a full-particle simulation of a typical 1 kW-class SPT-100 Hall thruster using four neutral algorithms, including the fixed-neutral algorithm (FNA), the algorithm of direct simulation of Monte Carlo (DSMC), the collisionless-neutral algorithm (CLNA), and the fluid algorithm (FA), to analyze the effects of different neutral iteration approaches on the simulation results. We found that FNA is sensitive to the initial number density of neutrals, and is difficult to converge properly, while the other algorithms not neglecting the atomic dynamics can get stable results. We count the parameters of the thruster, that is, thrust, specific impulse, and plasma density using different neutral algorithms. The time-averaged results match well with those of the experiment. However, the results differ in the time scale due to the low-frequency oscillations in Hall thrusters. We verify that the oscillations are due to the periodic change of neutrals and establish a zero-dimensional model to analyze the properties of the oscillations in the time scale. It indicates that the ratio of ion migration to neutral migration is the essential factor that significantly affects the calculation results. The model reveals that the direct neutral iteration methods, like DSMC and CLNA, can better simulate the characteristics of discharge fluctuations in Hall thrusters than the quasi-steady-state method, like FA. Finally, we proposed practical suggestions for the selection of the neutral algorithms for the SPT-100 thruster, which can also be generalized to other low- and medium-power Hall thrusters.

3D particle-in-cell study of the electron drift instability in a Hall Thruster using unstructured grids

In a Hall Thruster, the E×B current generates a strong electron drift with respect to the ions, which can trigger plasma instabilities, such as the electron drift instability (EDI), also called the electron cyclotron drift instability. The EDI has drawn a great deal of attention in the E×B community as previous one- and two-dimensional Particle-In-Cell (PIC) studies suggest it plays a major role in the anomalous transport of electrons across the magnetic barrier. However, experiments showed that the EDI has an inherent three-dimensional nature, which cannot be accurately described in a 1D or 2D configuration. Unfortunately, due to their prohibitive computational cost, needed 3D PIC simulations remained inaccessible without scaling plasma parameters, which inevitably modified the physics in a Hall Thruster. Thanks to recent computational developments, this paper presents a 3D fully kinetic investigation of the EDI in a typical Hall Thruster channel and near plume region. The study was conducted using an unstructured grid, thus demonstrating the feasibility to model more complicated geometries in the future. The growth and development of the EDI are described along with other plasma fluctuations, possibly the signature of another plasma instability, the modified-two-stream-instability. 3D effects on the anomalous transport are also assessed and found to be lower than in an analogous 2D simulation. This is due to lower losses in 2D, which lead to the saturation of the EDI occurring at higher energy levels.

Comparative analysis of simulation and experiment for the Hall-type thruster BPT-4000

Since 2004, the Plasma Physics Laboratory (PPL/PI/UnB) has been developing permanent magnet Hall thrusters due to their high efficiency. However, permanent magnets have limited use due to their maximum working temperature (the point at which they begin to demagnetize). Therefore, strict control of the temperature of the magnets must be carried out. In the present work we perform a numerical thermal simulation of a Hall thruster taken from the literature (e.g., the BPT-4000) and compare the obtained simulated thruster temperatures with experimental values taken in the laboratory. This work aims to verify the reliability of our simulation strategy in order to simulate other Hall-type thrusters in the future. The obtained simulation data was consistent with experimental results, demonstrating that the used simulation tool is reliable. In the future we will use this strategy for the simulation of improved plasma Hall thrusters developed at PPL aiming at improving its engineering model in order to prepare for future space qualification tests.

Simulation of effective parameters on the anomalous electrons drifts in the ‎Hall Effect thruster by PIC method

Simulation of effective parameters on the anomalous electrons drifts in the ‎Hall Effect thruster by PIC method

A Coupled 0-D Plasma Thermal Model for Hollow Cathodes

Hollow cathodes are essential components of dc electric thrusters for space applications, such as ion and Hall thrusters. Since the late 1970’s, several mathematical models have been proposed with the goal of characterizing the working principle and the plasma properties of such devices. Currently the more advanced 2-D models are used to effectively describe the onset of instabilities inside the plasma plume, but the increased complexity and the required calibrations make them not particularly suitable for cathode prototyping. Zero-dimensional models, on the other hand, can be used quickly and effectively to compute the main plasma parameters. In spite of their good qualities, reduced models usually do not perform well when used for very different cathodes with respect to the ones they were created for, especially due to the strong assumptions and free parameters which must be tuned to the specific case. By coupling a newly developed 0-D plasma model with a robust finite element analysis thermal simulation, the proposed model aims at filling this lack of flexibility, enabling the fast simulation of cathodes in a wide range of discharge currents and geometries. The model is able to compute self consistently all the physical quantities of interest, except the effective emission length, being the only free parameter. The model includes the approximate computation of the plasma sheath density on the emitter surface and the charge exchange heating (CEX) for the heavy species temperature. The thermal simulation is fully parametrized to quickly test different geometries and materials, while the prototyping tool allows great flexibility in terms of propellants and emissive insert materials.