Near-Wall Pathways of Anomalous Electron Transport in Hall Thrusters Revealed by 3D PIC Simulations

Abstract

Cross-field electron transport in Hall thrusters is widely attributed to high-frequency $E\times B$ instabilities, yet its net spatial pathway remains poorly resolved. Here we perform instability-resolving three-dimensional particle-in-cell simulations of a Hall thruster using a boundary-faithful and highly integrated framework. The model incorporates a realistic magnetic-field configuration, self-consistent dielectric wall charging, secondary electron emission, Monte Carlo ionization collisions, a self-consistent continuum neutral-gas evolution model, and an open near-plume outflow treatment. From the strongly oscillatory three-dimensional fields, we extract the net instability-driven transport by time and azimuthal averaging of the correlation term $\langle n_e E_y\rangle$ and the corresponding effective perpendicular mobility. The simulations reveal that anomalous electron transport is not distributed uniformly across the channel cross section. Instead, it self-organizes into persistent near-wall pathways connected to the near-exit region. By comparing conducting-wall, ceramic-wall-with-secondary-emission, and open-outflow closures, we show that the near-wall transport topology is robust, while the boundary treatment mainly redistributes the detailed strength of the pathway and its coupling to the exit and near-plume region. These results demonstrate a previously unresolved spatial organization of instability-driven anomalous transport in Hall thrusters and highlight the unique role of 3D PIC simulations in revealing it.

Figures (18)

• Figure 1: Physical configuration and computational domain. (a) Schematic of the annular Hall thruster and the modeled azimuthal sector. (b) Three-dimensional decomposition of the simulation domain into the channel region (blue) and plume region (red) in the $(x,y,z)\equiv(r,\theta,z)$ coordinate system, with the nominal $\mathbf{E}$, $\mathbf{B}$, and $\mathbf{E}\!\times\!\mathbf{B}$ directions indicated. (c) Meridional $(x,z)$ view defining the channel size $(L_{xc},L_{zc})$ and plume extension $(L_{xp},L_{zp})$. (d) Azimuthal $(y,z)$ view showing the simulated sector length $L_y$ with periodic boundary conditions in $y$.
• Figure 2: Summary of the simulation cases and their computational cost. Here, $\Delta t$ is the PIC time step, $t_{\mathrm{run}}$ is the total simulated physical time, $t_{\mathrm{wall}}$ is the measured wall-clock runtime on the target machine, $\bar{t}_{\mathrm{step}}$ is the average wall-clock time per time step, and $N_{i,\mathrm{peak}}$ is the peak number of macro-ions.
• Figure 3: Prescribed initial plasma loading. Normalized seed density $n_{\mathrm{seed}}/n_0$ is shown on three slices: $x$--$y$ at $i_z=72$, $x$--$z$ at $i_y=32$, and $y$--$z$ at $i_x=128$, where $i_x$, $i_y$, and $i_z$ denote grid indices. The yellow curve in the $x$--$z$ plane indicates the imposed initial ion axial drift profile $v_{z,i}$ (m/s). The inset shows the slice locations in the 3D computational domain.
• Figure 4: Background magnetic-field configurations in the $x$--$z$ plane. Colors show the magnetic-field magnitude $|\mathbf{B}|$ (Gauss), and white contours denote the magnetic vector potential. (a) Baseline export used for cases D, D$_{2\Delta t}$, C, O, and O$_{\text{loadC}}$. (b) Refined export over the same physical region, used for Case D$_{\text{finer}}$. (c) Extended plume-domain export, used for Case O$_{\text{bigger}}$; the dashed box indicates the baseline-domain extent. The inset summarizes the total cell count and relative cell-count ratio for the three configurations.
• Figure 5: Verification of the continuum neutral model against the free-molecular pre-processing. (a) Normalized neutral density $n_{0}/n_{0,\max}$ from the free-molecular method (left) and the finite-volume Lax--Friedrichs solution (right); the dashed line indicates the centerline used for the one-dimensional comparison. (b) Left: centerline profiles of $n_{0}/n_{0,\max}$ from the two methods; the shaded region denotes the pointwise difference. Right: relative-error map $RE=100\,(n_{0,F}-n_{0,LF})/n_{0,F}$, evaluated only in cells with $n_{0,F}/n_{0,\max}>0.01$. (c) Time evolution of the total number of neutral macroparticles in the free-molecular simulation, saturating at $4.39\times 10^{5}$. (d) Mean velocity fields $u_{x0}$ and $u_{z0}$ (m/s) obtained from the free-molecular run and used as prescribed advection velocities in the coupled continuum neutral solver.