Two-dimensional axial-azimuthal (Z-Ø) simulation of cross-field electron transport in a hall thruster plasma discharge [electronic resource]
Keywords: Mechanical Engineering.

The Hall thruster (or Hall effect thruster) is an electric propulsion device used for space flight applications. Despite its use as a deployed production technology, much of the underlying plasma physics which governs thruster behavior and performance is not well understood. Specifically, laboratory experiments indicate an anomalously high electron mobility in the direction perpendicular to the magnetic field, which exceeds that predicted by classical theory. Predicting this so-called anomalous electron transport remains a key research challenge. One possible mechanism for the generation of super-classical electron transport is the interaction of correlated quasi-coherent fluctuations in the plasma properties. Instabilities in the plasma can lead to quasi-coherent wave fluctuations in the electric potential, electron number density, and electron velocities; if these fluctuations are appropriately correlated, they can serve to either enhance or reduce electron transport across the magnetic field. In this work, we use numerical simulations as a tool to characterize axial and azimuthal fluctuations in the plasma discharge properties and study their impact on cross-field electron transport. We employ a two-dimensional axial-azimuthal (z-theta) model to simulate an annular Hall thruster discharge. We use a hybrid fluid-Particle-In-Cell approach in which the positive ion (Xe+) and neutral (Xe) species are modeled using a Particle-In-Cell (PIC) treatment and the electrons are modeled as a fluid continuum. The ion and neutral species are modeled as discrete collisionless superparticles; due to their large mass and consequently large Larmor radius, we neglect the magnetic field effect on the ions. For the electron fluid, we include the first three moments of the Boltzmann equation to obtain 2D continuity and momentum equations, using the drift-diffusion approximation, and a quasi-1D energy equation. The PIC and fluid treatments are coupled by assuming space charge neutrality, or quasineutrality, between the ions and electrons. We chose a simulated thruster model geometry and operating conditions to enable comparisons to experimental measurements of the Stanford Hall Thruster (SHT) laboratory discharge. The simulated thruster channel is 8 cm long, with an outer diameter of 9.4 cm; we include the full azimuth throughout the simulated domain, which includes the entire channel length and the near-plume. Using a non-uniform spatial resolution of 3 mm - 10 mm and maximum time step of 10 ns, we can achieve a simulated time of extent on the order of milliseconds, using a single PC processor core for a wall clock time of several days. We present results for a representative simulated low voltage operating condition. Simulated plasma properties are compared to experimental measurements of the plasma properties and the effective electron mobility. We further analyze the simulated data to characterize predicted axial and azimuthal fluctuations in the electric potential, electron number density, and electron velocities. We consider the simulated wave fluctuations in the context of linearized fluid theory models for specific dispersive propagation modes, as we attempt to characterize their impact on the effective axial electron transport for various axial regions within the thruster discharge. For the simulated time and spatial scales presented here, correlated fluctuations appear to enhance electron transport in some regions of the discharge and inhibit electron transport in others. In the mid-channel region, where we believe gradients and in the electron density and magnetic field may contribute to gradient-driven waves, we observe enhancement of the electron mobility beyond classical mobility values. Near the channel exit plane, however, we observe a distinct electron transport barrier, similar to that observed in experimental measurements. Just upstream of the channel exit plane, correlated fluctuations in the electron number density and the axial electron velocity appear to generate negative current which opposes the positive bulk discharge current; in this region, we believe the axial shear in the electron velocity may play a role in disrupting fluctuations and reducing electron transport. In both cases, it is clear that simulated wave fluctuations impact axial electron transport. Even in regions of observed transport enhancement, however, the simulated fluctuation-driven transport does not fully account for the experimentally-observed super-classical mobility. We believe that an additional transport mechanism -- perhaps electron wall scattering or higher frequency, shorter wavelength fluctuations -- is necessary to account for the experimentally-observed electron mobility. Towards this end, we present results for additional simulations which include an artificially enhanced electron collision frequency; these simulations show improved agreement with experimental results and confirm the need to include additional physical mechanisms for anomalous electron transport. Finally, suggestions for future work are included.