A two-dimensional hybrid particle-in-cell numerical model has been constructed in the radial-axial plane with the intent of examining the physics governing Hall thruster operation. The electrons are treated as a magnetized quasi-one-dimensional fluid and the ions are treated as collisionless, unmagnetized discrete particles. The anomalously high electron conductivity experimentally observed in Hall thrusters is accounted for using experimental measurements of electron mobility in the Stanford Hall Thruster. While an experimental mobility results in improved simulation of electron temperature and electric potential relative to a Bohm-type model, results suggest that energy losses due to electron wall interactions may also be an important factor in accurately simulating plasma properties. Using a simplified electron wall damping model modified to produce general agreement with experimental measurements, an evaluation is made of differing treatments of electron mobility, background gas, neutral wall interactions, and charge exchange collisions. Although background gas results in two populations of neutrals, the increased neutral density has little effect on other plasma properties. Diffuse neutral wall interactions are in better agreement with experimental measurements than specular scattering. Also, charge exchange collisions result in an increase in average neutral velocity of 11% and a decrease in average ion velocity of 4% near the exit plane. The momentum exchange that occurs during charge exchange collisions is found to be negligible.
Two-dimensional hybrid numerical simulations of E ϫ B discharges used in Hall thruster propulsion point to the presence of strong fluctuations attributable to resistive instabilities in the frequency range of f Ϸ 0.1-10 MHz and the wavenumber range of −1 Ϸ 10-500 m −1. Analytical analyses confirm that these resistive modes are of the convective type, become increasingly unstable at low electron mobility, and are particularly intense at high voltage. The simulations, which model cross-field electron flow via an experimentally measured mobility, exhibit large fluctuation power in a region corresponding to a strong electron transport barrier. The analysis gives an electron mobility ͑ e ͒-dependent growth rate ͑␥͒ scaling as ␥ ϳ e −1/2. The predicted phase velocity of these waves is close to the ion velocity, somewhat lower than that seen in the simulations. Including the electron pressure contribution lowers the growth rate at high frequencies, and introduces a phase velocity that is shifted by ± the ion acoustic speed for the stable and unstable branch, respectively. Surprisingly, the phase velocity of the strong disturbances at high frequency seen in the simulations is found to be in agreement with that of the initially stable branch. Finite ionization/particle wall recombination does not change the overall conclusions at high frequencies. However, at lower f or larger , the growth rate of the instability is dominated by the ionization rate, and the disturbances are better described as "ionization" instabilities. The transition/competition between ionization, electron pressure, and resistive behavior gives rise to a "quiescent frequency band" where the growth rate is found to be small, consistent with what is seen in the numerical experiments. While simple linear analysis captures much of the observed simulation behavior, comparison with limited experimental data at low frequency suggests that other effects, in particular azimuthal dynamics, are very important, and further motivate extending the hybrid simulation models to three dimensions.
An electron cross-field transport model based on instantaneous simulated plasma properties is incorporated into a radial-axial hybrid simulation of a Hall plasma thruster. The model is used to capture the reduction of fluctuation-based anomalous transport that is seen experimentally in the region of high axial shear in the electron fluid. Similar transport barriers are observed by the magnetic confinement fusion community due to shear suppression of plasma turbulence through an increase in the decorrelation rate of plasma eddies. The model assumes that the effective Hall parameter can be computed as the sum of the classical term, a near-wall conductivity term, and a fluctuationbased term that includes the effect of shear. A comparison is made between shear-based, experimental, and Bohm-type models for cross-field transport. Although the shear-based model predicts a wider transport barrier than experimentally observed, overall, it better predicts measured plasma properties than the Bohm model, particularly in the case of electron temperature and electric potential. The shear-based transport model also better predicts the breathing-mode oscillations and time-averaged discharge current than both the Bohm and experimental mobility models. The plasma property that is most sensitive to adjustment of the fitting parameters used in the shear-based model is the plasma density. Applications of these fitting parameters in other operating conditions and thruster geometries are examined in order to determine the robustness and portability of the model. Without changing the fitting parameters, the simulation was able to reproduce macroscopic properties, such as thrust and efficiency, of an SPT-100-type thruster within 30% and match qualitative expectations for a bismuth-fueled Hall thruster.
Published differential cross section data for heavy particle collisions between xenon ions and neutral xenon has been incorporated into plasma simulations for electric propulsion modeling. A fit has been made to the published data in order to estimate the relative contribution from charge exchange and elastic collisions and to reduce the computational cost of utilizing the differential cross section in existing numerical models. Since the published profiles do not include scattering data near 0 degrees, the differential cross section was assumed to be constant at low angles. The angle at which the differential cross section was assumed to transition from the constant profile to the fit was chosen such that the differential cross section integrated to the published total cross section value for xenon scattering. In order to make the resulting differential scattering curve generally applicable to other types of collisions with dissimilar collision partners, the profile was converted from the laboratory frame into center of mass coordinates. Each time a scattering event was determined to take place in the electric propulsion modeling codes, a scattering angle of the incident particle was chosen using a cumulative distribution function. The behavior of the target particle was determined using conservation of energy and momentum.
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