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An analytical model for the dependence of the cathode coupling voltage in a Hall thruster on facility pressure is derived and investigated. The expression for the coupling voltage is determined by performing a line integral of the generalized Ohm's law from the cathode emitter to the thruster's main plume. The effects of pressure as well as non-classical resistance due to ion acoustic turbulence are included. The resulting model is applied to datasets from 12 different Hall thruster configurations and is shown in all cases to match the trends in the data within experimental uncertainty. The model in turn is used to extrapolate the experimental datasets to on-orbit conditions, and the confidence in these predictions is quantified through the lens of Bayesian parameter estimation. The derived model is discussed in the context of the underlying assumptions as well as previous models that have been proposed for this facility effect. [ABSTRACT FROM AUTHOR]

We employ the 2D (r–z) code Hall2De to conduct numerical simulations of the SPT-140, a Hall thruster that operates with an external hollow cathode. The simulations are informed by direct measurements of the plasma conditions in the acceleration channel that were obtained using the laser-induced fluorescence technique. We validate our simulation results with additional plasma measurements, wear test erosion rates, and performance data as a function of background pressure. The comparisons of the simulation results with thrust measurements provide insight into the longstanding question of how background pressure affects Hall thruster performance. We find that in thrusters with an external cathode changes in the thrust with varying backpressure can be partially explained by changes in the plasma density near the cathode. We argue that such changes in the density affect the voltage coupling and, eventually, the thrust. However, accounting for this mechanism alone in the simulations over-predicts the thrust measured during ground tests for backpressures less than 10 μTorr. Also, at these backpressures, the measurements showed a higher rate of change of the thrust compared to the simulations. We propose that one explanation for this discrepancy is that the acceleration region may be axially shifting downstream with decreasing backpressure. Though possible, we also recognize that such shifts are not observed in LIF measurements at the lowest pressures for which such diagnostics are possible. We discuss alternative explanations in Part II of this article. [ABSTRACT FROM AUTHOR]

A theoretical model of the thrust produced by a Hall thruster has been developed to provide insight into the longstanding problem of performance dependence on facility pressure. Inputs to the model have been provided by 2D (r–z) axisymmetric simulations that were guided by measurements of the ion velocity field from laser induced fluorescence diagnostics. The combined analyses yield very good agreement with thrust measurements from ground tests of the SPT-140, a Hall thruster operating with an external cathode, and suggest two new findings. First, at intermediate pressures (∼9–15 μTorr) the rise of the thrust with increasing pressure is largely due to fast atoms produced by charge exchange collisions with beam ions. The acceleration region remains spatially invariant and the thrust rise is linear with pressure. As the pressure increases further, displacements of the acceleration region towards the anode become sizeable and reduce the rate of increase in thrust. Second, the thrust increase from vacuum to the lower values of pressure (≲9 μTorr) is driven largely by transport of electrons along magnetic lines, from the cathode to the near-plume of the thruster, which explains why the rise is nonlinear with pressure. It is argued based on first-principles that this higher rate of thrust variation observed at the lowest pressures may be strongly linked to the highly asymmetric distribution of the external-cathode electrons around the discharge. This would explain the insensitivity of performance in thrusters with centrally-mounted cathodes as well as the longstanding challenges 2D axisymmetric simulations have had in uncovering the source of the thrust dependence on facility pressure. [ABSTRACT FROM AUTHOR]