A simple model is developed to capture the effect of background pressure on the cathode coupling voltage in a Hall effect thruster. The underlying hypothesis of this investigation is that the changes in cathode coupling voltage drop are dominated by the potential drop from the cathode exit to the thruster plume. This drop in turn is driven by the onset of anomalously high resistivity, resulting from ion acoustic turbulence. A one-dimensional model, based on quasi-linear formulation, is presented for how the growth of this ion acoustic turbulence drives the potential drop, and how this voltage drop depends on neutral density in the plume. Predictions from this model are compared to experimental data from the SPT-100 Hall thruster and it is shown that there is good agreement within uncertainty to the experimental data. This suggests that the facility effects on the cathode coupling voltage are largely driven by the ion acoustic turbulence in the plume of the hollow cathode. The results are then discussed in the context of performance effects on Hall thrusters.
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