Model for the dependence of cathode voltage in a Hall thruster on facility pressure

Abstract

Abstract 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.