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.

推导并研究了霍尔推力器中阴极耦合电压对设备压力的依赖性的分析模型。通过执行从阴极发射极到推进器主羽流的广义欧姆定律的线积分，可以确定耦合电压的表达式。包括压力的影响以及由于离子声湍流引起的非经典阻力。所得模型应用于来自12种不同霍尔推力器配置的数据集，并在所有情况下均显示为与实验不确定性内的数据趋势匹配。反过来，该模型用于将实验数据集外推到在轨条件下，并且通过贝叶斯参数估计的方法量化了对这些预测的信心。