Hollow cathode theory and experiment. II. A two-dimensional theoretical model of the emitter region

Despite their long history and wide range of applicability that includes electric propulsion, detailed understanding of the driving physics inside orificed hollow cathodes remains elusive. The theoretical complexity associated with the multicomponent fluid inside the cathode, and the difficulty of accessing empirically this region, have limited our ability to design cathodes that perform better and last longer. A two-dimensional axisymmetric theoretical model of the multispecies fluid inside an orificed hollow cathode is presented. The level of detail attained by the model is allowed by its extended system of governing equations not solved for in the past within the hollow cathode. Such detail is motivated in part by the need to quantify the effect(s) of the plasma on the emitter life, and by the need to build the foundation for future modeling that will assess erosion of the keeper plate. Results from numerical simulations of a 1.2-cm-diam cathode operating at a discharge current of 25A and a gas flow rate of 5SCCM show that approximately 10A of electron current, and 3.45A of ion current return back to the emitter surface. The total emitted electron current is 33.8A and the peak emitter temperature is found to be 1440K. Comparisons with the measurements suggest that anomalous heating of the plasma is possible near the orifice region. The model predicts heavy species temperatures as high as 2034K and peak voltage drops near the emitting surface not exceeding 8V.