The Impact of Planar-Geometry Cathodes on Hall Thruster Performance

Abstract

This thesis explores the viability of planar cathodes for improving Hall thruster performance. A mathematical model is presented that calculates how the total efficiency of a Hall thruster changes when operated with a planar cathode instead of the traditionally utilized hollow cathode. The model assumes that a Hall thruster’s anode efficiency is completely agnostic to the type of cathode employed and any difference in total efficiency will manifest in the thruster’s cathode and electrical efficiencies. A one-dimensional model of the planar cathode's sheath is used to calculate the electrical efficiency of a Hall thruster equipped with a centrally mounted planar cathode as a function of the thruster’s discharge voltage, discharge current, voltage utilization efficiency, current utilization efficiency, and the cathode’s geometry and material properties. This sheath model is also used to calculate the maximum, space charge limited, discharge current a planar cathode can provide. This model demonstrates that under the correct conditions, the electrical and cathode efficiencies of a Hall thruster will be larger when operated with a planar cathode, leading to an increase in total thruster efficiency. Conversely, planar cathodes are far more susceptible to space charge issues and their ability to provide discharge currents of the magnitude desired by Hall thrusters is heavily reliant on the thruster having a sufficiently low voltage utilization efficiency. Working under this restriction, planar cathodes could be a viable option on Hall thrusters that possess low voltage utilization efficiencies at their nominal operation conditions.