Model for the Increase in Thruster Efficiency from Cross-Channel Coupling in Nested Hall Thrusters

Multi-channel operation in nested Hall thrusters has been experimentally shown to enhance thruster efficiency compared to single-channel operation at constant power. This is the result of higher local neutral density due to the flow from adjacent channels, leading to two effects: neutral ingestion and decreased plume divergence. Analytical expressions for the impact of these cross-channel effects on efficiency are derived for a nested Hall thruster based on the flow of neutrals between channels. These expressions are dependent on the geometry and operation of a given thruster, as well as its performance in single-channel operation. The mass utilization efficiency increase from cross-channel neutrals is found to be primarily driven by the distance between adjacent channels. A comparison of the model predictions of efficiency to experiment also shows agreement within uncertainty. These results are discussed in the context of best practices for nested Hall thruster channel testing and optimal thruster design.