Force balance in Hall Effect Thrusters: insights from 2d3v (drift-plane) kinetic simulation

The acceleration mechanism in Hall Effect Thrusters (HETs) is commonly described in terms of force balance. Namely, the reactive force produced by accelerated ions has the same value as Ampère's force acting on a drift current loop. This balance written in integral form provides the basis for quantitative estimations of HETs' parameters and scaling models. However, the balance details are not trivial, and some publications lack a clear understanding of this process.

In this contribution, we report on the results from the 2d3v drift-plane kinetic simulation of HET discharge. Specifically, we consider force balance in a local form and how it emerges from collision-less kinetic. Effects of gradient drift and magnetic field distortion due to drift current were also considered. Analysis reveals that bulk forces applied to electrons and ions do not match in the active part of discharge and converges only in the region of cathode plasma. Mismatch occurs due to the effect of finite electrons' pressure. This pressure is anisotropic and goes beyond the ideal gas law. A significant contribution to the pressure emerges from particles' acceleration-deceleration cycle in crossed fields, i.e., it is a kinetic effect of the finite size of electrons' trajectories. Kinetic pressure term increases with a power density of discharge and could gain value comparable with electric and magnetic contributions. Thus, it should be essential to take it into account in quantitive calculations.