Theoretical Study of the Breathing Mode in Hall Thrusters

Abstract

A transient 1D numerical uid model of the Hall thruster discharge is gradually simpli ed so as to expose the root phenomena responsible for the breathing mode. In a rst step, a times scale separation procedure is applied from which a quasi-stationary (QS) model is derived where time-dependent terms appear only in the transport of neutrals and in the evolution of the discharge current. The suitability of this QS model is then demonstrated by comparison with the fully time-dependent model. Approximate solutions of the linearized QS model are subsequently sought in the long wave and short wave limits. The very good agreement observed between the short wave approximate frequency and the frequency of the QS model corroborates the predator-prey interpretation, and validates at the same time the improvements brought to the former theory.