Transit-time instability in Hall thrusters

TLDR

Hall thruster experiments and simulations repeatedly observe longitudinal waves with phase velocities comparable to ion speeds. The study investigates the origin of ion transit‑time instability using a one‑dimensional fluid model and calculates the resonance frequency and growth rate to show how ionization level and transit time affect onset. A 1D fluid model of cold ions accelerated between electrodes, analyzed with short‑wave asymptotics, reveals that ion acoustic waves superimposed on a discharge‑current‑generated standing wave form a resonance that amplifies the waves. At high ionization, the acoustic waves grow, producing large density and velocity perturbations, and the resulting traveling wave is seen in plasma density and velocity while the potential oscillates in phase along the discharge.

Abstract

Longitudinal waves characterized by a phase velocity of the order of the velocity of ions have been recurrently observed in Hall thruster experiments and simulations. The origin of this so-called ion transit-time instability is investigated with a simple one-dimensional fluid model of a Hall thruster discharge in which cold ions are accelerated between two electrodes within a quasineutral plasma. A short-wave asymptotics applied to linearized equations shows that plasma perturbations in such a device consist of quasineutral ion acoustic waves superimposed on a background standing wave generated by discharge current oscillations. Under adequate circumstances and, in particular, at high ionization levels, acoustic waves are amplified as they propagate, inducing strong perturbation of the ion density and velocity. Responding to the subsequent perturbation of the column resistivity, the discharge current generates a standing wave, the reflection of which sustains the generation of acoustic waves at the inlet boundary. A calculation of the frequency and growth rate of this resonance mechanism for a supersonic ion flow is proposed, which illustrates the influence of the ionization degree on their onset and the approximate scaling of the frequency with the ion transit time. Consistent with experimental reports, the traveling wave can be observed on plasma density and velocity perturbations, while the plasma potential ostensibly oscillates in phase along the discharge.