Plasma Physics Mathematical Physics // 2022

I. Plasma Instability in Hall Thrusters - An Analytical Study

Theoretical Analysis & Derivation of Generalized Dispersion Relation

I. Plasma Instability in Hall Thrusters - An Analytical Study

Abstract

Theoretical analysis of the microinstabilities involved in Hall Thrusters and derivation of a Generalized Dispersion Relation. Study involves Linearised perturbation of the collisionless Vlasov equations, stability, and growth rate analysis using asymptotic techniques.

Table of Contents / Outline

Theoretical Formulation

Linearized perturbation theory applied to collisionless Vlasov-Poisson equations for cross-field discharge plasmas.

Hall thrusters operate via azimuthal electron drift generated by orthogonal electric and magnetic fields (E×BE \times B). This geometry produces high-frequency drift instabilities (e.g. Electron Cyclotron Drift Instability - ECDI and Modified Two-Stream Instabilities - MTSI).

Analytical Highlights

  • Derived a Generalized Dispersion Relation incorporating non-neutral plasma effects, finite Larmor radius corrections, and density gradients.
  • Conducted asymptotic growth rate expansion in weak-field and strong-field limits.
  • Established analytical bounds on unstable wavenumber regimes.