Plasma Physics Mathematical Physics
// 2022
I. Plasma Instability in Hall Thrusters - An Analytical Study
Theoretical Analysis & Derivation of Generalized Dispersion Relation
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 (). 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.