Plasma Physics Mathematical Modelling
// 2023
II. Plasma Instability in Hall Thrusters - A Numerical Study
Numerical Analysis of the General Dispersion Relation
Abstract
Numerical analysis of the General Dispersion relation for Hall Thrusters previously proposed by the author. The study involved algorithms including fixed point iteration and conjugate gradient descent using multiprocessing self-made modules in Python.
Table of Contents / Outline
Overview
This project presents a rigorous numerical analysis of the General Dispersion relation for Hall Thrusters, formulated by Jovi Koikkara.
Hall thrusters exhibit complex electrostatic and electromagnetic microinstabilities that dictate anomalous electron transport and thruster efficiency.
Methodology & Computation
- Formulated custom numerical solvers utilizing fixed-point iteration and conjugate gradient descent.
- Developed modular Python packages accelerated with multiprocessing to compute the complex roots of the dispersion relation across multidimensional parameter spaces.
- Simulated growth rates and wave vectors under diverse propellant conditions and magnetic field profiles.
Key Insights
- Verified stability regimes against empirical data.
- Demonstrated numerical convergence across stiff dispersion regimes where classical analytical approximations diverge.