A Full-Matrix Approach for Solving General Plasma Dispersion Relation

TL;DR

This paper introduces a comprehensive matrix-based numerical method to solve complex plasma dispersion relations, enabling exact solutions and polarization analysis for multi-component fluid plasmas, with promising results for kinetic plasma approximations.

Contribution

It presents a novel full-matrix eigenvalue approach that transforms the plasma dispersion relation problem into a solvable numerical eigenvalue problem, overcoming previous convergence issues.

Findings

Exact solutions for complex plasma dispersion relations

Natural polarization determination for multi-scale plasmas

Effective approximation method for kinetic plasma dispersion functions

Abstract

A hitherto difficult and unsolved issue in plasma physics is how to give a general numerical solver for complicated plasma dispersion relation, although we have long known the general analytical forms. We transform the task to a full-matrix eigenvalue problem, which allows to numerically calculate all the dispersion relation solutions exactly free from convergence problem and give polarizations naturally for arbitrarily complicated multi-scale fluid plasma with arbitrary number of components. Attempt to kinetic plasma via $N$-point Pad\'e approximation of plasma dispersion function also shows good results.