PDRK: A General Kinetic Dispersion Relation Solver for Magnetized Plasma

TL;DR

This paper introduces a fast, accurate, and comprehensive numerical method for solving kinetic plasma dispersion relations by transforming them into matrix eigenvalue problems using a J-pole expansion, applicable to various plasma configurations.

Contribution

It develops a general approach that efficiently computes all solutions of plasma dispersion relations without convergence issues, surpassing traditional iterative methods.

Findings

Accurately computes plasma dispersion relations with J=8.

Capable of solving both electrostatic and electromagnetic cases.

Provides all solutions, including heavily damped modes.

Abstract

A general, fast, and effective approach is developed for numerical calculation of kinetic plasma dispersion relations. The plasma dispersion function is approximated by $J$-pole expansion. Subsequently, the dispersion relation is transformed to a standard matrix eigenvalue problem of an equivalent linear system. The result is accurate for $J=8$ except the solutions that are the little interesting heavily damped modes. In contrast to conventional approaches, such as Newton's iterative method, this approach can give either all the solutions in the system or a few solutions around the initial guess. It is also free from convergent problems. The approach is demonstrated from electrostatic one-dimensional and three-dimensional dispersion relations, to electromagnetic kinetic magnetized plasma dispersion relation for bi-Maxwellian distribution with parallel velocity drift.