Toward developing a comprehensive algorithm for solving kinetic plasma dispersion relations for parallel propagation with a kappa distribution

Abstract

In general, it is challenging to numerically solve all the roots of plasma wave dispersion relations. The velocity distributions of multi-component particles in an anisotropic high-energy plasma can be better described by a drift loss-cone bi-Kappa distribution or a mixed drift loss-cone distribution containing bi-Kappa and bi-Maxwellian plasma in space and laboratories. In this work, we have developed a code with a new numerical algorithm to solve all roots of the kinetic dispersion relation for parallel propagation in hot magnetized plasmas with drift loss-cone bi-Kappa distribution. Solving all roots of the rational expansions of the kinetic dispersion relation is equivalent to a matrix eigenvalue problem of a linear system. We have performed detailed numerical solutions for three kinds of plasmas: bi-Maxwellian, bi-Kappa, and cold plasmas. We have also proposed a unified numerical method to solve the mixed dispersion relation based on the bi-Kappa and bi-Maxwellian distributions. The numerical results and benchmark studies demonstrate that the new algorithm is in agreement with the data from previous studies. This is a crucial step toward revealing a full picture of kinetic plasma waves and instabilities.