The oblique firehose instability in a bi-kappa magnetized plasma

TL;DR

This paper derives a dispersion equation for the oblique firehose instability in bi-kappa plasmas, analyzes its solutions under solar wind conditions, and explores how superthermal particles influence instability growth.

Contribution

It introduces a new dispersion equation for the oblique firehose instability in bi-kappa plasmas, including novel mathematical properties of special functions and analysis of superthermal effects.

Findings

Superthermal particles reduce maximum growth rates.

Spectral range of instability is decreased by superthermal effects.

Equation applies to any propagation direction and particle gyroradius.

Abstract

In this work, we derive a dispersion equation that describes the excitation of the oblique (or Alfv\'en) firehose instability in a plasma that contains both electron and ion species modelled by bi-kappa velocity distribution functions. The equation is obtained with the assumptions of low-frequency waves and moderate to large values of the parallel (respective to the ambient magnetic field) plasma beta parameter, but it is valid for any direction of propagation and for any value of the particle gyroradius (or Larmor radius). Considering values for the physical parameters typical to those found in the solar wind, some solutions of the dispersion equation, corresponding to the unstable mode, are presented. In order to implement the dispersion solver, several new mathematical properties of the special functions occurring in a kappa plasma are derived and included. The results presented here suggest that the superthermal characteristic of the distribution functions leads to reductions to both the maximum growth rate of the instability and of the spectral range of its occurrence.