Gyrokinetic Theory of Low-frequency Electromagnetic Waves in Finite-$\beta$ Anisotropic Plasmas

TL;DR

This paper develops a gyrokinetic theory for low-frequency electromagnetic waves in finite-$eta$ anisotropic plasmas, incorporating kinetic effects and analyzing mode stability and polarization.

Contribution

It introduces a comprehensive gyrokinetic framework for finite-$eta$ plasmas, including new dispersion relations and instability criteria for various modes.

Findings

Finite ion Larmor radius couples ion-sound, mirror, and shear Alfven waves.

Derived explicit criteria for firehose and mirror instabilities.

Numerical analysis of mode stability and polarization across parameter space.

Abstract

We present a gyrokinetic theory for the electromagnetic waves and instabilities with frequencies much lower than the ion cyclotron frequency in finite-$\beta$ anisotropic uniform plasmas. Here, $\beta$ is the ratio between plasma and magnetic pressures. Kinetic effects due to both the finite Larmor radii and wave-particle resonances are fully kept in the analysis. Corresponding linear dispersion relation and wave polarizations, valid for general $\beta$ value and perpendicular wavelength, are then specifically derived for a bi-Maxwellian plasma. Analytic expressions for the criteria of kinetic firehose and mirror instabilities are also given. The mode frequency, stability, and wave polarization of a broad spectrum of normal modes are then investigated numerically in a systematic study over a set of parameters. Our study clearly demonstrates that, due to the finite ion Larmor radius effect, the ion-sound wave, mirror mode, and shear Alfven wave are intrinsically coupled.