Hydromagnetic waves and instabilities in kappa distribution plasma

Abstract

Stability properties of hydromagnetic waves (shear and compressional Alfven waves) in spatially homogeneous plasma are investigated when the equilibrium particle velocity distributions in both parallel and perpendicular directions (in reference to the ambient magnetic field) are modeled by kappa distributions. Analysis is presented for the limiting cases |ξα|⪡1 and |ξα|⪢1 for which solutions of the dispersion relations are analytically tractable. Here ξα(α=e,i) is the ratio of the wave phase speed and the electron (ion) thermal speed. Both low and high β (=plasma pressure/magnetic pressure) plasmas are considered. The distinguishing features of the hydromagnetic waves in kappa distribution plasma are (1) both Landau damping and transit-time damping rates are larger than those in Maxwellian plasma because of the enhanced high-energy tail of the kappa distribution and (2) density and temperature perturbations in response to the electromagnetic perturbations are different from those in Maxwellian plasma when |ξα|⪡1. Moreover, frequency of the oscillatory stable modes (e.g., kinetic shear Alfven wave) and excitation condition of the nonoscillatory (zero frequency) unstable modes (e.g., mirror instability) in kappa distribution plasma are also different from those in Maxwellian plasma. Quantitative estimates of the differences depend on the specific choice of the kappa distribution. For simplicity of notations, same spectral indices κ∥ and κ⊥ have been assumed for both electron and ion population. However, the analysis can be easily generalized to allow for different values of the spectral indices for the two charged populations.