Linear Wave Propagation for Resistive Relativistic Magnetohydrodynamics

TL;DR

This paper analyzes wave modes in resistive relativistic magnetohydrodynamics, revealing how conductivity affects wave propagation, damping, and the transition between ideal and resistive regimes, with implications for plasma physics.

Contribution

It derives the dispersion relation for relativistic MHD with finite conductivity, identifying wave modes and their behavior across different conductivity limits.

Findings

Ten wave modes supported in the system.

In the resistive limit, matter and fields decouple, leading to light, acoustic, and damped modes.

In the ideal limit, modes match classical fast, slow, and Alfvén waves.

Abstract

We present a linear mode analysis of the relativistic MHD equations in the presence of finite electrical conductivity. Starting from the fully relativistic covariant formulation, we derive the dispersion relation in the limit of small linear perturbations. It is found that the system supports ten wave modes which can be easily identified in the limits of small or large conductivities. In the resistive limit, matter and electromagnetic fields decouple and solution modes approach pairs of light and acoustic waves as well as a number of purely damped (non-propagating) modes. In the opposite (ideal) limit, the frozen-in condition applies and the modes of propagation coincide with a pair of fast magnetosonic, a pair of slow and Alfv\'en modes, as expected. In addition, the contact mode is always present and it is unaffected by the conductivity. For finite values of the conductivity, the dispersion relation gives rise to either pairs of opposite complex conjugate roots or purely imaginary (damped) modes. In all cases, the system is dissipative and also dispersive as the phase velocity depends nonlineary on the wavenumber. Occasionally, the group velocity may exceed the speed of light although this does not lead to superluminal signal propagation.