Linear Wave Propagation for Resistive Relativistic Magnetohydrodynamics
Journal
Date Issued
2018
Author(s)
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.
Volume
25
Issue
9
Start page
092114
Issn Identifier
1070-664X
Ads BibCode
2018PhPl...25i2114M
Rights
open.access
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