Propagation of Electromagnetic Waves in Resistive Pair Plasma and Causal Relativistic Magnetohydrodynamics

TL;DR

This paper studies electromagnetic wave propagation in resistive pair plasmas, revealing superluminal group velocities at high resistivity but showing such conditions invalidate plasma assumptions, leading to a new causally consistent relativistic MHD framework.

Contribution

It introduces a new set of causal relativistic magnetohydrodynamics equations that incorporate resistivity while respecting causality constraints.

Findings

Superluminal group velocity occurs at high resistivity but invalidates plasma assumptions.

Plasma parameter drops below unity when superluminal propagation appears.

Proposes a new causal MHD model consistent with relativistic causality.

Abstract

We investigate the propagation of electromagnetic waves in resistive pair plasmas using a onefluid theory derived from the relativistic two-fluid equations. When the resistivity normalized by the electron/positron inertia variable exceeds a critical value, the dispersion relation for electromagnetic waves shows that the group velocity is larger than the light speed in vacuum. However, in such a case, it also is found that the plasma parameter is less than unity: that is, the electron-positron pair medium no longer can be treated as plasma. Thus the simple two-fluid approximation is invalid. This confirms that superluminal propagation of electromagnetic wave is forbidden in a plasma -- a conclusion consistent with the relativistic principle of causality. As an alternative, we propose a new set of equations for ``causal relativistic magnetohydrodynamics", which both have non-zero resistivity and yet are consistent with the causality principle.