Covariant Constitutive Relations and Relativistic Inhomogeneous Plasmas

TL;DR

This paper develops a covariant, relativistic framework for describing electromagnetic responses in inhomogeneous plasmas using a two-point susceptibility kernel, extending non-relativistic theories to include gravitational effects and non-stationary conditions.

Contribution

It introduces a fully covariant spacetime formulation of susceptibility kernels for relativistic plasmas, incorporating gravitational effects and non-stationarity, and derives explicit formulas for perturbed kernels.

Findings

Re-casts Maxwell-Vlasov equations with susceptibility kernel

Derives explicit formulas for perturbed kernels with/without gravity

Analyzes collisionless damping and Landau damping in relativistic plasmas

Abstract

The notion of a two-point susceptibility kernel used to describe linear electromagnetic responses of dispersive continuous media in non-relativistic phenomena is generalized to accommodate the constraints required of a causal formulation in spacetimes with background gravitational fields. In particular the concepts of spatial material inhomogeneity and temporal non-stationarity are formulated within a fully covariant spacetime framework. This framework is illustrated by re-casting the Maxwell-Vlasov equations for a collisionless plasma in a form that exposes a 2-point electromagnetic susceptibility kernel in spacetime. This permits the establishment of a perturbative scheme for non-stationary inhomogeneous plasma configurations. Explicit formulae for the perturbed kernel are derived in both the presence and absence of gravitation using the general solution to the relativistic equations of motion of the plasma constituents. In the absence of gravitation this permits an analysis of collisionless damping in terms of a system of integral equations that reduce to standard Landau damping of Langmuir modes when the perturbation refers to a homogeneous stationary plasma configuration. It is concluded that constitutive modelling in terms of a 2-point susceptibility kernel in a covariant spacetime framework offers a natural extension of standard non-relativistic descriptions of simple media and that its use for describing linear responses of more general dispersive media has wide applicability in relativistic plasma modelling.