Linearised electrodynamics and stabilisation of a cold magnetised plasma

TL;DR

This paper analyzes a linearized model of electromagnetic wave propagation in a magnetized plasma, establishing its stability, well-posedness, and convergence properties without restrictive assumptions on domain geometry.

Contribution

It provides a rigorous mathematical analysis of the linearized Euler-Maxwell model, including stability and convergence results under minimal geometric and topological assumptions.

Findings

Proves well-posedness of the model.

Establishes strong, polynomial, and exponential stability.

Shows convergence to the time-harmonic regime.

Abstract

We consider a linearized Euler--Maxwell model for the propagation and absorption of electromagnetic waves in a magnetized plasma. We present the derivation of the model, and we show its well-posedeness, its strong and polynomial stability under suitable and fairly general assumptions, its exponential stability in the same conditions as the Maxwell system, and finally its convergence to the time-harmonic regime. No homogeneity assumption is made, and the topological and geometrical assumptions on the domain are minimal. These results appear strongly linked to the spectral properties of various matrices describing the anisotropy and other plasma properties.