Numerical Simulation of Wave Propagation in Inhomogeneous Plasmas

Abstract: Several plasma wave phenomena play a major role in astro-

physical and experimental applications, specifically wave absorption,

mode conversion, and cyclotron damping. As it is often the case in

plasma physics, hierarchies of models exist to describe various aspects

of these phenomena, and this talk will focus on numerical simulations

of a full wave model. The presentation will start with modeling as-

pects for the cold plasma model, leading to partial differential equations

(PDEs) with variable coefficients, before turning to numerical methods

specifically tailored to handle such PDEs: the so-called quasi-Trefftz

methods.

Trefftz methods rely, in broad terms, on the idea of approximating solu-

tions to PDEs via Galerkin-type methods with basis functions solving

exactly the PDE locally, making explicit use of information about the

ambient medium. They are of particular interest for wave propagation

problems. But in general, for problems modeled by PDEs with vari-

able coefficients, no exact solutions are available. Hence quasi-Trefftz

methods have been introduced to address this problem: they rely not

on exact solutions to the PDE but instead on high order approximate

solutions constructed locally. We will discuss some of the fundamental

properties of these numerical methods for aeroacoustic problems. The

goal here will be to emphasize why they represent a promising alterna-

tive to more standard methods to tackle an important challenge related

to the boundary layer of air flow around planes.

Finally we will highlight the main difficulty in developing quasi-Trefftz

methods for electromagnetic wave propagation.