Well-posedness and generalized plane waves simulations of a 2D mode conversion model

TL;DR

This paper develops a mathematical and numerical framework using generalized plane waves to simulate 2D electromagnetic wave mode conversion in plasma, aiding plasma heating in fusion devices.

Contribution

It introduces a new basis function approach tailored for mode conversion models and implements it within a discontinuous Galerkin method for accurate simulations.

Findings

Simulations align with qualitative expectations from previous studies.

The basis functions effectively handle variable coefficients in the model.

The approach provides a foundation for further 2D mode conversion studies.

Abstract

Certain types of electro-magnetic waves propagating in a plasma can undergo a mode conversion process. In magnetic confinement fusion, this phenomenon is very useful to heat the plasma, since it permits to transfer the heat at or near the plasma center. This work focuses on a mathematical model of wave propagation around the mode conversion region, from both theoretical and numerical points of view. It aims at developing, for a well-posed equation, specific basis functions to study a wave mode conversion process. These basis functions, called generalized plane waves, are intrinsically based on variable coefficients. As such, they are particularly adapted to the mode conversion problem. The design of generalized plane waves for the proposed model is described in detail. Their implementation within a discontinuous Galerkin method then provides numerical simulations of the process. These first 2D simulations for this model agree with qualitative aspects studied in previous works.