Penalty Methods for the Hyperbolic System Modelling the Wall-Plasma Interaction in a Tokamak

TL;DR

This paper introduces a novel penalty method for a nonlinear hyperbolic system modeling plasma-wall interactions in tokamaks, effectively handling obstacle effects without boundary layer issues.

Contribution

A new penalty approach is proposed for hyperbolic plasma transport equations near tokamak walls, overcoming limitations of existing methods and ensuring optimal convergence.

Findings

Numerical evidence of Dirac measure formation at the plasma-limiter interface.

The proposed penalty method achieves optimal convergence rates.

No spurious boundary layers observed with the new method.

Abstract

The penalization method is used to take account of obstacles in a tokamak, such as the limiter. We study a non linear hyperbolic system modelling the plasma transport in the area close to the wall. A penalization which cuts the transport term of the momentum is studied. We show numerically that this penalization creates a Dirac measure at the plasma-limiter interface which prevents us from defining the transport term in the usual sense. Hence, a new penalty method is proposed for this hyperbolic system and numerical tests reveal an optimal convergence rate without any spurious boundary layer.