Some inverse problems around the tokamak Tore Supra

TL;DR

This paper investigates two inverse problems related to the Tore Supra tokamak, focusing on boundary magnetic data recovery and plasma shape reconstruction using complex analysis and shape optimization, with practical algorithms and simulations.

Contribution

It introduces new methods for boundary data recovery and plasma shape identification in tokamaks, combining complex analysis and shape optimization techniques with numerical validation.

Findings

Established stability and existence for boundary magnetic data recovery.

Developed a fast algorithm for plasma shape identification.

Validated methods through numerical simulations with Tore Supra data.

Abstract

We consider two inverse problems related to the tokamak \textsl{Tore Supra} through the study of the magnetostatic equation for the poloidal flux. The first one deals with the Cauchy issue of recovering in a two dimensional annular domain boundary magnetic values on the inner boundary, namely the limiter, from available overdetermined data on the outer boundary. Using tools from complex analysis and properties of genereralized Hardy spaces, we establish stability and existence properties. Secondly the inverse problem of recovering the shape of the plasma is addressed thank tools of shape optimization. Again results about existence and optimality are provided. They give rise to a fast algorithm of identification which is applied to several numerical simulations computing good results either for the classical harmonic case or for the data coming from \textsl{Tore Supra}.