Some inverse problems around the tokamak Tore Supra

Yannick Fischer (1) , Benjamin Marteau (2) , Yannick Privat (3)

1 APICS - Analysis and Problems of Inverse type in Control and Signal processing
2 ENSIMAG - École nationale supérieure d'informatique et de mathématiques appliquées
3 IRMAR - Institut de Recherche Mathématique de Rennes

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}.

Mots clés: Hardy Spaces; Bounded Extremal Problem; Conjugate Harmonic Function; Inverse Problems; Shape Optimization; Least Square Problems

Domaines: Equations aux dérivées partielles [math.AP]

Yannick Fischer, Benjamin Marteau, Yannick Privat. Some inverse problems around the tokamak Tore Supra. Communications on Pure and Applied Mathematics, 2012, 11 (6), pp.2327-2349. ⟨10.3934/cpaa.2012.11.2327⟩. ⟨hal-00537648v3⟩