Some inverse problems around the tokamak Tore Supra

Pages: 2327 - 2349, Volume 11, Issue 6, November 2012

doi:10.3934/cpaa.2012.11.2327       Abstract        References        Full Text (1105.0K)       Related Articles

Yannick Fischer - INRIA Sophia Antipolis Mediterranee, 2004 route des Lucioles, BP 93, 06902 Sophia-Antipolis, France (email)
Benjamin Marteau - ENSIMAG, 681, rue de la passerelle, Domaine universitaire, BP 72, 38402 Saint Martin D'Hères, France (email)
Yannick Privat - ENS Cachan Bretagne, CNRS, Univ. Rennes 1, IRMAR, av. Robert Schuman, F-35170 Bruz, France (email)

Abstract: We consider two inverse problems related to the tokamak 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 Tore Supra.

Keywords:  Hardy spaces, bounded extremal problem, conjugate harmonic function, inverse problems, shape optimization, least square problems
Mathematics Subject Classification:  Primary: 30H10, 49J20, 65N21; Secondary: 30H05, 42A50, 35N05

Received: March 2011;      Revised: May 2011;      Published: April 2012.

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