June 18,  19,  20   2003
 
 
 

11:30 AM - Thursday, June 19, 2003 - Amphitheater Darboux

Jacques Blum

Laboratoire Jean-Alexandre Dieudonné (UMR 6621)
Université de Nice Sophia-Antipolis
Parc Valrose, 06108 Nice Cedex 02, France

jblum@math1.unice.fr

Inverse Problems in Plasma Physics

In order to achieve controlled thermonuclear fusion, the plasma can be confined by a magnetic field in a closed toroidal magnetic configuration, called a Tokamak. The equilibrium of this plasma in an axisymmetric configuration is governed by a semi-linear elliptic partial differential equation. The right-hand side of this equation is a non-linear source, which represents the toroidal component of the plasma current density. The aim of this work is to perform the real-time identification of this non-linearity from experimental measurements, such as magnetic measurements (Cauchy boundary conditions), polarimetric measurements (integrals of the magnetic field over several chords), local magnetic measurements (motional Stark effect). This problem is formulated as an optimal control problem, where the control parameters are the coefficients that define the non-linearity of the equation. A new method of regularization for this ill-posed problem will be presented, and the various steps which have enabled to go from an inter-shot analysis to a real-time resolution will be explained.