Reconstruction of the equilibrium of the plasma in a Tokamak and identification of the current density profile in real time

摘要

The reconstruction of the equilibrium of a plasma in a Tokamak is a freeboundary problem described by the Grad-Shafranov equation in axisymmetricconfiguration. The right-hand side of this equation is a nonlinear source,which represents the toroidal component of the plasma current density. Thispaper deals with the identification of this nonlinearity source fromexperimental measurements in real time. The proposed method is based on a fixedpoint algorithm, a finite element resolution, a reduced basis method and aleast-square optimization formulation. This is implemented in a software calledEquinox with which several numerical experiments are conducted to explore theidentification problem. It is shown that the identification of the profile ofthe averaged current density and of the safety factor as a function of thepoloidal flux is very robust.