  The reconstruction of the equilibrium of a plasma in a Tokamak is a free
boundary problem described by the Grad-Shafranov equation in axisymmetric
configuration. The right-hand side of this equation is a nonlinear source,
which represents the toroidal component of the plasma current density. This
paper deals with the identification of this nonlinearity source from
experimental measurements in real time. The proposed method is based on a fixed
point algorithm, a finite element resolution, a reduced basis method and a
least-square optimization formulation. This is implemented in a software called
Equinox with which several numerical experiments are conducted to explore the
identification problem. It is shown that the identification of the profile of
the averaged current density and of the safety factor as a function of the
poloidal flux is very robust.
