  This paper deals with the numerical reconstruction of the plasma current
density in a Tokamak and of its equilibrium. The problem consists in the
identification of a non-linear source in the 2D Grad-Shafranov equation, which
governs the axisymmetric equilibrium of a plasma in a Tokamak. The experimental
measurements that enable this identification are the magnetics on the vacuum
vessel, but also polarimetric and interferometric measures on several chords,
as well as motional Stark effect or pressure measurements. The reconstruction
can be obtained in real-time using a finite element method, a non-linear
fixed-point algorithm and a least-square optimization procedure.
