  The real-time reconstruction of the plasma magnetic equilibrium in a Tokamak
is a key point to access high performance regimes. Indeed, the shape of the
plasma current density profile is a direct output of the reconstruction and has
a leading effect for reaching a steady-state high performance regime of
operation. In this paper we present the methodology followed to identify
numerically the plasma current density in a Tokamak and its equilibrium. In
order to meet the real-time requirements a C++ software has been developed
using the combination of a finite element method, a nonlinear fixed point
algorithm associated to a least square optimization procedure. The experimental
measurements that enable the identification are the magnetics on the vacuum
vessel, the interferometric and polarimetric measurements on several chords and
the motional Stark effect. Details are given about the validation of the
reconstruction on the JET tokamak, either by comparison with 'off-line'
equilibrium codes or real time software computing global quantities.
