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

Jacques Blum (1, 2) , Cedric Boulbe (1, 2) , Blaise Faugeras (1, 2)

1 JAD - Laboratoire Jean Alexandre Dieudonné
2 CASTOR - Control, Analysis and Simulations for TOkamak Research

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.

Domaines: Modélisation et simulation; Analyse numérique [math.NA]; Plasmas; Equations aux dérivées partielles [math.AP]; Optimisation et contrôle [math.OC]

Jacques Blum, Cedric Boulbe, Blaise Faugeras. Reconstruction of the equilibrium of the plasma in a Tokamak and identification of the current density profile in real time. Journal of Computational Physics, 2012, 231, pp.960-980. ⟨hal-00419608v3⟩