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

TL;DR

This paper presents a real-time method for reconstructing plasma equilibrium and identifying current density profiles in a Tokamak using a fixed point algorithm and finite element methods, demonstrating robustness in numerical experiments.

Contribution

It introduces a novel real-time identification technique for plasma current density profiles based on a fixed point algorithm and reduced basis methods.

Findings

Robust identification of current density profiles.

Effective real-time equilibrium reconstruction.

Validated through numerical experiments.

Abstract

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.