We propose an iterative finite element method for solving non-linear
hydromagnetic and steady Euler's equations. Some three-dimensional
computational tests are given to confirm the convergence and the high
efficiency of the method.
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.
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.
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.
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 problem of equilibrium of a plasma in a Tokamak is a free boundary
problemdescribed by the Grad-Shafranov equation in axisymmetric configurations.
The right hand side of this equation is a non linear source, which represents
the toroidal component of the plasma current density. This paper deals with the
real time identification of this non linear source from experimental
measurements. The proposed method is based on a fixed point algorithm, a finite
element resolution, a reduced basis method and a least-square optimization
formulation.