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

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

Modélisation, simulation numérique et problèmes inverses. Contributions en physique des plasmas de Tokamak, en écologie marine et autres travaux

Dans ce document je décris mon activité scientifique depuis la fin de ma thèse soutenue en octobre 2002. Il est constitué de deux parties. La première est une synthèse de mon travail et la seconde un recueil de mes articles les plus représentatifs en rapport avec les travaux décrits en première partie. La partie synthèse est constituée de deux chapitres. Le premier regroupe mes travaux les plus récents, depuis fin 2007, sur la thématique de la simulation numérique et des problèmes inverses pour les plasmas de Tokamak. Le second regroupe des travaux plus anciens concernant la modélisation et l'assimilation variationnelle de données en écologie marine ainsi que deux autres travaux isolés

An overview of the numerical methods for tokamak plasma equilibrium computation implemented in the NICE code

International audienceThe code NICE (Newton direct and Inverse Computation for Equilibrium) enables to solve numerically several problems of plasma free-boundary equilibrium computations in a tokamak: plasma free-boundary only reconstruction and magnetic measurements interpolation, full free-boundary equilibrium reconstruction from magnetic measurements and possibly internal measurements (interferometry, classical linear approximation polarimetry or Stokes model polarimety, Motional Stark Effect and pressure), direct and inverse, static and quasi-static free-boundary equilibrium computations. NICE unifies and upgrades 3 former codes VacTH [1], EQUINOX [2] and CEDRES++ [3]. The strength of NICE is to gather in a single finite element framework different equilibrium computation modes. It makes intensive use of Newton method and Sequential Quadratic Programming method to solve non linear problems. NICE is used routinely for WEST tokamak operation. It is also adapted to the IMAS (ITER Modelling and Analysis Suite) format which makes it usable on many different fusion tokamak reactors. In this document we give a general overview of the numerical methods implemented in NICE as well as a number of computation examples

EQUILIBRIUM RECONSTRUCTION FROM DISCRETE MAGNETIC MEASUREMENTS IN A TOKAMAK

International audienceWe describe an algorithm for the reconstruction of the equilibrium in a Tokamak from discrete magnetic measurements. In order to solve this inverse problem we first use toroidal harmonics to compute Cauchy boundary conditions on a fixed closed contour. Then we use these Cauchy boundary conditions to solve a non-linear source identification problem

FEM-BEM coupling methods for Tokamak plasma axisymmetric free-boundary equilibrium computations in unbounded domains

International audienceIncorporating boundary conditions at infinity into simulations on bounded computational domains is a repeatedly occurring problem in scientific computing. The combination of finite element methods (FEM) and boundary element methods (BEM) is the obvious instrument, and we adapt here for the first time the two standard FEM-BEM coupling approaches to the free-boundary equilibrium problem: the Johnson-Nédélec coupling and the Bielak-MacCamy coupling. We recall also the classical approach for fusion applications, dubbed according to its first appearance von-Hagenow-Lackner coupling and present the less used alternative introduced by Albanese, Blum and de Barbieri in [2]. We show that the von-Hagenow-Lackner coupling suffers from undesirable non-optimal convergence properties, that suggest that other coupling schemes, in particular Johnson-Nédélec or Albanese-Blum-de Barbieri are more appropriate for non-linear equilibrium problems. Moreover, we show that any of such coupling methods requires Newton-like iteration schemes for solving the corresponding non-linear discrete algebraic systems

Equilibrium reconstruction at JET using Stokes model for polarimetry

This paper presents the first application to real JET data of the new equilibrium code NICE which enables the consistent resolution of the inverse equilibrium reconstruction problem in the framework of non-linear free-boundary equilibrium coupled to the Stokes model equation for polarimetry. The conducted numerical experiments enable first of all to validate NICE by comparing it to the well-established EFIT code on 4 selected high performance shots. Secondly the results indicate that the fit to polarimetry measurements clearly benefits from the use of Stokes vector measurements compared to the classical case of Faraday measurements, and that the reconstructed profiles are better constrained with smaller error bars and are closer from theprofiles reconstructed by EFTM, the EFIT JET code using internal MSE constraints.Ce travail présente la première utilisation de données réelles du tokamak JET avec le code NICE pour la reconstruction de l'équilibre d'un plasma à frontière libre et utilisant le modèle de Stokes pour la polarimétrie

Equilibrium reconstruction at JET using Stokes model for polarimetry

International audienceThis paper presents the first application to real JET data of the new equilibrium code NICE which enables the consistent resolution of the inverse equilibrium reconstruction problem in the framework of non-linear free-boundary equilibrium coupled to the Stokes model equation for polarimetry. The conducted numerical experiments enable first of all to validate NICE by comparing it to the well-established EFIT code on 4 selected high performance shots. Secondly the results indicate that the fit to polarimetry measurements clearly benefits from the use of Stokes vector measurements compared to the classical case of Faraday measurements, and that the reconstructed p and ff profiles are better constrained with smaller error bars and are closer to the profiles reconstructed by EFTM, the EFIT JET code using internal MSE constraints