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Accueil > Plus d’actualités > Hanen Oueslati defended her PhD "Modeling and numerical simulation of tokamak plasmas : axisymmetric steady states with finite flows"

Hanen Oueslati defended her PhD "Modeling and numerical simulation of tokamak plasmas : axisymmetric steady states with finite flows"

On July 13, 2021, Hanen Oueslati defended her PhD "Modeling and numerical simulation of tokamak plasmas : axisymmetric steady states with finite flows", under the supervisons of Marie-Christine Firpo

Abstract
The usual equilibrium states in tokamak plasmas are solutions of the Grad-Shafranov equation. It is assumed that the plasma, seen as a conductive fluid, has zero velocity. Experimentally, there are many observations of spontaneous rotation in tokamaks, especially in the toroidal direction. This rotation proves to have important effects on the improvement of the confinement and on the entrance into the H-mode of improved confinement in tokamaks. To clarify these experimental observations, we propose to determine numerically the axisymmetric steady-states of the non-linear equations of visco-resistive magnetohydrodynamics obtained by reintroducing the convective term(v. grad)v. We take into account the external electric field in the toroidal direction used to create the toroidal current required in a tokamak to create the poloidal component of the magnetic field. We present numerical results obtained using the open source code FreeFem ++ in the geometries of tokamaks of the JET and ITER in the case of a uniform resistivity and with no magnetic perturbation. We have considered realistic values of the resistivity η and we have varied the viscosity 𝜈, of which the realistic order of magnitude is poorly known. We define a control parameter called the Hartman number H, a dimensionless number which evaluates both the viscosity and the resistivity H= (η𝜈)-1/2. We observe that, the more H increases, the more the velocity in the toroidal direction increases. Moreover, all other things being equal, the toroidal speed is a growing function of the plasma temperature and is greater in ITER than in JET. We show in a second step the effect of a small perturbation of the magnetic configurations on the plasma velocity in the toroidal direction. The tokamak up-down symmetry is broken for weak axisymmetric perturbation, and the rotation of the plasma increases. Another way to increase plasma rotation is to introduce a resistivity η(T) which depends on the plasma temperature. We present results for various up-down temperature variation (∆T). The latter has an effect of increasing the the plasma velocity. In all these simulations, the visco-resistive MHD model is solved with the finite element method using the FreeFem++ open source code for numerical solution of partial differential equations.

Jury :
Mr Xavier Leoncini : Rapporteur (Centre de Physique Théorique - Campus de Luminy Marseille)
Mr Maxime Lesur : rapporteur (Institut Jean Lamour - Université de Lorraine)
Mr Maxime Mikikian : examinateur ( Université d’Orléans )


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CNRS Ecole Polytechnique Sorbonne Université Université Paris-Saclay Observatoire de Paris
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Exploitant du site : Laboratoire de Physique des Plasmas, Ecole Polytechnique route de Saclay F-91128 PALAISEAU CEDEX
Hébergeur : Laboratoire de Physique des Plasmas, Ecole Polytechnique route de Saclay F-91128 PALAISEAU CEDEX
Directeur de la publication : Dominique Fontaine (Directrice)