Steady-state flows in a visco-resistive magnetohydrodynamic model of tokamak plasmas with inhomogeneous heating

E Roverc'H,H Oueslati,M.-C Firpo

doi:10.1017/s0022377821000313

Abstract

The axisymmetric visco-resistive magnetohydrodynamic steady states allowing flows (i.e. non-vanishing velocity fields) are computed for a toroidal JET-like geometry. It is shown that a spatially inhomogeneous heating of moderate magnitude leads to an increase of typical toroidal speeds with respect to the situation with uniform temperature with identical mean Hartmann numbers. A symmetry argument is introduced to capture the symmetry breaking, induced by the temperature gradient, that produces a net toroidal plasma flow.

Highlights

Plasma rotation has been recognized as a key ingredient in the confinement properties of heat and particles in tokamak plasmas
We introduce the modelling frame used to compute axisymmetric visco-resistive MHD steady states allowing for non-vanishing velocity fields
It appears that the uniform-temperature, purely antisymmetric solution is unstable with respect to finite-temperature perturbations

Summary

Introduction

Plasma rotation has been recognized as a key ingredient in the confinement properties of heat and particles in tokamak plasmas. This symmetry breaking may enter through boundary conditions and through the geometry An example of this is by using external magnetic perturbations which has recently been shown (Oueslati & Firpo 2020) to enhance plasma steady-state speeds and produce a net toroidal flow. One chooses some vertically inhomogeneous heating that fixes the boundary condition for T; whereas one assumes, with some arbitrariness, that the toroidal vorticity vanishes on the plasma border. This is written explicitly in Appendix A. The equations were solved under their weak form using the finite element method with FreeFem++ (Hecht 2012; Oueslati et al 2019)

Simulation results with localized heating

Link between velocity and symmetry

Conclusions