VMS finite element for MHD and reduced-MHD in Tokamak plasmas

The understanding of magnetohydrodynamic (MHD) instabilities is quite essential for the optimization of magnetically confined plasmas, a subject raising increasing interest as tokamak reactor design advances and projects such as ITER (International Thermonuclear Experimental Reactor) develop. Given the need and importance of numerically simulating and studying these instabilities, in this paper we report our effort in developing a stabilized full MHD numerical model to study tokamak plasmas in the frame of the Variational Multi-Scale formulation (VMS). Special attention is given to the plasma equilibrium calculation in limiter and x-point configurations. Several properties of the internal kink instability for a circular geometry were studied, e.g., dependence of the growth rate and mode sizes on the Reynolds Magnetic number and magnetic reconnection. The test cases were compared to other results numerically obtained before, as well as analytical developments. The effects of the VMS stabilization were rigorously verified in order to ensure a numerical stability without supressing the physical instabilities. The validation of this model gives rise to the possibility of simulating Edge-localized modes instabilities in the frame of full MHD equations.