Numerical study of linear plasma dynamics in a spherical tokamak

Abstract

The magnetohydrodynamic equilibrium is the starting point to study macro- instabilities in a confined plasma; for the particular case, where the system is axially symmetric, the static and stationary equilibrium is due by the Grad-Shafranov equation. We present the equilibrium state for a toroidal plasma confined by a spherical Tokamak with aspect ratio A ∼1.6, total plasma current 1.3 MA and beta parameter β ∼0.35. The Grad-Shafranov equation is solved numerically in a rectangular region of the poloidal plane, using the finite differences method under a successive over-relaxation scheme. Profiles of poloidal magnetic flux, pressure, safety factor and magnetic field are presented. Subsequently, by using the resistive magnetohydrodynamic model, said equilibrium is subjected to perturbations in the velocity to study the dynamics of the plasma in the linear regime. The plasma dynamics simulation is carried out under a fourth order finite difference scheme for the spatial derivatives and implementing the Runge-Kutta algorithm as a temporal integrator. The results show that the perturbations are located in the plasma outer edge; however, some poloidal modes move toward the central zone around the magnetic axis.