Numerical calculations demonstrating complete stabilization of the ideal magnetohydrodynamic resistive wall mode by longitudinal flow

Abstract

The cylindrical ideal magnetohydrodynamic (MHD) stability problem, including flow and a resistive wall, is cast in the standard mathematical form, ωA⋅x=B⋅x, without discretizing the vacuum regions surrounding the plasma. This is accomplished by means of a finite element expansion for the plasma perturbations, by coupling the plasma surface perturbations to the resistive wall using a Green’s function approach, and by expanding the unknown vector, x, to include the perturbed current in the resistive wall as an additional degree of freedom. The ideal MHD resistive wall mode (RWM) can be stabilized when the plasma has a uniform equilibrium flow such that the RWM frequency resonates with the plasma’s Doppler-shifted sound continuum modes. The resonance induces a singularity in the parallel component of the plasma perturbations, which must be adequately resolved. Complete stabilization within the ideal MHD model (i.e., without parallel damping being added) is achieved as the grid spacing in the region of the resonance is extrapolated to 0 step size.