Magnetohydrodynamics stability of compact stellarators

Recent stability results of external kink modes and vertical modes in compact stellarators are presented. The vertical mode is found to be stabilized by externally generated poloidal flux. A simple stability criterion is derived in the limit of large aspect ratio and constant current density. For a wall at infinite distance from the plasma, the amount of external flux needed for stabilization is given by F_i=(κ²-κ)/(κ²+1), where κ is the axisymmetric elongation and F_i is the fraction of the external rotational transform. A systematic parameter study shows that the external kink mode in a quasiaxisymmetric stellarator (QAS) can be stabilized at high beta (∼5%) without a conducting wall by magnetic shear via three-dimensional (3D) shaping. It is found that external kinks are driven by both parallel current and pressure gradient. The pressure contributes significantly to the overall drive through the curvature term and the Pfirsch-Schluter current.