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 = (kappa(2) - kappa)/(kappa(2) + 1), where kappa 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 (similar to 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. (C) 2000 American Institute of Physics. [S1070-664X(00)91005-X].