Ideal ballooning stability near an equilibrium magnetic island

Abstract

The stability properties of ideal ballooning modes on toroidal flux surfaces near a quasistatic magnetic island is examined. On these surfaces, magnetic field-line trajectories tend to bunch on that part of the magnetic surface closest to the X-point of the magnetic island. Because of this preferential bunching, the stabilizing effect of field-line bending due to magnetic shear can be reduced. Eigenfunctions localized in helical angle near the Xpoint and in poloidal angle on the bad curvature side of the tokamak a.re more susceptible to " ballooning instability than are modes in corresponding equilibria without the magnetic '_ island. For a slowly growing island, a growing number of flux surfaces located near the II separatrix become ballooning unstable. Secondary ballooning instabilities may play a part in the crash phase of sawteeth or macroscopic island dynamics.