Ideal ballooning stability near an equilibrium magnetic island

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 closet 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 X-point and in poloidal angle on the bad curvature side of the tokamak are 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 separatrix become ballooning unstable. Secondary ballooning instabilities may play a part in the crash phase of sawteeth or macroscopic island dynamics