Stability criterion for edge-localized, high-n external modes in tokamaks

The ideal-magnetohydrodynamics (MHD) energy principle is used to derive a n ecessary stability criterion for high-toroidal-number (n) external modes in axisymmetric equilibria. The corresponding trial functions are expressed i n the ballooning representation, but have a finite amplitude at the plasma boundary and can apply to equilibria where the conventional, high-n interna l ballooning criterion predicts stability. These trial functions are constr ucted by solving the standard local ballooning equation at the plasma bound ary flux surface with the radial wave number parameter as a complex eigenva lue, such that the radial envelope of the mode is an exponential decaying i nto the plasma. The resulting stability criterion includes the surface and vacuum contributions to the MHD potential energy associated with the mode f inite edge amplitude, and provides a framework for analyzing free-boundary ballooning and peeling modes. (C) 2001 American Institute of Physics.