Generalized moments for low-frequency modes in tokamaks and their application to drift and ballooning instabilities

Abstract

It is shown that the recently proposed electrostatic ballooning formulation in tokamak geometry absolutely destabilizes electrostatic drift waves (universal instability), and also further destabilizes the magnetohydrodynamic ballooning instability (finite ion Larmor-radius destabilization). The ion-density perturbation responsible for electrostatic ballooning effects have been derived by three independent methods: fluid approximation, the gyro-kinetic equation in a toroidal geometry, and the full kinetic equation in a plane-slab geometry with effective g (gravitational acceleration). All have yielded a consistent result. Toroidicity-induced frequency downshift is responsible for the universal mode, which smoothly reduces to the (stable) drift mode in slab geometry. For finite ion Larmor-radius destabilization of ballooning modes, toroidicity (due to magnetic drifts)-induced coupling with drift waves is also responsible.