Influence of continuous spectrum on ballooning instabilities in plasmas with shear-flow

Abstract

The influence of shear-flow on stability of plasma ballooning modes is important for Tokamak experiments. In a static plasma, the growth rate of ballooning modes is readily determined using the “ballooning transformation,” but this is ineffective for plasmas with flow. One then has only the quasi-static approximation. This gives the growth rate in the limit that shear velocity Ω′→0, but no other information on the effect of shear-flow. Furthermore, it is invalid in typical cases because of the intervention of the stable magnetohydrodynamic continuum. In this paper, a simple model is used to investigate the influence of shear-flow on ballooning modes. This shows that the intervention of the continuum leads to a reduction in the growth rate proportional to |Ω′| for small Ω′. This is in accord with some numerical simulations—but contrary to the (Ω′)2 variation expected from a perturbation expansion. In fact, since the effect is nonanalytic in Ω′, it cannot be obtained from a perturbation expansion in Ω′ and an alternative formalism is first developed for dealing with this problem.