Ideal MHD Ballooning modes, shear flow and the stable continuum

TL;DR

This paper investigates the impact of shear flow on ballooning mode stability in toroidal plasmas, concluding that small shear flows do not cause significant damping or alter stability boundaries.

Contribution

It introduces a simplified model to analyze the effect of shear flow on the stable continuum and shows that small shear flows do not lead to appreciable damping of ballooning modes.

Findings

Small shear flow does not cause significant damping.

The stable continuum does not lead to damping in the presence of small shear flow.

Shear flow does not affect ballooning mode stability boundaries.

Abstract

There is a well established theory of Ballooning modes in a toroidal plasma. The cornerstone of this is a local eigenvalue lambda on each magnetic surface - which also depends on the ballooning phase angle k. In stationary plasmas lambda(k) is required only near its maximum, but in rotating plasmas its average over k is required. Unfortunately in many case lambda(k) does not exist for some range of k, because the spectrum there contains only a stable continuum. This limits the application of the theory, and raises the important question of whether this "stable interval" gives rise to significant damping. This question is re-examined using a new, simplified, model - which leads to the conclusion that there is no appreciable damping at small shear flow. In particular, therefore, a small shear flow should not affect Ballooning mode stability boundaries.