Ideal MHD Ballooning modes, shear flow and the stable continuum

There is a well established theory of Ballooning modes in a toroidal plasma. The cornerstone of this is a local eigenvalue λ on each magnetic surface- which also depends on the Ballooning phase angle k. In stationary plasmas, λ(k) is required only near its maximum, but in rotating plasmas its average over k is required. Unfortunately in many cases λ(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. 1 a