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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 plasmaslambda(k) is required only near its maximum, but in rotating plasmas itsaverage over k is required. Unfortunately in many case lambda(k) does not existfor some range of k, because the spectrum there contains only a stablecontinuum. This limits the application of the theory, and raises the importantquestion of whether this "stable interval" gives rise to significant damping.This question is re-examined using a new, simplified, model - which leads tothe conclusion that there is no appreciable damping at small shear flow. Inparticular, therefore, a small shear flow should not affect Ballooning modestability boundaries.

Ideal MHD Ballooning modes, shear flow and the stable continuum