Finite shift stabilization of ballooning modes in a high-beta tokamak

The widely used s vs α stability diagram for ballooning modes is based on the assumption of circular flux surfaces with small shifts. (Here s=rq′/q and α=−R0q2β′.) This analysis is extended to include finite shifts. There again results a universal stability diagram, although in this case it is parametrized by three quantities s, α, and σ′, the differential shift between flux surfaces. The analysis shows that the inclusion of a finite shift leads to a significant further stabilization of the ballooning modes over that from the standard case.