Ideal-MHD stability of finite-beta plasmas

Abstract

An analytical theory of ideal-MHD ballooning modes that can be excited in finite-β equilibria is carried out on model configurations which include the effects of the increase of the poloidal field toward the outer edge of the plasma column and the dependence of the rate of magnetic shear on the poloidal angle. The relevant growth rates and eigensolutions are, in fact, significantly different from those derived on the basis of ‘low-β’ model configurations that omit one or both of the effects mentioned above, and provide different indications for the expected interaction between ideal-MHD and kinetic modes. For each value of the shear parameter ŝ, the normalized growth rate Γ becomes real at a critical value of the dimensionless pressure gradient parameter G. When the latter is increased at constant ŝ, Γ is found to increase only up to a saturation point, after which it decreases and tends to vanish at a second critical value of G.