Stability of the N = 1 Ideal Internal Kink for Large Aspect Ratio Shafranov Equilibria

Stability limits for the ideal internal kink mode are calculated analytically for the Shafranov current profile using the large aspect ratio expansion. For equilibria with q(a) > 2 and circular cross-section, the maximum stable poloidal beta is below 0.1. In the absence of a conducting wall, an equilibrium with q(a) < 2 is unstable at arbitrarily small positive poloidal-beta or shear inside the q = 1 surface. The effects of non-circularity are discussed and quantitative results are given for elliptic cross-sections.