Ballooning β Limit of a Non-Circular Small-Aspect-Ratio Tokamak

High mode number ballooning instabilities have been studied to obtain the maximum beta values for the quasi-uniform current equilibrium model (Soloviev). For circular boundary plasmas, the reduction of the aspect ratio does not lead to the increase of the ballooning mode stable β-value. The critical β is approximately given by 0.03/A{0.25+(1/A)2}, where A is the plasma aspect ratio. For the stability of non-circular cases against high n ideal ballooning modes, the moderate vertical elongation of D-shapes is appropriate for large-aspect-ratio tokamaks, while horizontally elongated inverse-D shapes are favorable for small-aspect-ratio plasmas.