Stability of internal transport barriers to ideal MHD ballooning modes

Internal transport barriers (ITB) in tokamaks can form near a minimum in the q profile, q(min), where magnetic shear is weak. We have analyzed their stability to short wavelength (n>1, where n is the toroidal mode number) ideal MHD ballooning modes, by considering the s-alpha model equilibrium. We show that the ballooning transformation fails in regions of low shear but that one can then adopt a complementary approach based on the recurrence relation describing the toroidal coupling of radially localized modes on adjacent rational surfaces. Inclusion of the stabilizing effects of favorable average curvature or finite-n using this technique leads to stable high-pressure ITB configurations. The theory also shows the advantages of operating with low-order rational values of q(min).