Stability of Tokamak Equilibrium with Internal Transport Barrier against High-n MHD Ballooning Mode

A new eigen-mode equation for the tokamak high-n (the toroidal mode number) ideal magnetohydrodynamic (MHD) ballooning mode in tokamak plasmas is derived to include the toroidal effects that are significant for stability of configurations with internal transport barriers (ITBs). For tokamak equilibria of shift circular flux surfaces, these toroidal effects basically are the finite inverse aspect ratio and the Shafranov shift. The former yields the averaged favorable curvature stabilization while the latter further strengthens this effect, leading to a low shear stable channel connecting the first and second stability regions, and to the shrinkage of unstable region in the (s,α) diagram. The dependence of the critical shear, below which the plasma is stable, on these effects is given. These results are important for understanding the ITB physics to some regards.