Magneto-Hydrodynamic High-n Ballooning Mode Instability of an Analytic Axi-Symmetric Toroidal Equilibrium with Arbitrary Aspect Ratio

An exact ballooning mode eigen-equation is derived to study stability of axi-symmetric toroidal plasma with arbitrary aspect ratio, including the tokamak, the finite aspect ratio and the spherical torus plasmas. For comparison with the widely used (s-α) model, an analytic exact equilibrium configuration with circular magnetic surfaces is analysed in detail. It is indicated that the (s-α) model needs to be improved for more realistic configurations.