Simplified Ideal MHD Normal Mode Equations for Toroidal Axisymmetric Plasmas

The ideal MHD normal mode equations for general toroidal axisymmetric plasmas can be significantly simplified by properly treating the compressibility team limiting cases: and c_s is the plasma sound velocity.These equations describing the general global modes (the low n, m mode) contain only two scalar functions. For tokamak plasmas, a further simplification, the shear Alfven approkimation, is introduced. It makes possible to describe the global mode by a simplified eigenmode equation with only one scalar function. This eigenequation, similar to the reduced tokamak equations widely used in recent literatures, provides a unified way to analyze the kink, Alfven spectrum and MHD TAE modes.