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.