SIMPLIFIED IDEAL MHD NORMAL-MODE EQUATIONS FOR TOROIDAL AXISYMMETRICAL PLASMAS

The ideal MHD normal mode equations for general toroidal axisymmetric plasmas can be significantly simplified by properly treating the compressibility team del . xi over arrow pointing right in two limiting cases: omega2 << k(parallel-to)2c(s)2 and omega2 >> k(parallel-to)2c(s)2, where k(parallel-to) = k over arrow pointing right . B over arrow pointing right/B 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 approximation, 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.