STABILITY ANALYSIS OF THE IDEAL M=N=1 KINK MODE IN TOROIDAL GEOMETRY BY DIRECT EXPANSION OF THE HYDROMAGNETIC EQUATIONS

The stability condition and growth rate of the ideal, internal m = n = 1. kink mode in a toroidal plasma are calculated by means of a direct inverse-aspect-ratio expansion of the magnetohydrodynamic (MHD) equat ions, rather than by using the energy principle. The analysis is based on the use of computer-aided algebra. The general equation for incomp ressible MHD oscillations in a low-beta circular tokamak is derived to lowest order in the inverse aspect ratio. This derivation generalizes the Pfirsch-Schluter factor for the kinetic energy in toroidal geomet ry.