Abstract
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) equations, rather than by using the energy principle. The analysis is based on the use of computer-aided algebra. The general equation for incompressible MHD oscillations in a low-β circular tokamak is derived to lowest order in the inverse aspect ratio. This derivation generalizes the Pfirsch-Schlüter factor for the kinetic energy in toroidal geometry.
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