Tokamak MHD instabilities: particular results of the internal-kink-mode theory

In order to understand the specificity of the tokamak kink modes, the author analyzes equations with the simplest case of low-pressure plasma and small current gradient when the ballooning effects are unimportant. It is shown that for small pressure and a small negative (usual) gradient of the longitudinal current, the m = 1 kink mode in a circular tokamak is stable (in contrast to the case of a circular cylinder). The ballooning effects are analyzed and it is shown that an increase of the plasma pressure is favorable for stability of the m = 1 mode if the current gradient is sufficiently small. The author considers the role of a negative current gradient in the high-pressure plamsa and points out that a destabilization of the m = 1 mode takes place if the gradient is increased