Finite β effects on the nonlinear evolution of the (m = 1; n = 1) mode in tokamaks

Abstract

The stability and evolution of ISX‐B‐like plasmas are numerically studied using a reduced set of resistive magnetohydrodynamic equations. For a sequence of equilibria stable to ideal modes, the n = 1 mode changes from a tearing branch to a pressure‐driven branch as β_p is increased. When this mode is unstable at low β, it is just the (m = 1; n = 1) tearing mode. Higher n modes also become linearly unstable with increasing β_p; they are essentially pressure‐driven and have ballooning character. For low values of β, the instability is best described as a β_p distortion of the (m = 1; n = 1) tearing mode. This mode drives many other helicities through toroidal and nonlinear couplings. As β_p is increased, the growth of the m = 1 island slows down in time, going from exponential to linear before reconnection occurs. If β_p is large enough, the island saturates without reconnection. A broad spectrum of other modes, driven by the (m = 1; n = 1) instability, is produced. These results agree with some observed features of magnetohydrodynamic activity in ISX‐B.