Content area
Abstract
Several aspects of the magnetohydrodynamic tearing mode have been studied.
The structure of the resistive m = 1 layer is investigated with quasilinear analysis. For profiles corresponding to ideal-MHD stability, the structure at the m = 1 mode is similar to m (GREATERTHEQ) 2, while for MHD-unstable profiles, the mode structure at the tearing layer turns out to be different and less affected by quasilinear corrections. The quasilinear effect on the growth rate is calculated numerically. For linear shear, a variational prescription to calculate the m = 1 tearing growth rates is given both for resistive and for viscous tearing.
The effect of a fast ion beam on tearing modes is treated in two limits. When beam-particle gyro-orbits are large, a rigid-beam model is justified, and the beam affects the ideal out region by changing (DELTA)' for m (GREATERTHEQ) 2 modes and by breaking the zero-order cancellation for m = 1 modes. A related correction to the finite-pressure Suydam criterion is found for m (GREATERTHEQ) 2. A counter-injected high-Z beam will increase tearing-instability in all cases. When beam-particle orbits are small, a consistent set of equations is obtained by combining a gyro-kinetic treatment of beam particles with a rederivation of Ohm's law. The ideal region is taken into account only through (DELTA)' and the asymptotic behaviour it imposes. The resistive layer is found to split into a substructure, where the beam effect changes the functional behaviour in an intermediate inner region. When the energy density in the beam is large enough the tearing mode growth rate becomes larger than that given by Furth, Killeen and Rosenbluth. The ion beam has been proposed for the purpose of driving a steady-state tokamak, but our results show that this would lead to a further destabilization of the tearing mode.
The tearing-layer equations are shown to be higher-order terms in the asymptotic expansion of the force laws in terms of the inverse tearing-layer width. Flows in the invariant direction are related to finite compressibility. Flowpatterns for the m = 1 ideal kink mode consistent with Newcomb-minimization are explicitly given, indicating singular behaviour of flows in the invariant direction at the rational surface.