Resistive instabilities and field line reconnection

A review is given of the linear theory of reconnection for a plane current layer. The three basic modes are the Rippling Mode, the Gravitational Interchange Mode, and the Tearing Mode. A derivation is given of the magnetic field energy which provides the driving force for the tearing mode. The necessary concepts for the analysis of tearing modes in cylindrical geometry are introduced. The equations governing tearing mode evolution in a tokamak are expanded to lowest order in the inverse aspect ratio. The tearing mode in a toroidal device is closely related to the ideal magnetohydrodynamic kink mode, and this relationship is stressed in the derivations of the linear growth rates for modes with poloidal model number m > 2 and for the quite different m = 1 mode. The nonlinear theory of tearing mode development and the implications of this theory for the understanding of toroidal magnetic confinement devices is reviewed