Sawtooth oscillations and collisionless reconnection in tokamaks

Magnetic reconnection in collisionless plasmas and its relation to the frozen-in law for the generalized vorticity is discussed. Applications are made to two features of sawtooth collapse in tokamaks. The reformation of a configuration with q(0) < 1 after the sawtooth collapse, which was observed in simulations, is explained by the conservation of generalized vorticity. (Here q(0) is the safety factor in the center.) The experimental observation that the temperature and density profiles are flattened, although q(0) remains below unity throughout the sawtooth evolution, is explained by the drift of trapped particles under the influence of three-dimensional perturbations of the magnetic field. At the same time, reconnection is inhibited by the large parallel conductivity caused by the passing electrons. The large parallel conductivity leads to semi-ideal MHD behavior, but does not affect the perpendicular diffusion of heat and particles.