Stationary magnetic field line reconnection in a tearing-unstable plasma slab

A nonlinear theory of a collisionless tearing mode is developed for the case of a plasma slab immersed in a sheared magnetic field and applied to the problem of magnetic field line reconnection. The main nonlinear effect comes from the diffusion of the magnetic field lines due to overlapping of magnetic islands created by the growth of the tearing mode. This effect is described by the effective collision integral in the kinetic equation for the particle distribution function which conserves both momentum and energy in the system. Nonlinear effects reduce the growth rate, but the instability saturation achieved is only due to quasi-linear relaxation. The reconnection rate of the magnetic field lines is calculated on the basis of the nonlinear theory of the tearing mode.