Three-dimensional simulations of magnetic reconnection in slab geometry

Magnetic reconnection in an incompressible plasma in three-dimensional slab geometry has been studied through magnetohydrodynamics numerical simulations. Particular attention has been paid to the case in which several unstable modes that correspond to resonant surfaces in different positions of the simulation domain, are excited at the beginning of the simulation. The dynamical evolution of such a system leads to a behavior different than what is expected from the linear theory. In particular the effects of the equilibrium field dissipation and the fact that several resonant surfaces are initially excited both concur in modifying the initial growth rates of the instability. In the nonlinear phase two basic phenomena are observed: first, the rapid transfer of energy to large wave numbers, corresponding to a direct cascade of the energy in the spectrum, which approaches, with increasing time, a power law; second, an energy transfer towards smaller wave numbers, which corresponds in the physical space to a coalescence of magnetic islands. Finally, the spectra in the periodic directions exhibit a strongly anisotropic behavior.