Three-Dimensional Simulations of Magnetic Reconnection with or Without Velocity Shears

The properties of spontaneous reconnection of a current sheet analyzed via direct three-dimensional simulations are presented. In particular the non-linear dynamics of resistive instabilities has been studied in absence or in presence of velocity shears. It is shown that full three-dimensional simulations allow the inclusion of a rich variety of (ideal) secondary instabilities which, depending on the initial equilibrium magnetic field configuration, determine the final fate of the system in the fully non linear regime. In particular in presence of a guide-field the dynamic is similar to what observed in two-dimensional simulations with energy driven toward both smaller and larger scales and energy spectra anisotropy. For different magnetic field configurations, the final state is characterized by the disruption of the coalesced structure created during the resistive phase and the system is characterized by a more chaotic state. A discussion on the importance of high-order numerical techniques in numerical simulations of magnetic reconnection is also present.