Numerical investigation of a three-dimensional four field model for collisionless magnetic reconnection

In this paper we present the numerical investigation of a three-dimensional four field model for magnetic reconnection in collisionless regimes. The model describes the evolution of the magnetic flux and vorticity together with the perturbations of the parallel magnetic and velocity fields. We explored the different behavior of vorticity and current density structures in low and high beta regimes, beta being the ratio between the plasma and magnetic pressure. A detailed analysis of the velocity field advecting the relevant physical quantities is presented. We show that, as the reconnection process evolves, velocity layers develop and become more and more localized. The shear of these layers increases with time ending up with the occurrence of secondary instabilities of the Kelvin-Helmholtz type. We also show how the beta parameter influences the different evolution of the current density structures, that preserve for longer time a laminar behavior at smaller beta values. A qualitative explanation of the structures formation on the different z-sections is also presented.