Extension of the Sweet-Parker Magnetic Reconnection to the Relativistic Plasma

We study the magnetic reconnection for relativistic plasma in the framework of magnetohydrodynamics and by means of the Particle-In-Cell (PIC) simulation. In the former approach, the magnetic fields are assumed to reconnect steadily inside the diffusion region as assumed in the conventional Sweet-Parker model. The model takes account of the pressure gradient between the diffusion and outflow regions as well as increase in the inertia due to the thermal energy. At a given inflow velocity (reconnection rate), the outflow velocity is faster when the Poynting to plasma kinetic fluxes in the inflow region (namely the magnetization parameter σi) is larger. For σi � 1, the plasma outflow velocity decreases with the increase in the inflow velocity since the larger heating rate enhances the inertia. We also carried out 2-dimensional PIC simulations to study the σi-dependence of the outflow speed. The results indicate that the outflow velocity converges to a saturation value in the limit of large σi. On the other hand, the thermal energy increases with σi without saturation. These results are consistent with those based on the MHD analysis.