Numerical simulations of high Lundquist number relativistic magnetic reconnection

We present the results of 2D and 3D magnetohydrodynamical numerical simulations of relativistic magnetic reconnection, with particular emphasis on the dynamics of the plasma in a Petschek-type configuration with high Lundquist numbers, S˜ 105-108. The numerical scheme adopted, allowing for unprecedented accuracy for this type of calculations, is based on high-order finite volume and discontinuous Galerkin methods as recently proposed by Dumbser & Zanotti. The possibility of producing high Lorentz factors is discussed, showing that Lorentz factors close to ˜4 can be produced for a plasma parameter σm= 20. Moreover, we find that the Sweet-Parker layers are unstable, generating secondary magnetic islands, but only for S > Sc˜ 108, much larger than what is reported in the Newtonian regime. Finally, the effects of a mildly anisotropic Ohm's law are considered in a configuration with a guide magnetic field. Such effects produce only slightly faster reconnection rates and Lorentz factors of about 1 per cent larger with respect to the perfectly isotropic Ohm's law.