Numerical simulations of high Lundquist number relativistic magnetic reconnection

TL;DR

This paper reports high-accuracy numerical simulations of relativistic magnetic reconnection at high Lundquist numbers, revealing plasma dynamics, instability thresholds, and effects of anisotropic resistivity in relativistic regimes.

Contribution

It introduces advanced numerical methods to simulate relativistic reconnection at unprecedented Lundquist numbers, analyzing plasma behavior, instabilities, and resistivity effects.

Findings

Lorentz factors up to ~4 can be achieved.

Sweet-Parker layers become unstable for S > 10^8.

Anisotropic Ohm law slightly increases reconnection rates.

Abstract

We present the results of two-dimensional and three-dimensional 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\sim 10^5-10^8. 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 \citet{Dumbser2009}. The possibility of producing high Lorentz factors is discussed, showing that Lorentz factors close to \sim 4 can be produced for a plasma parameter \sigma_m=20. Moreover, we find that the Sweet-Parker layers are unstable, generating secondary magnetic islands, but only for S > S_c = 10^8, much larger than what is reported in the Newtonian regime. Finally, the effects of a mildly anisotropic Ohm 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% larger with respect to the perfectly isotropic Ohm law.