Numerical simulations of relativistic magnetic reconnection with Galerkin methods

TL;DR

This paper uses advanced numerical methods to simulate relativistic magnetic reconnection, revealing high Lorentz factors and the instability of Sweet-Parker layers at extremely high Lundquist numbers.

Contribution

It introduces high-order finite volume and discontinuous Galerkin methods for accurate simulations of relativistic magnetic reconnection, exploring dynamics at high Lundquist numbers.

Findings

Lorentz factors up to ~4 for sigma=20

Sweet-Parker layers become unstable at S > 10^8

Secondary magnetic islands form at very high Lundquist numbers

Abstract

We present the results of two-dimensional magnetohydrodynamical numerical simulations of relativistic magnetic reconnection, with particular emphasis on the dynamics of Petschek-type configurations with high Lundquist numbers, S ~ 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 Dumbser & Zanotti (2009). The possibility of producing high Lorentz factors is discussed, by studying the effects produced on the dynamics by different magnetization and resistivity regimes. We show that Lorentz factors close to ~4 can be produced for a plasma magnetization parameter sigma=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.