2D Relativistic MHD Simulations of the Kruskal-Schwarzschild Instability in a Relativistic Striped Wind

Abstract

We study the linear and non-linear development of the Kruskal-Schwarzchild Instability in a relativisitically expanding striped wind. This instability is the generalization of Rayleigh-Taylor instability in the presence of a magnetic field. It has been suggested to produce a self-sustained acceleration mechanism in strongly magnetized outflows found in active galactic nuclei, gamma-ray bursts, and micro-quasars. The instability leads to magnetic reconnection, but in contrast with steady-state Sweet-Parker reconnection, the dissipation rate is not limited by the current layer's small aspect ratio. We performed two-dimensional (2D) relativistic magneto-hydrodynamic (RMHD) simulations featuring two cold and highly magnetized ($1\leqσ\leq10^{3}$) plasma layers with an anti-parallel magnetic field separated by a thin layer of relativistically hot plasma with a local effective gravity induced by the outflow's acceleration. Our simulations show how the heavier relativistically hot plasma in the reconnecting layer drips out and allows oppositely oriented magnetic field lines to reconnect. The instability's growth rate in the linear regime matches the predictions of linear stability analysis. We find turbulence rather than an ordered bulk flow near the reconnection region, with turbulent velocities up to $\sim0.1$c, largely independent of model parameters. However, the magnetic energy dissipation rate is found to be much slower, corresponding to an effective ordered bulk velocity inflow into the reconnection region $v_{\rm in}=β_{\rm in}c$, of $10^{-3}\lesssimβ_{\rm in}\lesssim 5\times10^{-3}$. This occurs due to the slow evacuation of hot plasma from the current layer, largely because of the Kelvin-Helmholtz instability experienced by the dripping plasma. 3D RMHD simulations are needed to further investigate the non-linear regime.