Quenching of Tearing Mode Instability by Transverse Magnetic Fields in Reconnection Current Sheets

Abstract: The tearing mode instability is a key process for magnetic energy conversion in magnetohydrodynamics, once anti-parallel components are allowed to reconnect, leading to the formation of magnetic islands. It has been employed to explain phenomena at different scales in nature, from galactic nuclei, to solar flares and laboratory fusion devices. In this study, we investigate the dynamics of a current sheet in the presence of a transverse magnetic field component, in the framework of viscoresistive, incompressible magnetohydrodynamics (MHD), both analytically and by means of direct numerical simulations. Firstly, we obtain analytical solution for the time-varying one-dimensional profile of an initial Harris current sheet in the presence of a transverse field. We find that the introduction of a transverse magnetic field disrupts the system's equilibrium, leading to the natural development of a neutral layer with shear flows within the current sheet, one along the antiparallel magnetic component and another along the guide field direction. Secondly, through numerical analysis, we examine the dispersion relation of the incompressible MHD equations in the context of a modified equilibrium profile due to the transverse field. Our findings indicate a rapid suppression of unstable modes of tearing instability with the width of the neutral layer, confirming the analytical predictions. These results offer new insightful understanding on the interplay between transverse magnetic fields, shear flows, and tearing mode instabilities in current sheet environments.