Three-dimensional simulations of compressible tearing instability

Abstract

Three-dimensional numerical simulations of the tearing instability in the framework of compressible and resistive magnetohydrodynamics are presented. Simulations have been performed with a novel Eulerian conservative high order code, including an explicit resistivity, which uses implicit high order numerical schemes having higher spectral resolution than classical schemes. The linear and non linear evolution of the tearing instability has been followed for force-free and pressure-balanced initial equilibrium configurations. Pressure equilibrium configurations are subject to a secondary instability which drives the system toward a quasi two dimensional structure oriented perpendicularly to the initial configuration. The development of secondary instabilities is suppressed by a guide field allowing the coalescence instability to fully develop in the system. Force-free initial configurations follow an intermediate path with respect the previous cases: Strong coalescence of magnetic islands, due to the non linear evolution of the tearing instability, is observed before the system enters in a phase dominated by 3D modes. The histories of the differing initial current-sheet equilibria have counterparts in the energy spectra that, for all three cases, are observed to be strongly anisotropic.

Resistive Magnetohydrodynamics Simulations of the Ideal Tearing Mode

“…This behavior is compatible with other 2D simulations of the tearing instability (see, for example, Figure 3 in Landi et al 2008).…”

“…We have verified that this relatively low resolution along the periodic direction is adequate, due the extreme accuracy of Fourier methods and the rather smooth gradients observed in the y direction. In spite of the relatively high values of S, in addition to instability, the equilibrium diffuses on timescales which although long compared to the instability, are still sufficient to affect linear evolution leading to slightly underestimate the growth rates of linear modes (Landi et al 2008). To avoid this, in the single mode linear analysis described below, the diffusion term of the initial equilibrium is subtracted on the rhs of the induction equation at all times.…”

“…Moreover, here only 2D MHD reconnection has been considered, while additional dynamics is expected in 3D simulations, with or without the presence of a guide field and/or shear flows, where the onset of the secondary plasmoid instability may be heavily modified by the interaction with other modes (Onofri et al 2004;Landi et al 2008;Bettarini et al 2009;Landi & Bettarini 2012). …”

Fast reconnection in relativistic plasmas: the magnetohydrodynamics tearing instability revisited

“…This is enforced by the fact that even in the fully nonlinear MHD case of our previous paper, when diffusion of B0 was not removed from the induction equation, growth rates were found to be smaller by the same amount as in the present study. For further details on the classical MHD code and deeper technical discussions see Landi, Velli & Einaudi (2005); Landi et al (2008).…”

High-order methods for the simulation of hydromagnetic instabilities in core-collapse supernovae

“…We performed 2D simulations of the tearing instability in a current sheet in force-free magneto-hydrostatic equilibrium with constant gas pressure and density using similar physical parameters as in Landi et al (2008) for different resistivities. The initial configuration is perturbed with transverse velocity fluctuations, which are much smaller than both the Alfvén and the sound speed.…”