On the explosive phase of the tearing mode in double current sheet plasmas: effect of the equilibrium magnetic configuration on the onset threshold and growth rate

Abstract

Magnetic reconnection associated with the tearing instability occurring in double-current sheet systems is investigated within the framework of reduced resistive magnetohydrodynamics (MHD) in a two-dimensional Cartesian geometry. The explosive non linear phase is particularly explored using the adaptive finite-element FINMHD code. The critical aspect ratio, that is defined as the minimum $L/x_s$ ratio (with $L$ and $x_s$ being the periodic system length and half-distance between the two current layers respectively) necessary for non linear destabilization after the linear and early non linear saturation phases, is obtained. The latter threshold is independent of the details of the chosen initial equilibrium (double Harris-like magnetic profile) and of the resistivity. Its value is shown to be $4.7$, that is close and slightly smaller than the value of order $5$ deduced using a more particular equilibrium configuration in previous studies. The time dependence of the kinetic energy ($E_K$) is shown to follow a double exponential law, $E_K \propto \exp \ [e^{(\gamma^* t)} ]$, with a pseudo-growth rate $\gamma^* \simeq 0.1 \ t_A^ {-1}$ ($t_A$ being the characteristic Alfv\'en time) that is again independent of the configuration and resistivity. The mechanism offers a possible explanation for the sudden onset of explosive magnetic energy release occurring on the fast Alfv\'en time scale in disruptive events of astrophysical plasmas with pre-existing double current sheets like in the solar corona.