Explosive magnetic reconnection caused by an X-shaped current-vortex layer in a collisionless plasma

Abstract

A mechanism for explosive magnetic reconnection is investigated by analyzing the nonlinear evolution of a collisionless tearing mode in a two-fluid model that includes the effects of electron inertia and temperature. These effects cooperatively enable a fast reconnection by forming an Xshaped current-vortex layer centered at the reconnection point. A high-resolution simulation of this model for an unprecedentedly small electron skin depth d e and ion-sound gyroradius ρ s , satisfying d e = ρ s , shows an explosive tendency for nonlinear growth of the tearing mode, where it is newly found that the explosive widening of the X-shaped layer occurs locally around the reconnection point with the length of the X shape being shorter than the domain length and the wavelength of the linear tearing mode. The reason for the onset of this locally enhanced reconnection is explained theoretically by developing a novel nonlinear and nonequilibrium inner solution that models the local X-shaped layer, and then matching it to an outer solution that is approximated by a linear tearing eigenmode with a shorter wavelength than the domain length. This theoretical model proves that the local reconnection can release the magnetic energy more efficiently than the global one and the estimated scaling of the explosive growth rate agrees well with the simulation results.

An Explosive Scaling Law for Nonlinear Magnetic Reconnection and Its Insensitivity to Microscopic Scales

“…In this case, we find an X-shaped current sheet to be generated nonlinearly, and we obtain an accelerated reconnection, as found in earlier works [8,11,12]. Our recent work [15] shows that this X-shaped layer emerges locally near the reconnection point (as shown in the panel withˆ = 0.02 in Fig. 2) and then expands rapidly and explosively.…”

“…Nevertheless, we show that almost the same explosive reconnection speed as found in Ref. [15] is obtained whenever a local X-shaped layer emerges, even though the layer width varies, depending on the values of the microscale parameters. This explosive scaling law may therefore be universal in that it is insensitive to the microscale physics.…”

“…We accomplish this by replacing the small scale d by the inner layer width δ in and the potential U by the magnetic energy W = (1/2) |∇ψ| 2 dxdy. The following discussion is a brief review of our previous theory [15], but here we greatly simplify the logic by ignoring the microscale physics inside the current layer.…”

“…For small aspect ratios, where Δ 1/δ in , the growth of is likely to be saturated below the level of δ in (a survey of the dependence on Δ is given in Ref. [15] for an ideal two-fluid case). Conversely, in the large-Δ case (Δ 1/δ in ), the growth will not saturate, since there is no stabilizing mechanism in our problem.…”

“…Many simulation results [8][9][10][11][12][13] that when ρ S and ρ i are comparable to the electron skin depth d e , the reconnection rate is nonlinearly accelerated by an X-shaped current layer (which is only visually similar to the Petschek model [14]). Using an ideal two-fluid model (d e = ρ S 0, ρ i = 0, and no resistivity η = 0), our recent work [15] has shown that this X-shaped layer is actually localized around the reconnection point and that this spatially concentrated reconnection is responsible for persistent nonlinear acceleration which, moreover, appears to be explosive.…”