Faster Form of Electron Magnetic Reconnection with a Finite Length X-Line

Observations in Earth’s turbulent magnetosheath downstream of a quasiparallel bow shock reveal a prevalence of electron-scale current sheets favorable for electron-only reconnection where ions are not coupled to the reconnecting magnetic fields. In small-scale turbulence, magnetic structures associated with intense current sheets are limited in all dimensions. And since the coupling of ions are constrained by a minimum length scale, the dynamics of electron reconnection is likely to be 3D. Here, both 2D and 3D kinetic particle-in-cell simulations are used to investigate electron-only reconnection, focusing on the reconnection rate and associated electron flows. A new form of 3D electron-only reconnection spontaneously develops where the magnetic X-line is localized in the out-of-plane ($z$) direction. The consequence is an enhancement of the reconnection rate compared with two dimensions, which results from differential mass flux out of the diffusion region along $z$, enabling a faster inflow velocity and thus a larger reconnection rate. This outflow along $z$ is due to the magnetic tension force in $z$ just as the conventional exhaust tension force, allowing particles to leave the diffusion region efficiently along $z$ unlike the 2D configuration.

Figure 1

(a) $E_{\parallel }$ over half the 3D simulation domain at $t=152{\mathrm{\Omega }}_{ce}^{-1}$ in the $xz$ plane at $y=32.13$. The black circles are locations of X-lines associated with intense $E_{\parallel }$. The time evolution of one reconnection site located at $(x,y,z)=(14.14,32.13,55.27)$ is examined in (b). (b) Time evolution of peak $E_{\parallel }$ values are shown for 2D (red) and 3D (black) simulations. The solid curves show measurements of peak $E_{\parallel }$ around the X-line, while the dashed red line is calculated using the magnetic vector potential $\psi$.

Figure 2

2D (left column) and 3D (right column at $z=55.27$) results at $\sim 100{\mathrm{\Omega }}_{ce}^{-1}$ and $\sim 152{\mathrm{\Omega }}_{ce}^{-1}$, respectively, for the X-lines investigated in Fig. 1. The black contour lines in (a) and (c) are magnetic field lines while the black curves in (b) and (d) are short segments approximating projected magnetic field lines. The parallel electric field $E_{\parallel }$ is in (a) and (b). Panels (c) and (d) are inflows $V_{ey}$. In (e) and (f) are vertical cuts of $B_x$,$V_{ey}$, $V_{e\perp y}$, $E_z$, and $E_{\parallel }$ along the vertical yellow lines in panels (a)–(d). The projection of electron flows on the $xy$ plane are the perpendicular flows ${\mathbf{V}}_{e\perp }$ in panel (g),(h).

Figure 3

(a) 3D electron flows ${\mathbf{V}}_{e\perp }$ at $y=32.13$ in the $xz$ plane are diverging from the slanted dashed black line. (b) 3D electron flows ${\mathbf{V}}_{e\perp }$ converge inside the red boxed boundary in the $yz$ plane. The images of $E_{\parallel }$ in the (a) and (b) are overlaid, showing its finite and localized structure. (c) Cuts along the dashed black line in (a) are shown for $V_{ez}$, $E_{\parallel }$, and $B^2{b}_y\partial b_z/\partial y$. The dashed vertical red lines denote $z$ boundaries of the red boxes in (a),(b).

Figure 4

3D flow into and out of the diffusion region, where ${\overline{\mathbf{V}}}_e={\mathbf{V}}_e\times {10}^2$. Panels (a) and (b) show normal flow through each of the six faces of the diffusion region, which are numbered. For example, normal flow through face 1 at $z=49.46$ is given by $V_{ez}$. The integrated mass flux [Eq. (1)] through each face is: ${\mathrm{\Phi }}_{1,\dots ,6}\approx 20.6,1.5,-2.7,-17.9,1.22,-2.91$.