The self-generation of core fields and electron scattering in flux ropes during magnetic reconnection

Abstract

Two-dimensional particle-in-cell simulations with a realistic mass ratio reveal the generation mechanisms of the out-of-plane magnetic field in magnetic islands/flux ropes during magnetic reconnection. In the absence of an initial guide field, reconnection produces a large electron temperature anisotropy (around 4.5) inside magnetic islands that drives the Weibel instability. Strong out-of-plane magnetic fields (Bz/B0 around 0.4, greatly exceeding the Hall field) with a regular bipolar structure grow inside islands. A space-time analysis reveals a one-to-one correspondence between the temperature anisotropy and the development of the Weibel magnetic field. The instability relaxes the anisotropy, but island merging leads to anisotropy reemergence and re-excitation. In the presence of a strong ambient guide field (Bg/B0 = 0.5), the electron outflow from the X-point deflects along the separatrices and forms a circular current loop wrapping the flux ropes. This flux-rope separatrix current generates an out-ofplane magnetic field that reinforces the ambient guide field, reaching Bz/B0 around 1.4. The current can, in some cases, drive the electron Kelvin-Helmholtz instability, which produces electron vortices and strengthens the magnetic field. Mergers significantly broaden the islands and further strengthen the field. These self-generated out-of-plane magnetic fields scatter electrons and reduce their temperature anisotropy, which can potentially affect electron heating via Fermi reflection. The simulation results are supported by spacecraft observations suggesting that ambient guide fields can be enhanced within flux ropes in Earth's magnetotail.

Figures (9)

• Figure 1: Structure of the lower current sheet (the simulation domain contains two current sheets) at (a) $t\Omega_i =0.1$, (b) $t\Omega_i=0.3$ and (c) $t\Omega_i=0.4$. Black lines denote magnetic field lines and the color scale shows the electron temperature anisotropy $T_x/T_y$.
• Figure 2: (a) Out-of-plane magnetic field $B_z$ at $t\Omega_i \approx 0.37$. Black contours indicate magnetic field lines. (b) The $x$-direction electron current $J_{ex}$ at the same time. The electron current is normalized by $J_{e0}=en_0v_{Ae}$ where $v_{Ae}$ is the electron Alfv$\acute{e}$n speed. (c) Magnetic field components along the vertical dashed line in (a). The perturbations due to the usual Hall field are indicated.
• Figure 3: Space--time plot of the out-of-plane magnetic field $B_z$ and electron temperature anisotropy $T_x/T_y$ in the center of the lower current sheet.
• Figure 4: Weibel evolution during magnetic island merger. Black contours denote magnetic field lines, and the color scale shows the out-of-plane magnetic field $B_z/B_0$.
• Figure 5: The lower current sheet at (a) $t\Omega_i = 0.25$ and (b) $t\Omega_i = 1$ in a simulation with an initial guide field $B_g/B_0 = 0.5$. Black contours denote magnetic field lines, and the color scale shows the out-of-plane magnetic field $B_z/B_0$.