Spacecraft Observations and Analytic Theory of Crescent-Shaped Electron Distributions in Asymmetric Magnetic Reconnection

Supported by a kinetic simulation, we derive an exclusion energy parameter ${\mathcal{E}}_X$ providing a lower kinetic energy bound for an electron to cross from one inflow region to the other during magnetic reconnection. As by a Maxwell demon, only high-energy electrons are permitted to cross the inner reconnection region, setting the electron distribution function observed along the low-density side separatrix during asymmetric reconnection. The analytic model accounts for the two distinct flavors of crescent-shaped electron distributions observed by spacecraft in a thin boundary layer along the low-density separatrix.

Figure 1

(a) Schematic illustration of the reconnection region encountered by the MMS mission on October 16, 2015. (b) The trajectories of the MMS spacecraft were determined in Ref. [7] and are indicated by the black arrows. In addition, distinct orbit types are labeled. (c)–(e) Electron distribution function recorded during the separatrix crossing by MMS3 and MMS4, respectively. Times are given relative to 13∶07:02.000 UT. The velocity axes are normalized by $v_0=10^7\mathrm{m}/\mathrm{s}$, and all distributions are computed from the full 3D MMS measurements. In (c) and (e), $\overline{f}(v_{\parallel },v_{\perp })$ are gyro-averaged distributions, and regions of distinct orbit types are labeled consistently with the trajectories in (b). The data in (d) are cuts of the full 3D electron distributions at $v_{\parallel }=0$.

Figure 2

(a) Trapped magnetosheath electrons propagating across the diffusion region into the magnetospheric inflow. Nongyrotropic regions ($\sqrt{{\rho }_l/R_B}>0.25$) are identified by the background color. (b) Guiding center trajectories are characterized by $A_M=\text{const}$, and electrons with $\mathcal{E}>{\mathcal{E}}_X$ may jump across the diffusion region. The color contours document the strong $E_N$ electric fields along the separatrix. (c) $q{\mathrm{\Phi }}_N$ is a measure of the electron energization, obtained by integrating $E_N$ along the white line in (b). In areas of no pitch angle mixing [for $({\rho }_l/R_B{)}^{1/2}<0.25$], the energization ${\mathcal{E}}_{X\perp }$ is purely perpendicular. (d) ${\mathcal{E}}_{\mathrm{sheath}}$ of Eq. (2) and energization by $q{\mathrm{\Phi }}_N$ add to provide the minimum kinetic energy ${\mathcal{E}}_X$ of sheath electrons in the magnetospheric inflow. In (c) and (d), values are normalized by $m{c}^2$, and those used for computing the distributions in Fig. 3 are marked by circles.

Figure 3

(a),(c) Rows of distributions for magnetosheath electrons collected from the location in Fig. 2 as a function of $\mathrm{\Delta }{A}_{Mx}$. Row (a) shows the local distribution $f(\mathbf{x},v_{\perp 1},v_{\perp 2})=\int f(\mathbf{x},\mathbf{v})d{v}_{\parallel }$, while row (b) is calculated based on the location of the electrons’ guiding centers $f_g({\mathbf{x}}_g,v_{\perp 1},v_{\perp 2})=\int f_g({\mathbf{x}}_g,\mathbf{v})d{v}_{\parallel }$. In (b), the magenta lines show the predicted cutoff energy ${\mathcal{E}}_X$ at values marked in Fig. 2, shifted by the $E\times B$ drift. Rows (c) and (d) display ${\overline{f}}_g(v_{\parallel },v_{\perp })$ obtained from the simulation data and Eq. (3), respectively. Again, the magenta lines represent the total cutoff energy ${\mathcal{E}}_X$, while the yellow lines are the perpendicular cutoff energy ${\mathcal{E}}_{X\perp }$; both are calculated relativistically based on the values indicated in Fig. 2. The green lines mark the boundary to the velocity region of incoming passing magnetosphere electrons, calculated based on the local values of $B$ and ${\mathrm{\Phi }}_{\parallel }$ [14].