Electron Acceleration during Macroscale Magnetic Reconnection

The first self-consistent simulations of electron acceleration during magnetic reconnection in a macroscale system are presented. Consistent with solar flare observations, the spectra of energetic electrons take the form of power laws that extend more than two decades in energy. The drive mechanism for these nonthermal electrons is Fermi reflection in growing and merging magnetic flux ropes. A strong guide field suppresses the production of nonthermal electrons by weakening the Fermi drive mechanism. For a weak guide field the total energy content of nonthermal electrons dominates that of the hot thermal electrons even though their number density remains small. Our results are benchmarked with the hard x-ray, radio, and extreme ultraviolet observations of the X8.2-class solar flare on September 10, 2017.

Figure 1

(a),(b), and (c) $⟨W⟩$ for a simulation with $B_g/B_0=0.25$ at $t/{\tau }_A=2.5$, 5, and 8 with field lines overplotted. (d) The firehose parameter at late time from a simulation with $B_g/B_0=0.1$.

Figure 2

(a) A log-log plot of $F(W)$ versus energy at multiple times for the $B_g/B_0=0.25$ simulation. Inset in (a): the late time $F(W)$ for several guide fields. (b) The late time $F(W)$ for $B_g/B_0=0.25$ with various values of $S_{\nu }$ (effective system size). The dashed line in both (a) and (b) is a power-law with ${\delta }^{\prime }=3.3$.

Figure 3

(a) ${\delta }^{\prime }$ (black) versus $B_g$ and the theoretical fit (red). (b) Energy versus $x$ position of a nonthermal electron. (c) A schematic depicting the flux rope merging mechanism that leads to electron power-law distributions.

Figure 4

(a) $F(W)$ (black) along with the fit (red) described in Ref. [25] versus energy on a log-log scale. (b) The same data on a linear-linear scale, zoomed in to low energies to reveal the thermal electrons. (c) The percentage of energy (black) and density (red) of nonthermals versus guide field. (d) the average energy per particle of particle electrons (black) and thermals (red) versus $B_g$. The dotted line is the energy from the initial Maxwellian distribution of particle electrons.