Effects of Multi-scale Coupling on Particle Acceleration and Energy Partition in Magnetic Reconnection

TL;DR

The study addresses how multi-scale coupling between kinetic microphysics and large-scale flow structures governs energy partition and particle acceleration during magnetic reconnection in a relativistic pair plasma. It uses fully-kinetic PIC simulations of large-scale island coalescence with self-consistent outflows, coupled with a region-decomposition scheme and the electron-frame dissipation measure $D_e$ to dissect energy transfer across islands, downstream zones, and the primary current sheet. For large system sizes, downstream turbulence and secondary current sheets become the dominant sites of energy dissipation and non-thermal particle acceleration, decoupled in space and time from the primary reconnection site, while the primary current sheet still accelerates the highest-energy particles. The electron spectra develop an ankle near $\gamma-1 \approx 15$, indicating multiple concurrent acceleration channels that broaden the non-thermal tail beyond what is seen in isolated current-sheet setups. These results imply that multi-scale modeling is essential to capture realistic energy partition and acceleration in reconnecting systems, with potential relevance for solar flares and magnetotail dynamics where outflows drive turbulence and secondary reconnection.

Abstract

The interplay between kinetic and macroscopic scales during magnetic reconnection is investigated using particle-in-cell simulations of magnetic island coalescence in the strongly-magnetized, relativistic pair plasma regime. For large system sizes, secondary current sheet formation and downstream turbulence driven by the reconnection outflows dominate the global energy dissipation so that it is causally connected, but spatially and temporally de-coupled from the primary reconnecting current sheet. When compared to simulations of an isolated, force-free current sheet, these dynamics activate additional particle acceleration channels which are responsible for a significant population of the non-thermal particles, modifying the particle energy spectra.

Figures (11)

• Figure 1: (Top) Reconnection rate $E_R$ versus time for island coalescence at several system sizes. (Bottom) Island O-point separation normalized to initial separation.
• Figure 2: Left side: Current density magnitude $|J|$ at several times for $L/d_e=320$ associated with: (top) $E_{R,\mathrm{max}}$, (center) first local minimum in $\lambda$, (bottom) $\lambda_{b1}$. Right side: $D_e$ at the same times.
• Figure 3: (Top) Region decomposition at time of $E_{R,\mathrm{max}}$ for $L/d_e=320$. Red: magnetic islands; orange: primary current sheet; blue: downstream region; green: top and bottom regions. (Center) Cumulative $\mathcal{D}_i$ normalized by initial magnetic energy, decomposed by region for $L/d_e=40$. Colors match regions in top plot, with the system-wide total in black. (Bottom) Same as center for $L/d_e=320$.
• Figure 4: (Top) Volume integrated $D_e$ normalized to initial magnetic energy versus time for $L/d_e=40$ in blue, compared to $E_R$ in red, up to $\tau_{99}$. (Bottom) Same for $L/d_e=320$, with vertical dash-dotted lines indicating the times in Fig. \ref{['fig:temp2D']}.
• Figure 5: Electron energy spectra $f(\gamma-1)$ for $L/d_e=320$ (blue) and FFCS (red). Only the particles starting in the islands at $t/t_A=0$ are included in the $L/d_e=320$ spectra. Increasing opacity indicates later times: $t/t_A=0,1.3$ (just after $E_{R,\mathrm{max}}$), $\tau_{99}$ in blue and $t/t_A=0,5$ in red. The inset plot compares the second $L/d_e=320$ spectrum to the final FFCS spectrum (scaled to overlap), alongside a power law with index $p=3$. The green (purple) region indicates energy band $\gamma_{\mathrm{nt}}<\gamma<\gamma_{\mathrm{hi}}$ ($\gamma >\gamma_{\mathrm{hi}}$).