Efficient Nonthermal Ion and Electron Acceleration Enabled by the Flux-Rope Kink Instability in 3D Nonrelativistic Magnetic Reconnection

The relaxation of field-line tension during magnetic reconnection gives rise to a universal Fermi acceleration process involving the curvature drift of particles. However, the efficiency of this mechanism is limited by the trapping of energetic particles within flux ropes. Using 3D fully kinetic simulations, we demonstrate that the flux-rope kink instability leads to strong field-line chaos in weak-guide-field regimes where the Fermi mechanism is most efficient, thus allowing particles to transport out of flux ropes and undergo further acceleration. As a consequence, both ions and electrons develop clear power-law energy spectra that contain a significant fraction of the released energy. The low-energy bounds are determined by the injection physics, while the high-energy cutoffs are limited only by the system size. These results have strong relevance to observations of nonthermal particle acceleration in space and astrophysics.

Figure 1

Current density for simulations with $L_x=150d_i$ and different $y$ dimensions (a) $L_y=12.5d_i$ and (b) $L_y=6.25d_i$, respectively. (c),(d) The $y$-averaged energetic electron density in these two simulations, respectively, overplotted with Poincaré-type plots of magnetic field lines—traced from $x=0$ with their locations in the $x–z$ plane recorded every $6.25d_i$ in $y$ and with different colors for different starting points.

Figure 2

(a) The averaged separation of initially adjacent field lines in the $x–z$ plane traced from the center of flux ropes with $D\sim 15d_i$. (b) The mean-square displacement in $x$ for test-particle electrons and parallel-streaming particles traced from the cores of the flux ropes. Test-particle electrons are injected with an initial isotropic velocity $\sim 3.5V_A$, while the parallel-streaming particles have a parallel velocity equal to the test-particles’ root-mean-square parallel velocity. (c) The enhancement of energetic electrons in 3D compared with a 2D simulation.

Figure 3

Evolution of energy spectra for (a) electrons and (b) protons in the $L_x=300d_i$ simulation. The spectral indices of this and a $L_x=150d_i$ simulation are shown in the insets. (c) The high-energy cutoff of the power laws, determined by the energy at which the spectrum deviates from the fitted power law by 50%. (d) The energization history of different generations of injected particles. The dash-dotted lines represent the $ϵ\propto t^{0.8}$ scaling in (c) and (d).