Fast particle acceleration in three-dimensional relativistic reconnection

Magnetic reconnection is invoked as one of the primary mechanisms to produce energetic particles. We employ large-scale three-dimensional (3D) particle-in-cell simulations of reconnection in magnetically-dominated ($\sigma=10$) pair plasmas to study the energization physics of high-energy particles. We identify a novel acceleration mechanism that only operates in 3D. For weak guide fields, 3D plasmoids / flux ropes extend along the $z$ direction of the electric current for a length comparable to their cross-sectional radius. Unlike in 2D simulations, where particles are buried in plasmoids, in 3D we find that a fraction of particles with $\gamma\gtrsim 3\sigma$ can escape from plasmoids by moving along $z$, and so they can experience the large-scale fields in the upstream region. These "free" particles preferentially move in $z$ along Speiser-like orbits sampling both sides of the layer, and are accelerated linearly in time -- their Lorentz factor scales as $\gamma\propto t$, in contrast to $\gamma\propto \sqrt{t}$ in 2D. The energy gain rate approaches $\sim eE_{\rm rec}c$, where $E_{\rm rec}\simeq 0.1 B_0$ is the reconnection electric field and $B_0$ the upstream magnetic field. The spectrum of free particles is hard, $dN_{\rm free}/d\gamma\propto \gamma^{-1.5}$, contains $\sim 20\%$ of the dissipated magnetic energy independently of domain size, and extends up to a cutoff energy scaling linearly with box size. Our results demonstrate that relativistic reconnection in GRB and AGN jets may be a promising mechanism for generating ultra-high-energy cosmic rays.