Reconnection and particle acceleration in interacting flux ropes -- II. 3D effects on test particles in magnetically dominated plasmas

We analyze particle acceleration in explosive reconnection events in magnetically dominated proton-electron plasmas. Reconnection is driven by large-scale magnetic stresses in interacting current-carrying flux tubes. Our model relies on development of current-driven instabilities on macroscopic scales. These tilt-kink instabilities develop in an initially force-free equilibrium of repelling current channels. Using MHD methods we study a 3D model of repelling and interacting flux tubes in which we simultaneously evolve test particles, guided by electromagnetic fields obtained from MHD. We identify two stages of particle acceleration; Initially particles accelerate in the current channels, after which the flux ropes start tilting and kinking and particles accelerate due to reconnection processes in the plasma. The explosive stage of reconnection produces non-thermal energy distributions with slopes that depend on plasma resistivity and the initial particle velocity. We also discuss the influence of the length of the flux ropes on particle acceleration and energy distributions. This study extends previous 2.5D results to 3D setups, providing all ingredients needed to model realistic scenarios like solar flares, black hole flares and particle acceleration in pulsar wind nebulae: formation of strong resistive electric fields, explosive reconnection and non-thermal particle distributions. By assuming initial energy equipartition between electrons and protons, applying low resistivity in accordance with solar corona conditions and limiting the flux rope length to a fraction of a solar radius we obtain realistic energy distributions for solar flares with non-thermal power law tails and maximum electron energies up to 11 MeV and maximum proton energies up to 1 GeV.