Reconnection and particle acceleration in interacting flux ropes I. Magnetohydrodynamics and test particles in 2.5D

Magnetic reconnection and non-thermal particle distributions associated with current-driven instabilities are investigated by means of resistive magnetohydrodynamics (MHD) simulations combined with relativistic test particle methods. We propose a system with two parallel, repelling current channels in an initially force-free equilibrium, as a simplified representation of flux ropes in a stellar magnetosphere. The current channels undergo a rotation and separation on Alfv\'enic timescales, forming secondary islands and (up to tearing unstable) current sheets in which non-thermal energy distributions are expected to develop. Using the recently developed particle module of our open-source grid-adaptive MPI-AMRVAC software, we simulate MHD evolution combined with test particle treatments in MHD snapshots. We explore under which plasma-$\beta$ conditions the fastest reconnection occurs in two-and-a-half dimensional (2.5D) scenarios and in these settings test particles are evolved. We quantify energy distributions, acceleration mechanisms, relativistic corrections to the particle equations of motion and effects of resistivity in magnetically dominated proton-electron plasmas. Due to large resistive electric fields and indefinite acceleration of particles in the infinitely long current channels, hard energy spectra are found in 2.5D configurations. Solutions to these numerical artifacts are proposed for both 2.5D setups and future 3D work. We discuss the magnetohydrodynamics of an additional kink instability in 3D setups and the expected effects on energy distributions. The obtained results hold as a proof-of-principle for test particle approaches in MHD simulations, relevant to explore less idealised scenarios like solar flares and more exotic astrophysical phenomena, like black hole flares, magnetar magnetospheres and pulsar wind nebulae.