Solar particle acceleration at reconnecting 3D null points

Context: The strong electric fields associated with magnetic reconnection in solar flares are a plausible mechanism to accelerate populations of high energy, non-thermal particles. One such reconnection scenario occurs at a 3D magnetic null point, where global plasma flows give rise to strong currents in the spine axis or fan plane. Aims: To understand the mechanism of charged particle energy gain in both the external drift region and the diffusion region associated with 3D magnetic reconnection. In doing so we evaluate the efficiency of resistive spine and fan models for particle acceleration, and find possible observables for each. Method: We use a full orbit test particle approach to study proton trajectories within electromagnetic fields that are exact solutions to the steady and incompressible magnetohydrodynamic equations. We study single particle trajectories and find energy spectra from many particle simulations. The scaling properties of the accelerated particles with respect to field and plasma parameters is investigated. Results: For fan reconnection, strong non-uniform electric drift streamlines can accelerate the bulk of the test particles. The highest energy gain is for particles that enter the current sheet, where an increasing "guide field" stabilises particles against ejection. The energy is only limited by the total electric potential energy difference across the fan current sheet. The spine model has both slow external electric drift speed and weak energy gain for particles reaching the current sheet. Conclusions: The electromagnetic fields of fan reconnection can accelerate protons to the high energies observed in solar flares, gaining up to 0.1 GeV for anomalous values of resistivity. However, the spine model, which gave a harder energy spectrum in the ideal case, is not an efficient accelerator after pressure constraints in the resistive model are included.