Scaling of particle acceleration in 3D reconnection at null points

Context. The strong electric fields associated with magnetic reconnection are likely to be responsible for the presence of high energy protons and electrons observed in solar flares. There is much evidence for 3D reconnection in the solar corona, and we discuss particle acceleration at 3D reconnection sites. The simplest configuration for 3D reconnection is at a 3D null point, where reconnection can take place in spine and fan modes. Aims. The aim is to understand the properties of accelerated particles generated by 3D magnetic reconnection, using a test particle approach, and thus contribute to understanding the origin of high energy protons and electrons in solar flares. We analyse the properties of electrons in the magnetic configuration we previously used to study protons. In addition, we discuss the dependence of the particle properties on the parameters of the reconnection, such as strengths of electric and magnetic fields. Methods. A theoretical framework is presented which can be used to interpret particle acceleration at 3D null points, and which shows how strong acceleration can arise. We also use a test particle approach to calculate particle trajectories in simple model 3D reconnecting nulls. A modified guiding-centre approach is used for electrons, whilst the full equation of motion is solved for protons. Results. Most particle acceleration takes place when particles closely approach the spine or fan, and we have derived scalings for the sizes of the localised regions in which strong acceleration occurs. The energy spectra of protons and electrons are compared, and it is shown that the spatial distribution of accelerated electrons differs from protons. A significant number of trapped, high-energy particles can be generated, which may be observed as coronal HXR sources. The effectiveness of acceleration increases with the electric-field magnitude, and decreases with magnetic-field magnitude. Conclusions. Both protons and electrons can be effectively accelerated at 3D reconnecting null points. The particle properties depend on the geometry and field parameters, so that, in principle, the field configuration may be inferred from observed properties of particles