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Context. Non-thermal particle acceleration in the solar corona is thought to constitute a substantial part of the energy budget of explosive events such as solar flares. One well-established mechanism of non-thermal acceleration is directly via fields in current sheets.\ud \ud Aims. In this paper we study proton acceleration during “spine-fan reconnection” at a 3D magnetic null point. This type of reconnection has recently been implicated in some flares known as circular-ribbon flares. It has also recently been discovered that the reconnecting current sheet may undergo a non-linear tearing-type instability. This tearing leads to the formation of flux ropes and quasi-turbulent dynamics.\ud \ud Methods. A predictor-corrector test particle code is used to model the trajectories of protons at different stages of sheet tearing: when the sheet is intact, just after the formation of the first major flux rope, and once the non-linear phase of the instability has become more fully developed. The fields for these proton trajectories were taken from snapshots of a 3D magnetohydrodynamics simulation treated as three static field geometries represented by interpolated grids. Acceleration in the intact current sheet is compared to earlier simulations of infinite static current sheets and then used as a control case with which to compare the later snapshots.\ud \ud Results. Protons are found to be predominantly accelerated along the fan surface, especially in the absence of current sheet tearing. Most of the highest energy protons are accelerated in the main body of the current sheet, along the direction of strongest parallel electric field. A high energy tail is present in the kinetic energy distribution. After tearing commences, this direct acceleration no longer dominates and acceleration in the outflow regions makes a proportionally greater contribution. Sheet tearing appears overall to hinder the acceleration of protons in the fan plane, at least in the absence of time-dependent acceleration mechanisms. Some correlation is found between high energy protons and locations of flux ropes formed by the instability, but the nature of the link remains at present unclear.

Recent advances in theory and computational experiments have shown the need to refine the previous categorisation of magnetic reconnection at three-dimensional null points -- points at which the magnetic field vanishes. We propose here a division into three different types, depending on the nature of the flow near the spine and fan of the null. The spine is an isolated field line which approaches the null (or recedes from it), while the fan is a surface of field lines which recede from it (or approach it). So-called "torsional spine reconnection" occurs when field lines in the vicinity of the fan rotate, with current becoming concentrated along the spine, so that nearby field lines undergo rotational slippage. In "torsional fan reconnection" field lines near the spine rotate and create a current that is concentrated in the fan with a rotational flux mismatch and rotational slippage. In both of these regimes, the spine and fan are perpendicular and there is no flux transfer across spine or fan. The third regime, called "spine-fan reconnection", is the most common in practice and combines elements of the previous spine and fan models. In this case, in response to a generic shearing motion, the null point collapses to form a current sheet that is focused at the null itself, in a sheet that locally spans both the spine and fan. In this regime the spine and fan are no longer perpendicular and there is flux transfer across both of them., Comment: 16 pages, 10 figures. Accepted for publication in Physics of Plasmas

The behaviour of magnetic perturbations of an initially potential three-dimensional equilibrium magnetic null point are investigated. The basic components which constitute a typical disturbance are taken to be rotations and shears, in line with previous work. The spine and fan of the null point (the field lines which asymptotically approach or recede from the null) are subjected to such rotational and shear perturbations, using three-dimensional magnetohydrodynamic simulations. It is found that rotations of the fan plane and about the spine lead to current sheets which are spatially diffuse in at least one direction, and form in the locations of the spine and fan. However, shearing perturbations lead to 3D-localised current sheets focused at the null point itself. In addition, rotations are associated with a growth of current parallel to the spine, driving rotational flows and a type of rotational reconnection. Shears, on the other hand, cause a current through the null which is parallel to the fan plane, and are associated with stagnation-type flows and field line reconnection across both the spine and fan. The importance of the parallel electric field, and its meaning as a reconnection rate, are discussed., Comment: Accepted for publication in JGR (Space Physics)