Proton Acceleration in Analytic Reconnecting Current Sheets

Particle acceleration provides an important signature for the magnetic collapse that accompanies a solar flare. Most particle acceleration studies, however, invoke magnetic and electric field models that are analytically convenient rather than solutions of the governing magnetohydrodynamic equations. In this paper a self-consistent magnetic reconnection solution is employed to investigate proton orbits, energy gains, and acceleration timescales for proton acceleration in solar flares. The magnetic field configuration is derived from the analytic reconnection solution of Craig and Henton. For the physically realistic case in which magnetic pressure of the current sheet is limited at small resistivities, the model contains a single free parameter that specifies the shear of the velocity field. It is shown that in the absence of losses, the field produces particle acceleration spectra characteristic of magnetic X-points. Specifically, the energy distribution approximates a power law ~ξ-3/2 nonrelativistically, but steepens slightly at the higher energies. Using realistic values of the “effective” resistivity, we obtain energies and acceleration times that fall within the range of observational data for proton acceleration in the solar corona