Proton acceleration during coalescence of two parallel current loops in solar flares

We investigate the plasma dynamics during coalescence of two parallel current loops in solar flares by using a resistive three-dimensional MHD simulation code, paying particular attention finding the most effective electromagnetic fields for the production of high-energy protons. Next we investigate the orbit of many protons in the electromagnetic fields obtained from the MHD simulations. We investigate two cases of the coalescence process: (1) co-helicity reconnection where only the poloidal magnetic field produced from the axial currents dissipates and (2) counter-helicity reconnection where both poloidal and axial magnetic fields dissipate. We found a bump-on-tail distribution in the same direction as the original loop current for both the cases of co-helicity and counter-helicity. It is shown that the maximum proton energy exceeds the energy (2.223 MeV) of the observed prompt nuclear de-excitation lines of gamma-ray, and that proton energy spectrum is neither a pure power-law type nor a pure exponential type. We may conclude that anisotropic proton acceleration along the loop can be realized both for co-helicity and counter-helicity reconnection during the coalescence of two parallel loops.