Early-stage Coronal Hard X-Ray Source in Solar Flares in the Collapsing Trap Model

A bright hard X-ray coronal source observed at the early stage of solar flares is considered. The plasma density in a quiet corona is not enough to explain the hard X-ray bremsstrahlung radiation. The generally accepted concept of increasing plasma density in the looptop is associated with the effect of evaporation of hot chromosphere plasma. We discuss the increase in plasma density at the looptop at the early stage of a flare, due to magnetic loop contraction during the relaxation of the magnetic field (the so-called collapsing trap model). In this case, the increase in the plasma density at the looptop occurs on a timescale of seconds-Tens of seconds, while the process of plasma evaporation increases the plasma density for much longer. The Fokker-Planck kinetic equation for accelerated electrons with a betatron and Fermi terms is solved numerically. We calculate increases in the energy of the accelerated electrons, the energy spectrum, and the pitch-Angle anisotropy due to betatron and Fermi first-order acceleration. For a collapse time of 8 s, the total energy of the accelerated electrons increases by a1/420%-200%, depending on the model parameters. The ratio of the looptop/total hard X-ray flux at 29-58 keV increases by 15%-30% in the collapsing trap model. It is shown that this model can explain the appearance of bright coronal hard X-ray sources in the first seconds-Tens of seconds after the hard X-ray flux starts growing.