ACCELERATION OF RUNAWAY ELECTRONS IN SOLAR-FLARES

The DC electric field acceleration of electrons out of a thermal plasma and the evolution of the runaway tail are studied numerically, using a relativistic quasilinear code based on the Ritz-Galerkin method and finite elements. A small field-aligned electric field is turned on at a certain time. The resulting distribution function from the runaway process is used to calculate the synchrotron emission during the evolution of the runaway tail. It is found that during the runaway tail formation, which lasts a few tens of seconds for typical solar flare conditions, the synchrotron emission level is low, almost of the same order as the emission from the thermal plasma, at the high-frequency end of the spectrum. However, the emission is enhanced explosively in a few microseconds by several orders of magnitude at the time the runaway tail stops growing along the magnetic field and tends toward isotropy due to the pitch-angle scattering of the fast particles. Our results indicate that in order to account for the observed synchrotron emission spectrum of a typical solar flare, the electric field acceleration phase must be accompanied or preceded by a heating phase which yields an enhanced electron temperature of about 2-15 keV in the flare region if the electric field is 0.1-0.2 times the Dreicer field and cyclotron to plasma frequency ratios are of order 1-2.