Stochastic acceleration of electrons. I. Effects of collisions in solar flares

Stochastic acceleration of thermal electrons to nonrelativistic energies is studied under solar flare conditions. We show that, in turbulent regions, electron-whistler wave interactions can result in the acceleration of electrons in times comparable to or shorter than the Coulomb collision time. The kinetic equation describing the evolution of the electron energy distribution including stochastic acceleration by whistlers and energy loss via Coulomb interactions is solved for an initial thermal electron energy spectrum. In general, the shape of the resulting electron distributions are characterized by the energy E_c where systematic energy gain by turbulence equals energy loss due to Coulomb collisions. For energies less than E_c, the spectra are steep (quasi-thermal) whereas above E_c, the spectra are power laws. We find that hard X-ray spectra computed using the electron distributions obtained from our numerical simulations are able to explain the complex spectral shapes and variations observed in impulsive hard X-ray bursts. In particular, we show that the gradual steepening observed by Lin et al. could be due to a systematic increase in the density of the plasma (due to evaporation) and the increasing importance of collisions instead of the appearance of a superhot thermal component.