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Electron Acceleration in Solar Flares by Fast-Mode Waves: Coulomb Collisions

We consider solar-flare electron acceleration from thermal to hard X-ray-producing energies by MHD fast-mode waves. Fast-mode waves are an efficient acceleration agent when isotropizing pitch-angle scattering is present. Pitch-angle scattering increases the acceleration efficiency, since fast-mode waves affect only the parallel (with respect to the ambient magnetic field) electron energy and produce a parallel energization rate that is proportional to the square of the magnetic moment. We remove the isotropy condition and consider specifically the pitch-angle scattering that results from electron-electron Coulomb collisions in an impulsive solar flare environment. We compare results for the case of (1) no Coulomb collisions, (2) energy redistribution by Coulomb collisions in the parallel direction only, and (3) Coulomb pitch-angle scattering with energy loss. We find that Coulomb pitch-angle scattering strongly enhances the efficiency of fast-mode wave acceleration and produces bulk energization of the ambient electrons.