Stochastic electron acceleration by cascading fast mode waves in impulsive solar flares

We present a model for the acceleration of electrons from thermal to ultrarelativistic energies during an energy release fragment in an impulsive solar flare. Long-wavelength low-amplitude fast mode waves are assumed to be generated during the initial flare energy release (by, for example, large-scale restructuring of the magnetic field). These waves nonlinearly cascade to higher wavenumbers and eventually reach the dissipation range, whereupon they are transit-time damped by electrons in the tail of the thermal distribution. The electrons, in turn, are energized out of the tail and into substantially higher energies. We find that for turbulence energy densities much smaller than the ambient magnetic field energy density and comparable to the thermal particle energy density, and for a wide range of initial wavelengths, a sufficient number of electrons are accelerated to hard X-ray-producing energies on observed timescales. We suggest that MHD turbulence unifies electron and proton acceleration in impulsive solar flares, since a preceding study established that a second MHD mode (the shear Alfven wave) preferentially accelerates protons from thermal to gamma-ray line-producing energies.