Stochastic Acceleration of Electrons in Solar Flares

Stochastic particle acceleration (SPA) is a process in which turbulent fluctuations or randomly phased waves energize particles. We develop an SPA model for electron acceleration in solar flares based on turbulent fast magnetosonic waves and transit-time damping. Our model is two dimensional in both velocity space and wavenumber space, so that it takes into account anisotropy in the wave power spectrum P and electron distribution function f. We use quasilinear theory to obtain a set of equations that describes the coupled evolution of P and f. We solve these equations numerically, and find that the electron distribution function develops a power-law-like non-thermal tail between energies Emin and Emax. We obtain approximate analytic expressions for Emin and Emax that describe how these minimum and maximum energies depend upon plasma parameters such as the electron temperature and number density. We compare our results to previous studies that assume that P and f are isotropic and use our analysis to explain the observed hard x-ray spectrum seen in the June 27, 1980 flare. In our numerical simulations, the power-law indices of the electron energy spectra range from -2.3 to -4.4. The absolute values of these indices are larger than the corresponding values in studies with isotropic P and f and closer to the observed values in solar flares.