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We develop a model for stochastic acceleration of electrons in solar flares.As in several previous models, the electrons are accelerated by turbulent fastmagnetosonic waves ("fast waves") via transit-time-damping (TTD) interactions.(In TTD interactions, fast waves act like moving magnetic mirrors that push theelectrons parallel or anti-parallel to the magnetic field). We also include theeffects of Coulomb collisions and the waves' parallel electric fields. Unlikeprevious models, our model is two-dimensional in both momentum space andwavenumber space and takes into account the anisotropy of the wave powerspectrum $F_k$ and electron distribution function $f_{\rm e}$. We use weakturbulence theory and quasilinear theory to obtain a set of equations thatdescribes the coupled evolution of $F_k$ and $f_{\rm e}$. We solve theseequations numerically and find that the electron distribution function developsa power-law-like non-thermal tail within a restricted range of energies $E\in(E_{\rm nt}, E_{\rm max})$. We obtain approximate analytic expressions for$E_{\rm nt}$ and $E_{\rm max}$, which describe how these minimum and maximumenergies depend upon parameters such as the electron number density and therate at which fast-wave energy is injected into the acceleration region atlarge scales. We contrast our results with previous studies that assume that$F_k$ and $f_{\rm e}$ are isotropic, and we compare one of our numericalcalculations with the time-dependent hard-x-ray spectrum observed during theJune 27, 1980 flare. In our numerical calculations, the electron energy spectraare softer (steeper) than in models with isotropic $F_k$ and $f_{\rm e}$ andcloser to the values inferred from observations of solar flares.

Stochastic Acceleration of Electrons by Fast Magnetosonic Waves in Solar Flares: the Effects of Anisotropy in Velocity andWavenumber Space