Recent observations of high energy gamma-rays from electron-dominated solar flares indicate the acceleration of electrons to relativistic energies within a few seconds of the start of the flare. The process of producing these suprathermal particles is not well understood, but stochastic wave-particle interaction plays an important role. The effect of random multiple scatterings of particles can be described as a diffusion in energy, pitch angle, and physical space through the Fokker-Planck equation. This equation can be reduced to a simple form, a function of energy and time, if the acceleration region is homogeneous and the scattering mean free path is much smaller than both the energy change mean free path and the size of the acceleration region.; Analytic solutions can be found only for limited and simple cases. Previous analytical solutions of the Fokker-Planck equation suffered from ambiguous or incorrect treatment of the boundary conditions. By using the spectral theory of second-order differential equations, all existing controversies are resolved and a complete treatment of the analytic properties of singular Fokker-Planck equations is given.; For more general cases, numerical methods must be used. Six finite difference methods and a stochastic simulation method which uses the exact correspondence between the Fokker-Planck equation and the Ito stochastic differential equation are examined. It is concluded that the most robust method is the fully implicit extended Chang-Cooper finite difference method.; Finally, three specific stochastic acceleration models are applied to four electron-dominated solar flares, whose photon emissions are almost entirely from electron bremsstrahlung radiation. One model, the hard sphere, is eliminated. The others give constraints on the relevant physical parameters of the stochastic acceleration model for the first time.
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