Generalized Fokker-Planck Approximations of Particle Transport with Highly Forward-Peaked Scattering

The Fokker-Planck equation is often used to approximate the description of particle transport processes with highly forward-peaked scattering. Pomraning has shown that if the physical scattering kernel is sufficiently dominated by small-angle scattering, then the Fokker-Planck equation is an asymptotic approximation to the linear Boltzmann equation. However, most physically-meaningful scattering kernels contain a sufficient amount of large-angle scattering that the asymptotic criterion is not met. Thus, in many physical problems, solutions of the Fokker-Planck equation are substantially in error. In this paper, Pomraning's asymptotic results are generalized and a new generalized Fokker-Planck (GFP) theory that robustly incorporates large-angle scattering is developed. Numerical experiments demonstrate that the resulting GFP equations are much more accurate than the standard Fokker-Planck equation.