Generation of isotropic and anisotropic scattering cross section for boltzmann-fokker-planck equation via extrapolation exponential function and minimized RMS errors

Abstract

Handling highly anisotropic scattering of fast neutrons with conventional methods usually means that high order Legendre expansions are necessary to obtain correct angular fluxes. This drawback in standard transport calculations is avoided by applying the Boltzmann-Fokker-Planck (BFP) equation which has been used in both neutral and charged-particle transport problems. Previously, Caro and Ligou, and Morel have introduced Fokker-Planck decomposition methods, which decompose elastic scattering cross section into forward-peaked and smooth components. A new method for decomposing scattering cross sections for Boltzmann-Fokker-Planck equation is presented. We start from the basic data σ(μ, E) (given by ENDF/B-VI) to get more correctly determined BFP data. In this method, we use Legendre expansion for smooth component and exponential function which Caro and Ligou used for forward-peaked component. In addition, by using RMS errors and an extra degree of freedom $\sigma_{ext}$, we conserve both moments and scattering cross section. To show the superiority of the new decomposition method, we evaluate generated BFP data with $^{238}U$ and $^{235}U$ multi-slab problems.