The Asymptotic Drift-Diffusion Limit of Thermal Neutrons

Abstract

It is well known that in an infinite, source-free, purely scattering medium with physi cally realizable cross sections, neutrons attain a Maxwell-Boltzmann distribution char acterized by the material temperature. In this work we look at how small variations to these conditions change the behavior of the thermal-neutron distribution in space and energy. Specifically, our analysis examines the influence of small amounts of absorp tion and a small source as well as temperature variations in the material. We restrict our study to regions away from boundary and initial layers. The result of the asymp totic analysis is that the amplitude of the neutron scalar flux satisfies a drift-diffusion equation in which the diffusion coefficient and drift velocity depend on the first-order anisotropy of the scattering kernel as well as the gradient of the material tempera ture. Additionally, through first order in the asymptotic expansion the neutron energy distribution is Maxwell-Boltzmann at the local material temperature.