The Boltzmann Equation with an Average Force Field Caused by Anisotropic Momentum Changes

Abstract

In non-equilibrium gases of low density, the angular distribution of momentum changes in binary collisions becomes anisotropic. As the result of the biased counteractions, an internal force field is brought forth in the direction depending on the anisotropy. The effect of momentum changes biased from isotropic ones is introduced into the Boltzmann equation, here, as a force field averaged over the distribution function. This average force field complements the rotational invariance in the macroscopic cross section used customarily in the collision term. The equation with the average force field is applied to the neutron transport problem in a medium. The results have shown that the average force field contributes to making the spatial distribution of neutron flux flatter and to growing a new mode which decays more slowly than the fundamental mode.