Symmetries of the [formula omitted] approximation to the Boltzmann neutron transport equation

Abstract

This work explores conditional translation and scaling symmetries of a P3 approximation to the one-dimensional (1D) Boltzmann neutron transport equation with arbitrary material properties. The principal outcomes of this analysis are twofold: 1) the identification of symmetries using Lie group theory is exhaustive, and thus provides definitive insight into scenarios where the differential equation(s) under consideration are expected to hold across phase space position or dimensional scale; and 2) invariance under transformations may be leveraged to construct changes of variables under which reduced-order structures or exact solutions with special properties may be derived. In support of these goals, this work includes the application of Lie group theory to the aforementioned neutron transport model. A variety of conditional translation and scaling symmetries are obtained (e.g., depending on the functional form of various macroscopic cross section functions), and an example scaleinvariant numerical solution of the 1D spherical P3 equations is provided.