On the Equivalence of Boundary and Boundary Condition Perturbations in Transport Theory and Its Diffusion Approximation

Abstract

It is shown that a perturbation in the external boundary of a system can be converted into (treated as) a perturbation in the boundary condition of the neutron balance equation. As a result, one may then use existing boundary condition perturbation or variational methods to estimate the change in the parameters of interest. The equivalent perturbation in the boundary condition is derived both in transport theory and its diffusion approximation for eigenvalue as well as fixed-source problems. Generalized boundary conditions in both diffusion and transport theory are considered. The existence of a solution to the problem with the equivalent boundary conditions that are nonstandard is investigated through analytic examples. The analysis is limited to first-order perturbation theory.