Singular Perturbation Solutions of the Neutron Transport Equation

A singular perturbation technique is applied to the time-independent one-dimensional neutron transport equation with isotropic neutron scattering. The technique reduces the transport problem to a series of diffusion theory problems in the interior medium and a series of simplified transport problems solved analytically in the boundary layer. The analysis provides a consistent method for deriving and comparing various diffusion theory approximations to the transport equation. In addition, the resulting scheme provides a systematic method for enhancing the accuracy of diffusion theory calculations of global flux distributions. A general asymptotic expansion of c, the number of secondary neutrons per collision, is obtained and an O(ε²) correction to the diffusion theory boundary condition at a material interface is derived. The perturbation technique has been applied analytically to both fixed source and criticality problems. The technique is also incorporated in a multigroup diffusion theory computer code. In test calculations, the error in flux distributions is reduced to about one-half that achieved with standard diffusion theory techniques.