Singular perturbation solutions of the neutron transport equation

Thesis/Dissertation · Fri Jan 01 04:00:00 EST 1982

OSTI ID:6735281

Losey, D C

In this research the singular perturbation technique is used to solve the one-dimensional neutron transport equation with isotropic neutron scattering. Both analytic and numerical solutions demonstrate that the singular perturbation provides a systematic method for enhancing the accuracy of diffusion theory calculations of global neutron flux distributions in nuclear reactors. The study demonstrates a systematic method for obtaining solutions to the higher-order perturbation equations for realistic calculations, including those with material interfaces and distributed sources. With the singular perturbation technique, transport problems have two separate domains in which solutions are calculated. In the interior regions distant from boundaries, diffusion equations have been derived which model the asymptotic components of the transport solutions for both homogeneous and inhomogeneous transport problems. Boundary layer solutions model the transient components of the transport solutions which arise near material interfaces, localized sources, and vacuum boundaries. An important result of our perturbation analyses is a consistent method by which various diffusion theory approximations to the transport equation may be derived and compared. The boundary layer analysis for a material interface is another important result because it provides a model for improving the accuracy of diffusion theory calculations. The perturbation technique is applied to analytically solve fixed source and criticality problems. The perturbation technique is also incorporated in a multi-group diffusion theory computer code which is used to numerically evaluate the flux distributions in several reactor configurations.

• Research Organization: Michigan Univ., Ann Arbor (USA)
• OSTI ID: 6735281
• Country of Publication: United States
• Language: English

Related Subjects

654003* -- Radiation & Shielding Physics-- Neutron Interactions with Matter
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
ANALYTICAL SOLUTION
ASYMPTOTIC SOLUTIONS
BOUNDARY LAYERS
DIFFUSION
LAYERS
NEUTRAL-PARTICLE TRANSPORT
NEUTRON FLUX
NEUTRON TRANSPORT
NUMERICAL SOLUTION
ONE-DIMENSIONAL CALCULATIONS
PERTURBATION THEORY
RADIATION FLUX
RADIATION TRANSPORT
SCATTERING