COMPARISON OF SOLUTIONS TO THE ONE-VELOCITY NEUTRON DIFFUSION PROBLEM

Technical Report · Mon Oct 21 04:00:00 EDT 1957

OSTI ID:4311573

Beach, L A; Theus, R B; Shapiro, P; O'Rourke, R C; Faust, W R; Lepson, B

By Fourier transform techniques the exact solutions of the one-velocity neutron diffusion problem were derived for plane isotropic, plane parallel monodirectional, and plane parallel bidirectional source terms. These exact solutions in terms of Fourier inversion integrals were numerically evaluated upon the Narec to give the angular distribution of the scattered intensity, total scattered intensity, and total intensity. By solving the integrals by contour integration in the complex plane, asymptotic solutions were obtained which are good approximate solutions for deep penetrations and problems with little absorption. Moment method solutions were derived and evaluated to be in good agreement with the exact solutions for symmetric source and intensity functions. Monte Carlo esimates can be obtained that correctiy account for source asymmetries and boundary discontinuities and which can be extended to at least 20 mean free paths utilizing suitable bias techniques such as the exponential transformation. (auth)

• Research Organization: Naval Research Lab., Washington, D.C.
• NSA Number: NSA-12-004915
• OSTI ID: 4311573
• Report Number(s): NRL-5052
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

ABSORPTION
ANGULAR DISTRIBUTION
COMPUTERS
DIFFERENTIAL EQUATIONS
DIFFUSION
FOURIER ANALYSIS
INTEGRALS
MATHEMATICS
MONTE CARLO METHOD
NEUTRON FLUX
NUMERICALS
OSCILLATIONS
PHYSICS
SCATTERING