ENERGY-DEPENDENT NEUTRON TRANSPORT THEORY NEAR A TEMPERATURE DISCONTINUITY,
Abstract
An exact solution is obtained for the energy-dependent Boltzman transport equation for thermal neutrons near a temperature discontinuity. The medium is nonabsorbing and infinite in extent. The method of solution consists of expanding the energy-transfer kernel in a degenerate form and then solving directly for the solutions of the resulting homogeneous equation. Both discrete and singular solutions are found. The angular flux is then expanded in terms of a complete set of these solutions. Finally, the expansion coefficients are determined by applying the boundary conditions associated with the temperature-discontinuity problem. Numerical calculations of both scalar neutron flux and total neutron density are included for various temperature ratios and neutron-to-moderator mass ratios. A comparison of the transport-theory results with diffusion-theory results shows that diffusion theory describes the neutron flux quite accurately for small values of temperature discontinuity. Diffusion-theory calculations become less accurate, however, as the higher energy modes become important. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1967
- Accession Number
- AD0663369
Entities
People
- Anthony Leonard
- Eugene C. Gritton
Organizations
- RAND Corporation