Energy-Dependent Neutron Transport Theory Near a Temperature Discontinuity.

by Eugene C. Gritton, Anthony Leonard

Purchase Print Copy

 FormatList Price Price
Add to Cart Paperback81 pages $25.00 $20.00 20% Web Discount

An exact solution is obtained for the energy-dependent Boltzmann transport equation for thermal neutrons near a temperature discontinuity. The medium is nonabsorbing and infinite. 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 accurately for small values of temperature discontinuity. Diffusion-theory calculations become less accurate, however, as the higher energy modes become important. 81 pp. Ref.

This report is part of the RAND Corporation research memorandum series. The Research Memorandum was a product of the RAND Corporation from 1948 to 1973 that represented working papers meant to report current results of RAND research to appropriate audiences.

The RAND Corporation is a nonprofit institution that helps improve policy and decisionmaking through research and analysis. RAND's publications do not necessarily reflect the opinions of its research clients and sponsors.