Boltzmann Transport Equation Algorithms for Infinite-Slab Buildup and Albedo Factors.

摘要

This report describes the development of improved algorithms for use in the Mathematical Radiation Environment Model for Ships (MREMS) code, which estimates dose equivalent at a matrix of many detector points due to a set of gamma-ray and neutron emitting source points. The algorithms consist of models with adjustable parameters, which are averageable over arbitrary source spectra, for buildup and albedo factors; these models can be used directly in the point-kernal model that MREMS employs. Buildup and albedo factors were calculated for six materials in a point source, slab, point-detector geometry using a decomposition of the solution to the Boltzmann transport equation (and appropriate boundary conditions) into single- and multiple-scatter components. A rigorous solution for the single-scatter component was used that improves the efficiency of the calculations. A detailed model-fitting procedure was employed to fit these factors to simplified models, and the model constants were evaluated for each of several source energies. Finally, a procedure was implemented to determine average model constants for arbitrary source spectra. Slab buildup and albedo factors are presented for various source-slab-detector configurations, both in tabular form and in graphs that also show the fitted models.