Afwl-Atac Joint Shielding Program. Investigation of Analytical Methods, Solution Sensitivity, and Structural Scattering in Neutron Transport

摘要

A limited investigation has been made of the effect of cross-section measurement error and of cross-section approximation upon the transport-equation solution at deep penetration. The most serious error in deep penetration calculations appears to arise from inadequate treatment of anisotropic scattering; a P1 scattering kernel is not adequate. Other aspects of the problem are included in the study. It is recommended that calculations be made to deep penetration with transport codes capable of handling anisotropic scattering. An analytical approach to the solution of the multigroup formulation of the transport equation has been studied and the method yields the correct functional form of the vector flux in terms of the penetration distance and neutron directions of motion. Complete solution requires the inversion of large matrices. A method of inclusion of theta-dependence in the multigroup transport equation applicable to slab geometry has been investigated. The method should be practical for crew-compartment shielding calculations. The scattering of fast neutrons from structures was subjected to a limited investigation by means of Monte Carlo methods, and approximate analytical formulas applicable to materials with strongly peaked forward scattering were derived. (Author)