The theory of pulsed neutron experiments in polycrystalline moderators

This thesis is a theoretical investigation of pulsed neutron experiments in thermal non-multiplying, polycrystalline moderators. A transport approximation is used to model the spatial dependence of the neutron distribution function. The first part is concerned with the initial value problem for the Boltzmann equation describing the decay of thermal neutrons in a finite, polycrystalline system. The scattering kernel employed contains an isotropic. square-integrable component describing inelastic scattering and a term of the form vΣ el (v)δ(v' 2 -v 2 ) that models elastic scattering. Laplace transform methods are applied to the Boltzmann equation which lead to an unsuspected structure in the transform variable plane. Discrete eigenvalue existence theorems are re-examined and the role of new continuum terms in the total solution are considered. The variation of the lowest eigenvalue with system size, i.e., the dispersion law, is thoroughly investigated. An alternate representation of the dispersion law is developed which aids in explaining experimental results. In the second part of this thesis, a simplified model of the inelastic scattering kernel is used to investigate and expand the ideas in the first part ad to examine the role of various continuum contributions to the total solution. The dispersion law is examined in some detail both analytically and numerically. Comparisons are made with experimental data and multi-group calculations in beryllium and graphite. The implication of results for experiment and multi-group calculations are indicated throughout chapters II and III. Several results of major significance are examined together with suggestions for future work.