Implantation of the continuous slowing down theory separable kernel into conventional space dependent analysis

A conventional space dependent transport computer code has been altered through a model that reduces data storage and time of execution required to calculate values of the multigroup flux. During development of the model, a change in a basic assumption yielded an increase in accuracy without any storage or time penalties. The model uses Continuous Slowing Down Theory (CSDT) and the Separable Kernel Approximation in which the probability of neutron scatter between any two groups can be determined by two parameters; one dependent only on the energy group from which the neutron scatters, the other parameter dependent only on the energy group into which the neutron scatters. It will be shown that this basic premise provides the framework for the entire model. In other words, use of this model implies that finding the inscatter source to a given group g depends only on the value of the scattering parameter in group g and one flux-like term in the previous energy group. Thus, the need for large tables of cross section transfer pairs and the time to access these pairs is eliminated. A standard 49 group cross section table consisting of 2548 elements can now be reduced to 294 entries; a decrease of almost 89%. This method has been applied to some simple single region problems and also to some typical fast reactor problems. In all instances there is good agreement between a base case and the flux as predicted by the model. The criticality, k, calculated with the model agrees with the base case result to within 1%. The model provides a more rapid and yet still accurate means of finding the spatial flux distribution. By the very nature of the model, as the number of energy groups used increases, the potential for computer savings (storage and time) increases at an exponential rate