Neutron Transport Calculations Involving a Mixture of Group and Discrete-Energy Fluxes.

In numerical computation of neutron transport problem the continuous energy variable is almost always transformed into a discrete index by the process of multigrouping. The integral of the flux spectrum over the group interval is the group flux, and no information is provided about the variation of the spectrum within the group. However, an a-priori guess as to the continuous energy dependence of the flux within the group is incorporated through the weight function used in finding group constants. An alternative procedure leads to values of the flux on a discrete energy grid. The pertinent cross section coefficients for many hundreds of discrete energy points can be processed in a small fraction of the time required for the corresponding multigroup cross sections. Hence the discrete-energy approach is attractive when one seeks fine details of the energy spectrum or where it is desired to experiment with various energy grids. However the discrete-energy method has some obvious drawbacks. It is unsuited to the unresolved resonance range. It cannot handle large energy intervals with any degree of confidence. In order therefore to treat problems typically calling for fine detail is a resonance region covering only a small portion of the overall energy range, a mixed or hybrid treatment has been developed. It envisions one or more restricted energy intervals where the flux is calculated on a discrete energy grid, while elsewhere the spectrum is treated on a multigroup basis. The scattering matrix in the hybrid formulation requires the calculation of four types of "transfer" coefficients: group-to-group, group -to-point, point-to-point, and point-to-group. Correspondingly there are one-dimensional arrays of cross sections representing, e.g. the total cross section, which contain group-averaged cross section in the energy ranges described by groups, and "point" cross sections where there is a discrete energy description. These cross sections may be used as the input library to standard transport codes, such as ANISN, which will then compute group fluxes and discrete-energy fluxes in the appropriate regions. No changes need be made in these codes except for such auxiliary portions as involve an integration over energy, e.g. an overall-system checking routine. Preparation of the cross section quantities required in this mixed group-discrete energy scheme has been implemented in the frame work of the MINX processing code, and associated handling programs. The processing code incorporates a program for calculating the infinite-medium spectrum and the corresponding slowing-down rate in an infinite medium, thus providing a check to insure the cross sections conserve neutrons. Several illustrative problems have been run, for various combinations of groups and points, in iron and iron-water mixtures. Typical spectra are presented, showing the detail that can be calculated for the flux spectrum in the resolved resonance region for iron.