Understanding the Macroscopic Cross Section Treatment in Hybrid Continuous Energy and Multigroup Depletion using the Shift Monte Carlo Code

This paper establishes the methodology required for hybrid depletion using continuous energy and multigroup Monte Carlo. Hybrid depletion is necessary to combine previous substepping techniques that either looked to update the flux spectrum or distribution on the substep. Hybrid depletion allows for this by using multigroup Monte Carlo as reduced order model to obtain a new spectrum and spatial distribution of the flux. However, the treatment of the macroscopic cross sections in this novel approach is important and must be analyzed thoroughly before any other analysis can be done. As such, the macroscopic cross sections are updated using the varied isotopic number densities and multigroup microscopic cross sections. This paper explores how treating multigroup microscopic cross sections for each substep can be used to update macroscopic cross section. The perturbed macroscopic cross sections are used in multigroup Monte Carlo to obtain a new solution for the substep and then the substep solution is compared to reference depletion using standard methods. While the perturbation method outlined in this paper is demonstrated to be inadequate for substep results, the accuracy of this method in predicting the change in number densities implies that further treating of the multigroup cross sections could be used to improve these results.