Development of Uncertainty Analysis Techniques for the Fission Matrix–Based Neutron Transport Code RAPID

The combined fission matrix (CFM) method is a newly developed neutron transport theory. This method estimates the fission matrix of the reactor core or spent fuel pool by combining a set of database fission matrices. The RAPID neutron transport code based on the CFM routine was developed originally for the spent fuel storage system and has been applied to the reactor core calculation in recent years. It can perform high-fidelity whole-core transport calculations within minutes. However, since the fission matrix database is obtained from Monte Carlo calculations, the uncertainty in the fission matrix will inevitably pass to its eigenvalue and eigenvector. The RAPID code also uses the fission matrix homogenization and interpolation techniques to further improve the calculation efficiency. Therefore, it is difficult to establish a relationship between the fission matrix elements’ uncertainty and the resulting eigenvalue and eigenvector uncertainties. This paper proposes two uncertainty analysis methods to obtain the eigenvalue and eigenvector uncertainties. The fission matrix resampling method resamples the database fission matrix elements according to each individual uncertainty. This method could generate many fission matrix databases at little additional costs and analyze the eigenvalue and eigenvector uncertainties from these resampled fission matrix coefficients. The analog uncertainty analysis method predicts the eigenvalue uncertainty from the uncertainty of the total fission rate in a fixed-source calculation, which yields a fission matrix column. Both uncertainty analysis methods have been validated against the reference brute-force calculations on a single-pin model and the BEAVRS whole-core model. It shows that the fission matrix resampling method could well estimate the uncertainties in the fission matrix eigenvalue and eigenvector. The analog uncertainty analysis method can accurately predict the eigenvalue uncertainty, which provides a guideline for the number of neutron histories simulated per fixed-source calculation.