A Monte Carlo framework for nuclear data uncertainty propagation via the windowed multipole formalism

Abstract

A new framework has been developed that calculates the uncertainty in calculated quantities, such as K[subscript eff], reactivity coefficients, multigroup cross sections, and reaction rate ratios, that arise due to uncertainties in the underlying nuclear data. This framework relies on first order uncertainty analysis using sensitivity methods. The major innovation in the proposed framework is the use of the windowed multipole formalism for calculating the sensitivities. The use of the windowed multipole formalism provides a natural, physics-inspired binning strategy for the sensitivity coefficients, while also aiding in the statistical convergence of the calculated sensitivity tallies. Additionally, our framework improves on existing methods by fully accounting for temperature effects. The proposed method allows for identifying exactly the resonances and parameters that are driving the uncertainty, and thus provides guidance to nuclear data evaluators and experimenters on how to reduce the uncertainty in the most efficient manner. Calculating the uncertainty requires two key pieces of information; the windowed multipole sensitivity coefficients, and the windowed multipole covariance matrix. A sensitivity coefficient calculation algorithm based on the CLUTCH-FM methodology was implemented in OpenMC. Several methods for obtaining the windowed multipole covariance matrix from the resonance parameter covariance matrix were explored, and ultimately an approach based on random-sampling was selected. Along the way, an analytical benchmark was developed for the purposes of validating the framework, as well as the implementation. This analytical benchmark consists of a solution to the forward and adjoint neutron transport equations. The windowed multipole covariance matrix was calculated for three isotopes; ²³⁸U , ¹⁵⁷Gd , and ²³Na . The uncertainty in K[subscript eff] due to the uncertainty in the ²³⁸U and ¹⁵⁷Gd cross sections was calculated for two criticality safety benchmarks, and a beginning-of-life PWR model. The uncertainty of several reaction rate ratios due to the uncertainty in the ¹⁵⁷Gd cross section was also calculated for the PWR model. The resonances of ²³⁸U and ¹⁵⁷Gd that have the largest contribution to the uncertainty were identified for the criticality safety benchmarks.