Second-order adjoint sensitivity analysis of a general ratio of functionals of the forward and adjoint fluxes in a multiplying nuclear system with source

Abstract

In the present work, the Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) is applied to a generic multiplying subcritical nuclear system comprising a non-fission neutron source in order to compute efficiently and exactly all of the 1st- and 2nd-order functional derivatives (“sensitivities”) of a system response with respect to the system’s many parameters. The system response is defined to be a ratio of two general nonlinear functionals of the forward and adjoint particle fluxes, while the system parameters include isotopic number densities, microscopic cross sections, fission spectrum parameters, neutron sources, and detector response functions. Such ratios of functionals represent the most general models for quantities of fundamental importance in reactor physics, including eigenvalues, ratios of reaction rates and forward/adjoint flux-weighted multi-group cross sections. The exact expressions obtained in this work will be used in subsequent works to perform a large-scale sensitivity analysis of a polyethylene-reflected plutonium metal sphere experimental benchmark to the nuclear data characterizing this benchmark, comprising 21,976 first-order sensitivities and 482,944,576 second-order sensitivities.