Second-order sensitivity and uncertainty analysis of the Roussopoulos-functional for a subcritical multiplying nuclear system with source

Abstract

The Roussopoulos-functional has long been used for selecting trial functions for the forward and adjoint fluxes when computing reaction rates in nuclear systems and/or particle detector responses, because this functional was considered in previous works and textbooks to be accurate to second-order in variations of the model’s forward and adjoint fluxes. However, by applying the Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM), this work shows that the first-order sensitivities of the Roussopoulos-functional to the system’s parameters (including isotopic number densities, microscopic cross sections, fission spectrum, forward and adjoint sources) are not identically zero. This means that the Roussopoulos-functional is not accurate to second-order in the flux variations if the system parameters are imprecisely (rather than perfectly well) known, as is invariably the case in practice. This work also illustrates the application of the 2nd-ASAM for computing efficiently the correct expressions of the second-order sensitivities of the Roussopoulos-functional to model parameters. The results presented in this work indicate the correct path for future possible uses of the Roussopoulos-functional for performing sensitivity and uncertainty analyses of both forward and inverse problems in nuclear systems.