Second-order sensitivities of a general functional of the forward and adjoint fluxes in a multiplying nuclear system with source

Abstract

This work presents an application of the Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) to compute efficiently and exactly all of the 1st- and 2nd-order functional derivatives (“sensitivities”) of a generic scalar-valued response to parameters for a multiplying subcritical system comprising a non-fission neutron source. The response is defined to be a nonlinear functional of the forward and adjoint particle fluxes while the system parameters include isotopic number densities, microscopic cross sections, fission spectrum, sources, and detector response functions. As indicated by the general theoretical considerations underlying the 2nd-ASAM, the number of computations required to obtain the 1st- and 2nd-order increases linearly in augmented Hilbert spaces as opposed to increasing exponentially in the original Hilbert space. This unique feature provides the fundamental reason for the unmatched efficiency of the 2nd-ASAM for computing exactly all of the 1st- and 2nd-order responses sensitivities to model parameters. The results presented in this work are currently being implemented in several production-oriented three dimensional neutron transport code systems for analyzing specific subcritical systems.