Second-Order Analysis: Effects of Fission Cross Sections

Abstract

The Comprehensive Second-Order Adjoint Sensitivity Analysis Methodology for Linear Systems (2nd-CASAM-L) is applied to compute the second-order sensitivities of the leakage response of the PERP (polyethylene-reflected plutonium) benchmark with respect to the group-averaged isotopic fission microscopic cross sections, mixed fission/total, and fission/scattering microscopic cross sections. The numerical results obtained indicate that the vast majority of the second-order unmixed sensitivities are smaller than the corresponding first-order ones, but several second-order mixed relative sensitivities are larger than the first-order ones. In particular, several second-order sensitivities for isotope ²³⁹Pu are significantly larger than the corresponding first-order sensitivities. It is also shown that the effects of the second-order sensitivities of the PERP benchmark’s leakage response with respect to the benchmark’s fission cross sections on the moments (expected value, variance, and skewness) of the PERP benchmark’s leakage response distribution are negligible by comparison to the corresponding effects (on the response distribution) stemming from uncertainties in the total cross sections but are larger than the corresponding effects (on the response distribution) stemming from uncertainties in the scattering cross sections.