Second-Order Analysis: Effects of Source Parameters

Abstract

This chapter presents the application of the Second-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Linear Systems (2nd-CASAM-L) to compute the mixed second-order sensitivities of the PERP (polyethylene-reflected plutonium) benchmark’s leakage response with respect to the benchmark’s imprecisely known source parameters and the following other parameters: (i) the 12 × 180 mixed second-order sensitivities involving the total microscopic cross sections, (ii) the 12 × 21600 mixed second-order sensitivities involving the scattering microscopic cross sections, (iii) the 12 × 60 mixed second-order sensitivities involving the fission microscopic cross sections, (iv) the 12 × 60 mixed second-order sensitivities involving the average number of neutrons produced per fission, and (v) 12 × 6 mixed second-order sensitivities involving the isotopic number densities of all isotopes in the PERP benchmark. The numerical results obtained for these sensitivities indicate that the first- and second-order relative sensitivities with respect to the source parameters for ²³⁹Pu are very small (10⁻⁴ or less). In contradistinction, the first-order and several second-order relative sensitivities of the leakage response with respect to the source parameters of ²⁴⁰Pu are large (e.g., near or greater than 1.0). Large values are also displayed by several mixed second-order relative sensitivities of the leakage response with respect to parameters involving the source and (i) the total cross sections, (ii) the average neutrons per fission, and (iii) the isotopic number densities. Among them, the largest mixed second-order relative sensitivity has a value of 5.967, involving the source parameter of isotope ²⁴⁰Pu and the isotopic number density of isotope ²³⁹Pu. It is also shown that the effects of the first- and second-order sensitivities involving the benchmark’s source parameters on the moments (expected value, variance, and skewness) of the benchmark’s leakage response distribution are negligibly smaller than the corresponding effects involving the total, fission, and scattering microscopic cross sections.