Second-Order Analysis: Effects of Average Number of Neutrons Per Fission

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 PERP leakage response with respect to the following nuclear data: average number of neutrons per fission (ν), mixed ν and total cross sections, mixed ν and scattering cross sections, and mixed ν and fission cross sections. The numerical results obtained indicate that for energy groups g = 7, …, 14 of isotope ²³⁹Pu, the values of the second-order unmixed sensitivities of the PERP leakage response with respect to the average number of neutrons per fission are significantly larger than the corresponding values of the first-order ones. For the other energy groups, the values of the second-order unmixed sensitivities are smaller than the corresponding values of the first-order ones. For isotope ²⁴⁰Pu, the values for both the first- and second-order relative sensitivities are all very small, and the values of the second-order unmixed relative sensitivities are an order of magnitude smaller than the corresponding values of the first-order ones. The results also indicate that many mixed second-order relative sensitivities in the matrices ${\textbf{S}}^{(2)}\left({\nu}_i^g,{\nu}_k^{g^{\prime }}\right)$, ${\textbf{S}}^{(2)}\left({\nu}_i^g,{\sigma}_{t,k}^{g^{\prime }}\right)$, and ${\textbf{S}}^{(2)}\left({\nu}_i^g,{\sigma}_{f,k}^{g^{\prime }}\right)$ are significantly larger than the unmixed second-order sensitivities of the leakage response with respect to the average number of neutrons per fission. It is also shown that the effects of the second-order sensitivities of the PERP benchmark’s leakage response with respect to the average number of neutrons per fission, ν, on the moments (expected value, variance, and skewness) of the PERP benchmark’s leakage response distribution are negligible by comparison to the corresponding effects stemming from uncertainties in the microscopic total cross sections but are larger than the corresponding effects stemming from uncertainties in the fission and scattering microscopic cross sections.