Second-Order Analysis: Effects of Isotopic Number Densities

Abstract

This chapter applies the Second-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Linear Systems (2nd-CASAM-L) to compute the mixed second-order sensitivities of the PERP benchmark’s leakage response involving the benchmark’s imprecisely known isotopic number densities and the following parameters: (i) the 6 × 6 second-order sensitivities between the isotopic number densities, (ii) the 6 × 180 mixed second-order sensitivities involving the total microscopic cross sections, (iii) the 6 × 21,600 mixed second-order sensitivities involving the scattering microscopic cross sections, (iv) the 6 × 60 mixed second-order sensitivities involving the fission microscopic cross sections, and (v) the 6 × 60 mixed second-order sensitivities involving the average number of neutrons produced per fission. It is shown that many of these mixed second-order sensitivities involving the isotopic number densities have very large values. Most of the large sensitivities involve the isotopic number density of ²³⁹Pu and the microscopic total, scattering, or fission cross sections for the 12th or 30th energy groups of ²³⁹Pu or ¹H, respectively. The largest in absolute value (of −94.91) is attained by the second-order mixed sensitivity of the PERP leakage response involving the isotopic number density of ²³⁹Pu and the microscopic total cross section for the 30th energy group of ¹H.