Abstract
The Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) is applied to compute the first-order and second-order sensitivities of the leakage response of a polyethylene-reflected plutonium (PERP) experimental system with respect to the following nuclear data: Group-averaged isotopic microscopic fission cross sections, mixed fission/total, fission/scattering cross sections, average number of neutrons per fission (), mixed /total cross sections, /scattering cross sections, and /fission cross sections. The numerical results obtained indicate that the 1st-order relative sensitivities for these nuclear data are smaller than the 1st-order sensitivities of the PERP leakage response with respect to the total cross sections but are larger than those with respect to the scattering cross sections. The vast majority of the 2nd-order unmixed sensitivities are smaller than the corresponding 1st-order ones, but several 2nd-order mixed relative sensitivities are larger than the 1st-order ones. In particular, several 2nd-order sensitivities for 239Pu are significantly larger than the corresponding 1st-order ones. It is also shown that the effects of the 2nd-order sensitivities of the PERP benchmark’s leakage response with respect to the benchmark’s parameters underlying the average number of neutrons per fission, , 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 fission and scattering cross sections.
Highlights
This work, designated as “Part III,” continues the presentations of results, commenced in Part I [1] and set forth in Part II [2], produced within the ongoing second-order comprehensive sensitivity analysis to nuclear data of the polyethylene-reflected plutonium (PERP) metal sphere benchmark describedEnergies 2019, 12, 4100; doi:10.3390/en12214100 www.mdpi.com/journal/energiesEnergies 2019, 12, 4100 in [3]
The largest absolute value in this submatrix is attained by the relative 2nd-order mixed sensitivity S(2) νig==112, σtg,k==112 = −3.785, involving the parameters representing the average number of neutrons per fission and total cross section of isotope 239Pu in the 12th energy group
For the sensitivities with respect to the fission cross sections, the following conclusions can be drawn from the results reported in this work: 1. The 1st-order relative sensitivities of the PERP leakage response with respect to the group-averaged microscopic fission cross sections for the two fissionable PERP isotopes are positive, as shown in Tables 2 and 3, signifying that an increase in σgf,i, i = 1, 2; g = 1, . . . , 30 will cause an increase in the PERP leakage response L
Summary
This work, designated as “Part III,” continues the presentations of results, commenced in Part I [1] and set forth in Part II [2], produced within the ongoing second-order comprehensive sensitivity analysis to nuclear data of the polyethylene-reflected plutonium (PERP) metal sphere benchmark described. 30, of the leakage response with respect to the fission microscopic cross sections for the six isotopes contained in the PERP benchmark will be presented, below, in tables that will include comparisons with the numerical values of the corresponding 2nd-order unmixed relative sensitivities S(2) σgf ,i, σgf ,i. We present the computation and analysis of the numerical results for the 2nd-order mixed sensitivities ∂2L(α)/∂σ f ∂σt, of the leakage response with respect to the group-averaged fission and total microscopic cross sections of all isotopes of the PERP benchmark. As has been shown by Cacuci [5], these mixed sensitivities can be computed using two distinct expressions, involving distinct 2nd-level adjoint systems and corresponding adjoint functions, by considering either the computation of ∂2L(α)/∂σ f ∂σt or the computation of ∂2L(α)/∂σt∂σ f These two distinct paths for computing the 2nd-order sensitivities with respect to group-averaged fission and total microscopic cross sections will be presented in Section 3.1 and, respectively, Section 3.2.
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