Comprehensive Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) Applied to a Subcritical Experimental Reactor Physics Benchmark: III. Effects of Imprecisely Known Microscopic Fission Cross Sections and Average Number of Neutrons per Fission

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.

Comprehensive Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) Applied to a Subcritical Experimental Reactor Physics Benchmark: IV. Effects of Imprecisely Known Source Parameters

“…Therefore, the 0th-order order scattering cross sections must be considered separately from the higher order scattering cross sections. As described in [1][2][3] and Appendix A, the total number of 0th-order scattering cross sections comprised in σ s is denoted as J σs,l=0 , where J σs,l=0 = G × G × I, while the total number of higher order scattering cross sections comprised in σ s is denoted as…”

“…(127) 127), requires 7101 adjoint PARTISN computations to obtain the needed second level adjoint functions. As has been discussed in Part III [3], the reason for needing "only" 7101, rather than 21600, PARTISN computations is that all of the up-scattering and some of the down-scattering cross sections are zero for the PERP benchmark. Therefore, computing ∂ 2 L(α)/∂q∂σ s using Equations (104) and (106) is about 590 (≈7101/12) times more efficient than computing ∂ 2 L(α)/∂σ s ∂q by using Equations (114)-(119) and (122)-(127).…”

“…. , G are the solutions of the 2nd-Level Adjoint Sensitivity System presented in Equations (21) and (30) of Part III [3], which are also reproduced below for convenient reference:…”

“…Correlations between the source parameters or correlations between these source parameters and other cross section parameters are not available for the PERP benchmark. As discussed in [1][2][3], when such correlations are unavailable, the maximum entropy principle (see, e.g., Ref. [14]) indicates that neglecting them minimizes the inadvertent introduction of spurious information into the computations of the various moments of the response's distribution in parameter space.…”

“…In previous works [1][2][3], the Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) conceived by Cacuci [4][5][6] has been applied to the subcritical polyethylene-reflected plutonium (acronym: PERP) metal OECD/NEA-benchmark [7], to compute efficiently the exact values of the 1st-order and 2nd-order sensitivities of the PERP's leakage response with respect to the following model parameters: (i) 180 group-averaged total microscopic cross sections [1]; (ii) 21,600 group-averaged scattering microscopic cross sections [2]; and (iii) 120 fission process parameters [3]. This work, designated as Part IV, presents the results of having applied the 2nd-ASAM to compute the 1st-and 2nd-order sensitivities of the PERP's leakage response with respect to the PERP benchmark's 12 source parameters.…”