Abstract
This work extends to third-order previously published work on developing the adjoint sensitivity and uncertainty analysis of the numerical model of a polyethylene-reflected plutonium (acronym: PERP) OECD/NEA reactor physics benchmark. The PERP benchmark comprises 21,976 imprecisely known (uncertain) model parameters. Previous works have used the adjoint sensitivity analysis methodology to compute exactly and efficiently all of the 21,976 first-order and (21,976)2 second-order sensitivities of the PERP benchmark’s leakage response to all of the benchmark’s uncertain parameters, showing that the largest and most consequential 1st- and 2nd-order response sensitivities are with respect to the total microscopic cross sections. These results have motivated extending the previous adjoint-based derivations to third-order, leading to the derivation, in this work, of the exact mathematical expressions of the (180)3 third-order sensitivities of the PERP leakage response with respect to these total microscopic cross sections. The formulas derived in this work are valid not only for the PERP benchmark but can also be used for computing the 3rd-order sensitivities of the leakage response of any nuclear system involving fissionable material and internal or external neutron sources. Subsequent works will use the adjoint-based mathematical expressions obtained in this work to compute exactly and efficiently the numerical values of these (180)3 third-order sensitivities (which turned out to be very large and consequential) and use them for a third-order uncertainty analysis of the PERP benchmark’s leakage response.
Highlights
Until recently, only the first-order sensitivities of a computational model’s responses to the respective model’s imprecisely known parameters have been taken into account when assessing the uncertainties induced in the respective responses by the parameter uncertainties
The formulas derived in this work are valid for the Polyethylene-Reflected Plutonium (PERP) benchmark but can be used for computing the 3rd-order sensitivities of the leakage response of any nuclear system involving fissionable material and internal or external neutron sources
Subsequent works will use the adjoint-based mathematical expressions obtained in this work to compute exactly and efficiently the numerical values of these (180)3 third-order sensitivities and use them for a third-order uncertainty analysis of the PERP benchmark’s leakage response
Summary
Only the first-order sensitivities (i.e., functional derivatives) of a computational model’s responses (i.e., quantities of interest) to the respective model’s imprecisely known (i.e., uncertain) parameters have been taken into account when assessing the uncertainties induced in the respective responses by the parameter uncertainties. Cacuci’s results [12] are applied in this work to the PERP benchmark in order to derive the exact analytical expressions of the 3rd-order sensitivities of the PERP benchmark’s leakage response with respect to this benchmark’s microscopic total cross sections. We present the derivation of the exact analytical expressions of the 3rd-order sensitivities of the polyethylene-reflected plutonium (acronym: PERP) metal sphere OECD/NEA benchmark [11] total leakage response with respect to this benchmark’s total cross sections, continuing the work presented in [5]-[10]. =1, , Jσt of the PERP leakage response with respect to the group-averaged microscopic total cross sections These 3rd-order sensitivities will be derived by using two alternative procedures, which will be presented in sections 3.1 and 3.2, respectively. It will be shown that these two alternative procedures will yield identical expressions for the corresponding 3rd-order sensitivities, as would be expected
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