Abstract
This work extends the investigation of higher-order sensitivity and uncertainty analysis from 3rd-order to 4th-order for a polyethylene-reflected plutonium (PERP) OECD/NEA reactor physics benchmark. Specifically, by applying the 4th-order comprehensive adjoint sensitivity analysis methodology (4th-CASAM) to the PERP benchmark, this work presents the numerical results of the most important 4th-order sensitivities of the benchmark’s total leakage response with respect to the benchmark’s 180 microscopic total cross sections, which includes 180 4th-order unmixed sensitivities and 360 4th-order mixed sensitivities corresponding to the largest 3rd-order ones. The numerical results obtained in this work reveal that the number of 4th-order relative sensitivities that have large values (e.g., greater than 1.0) is far greater than the number of important 1st-, 2nd- and 3rd-order sensitivities. The majority of those large sensitivities involve isotopes 1H and 239Pu contained in the PERP benchmark. Furthermore, it is found that for most groups of isotopes 1H and 239Pu of the PERP benchmark, the values of the 4th-order relative sensitivities are significantly larger than the corresponding 1st-, 2nd- and 3rd-order sensitivities. The overall largest 4th-order relative sensitivity S(4)σt,6g=30,σt,6g=30,σt,6g=30,σt,6g=30=2.720×106 is around 291,000 times, 6350 times and 90 times larger than the corresponding largest 1st-order, 2nd-order and 3rd-order sensitivities, respectively, and the overall largest mixed 4th-order relative sensitivity S(4)σt,630,σt,630,σt,630,σt,530=2.279×105 is also much larger than the largest 2nd-order and 3rd-order mixed sensitivities. The results of the 4th-order sensitivities presented in this work have been independently verified with the results obtained using the well-known finite difference method, as well as with the values of the corresponding symmetric 4th-order sensitivities. The 4th-order sensitivity results obtained in this work will be subsequently used on the 4th-order uncertainty analysis to evaluate their impact on the uncertainties they induce in the PERP leakage response.
Highlights
The Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) conceived by Cacuci [1] has opened the way for the exact computation of the large number of 2ndorder sensitivities that arise in large-scale problems comprising many parameters
Benchmark’s leakage response with respect to the 180 group-averaged microscopic total cross sections are the largest and have, the largest impact on the uncertainties induced in the leakage response
Based on the trends indicated by the numerical results presented in Tables 2–7, it would be expected that the largest 4th-order sensitivities would be those which correspond to the largest 3rd-order ones
Summary
The Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) conceived by Cacuci [1] has opened the way for the exact computation of the large number of 2ndorder sensitivities that arise in large-scale problems comprising many parameters. 30, represents the 4th-order unmixed relative sensitivities of the PERP leakage response with respect g to the same microscopic total cross section (namely: σt,i ) for each isotope and for each energy group. 30 for the 30th energy group of in [11] that the microscopic total cross sections and σt, isotopes Pu and H are the two most important parameters affecting the PERP benchmark’s leakage response since they are involved in the largest mixed and unmixed 1st-, 2nd- and 3rd-order sensitivities.
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