Abstract
This invited keynote presentation compares the relative importance of 1st-order versus 2nd-order sensitivities of the leakage response of an OECD/NEA benchmark (polyethylene-reflected plutonium sphere) to the nuclear data characterizing this benchmark. The imprecisely known parameters underlying the neutron transport computational model for this benchmark include 180 group-averaged total microscopic cross sections, 21600 group-averaged scattering microscopic cross sections, 60 parameters describing the fission process, 30 parameters describing the fission spectrum, 10 parameters describing the system’s sources, and 6 isotopic number densities. Thus, this benchmark comprises 21886 1st-order sensitivities of the leakage response with respect to the model parameters, and 478,996,996 2nd-order sensitivities, of which 239,509,441 are distinct. The exact deterministic computation of all of these 1st- and 2nd-order sensitivities was made possible by the application of the Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) developed by Cacuci. Thousands (out of the 32 400 elements) of the 2nd-order sensitivities of the leakage response with respect to the total cross sections turned out to be significantly larger than the largest corresponding 1st-order sensitivities, contrary to some previously held beliefs in the reactor physics community. Hence, it will be shown that neglecting the 2nd-order sensitivities to total cross sections would cause very large non-conservative errors by under-reporting the response’s variance and expected value. The 2nd-order sensitivities also cause the response distribution to be skewed towards positive values relative to the expected value, which, in turn, is significantly larger than the computed value of the leakage response. The result presented in this paper also underscore the need for obtaining reliable cross section covariance data, which are not available at this time.
Highlights
Several important subcritical fundamental physics benchmarks within the Nuclear Energy Agency (NEA) International Criticality Safety Benchmark Evaluation Project (ICSBEP) Handbook [1] use as particle source a 4.5 kg alpha-phase plutonium sphere colloquially known as the “BeRP ball,” which was originally constructed at Los Alamos National Laboratory in 1980 [2] for conducting experiments aimed at estimating the reactivity worth of beryllium reflectors
In their computational evaluation of neutron multiplicity measurements for the “polyethylene-reflected BeRP” ball, Miller et al [3] showed that the computational results disagreed significantly with the corresponding measurements of neutron multiplicity and concluded that “only a subtle variation in the value of the average number of neutrons produced per fission” for 239Pu was able to improve the simulations of the plutonium sphere...”
This work summarizes the most significant results obtained for the 1st- and 2nd-order sensitivities of the “polyethylene-reflected BeRP ball” benchmark’s leakage response with respect to the benchmark’s groupaveraged isotopic total cross sections, highlighting the finding that many of the 2nd-order sensitivities are much larger than the corresponding 1st-order sensitivities
Summary
Several important subcritical fundamental physics benchmarks within the Nuclear Energy Agency (NEA) International Criticality Safety Benchmark Evaluation Project (ICSBEP) Handbook [1] use as particle source a 4.5 kg alpha-phase plutonium sphere colloquially known as the “BeRP ball,” which was originally constructed at Los Alamos National Laboratory in 1980 [2] for conducting experiments aimed at estimating the reactivity worth of beryllium reflectors ( the acronym “BeRP” for “berylliumreflected plutonium”). In their computational evaluation of neutron multiplicity measurements for the “polyethylene-reflected BeRP” ball, Miller et al [3] showed that the computational results disagreed significantly with the corresponding measurements of neutron multiplicity and concluded that “only a subtle variation in the value of the average number of neutrons produced per fission” for 239Pu was able to improve the simulations of the plutonium sphere...”. This work summarizes the most significant results obtained for the 1st- and 2nd-order sensitivities of the “polyethylene-reflected BeRP ball” benchmark’s leakage response with respect to the benchmark’s groupaveraged isotopic total cross sections, highlighting the finding that many of the 2nd-order sensitivities are much larger than the corresponding 1st-order sensitivities. 30 6.432 8.424 9.97 10.67 22.48 23.62 23.62 23.15 22.29 21.40 20.24 g=12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 g′=23
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