Fourth-Order Adjoint Sensitivity and Uncertainty Analysis of an OECD/NEA Reactor Physics Benchmark: I. Computed Sensitivities

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.

Evaluation of the Esfr End of Equilibrium Cycle State: Spatial Distributions of Reactivity Coefficients

The Horizon 2020 ESFR-SMART project investigates the behaviour of the commercial-size European Sodium-cooled Fast Reactor (ESFR) throughout its lifetime. This paper reports work focused on the End of Equilibrium Cycle (EOEC) loading of the ESFR, including neutronic analysis, core- and zone-wise reactivity coefficients, and more detailed local mapping of important safety-relevant parameters. Sensitivity and uncertainty analysis on these parameters have also been performed and a detailed investigation into decay heat mapping carried out. Due to the scope of this work the results have been split into three papers. The nominal operating conditions and both zone-wise and local mapping of reactivity coefficients are considered in this paper; the sensitivity and uncertainty analysis are detailed in Margulis et al. [1]; and the decay heat mapping calculations are reported in Jimenez-Carrascosa et al. [2]. The work was performed across four institutions using both continuous-energy Monte Carlo and deterministic reactor physics codes. A good agreement is observed between the methods, verifying the suitability of these codes for simulation of large, complicated reactor configurations; and giving confidence in the results for the most limiting ESFR EOEC core state for safety analysis. The results from this work will serve as basis for the transient calculations planned for the next stage of work on the ESFR, allowing for more in-depth studies to be performed on the multiphysics behaviour of the reactor.