Author(s)

Dan Gabriel Cacuci^*, Ruixian Fang

Center for Nuclear Science and Energy, Department of Mechanical Engineering, University of South Carolina, Columbia, SC, USA.

This work extends to fourth-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. Previous works showed that the third-order sensitivities of the PERP leakage response with respect to these total microscopic cross sections are far larger than the corresponding 1^st-order and 2^nd-order ones, thereby having the largest impact on the uncertainties induced in the PERP benchmark’s response. This finding has motivated the development of the original 4^th-order formulas presented in this work, which are valid not only for the PERP benchmark but can also be used for computing the 4^th-order sensitivities of 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 the largest fourth-order sensitivities of the PERP benchmark’s response to the total microscopic cross sections, and use them for a pioneering fourth-order uncertainty analysis of the PERP benchmark’s response.

Polyethylene-Reflected Plutonium Sphere, 4^th-Order Adjoint Sensitivity Analysis, Microscopic Total Cross Sections

Cacuci, D. and Fang, R. (2021) Fourth-Order Adjoint Sensitivity Analysis of an OECD/NEA Reactor Physics Benchmark: II. Mathematical Expressions and CPU-Time Comparisons for Computing 4^th-Order Sensitivities. American Journal of Computational Mathematics, 11, 133-156. doi: 10.4236/ajcm.2021.112010.