Third order adjoint sensitivity analysis of reaction rate responses in a multiplying nuclear system with source

Abstract

Until recently, the 2nd-order sensitivities of reactor physics model responses to the nuclear data characterizing the respective model were impractical to compute exactly and exhaustively, because of the so-called “curse of dimensionality.” Hence, the effects of the 2nd-order sensitivities on the uncertainties produced in responses by the uncertain nuclear data have been routinely neglected. Recently, the author has developed a general 2nd-order adjoint sensitivity analysis methodology which overcame the “curse of dimensionality” to perform the first-ever complete computation of the exact 21,976 first-order, and 482,944,576 s-order sensitivities for a OECD/NEA reactor physics benchmark response to the uncertain nuclear data that characterize the neutron transport computational model of this benchmark. In particular, the numerical results obtained for the benchmark’s leakage response with respect to the benchmark’s group-averaged isotopic total cross sections indicated that, contrary to the widely held belief that the 2nd-order response sensitivities in reactor physics systems are negligible, the opposite turned out to be the case, i.e., many of the 2nd-order sensitivities were orders of magnitude larger than the corresponding 1st-order ones. Consequently, neglecting the 2nd-order sensitivities would cause very large non-conservative errors by under-reporting the response variance and erroneously reporting its expected value.The fact that a large number of 2nd-order response sensitivities are significantly larger than the 1st-order sensitivities has motivated the development of the general expressions presented in this work for the efficient and exact computation of the 3rd-order response sensitivities of reaction rate responses to nuclear data for subcritical reactor physics systems modeled by the neutron transport equation. The mathematical results derived in this work are currently implemented in production-oriented three-dimensional neutron transport code systems to enable the computation of 3rd-order sensitivities of reactor physics systems, commencing with the OECD/NEA benchmark mentioned above.