Concluding Remarks

Abstract

The “nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Linear Systems” (nth-CASAM-L), which was presented in Volume 1 of this monograph, has been applied in this book (Volume 2) to the subcritical polyethylene-reflected plutonium metal (PERP) fundamental physics benchmark. This benchmark is included in the Nuclear Energy Agency (NEA) International Criticality Safety Benchmark Evaluation Project Handbook. The PERP benchmark has been selected to serve as a paradigm illustrative “linear system” because it is modeled by the neutron transport equation which, as has been shown in Chap. 4 of Volume 1 of this monograph, is a linear integro-differential equation that requires “large-scale computations” for solving it in order to determine the underlying neutron flux distribution in space, energy, and solid angle. In order to model the processes of neutron transport and slowing down (in energy) through scattering reactions, removal of neutrons through capture, and birth of neutrons through fission reactions and external sources, the neutron transport equation involves a large number of imprecisely known parameters, including nuclear cross sections, isotopic number densities, fission spectra, and source parameters. In particular, the numerical model of the PERP benchmark includes 21,976 parameters, as follows: (i) 180 group-averaged total microscopic cross sections, (ii) 120 fission process parameters, (iii) 60 fission spectrum parameters, (iv) 10 parameters describing the experiment’s nuclear sources, (v) 6 isotopic number densities, and (vi) 21,600 group-averaged scattering microscopic cross sections, of which 7101 have nonzero nominal values. Subcritical benchmarks, such as the PERP benchmark, are most often characterized for practical applications by their total leakage rather than by the count rate that a particular detector would see at a particular distance. This is because the total leakage does not depend on the detector configuration (as opposed to count rates) and is therefore more meaningful physically than the count rates. For this reason, the total leakage from the PERP benchmark has been considered to be the paradigm response of interest for the high-order sensitivity and uncertainty analysis described in this book (Volume 2).