Illustrating Important Effects of Second-Order Sensitivities on Response Uncertainties in Reactor Physics

Dan G Cacuci

doi:10.3390/jne2020012

Abstract

This paper illustrates the relative importance of the largest first- and second-order sensitivities of the leakage response of an OECD/NEA reactor physics benchmark (a polyethylene-reflected plutonium sphere) to the benchmark’s underlying total cross sections. It will be shown that numerous 2nd-order sensitivities of the leakage response with respect to the total cross sections are significantly larger than the largest corresponding 1st-order sensitivities. In particular, the contributions of the 2nd-order sensitivities cause the mean (expected) value of the response to differ appreciably from its computed value and also cause the response distribution to be skewed towards positive values relative to the mean. Neglecting these large 2nd-order sensitivities would cause very large non-conservative errors by under-reporting the response’s variance and expected value. The results presented in this paper also underscore the need for obtaining reliable cross section covariance data, which are currently unavailable. Finally, comparing the CPU-times needed for computations, this paper demonstrates that the Second-Order Adjoint Sensitivity Analysis Methodology is the only practical method for computing 2nd-order sensitivities exactly, without introducing methodological errors, for large-scale systems characterized by many uncertain parameters.

Highlights

The work reported in this work is based on the PHYSOR-2020 plenary invited conference paper entitled “On the importance of second-order response sensitivities to nuclear data in reactor physics uncertainty analysis.” This paper was selected by the PHYSOR-2020 Technical Committee to be published in the Special Issue of the Journal of Nuclear Engineering
The OECD Nuclear Energy Agency (OECD/NEA) International Criticality Safety Benchmark Evaluation Project (ICSBEP) Handbook [1] describes several fundamental subcritical reactor physics benchmarks that use a 4.5 kg alpha-phase plutonium sphere constructed at Los Alamos National Laboratory in 1980 [2]
The 2nd-order sensitivities of the leakage response to the parameters involved in the definitions of the total cross sections are given by the following expression:

Summary

Introduction

The work reported in this work is based on the PHYSOR-2020 plenary invited conference paper entitled “On the importance of second-order response sensitivities to nuclear data in reactor physics uncertainty analysis.” This paper was selected by the PHYSOR-2020 Technical Committee to be published in the Special Issue of the Journal of Nuclear Engineering. The expressions of the 1st-order sensitivities of the leakage response to the model parameters underlying the total cross section are as follows:. The 2nd-order sensitivities of the leakage response to the parameters involved in the definitions of the total cross sections are given by the following expression:. Not counting the “trial and error” the “correct” value to use for δαi, the CPU time (using a DELL computer with an 8-core processor, AMD FX-8350) needed to compute the 27,956,503 distinct non-zero 2nd-order sensitivities by using Equations (20) and (21) at the respective 111,811,058 “sampling points” would be 592 YEARS-CPU time! It is not feasible to compute the 2nd-order sensitivities using “sampling approaches”

Uncertainty Quantification

Uncorrelated Total Microscopic Cross Sections

Fully Correlated Total Microscopic Cross Sections

Concluding Remarks