Application of the Second-Order Comprehensive Adjoint Sensitivity Analysis Methodology to Compute First- and Second-Order Sensitivities of Flux Functionals in a Multiplying System with Source

Abstract

This work presents an application of the Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) to the neutron transport Boltzmann equation that models a multiplying subcritical system comprising a nonfission neutron source to compute efficiently and exactly all of the first-and second-order functional derivatives (sensitivities) of a detector's response to all of the model's parameters, including isotopic number densities, microscopic cross sections, fission spectrum, sources, and detector response function. As indicated by the general theoretical considerations underlying the 2nd-ASAM, the number of computations required to obtain the first and second orders increases linearly in augmented Hilbert spaces as opposed to increasing exponentially in the original Hilbert space. The results presented in this work are currently being implemented in several production-oriented three-dimensional neutron transport code systems for analyzing specific subcritical systems.

Comprehensive Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) Applied to a Subcritical Experimental Reactor Physics Benchmark: IV. Effects of Imprecisely Known Source Parameters

“…dΩ Ω · n ϕ g (r, Ω), (6) where S b is the external surface area of the PERP ball. Figure 1 shows the histogram plot of the leakage for each energy group for the PERP benchmark.…”

“…Figure 1 shows the histogram plot of the leakage for each energy group for the PERP benchmark. The total leakage computed using Equation (6) for the PERP benchmark is 1.7648 × 10 6 neutrons/sec. Table 2 summarizes the integrals for the source, fission source, absorption, in-scattering, self-scattering, out-scattering, and particle balance.…”

“…Nominal values of the source parameters for the PERP benchmark [10]. The first-order sensitivity of the PERP leakage response to the source parameters are computed from the following particular form of Equation (154) from Reference [6]:…”

“…In previous works [1][2][3], the Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) conceived by Cacuci [4][5][6] has been applied to the subcritical polyethylene-reflected plutonium (acronym: PERP) metal OECD/NEA-benchmark [7], to compute efficiently the exact values of the 1st-order and 2nd-order sensitivities of the PERP's leakage response with respect to the following model parameters: (i) 180 group-averaged total microscopic cross sections [1]; (ii) 21,600 group-averaged scattering microscopic cross sections [2]; and (iii) 120 fission process parameters [3]. This work, designated as Part IV, presents the results of having applied the 2nd-ASAM to compute the 1st-and 2nd-order sensitivities of the PERP's leakage response with respect to the PERP benchmark's 12 source parameters.…”

“…These imprecisely known source parameters also contribute to the accuracy of the neutron transport calculation. To evaluate the uncertainties induced in the leakage response by the imprecisely known source parameters, the 1st-order and 2nd-order sensitivities of the leakage response with respect to the source parameters will be computed by specializing the general expressions derived by Cacuci [6] to the PERP benchmark.…”