Jeffrey A. Favorite’s research while affiliated with Los Alamos National Laboratory and other places

Background Correlated sampling can be applied with batch statistics using MCNP6’s tally fluctuation chart (TFC) to reduce the uncertainty of a difference of tallies between a base case and a perturbed case without modifying the source code. The cases are correlated if they are run with the same random number sequence. Equations implemented Equations used to apply correlated sampling to the difference of two tallies are summarized from previous work. Equations used to apply correlated sampling to a ratio of two tallies, to the difference of two tallies divided by a third tally, and to other combinations of ratios are presented. New computer code A general-purpose, command-line-driven computer program, COSUBS (Correlated Sampling Using Batch Statistics), is presented that reads MCNP6 TFCs from output files and applies these equations. The user specifies the input relative perturbation, if desired, and any normalization tally, if desired. Example problems show how to run COSUBS and interpret the output.

Application of perturbation capabilities for density sensitivities in Monte Carlo radiation transport codes has been limited because changing source nuclide densities or source material densities changes the intrinsic source, and in most Monte Carlo codes, the user-input source is independent of the user-input materials. The perturbation capability then has no way of accounting for changes in the intrinsic source. This paper derives the sensitivity of a response with respect to a source nuclide density in terms of a portion due to the transport operator and a portion due to the source rate density. The Monte Carlo perturbation method computes the portion due to the transport operator, and the portion due to the source rate density is computed in postprocessing using parameters from the precomputed intrinsic source calculation. This paper derives first- and second-order sensitivities. The equations require the response to be separated by contribution from each of the sources modeled. A test problem containing several (α,n) and spontaneous fission neutron sources verifies the method.

Methods for approximately accounting for the terms neglected in a finite (L’th-order) Legendre expansion of the scattering source in the transport equation are called transport corrections. This paper derives adjoint-based sensitivities of a neutron or gamma-ray transport response for problems that use diagonal, Bell-Hansen-Sandmeier (BHS), or n’th-Cesàro-mean-of-order-2 (Cesàro) transport corrections in the discrete-ordinates method. For diagonal and BHS transport corrections, there is a sensitivity to the L + 1ʹth scattering cross-section moment, and the sensitivity to nuclide and material densities requires this contribution. For the Cesàro transport correction, the sensitivities to the scattering cross section for the l’th moment are multiplied by a simple function of l and the scattering expansion order L. Numerical results for a keff problem and a fixed-source problem verify the derivation and implementation of the sensitivity equations into the SENSMG multigroup sensitivity code. The Cesàro transport correction yields inaccurate responses for both problems.

Kilowatt Reactor Using Stirling TechnologY (KRUSTY) was a prototype for the U.S. National Aeronautics and Space Administration’s Kilopower Program. KRUSTY has a highly enriched uranium–molybdenum alloy (with 7.65 wt% molybdenum) annular core reflected by beryllium oxide with an outer stainless steel shield. Five configurations from the experimental campaign were chosen to be evaluated as benchmark cases. Uncertainties were evaluated in five categories: (1) criticality measurement, (2) mass and density, (3) dimensions, (4) material compositions, and (5) positioning. The largest contribution to the overall uncertainty in each case was from the radial alignment of the movable platen. A simplified model was created to increase computational efficiency, and an average bias of –16 pcm was calculated due to the simplifications. Sample calculations were completed for each case using MCNP6.2, COG, and MC21, all with ENDF/B-VIII.0 nuclear data. For MCNP6.2, the average difference (absolute value) between the calculated and experimental keff for the five configurations was 14 pcm for both the detailed and the simplified models. The keff results from all three codes are within 1σ of the benchmark values. KRUSTY’s value as a benchmark is due to its sensitivity to beryllium and molybdenum. For beryllium, KRUSTY adds an 18th benchmark with a total cross-section sensitivity greater than 0.05%/%/(unit lethargy). For molybdenum, KRUSTY adds a 9th benchmark with a total cross-section sensitivity greater than 0.004%/%/(unit lethargy).

The multidual differentiation method has been implemented in a ray-tracing transport simulation for the purpose of calculating arbitrary-order sensitivities of the uncollided particle leakage. This method extends dual number differentiation by perturbing variables along multiple nonreal axes to calculate arbitrary-order derivatives. Numerical results of first-through third-order multidual sensitivities of the uncollided particle leakage with respect to isotope densities, microscopic cross sections, source emission rates, and material interface locations (including the outer boundary) are shown for a two-region sphere. The relative error of first and second partial derivatives with respect to isotopic parameters and first partial derivatives of the leakage with respect to interface locations are within 9.8E−10% of existing adjoint-based sensitivities. Higher-order multidual-based derivatives that are not available with the adjoint method are in excellent agreement with central difference approximations.

This paper derives a new formula for the sensitivities of Bondarenko resonance self-shielded cross sections with respect to nuclide densities and the subsequent adjoint-based sensitivities of keff with respect to nuclide densities. A previous derivation ignored the dependence of the self-shielded cross sections on some of the nuclide densities. The new formula accounts explicitly for tabular interpolation of the self-shielded cross sections. Numerical results for two test problems using the PARTISN multigroup discrete ordinates code and the SENSMG multigroup sensitivity code demonstrate the correctness of the equations and their implementation.

This work applies the Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) to compute the 1st-order and unmixed 2nd-order sensitivities of a polyethylene-reflected plutonium (PERP) benchmark’s leakage response with respect to the benchmark’s imprecisely known isotopic number densities. The numerical results obtained for these sensitivities indicate that the 1st-order relative sensitivity to the isotopic number densities for the two fissionable isotopes have large values, which are comparable to, or larger than, the corresponding sensitivities for the total cross sections. Furthermore, several 2nd-order unmixed sensitivities for the isotopic number densities are significantly larger than the corresponding 1st-order ones. This work also presents results for the first-order sensitivities of the PERP benchmark’s leakage response with respect to the fission spectrum parameters of the two fissionable isotopes, which have very small values. Finally, this work presents the overall summary and conclusions stemming from the research findings for the total of 21,976 first-order sensitivities and 482,944,576 second-order sensitivities with respect to all model parameters of the PERP benchmark, as presented in the sequence of publications in the Special Issue of Energies dedicated to “Sensitivity Analysis, Uncertainty Quantification and Predictive Modeling of Nuclear Energy Systems”.

The first-order sensitivities of the (α,n) neutron source rate density in a homogeneous material to isotopic (α,n) cross sections, elemental electronic stopping power data, and general coefficients for the nuclear stopping power are derived for the total neutron source and the energy-dependent neutron source. The physics bases for some of the equations in the SOURCES4C calculation of the stopping power are briefly discussed. The derivatives have been implemented in SOURCES4C. In simple PuO2 and PuB2 test problems, the computed derivatives compare extremely well with central differences. The first-order sensitivities are applied to show that improving the value of one of SOURCES4C’s stopping-power coefficients changes the (α,n) neutron source rate by 1.738 × 10⁻⁶% in the PuO2 problem.

This paper presents the first application of model calibration to neutron multiplicity counting (NMC) experiments for cross-section optimization that is informed by adjoint-based sensitivity analysis (SA) and first-order uncertainty quantification (UQ). We summarize previous work on SA applied to NMC and describe notable modifications and additions. We give the procedure for first-order UQ and Bayesian-inference-based parameter estimation (PE). We then discuss model calibration applied to NMC of a 4.5-kg sphere of weapons-grade, alpha-phase plutonium metal (the BeRP ball) with the nPod neutron multiplicity counter. For the BeRP ball in bare and polyethylene-reflected configurations, we discuss the sensitivity of the first- and second-moment detector responses (i.e., first and second moments of the NMC distribution, respectively) to the cross sections. We describe the sources of uncertainty in the measured and simulated responses. Specifically, uncertainty in the measured responses is due to both random and systematic sources. Uncertainty in the simulated responses is due to the cross-section covariances. We describe in detail the adjustment to the cross sections and cross-section covariances due to the optimization. Due to the contribution of systematic uncertainties to the measured response uncertainties, the adjustment to the cross sections is similar in trend but larger in magnitude compared to that recommended by previous work. We compare the measured responses to responses simulated with nominal and optimized cross sections, demonstrating that the best-estimate cross sections produce simulations of NMC experiments that are more accurate with reduced uncertainty.