Brian C. Kiedrowski’s research while affiliated with University of Michigan and other places

This paper presents mathematical formulations and methods to predict the effect of forced-flight variance reduction on Monte Carlo tally variance and calculation time. This includes deducing biasing operators that are then used to construct a history-score probability density function (HSPDF), which represents all possible Monte Carlo random walks and gives the probability of a Monte Carlo history scoring in a tally from a particular phase-space position. The history-score moment equations (HSMEs), the statistical moments of the HSPDF, are then derived to calculate the statistical behavior of the Monte Carlo tally when forced-flight variance reduction is applied. In addition, the future-time equation (FTE) is derived to predict the Monte Carlo computational time as a result of applying forced-flight variance reduction. The solutions of the HSMEs and FTE can be used to predict Monte Carlo computational cost. This work also describes a discrete ordinates method to solve the forced-flight HSMEs and FTE. Several 1-D and 2-D test problems verify that the derivations are performed and implemented correctly.

Rossi-alpha neutron experiments are used to estimate the prompt neutron decay constant of a fissile assembly, a quantity of widespread interest in applications including in nuclear nonproliferation and criticality safety. This work develops a mathematical model to efficiently estimate measurement uncertainty of Rossi-alpha neutron experiments inferred from a two-exponential fit model with histogram binning. The derived uncertainty estimates were validated using repeated Rossi-alpha measurements of a subcritical, 4.5-kg sphere of weapons-grade, α-phase plutonium with nickel, copper, tungsten, and polyethylene reflectors. The estimates of uncertainty for the histogram data produced by the model were conservative and agree with the reference uncertainties within noise. The estimates of the prompt neutron decay constant uncertainty agreed with the reference uncertainties within one standard deviation. The proposed model will reduce total measurement times, ultimately reducing operational and procedural costs in application.

Recent research has focused on the development of surrogate models for radiation source localization in a simulated urban domain. We employ the Monte Carlo N-Particle (MCNP) code to provide high-fidelity simulations of radiation transport within an urban domain. The model is constructed to employ a source location (x,y,z) as input and return the estimated count rate for a set of specified detector locations. Because MCNP simulations are computationally expensive, we develop efficient and accurate surrogate models of the detector responses. We construct surrogate models using Gaussian processes and neural networks that we train and verify using the MCNP simulations. The trained surrogate models provide an efficient framework for Bayesian inference and experimental design. We employ Delayed Rejection Adaptive Metropolis (DRAM), a Markov Chain Monte Carlo algorithm, to infer the location and intensity of an unknown source. The DRAM results yield a posterior probability distribution for the source’s location conditioned on the observed detector count rates. The posterior distribution exhibits regions of high and low probability within the simulated environment identifying potential source locations. In this manner, we can quantify the source location to within at least one of these regions of high probability in the considered cases. Employing these methods, we are able to reduce the space of potential source locations by at least 60%.

The reactivity and the k-effective multiplication factor ($k_\text{eff}$) of a fissionable assembly are quantities of widespread interest. These values can be inferred from Rossi-alpha measurements of the prompt neutron decay constant (or the inverse: $\alpha^{-1}$). It has been shown that $^3$He-gas proportional counter-based detection systems are insensitive to $\alpha^{-1}$ of fast assemblies (much faster than tens of microseconds). Therefore, it is of interest to investigate fast detection systems such as those based on organic scintillation detectors. In this work, an array of 12 cylindrical, 5.08 cm $\times$ 5.08 cm diameter \textit{trans}-stilbene organic scintillators was used to measure five subcritical assemblies. One assembly was a sphere of approximately 4.5 kg of alpha-phase, weapons-grade plutonium ($k_\text{eff} = 0.773$, $\alpha^{-1}=11.84$ ns) known as the BeRP ball encased in a thin stainless-steel clad. The other assemblies used the same encased sphere and 7.62 cm of iron, nickel, copper, or tungsten reflectors ($k_\text{eff} = 0.884, 0.916, 0.924, 0.939$, respectively and $\alpha^{-1} = 36.60, 41.56, 49.60, 70.32$ ns, respectively). This work (1) validates Rossi-alpha measurements with organic scintillators by demonstrating good agreement between measurements and simulations; and (2), demonstrates that organic scintillator-based systems are sensitive to $\alpha^{-1}$ on the order of 10 - 100~ns.

The meshless local Petrov–Galerkin (MLPG) method is applied to the steady-state and k-eigenvalue neutron transport equations, which are discretized in energy using the multigroup approximation and in angle using the discrete ordinates approximation. To prevent oscillations in the neutron flux, the MLPG transport equation is stabilized by the streamline upwind Petrov–Galerkin (SUPG) method. Global neutron conservation is enforced by using moving least squares basis and weight functions and appropriate SUPG parameters. The cross sections in the transport equation are approximated in accordance with global particle balance and without constraint on their spatial dependence or the location of the basis and weight functions. The equations for the strong-form meshless collocation approach are derived for comparison to the MLPG equations. The method of manufactured solutions is used to verify the resulting MLPG method in one, two and three dimensions. Results for realistic problems, including two-dimensional pincells, a reflected ellipsoid and a three-dimensional problem with voids, are verified by comparison to Monte Carlo simulations.

For a nuclear system in which the entire -eigenvalue spectrum is known, eigenfunction expansion yields the time-dependent flux response to any arbitrary source. Applications in which this response is of interest include pulsed-neutron experiments, accelerator-driven subcritical systems, and fast burst reactors, where a steady-state assumption used in neutron transport is invalid for characterizing the time-dependent flux. To obtain the -eigenvalue spectrum, the transition rate matrix method (TRMM) tallies transition rates describing neutron behavior in a discretized position-direction-energy phase space using Monte Carlo. Interpretation of the resulting Markov process transition rate matrix as the operator in the adjoint -eigenvalue problem provides an avenue for determining a large finite set of eigenvalues and eigenfunctions of a nuclear system. Results from the TRMM are verified using analytic solutions, time-dependent Monte Carlo simulations, and modal expansion from diffusion theory. For simplified infinite-medium and one-dimensional geometries, the TRMM accurately calculates eigenvalues, eigenfunctions, and eigenfunction expansion solutions. Applications and comparisons to measurements are made for the small fast burst reactor CALIBAN and the Fort St. Vrain high-temperature gas-cooled reactor. For large three-dimensional geometries, discretization of the large position-energy-direction phase space limits the accuracy of eigenfunction expansion solutions using the TRMM, but it can still generate a fair estimate of the fundamental eigenvalue and eigenfunction. These results show that the TRMM generates an accurate estimate of a large number of eigenvalues. This is not possible with existing Monte Carlo–based methods.

The heavy-gas model with specific energy-dependent absorption cross sections is used to construct analytical, semi-analytical, and numerical free-gas scattering benchmarks for the neutron spectrum, effective multiplication factor k, and temperature coefficient in an infinite, homogeneous medium. The energy dependences considered are piecewise constant, constant plus inverse in energy, and piecewise linear. Analytic forms for k and in terms of hypergeometric functions are obtained for piecewise-constant absorption with two energy ranges and for constant-plus-inverse-in-energy absorption. Analogous semi-analytical integral expressions are obtained for piecewise-linear absorption with two energy ranges. Numerical solutions of a linear system are obtained for piecewise-constant and piecewise-linear absorption for greater than two energy ranges. The heavy-gas model solutions of k are compared with continuous-energy Monte Carlo calculations; the results converge to the heavy-gas model with increasing target mass ratio A, demonstrating the heavy-gas model’s utility as a verification benchmark.

This paper presents a new method for performing angular biasing in Monte Carlo radiation transport codes using arbitrary convex polyhedra to define regions of interest toward which to project particles (DXTRAN regions). The method is derived and is implemented using axis-aligned right parallelepipeds (AARPPs) and arbitrary convex polyhedra. Attention is paid to possible numerical complications and areas for future refinement. A series of test problems are executed with void, purely absorbing, purely scattering, and 50% absorbing/50% scattering materials. For all test problems tally results using AARPP and polyhedral DXTRAN regions agree with analog and/or spherical DXTRAN results within statistical uncertainties. In cases with significant scattering the figure of merit (FOM) using AARPP or polyhedral DXTRAN regions is lower than with spherical regions despite the ability to closely fit the tally region. This is because spherical DXTRAN processing is computationally less expensive than AARPP or polyhedral DXTRAN processing. Thus, it is recommended that the speed of spherical regions be considered versus the ability to closely fit the tally region with an AARPP or arbitrary polyhedral region. It is also recommended that short calculations be made prior to final calculations to compare the FOM for the various DXTRAN geometries because of the influence of the scattering behavior.

We describe the new ENDF/B-VIII.0 evaluated nuclear reaction data library. ENDF/B-VIII.0 fully incorporates the new IAEA standards, includes improved thermal neutron scattering data and uses new evaluated data from the CIELO project for neutron reactions on ¹H, ¹⁶O, ⁵⁶Fe, ²³⁵U, ²³⁸U and ²³⁹Pu described in companion papers in the present issue of Nuclear Data Sheets. The evaluations benefit from recent experimental data obtained in the U.S. and Europe, and improvements in theory and simulation. Notable advances include updated evaluated data for light nuclei, structural materials, actinides, fission energy release, prompt fission neutron and γ-ray spectra, thermal neutron scattering data, and charged-particle reactions. Integral validation testing is shown for a wide range of criticality, reaction rate, and neutron transmission benchmarks. In general, integral validation performance of the library is improved relative to the previous ENDF/B-VII.1 library.

Monte Carlo methods are developed using adjoint-based perturbation theory and the differential operator method to compute the sensitivities of the k-eigenvalue, linear functions of the flux (reaction rates), and bilinear functions of the forward and adjoint flux (kinetics parameters) to system dimensions for uniform expansions or contractions. The calculation of sensitivities to system dimensions requires computing scattering and fission sources at material interfaces using collisions occurring at the interface—which is a set of events with infinitesimal probability. Kernel density estimators are used to estimate the source at interfaces using collisions occurring near the interface. The methods for computing sensitivities of linear and bilinear ratios are derived using the differential operator method and adjoint-based perturbation theory and are shown to be equivalent to methods previously developed using a collision history–based approach. The methods for determining sensitivities to system dimensions are tested on a series of fast, intermediate, and thermal critical benchmarks as well as a pressurized water reactor benchmark problem with iterated fission probability used for adjoint-weighting. The estimators are shown to agree within 5% and of reference solutions obtained using direct perturbations with central differences for the majority of test problems.