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Estimating List-Mode Data Sensitivities to Nuclear Data with MCNP6

Nuclear data are a vital component of predictive simulations used in applications like experiment design, stockpile stewardship, nuclear nonproliferation/safeguards, health physics, and criticality safety. A singular simulation requires the coalescence of different areas of nuclear data such as cross sections, angular distributions, and energy distributions of emitted neutrons for different materials and energy ranges. Improving nuclear data and thus reducing the uncertainty in simulated parameters could enable smaller, better-informed safety factors and ultimately reduce operational and procedural costs. There is a constant effort to garner a better understanding of the physical quantities represented by nuclear data through experiments. Integral experiment benchmarks use simulated and measured results to validate current nuclear data values. In the past, benchmarks primarily focused on the effective multiplication factor (k eff ); however, this limited scope has caused compensating errors and areas of nuclear data that lack validation. Compensating errors are inaccuracies in nuclear data that are obfuscated by cancellation when observing integrated values such as k eff . Diverse integral benchmark experiments that look for quantities of interest other than k eff and include multiple responses minimize the possibility of compensating errors and provides validation to areas of nuclear data previously lacking experimental validation. Benchmark experiments can be optimized during the design process to be highly dependent on specific areas of nuclear data. The dependence of a response in an experiment to a specific area/type of nuclear data is defined as sensitivity. A larger sensitivity means that nuclear data uncertainties will play a larger role in the response(s) resulting in larger bias. Currently, the sensitivity capabilities of the Monte Carlo N-Particle (MCNP ®1 ) transport code are limited to responses of k eff and tallied values (e.g., flux, surface current). As a part of the EUCLID project, this work explores estimating list-mode nuclear data sensitivities that can be used to design experiments aimed to constrain and reduce compensating errors in nuclear data by focusing on responses other than k eff . Tallied values are ideal quantities that are estimated with detectors during experiments. List-mode data (a list of neutron collection times) are the direct output of detector systems in subcritical neutron noise experiments. Expanding MCNP sensitivity capabilities to include the sensitivity of responses estimated from list-mode data, such as the prompt neutron decay constant (α) and multiplicity estimates (S and D), enables more direct comparison of simulated and measured experimental quantities. Additionally, deterministic tools such as SENSMG are capable of obtaining sensitivities to a wide variety of responses; however, these tools cannot handle complex geometries due to the assumptions made in discretizing the phase-space variables of the Boltzman transport equation.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Utilization of ACE nuclear data file toolkit ACEtk to calculate relative sensitivity coefficients of point-kinetics parameters

Sensitivity and uncertainty methods are quintessential for nuclear criticality safety and experiment design. This type of analysis relies on calculations of sensitivity coefficients; sensitivity coefficients of the effective neutron multiplication factor with respect to some nuclear data are predominantly calculated and used. As a part of the Laboratory Directed Research & Development project EUCLID (Experiments Underpinned by Computational Learning for Improvements in nuclear Data) at Los Alamos National Laboratory, sensitivity coefficients of many radiation detector measurement responses with respect to nuclear data were investigated. Specifically, this paper outlines a method to calculate point-kinetics parameters relative sensitivity coefficients with respect to nuclear data. Point-kinetics parameters such as the prompt neutron decay constant, effective delayed neutron fraction, and neutron generation time are especially important to experimenters and reactor operators designing systems with dynamic neutron populations. This method couples capabilities of the ACE (A Compact ENDF) nuclear data file toolkit, ACEtk, with the ability to load cross sections into the radiation transport code Monte Carlo N-Particle (MCNP). In conclusion, key aspects of optimizing this method for a particular application and sensitivity profiles of the Jezebel criticality experiment are examined and discussed.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗

Validation of the two-region Rossi-alpha model for reflected assemblies

Nuclear criticality safety, nonproliferation and safeguards, emergency response, and stockpile stewardship utilize estimates of the k eff multiplication factor. The value of k eff cannot be directly measured, but it can be inferred from the prompt neutron period. One modality of measuring the prompt neutron period is the Rossi-alpha method, which is predicated on fitting a histogram of detection time differences due to the nonrandom temporal distribution of same-fission-chain neutrons. Recent works have developed the motivation and theory to expand traditional one-region point kinetic models resulting in one-exponential histogram fits to two-region models that result in two-exponential fits. This paper validates the new two-region model using organic scintillator measurements of copper-reflected weapons-grade plutonium (0:83 ≤ k eff ≤ 0:94) and high-density- polyethylene-reflected highly enriched uranium (0:73 ≤ k eff ≤ 0:95). Furthermore, the results show that more thermal systems have shorter prompt neutron periods in the core region due to increased induced-fission probabilities for moderated neutrons. Here, a new parameter introduced by the two- region model is also shown to be correlated to the amount of reflection, and may be used to infer assembly properties such as type and amount of reflector.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Data Assimilation using Non-invasive Monte Carlo Sensitivity Analysis of Reactor Kinetics Parameters

Accurately predicting the criticality of an experiment before interacting with the experimental components is very important for criticality safety. Radiation transport software can be utilized to calculate the effective neutron multiplication factor of a nuclear system. Because of the integral nature of the effective neutron multiplication factor, the value calculated contains various sources of nuclear-data induced uncertainty. The sensitivity analysis and data assimilation technique presented in this paper exhibit one possible method of identifying and reducing the effective neutron multiplication factor nuclear-data induced uncertainty. The results presented in this work show that it is possible to use relative sensitivity coefficients of the prompt neutron decay constant and the effective delayed neutron fraction to 239 Pu nuclear data to reduce nuclear-data induced uncertainties in the effective neutron multiplication factor. This work has been utilized by members of the Los Alamos National Laboratory project EUCLID (Experiments Underpinned by Computational Learning for Improvements in Nuclear Data) for optimally designing a new experiment, which will be used to reduce compensating errors in 239 Pu nuclear data.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Subcritical Neutron and Gamma Noise Measurements at the Seven Percent Critical Experiment (7uPCX)

As part of a collaborative international effort organized by Lawrence Livermore National Laboratory (LLNL), with key participants from L’Institut de radioprotection et de sûreté nucléaire (IRSN), Los Alamos National Laboratory (LANL), and Sandia National Laboratories (SNL), a series of high-multiplication subcritical neutron and gamma noise measurements were planned and executed. The primary aim of this research was to advance detector technology, assess the validity of gamma noise for subcriticality measurements, and nuclear criticality safety, focusing on collecting list-mode or time-series data from various reactor configurations with multiplication values ranging from 20 to 310. This comprehensive dataset enabled a detailed comparative analysis of multiple detector systems and the results of both neutron and gamma noise measurements. In this work we focus on experimentally comparing the results from neutron and gamma noise measurements. We note good agreement between estimations of the prompt neutron decay constant and demonstrate the effects of changing reactor geometry on the efficiency of the differing methods.

Criticality↗

Welch Method and Bootstrapping Applied to Subcritical Gamma Noise

We measured the prompt neutron decay constant 𝛼 of the CROCUS zero-power reactor at the Swiss Federal Institute of Technology Lausanne using cross-power spectral density (CPSD) analysis of gamma-gamma correlations from two trans-stilbene organic scintillators positioned near the reactor core. We measured critical and subcritical states, with water levels ranging from 960 mm (critical) to 800 mm (𝜌=−1.4 $ subcritical). Our analysis used the Welch method, dividing signal segments for fast Fourier transform (FFT) frequency analysis and applying bootstrapping uncertainty quantification that uses Welch-defined segments. Results demonstrated a clear increase in the measured 𝛼 as reactor reactivity decreased, distinguishing critical from subcritical conditions. At the 960-mm critical level, 𝛼 was estimated at 155.9 ± 0.7 s −1 , and for the 800-mm subcritical level, 𝛼 increased significantly to 367.3 ± 6.9 s –1 . A linear regression of subcritical states yielded a critical estimate of 154.0 ± 3.1 s –1 , aligning with the static 𝛼 estimate at critical. The bootstrapping method produced normally distributed 𝛼 estimates, confirming data consistency. The gamma CPSD 𝛼 estimates clearly distinguish reactor states and improve monitoring of zero-power reactors. The future deployment of modular and microreactors as potential candidates for noise analysis is demonstrated in CROCUS, particularly zero-power mock-ups of new designs. The improvement of noise analysis in the subcritical domain from this work will support experimental data for reactor deployment and procedure.

CROCUS↗

Experimental Investigation of Subcritical Neutron and Gamma Noise Methods at the Seven Percent Critical Experiment (7uPCX)

As part of a collaborative international effort organized by the Lawrence Livermore National Laboratory (LLNL), with key participants from the Institut de radioprotection et de sûreté nucléaire (IRSN), Los Alamos National Laboratory (LANL), and the Sandia National Laboratories (SNL), a series of high-multiplication subcritical neutron and gamma noise measurements was planned and executed. The primary aim of this article was to advance detector technology, assess the validity of gamma noise for subcriticality measurements, and nuclear criticality safety, focusing on collecting list-mode or time-series data from various reactor configurations with multiplication values ranging from 20 to 310. This comprehensive dataset enabled a detailed comparative analysis of multiple detector systems and the results of both neutron and gamma noise measurements. In this work, we focus on experimentally comparing the results from neutron and gamma noise measurements. We note good agreement between estimations of the prompt neutron decay constant and demonstrate the effects of changing reactor geometry on the efficiency of the differing methods. Our results agree well with independent experimental measurements and simulations performed by LLNL.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Application of the Rossi-alpha method to simulations of HEU and organic scintillators

The International Criticality Safety Benchmark Evaluation Project (ICSBEP) Handbook contains thousands of high-quality benchmark measurements that include detailed descriptions of experiment designs and exhaustive accounting of uncertainties. These benchmarks are used extensively by the criticality safety and nuclear data communities. A subcritical benchmark involving bare, highly enriched uranium (HEU) has yet to be accepted to the handbook. The Measurement of Uranium Subcritical and Critical (MUSiC) was proposed to address this gap. MUSiC will be performed at the National Criticality Experiments Research Center (NCERC) and will leverage bare HEU hemisphere shells that can be assembled in a variety of configurations. The measurement has the following key benefits: it will be the first set of fast, subcritical measurements of HEU to be submitted to ICSBEP; ten configurations will be measured spanning from nearly no multiplication to critical (e.g., it is a measurement of similar systems with different re activities); measurements of an all-HEU system will be of value for nuclear data validation, providing results that assist in determining biases in both measurements and simulations. A variety of detector systems will be used including a Neutron Multiplicity Array Detector (NoMAD) system (similar to the MC-15), four small volume 0.635 cm (#8960;) × 7.59 cm 3He detectors (ideal for measuring prompt neutron decay constants due to their fast recovery speed), and an array of eight 5.08 cm (#8960;) × 5.08 cm EJ-309 organic scintillator detectors. The focus of this work is the simulation of the subcritical MUSiC configurations including the EJ-309 detectors and the application of the Rossi-α method. The EJ-309 organic scintillator detector array is a new detection system that will be deployed at NCERC. Organic scintillators are ideal for measurements of fast, subcritical systems due to their short time response on the order of nanoseconds.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Preliminary RAM-RODD results for the MUSiC subcritical configurations

The Measurement of Uranium Subcritical and Critical (MUSiC) was performed at the DOE’s National Criticality Experiments Research Center (NCERC) located in the Nevada National Security Site (NNSS). The measurement utilized the Rocky Flats shells to perform benchmark measurements of similar highly enriched uranium (HEU) systems that span a wide range of reactivities. The Rocky Flats (RF) shells are 93.16% U-235 enriched metal hemishells that can be stacked concentrically. Ten configurations were measured with effective multiplication factors spanning between deeply subcritical (~ 0.64) through delayed critical. Details of the measured configurations are listed in Table 1. This unique set of measurements with its large span of reactivies is being used to determine the range over which neutron noise techniques such as Feynman variance-to-mean, Rossi-alpha, and pulsed neutron source techniques can be accurately employed for a bare HEU system. The results of the measurements will be published as a benchmark in The International Criticality Safety Benchmark Evaluation Project (ICSBEP) Handbook. The results will support the growing amount of subcritical benchmark data, such as the SCRaP measurements, that is available to the community. The measurements were performed using several different detector systems for the purposes of cross-validation and obtaining detector independent results. Four detector systems were deployed, three by the NCERC team and one from the University of Michigan. The detector systems included a Neutron Multiplicity Array Detector (NoMAD) system (similar to the MC-15), four small volume 0.635 cm (Ø) × 7.59 cm 3 He detectors (ideal for measuring prompt neutron decay constants due to their fast recovery speed), the Rossi Alpha Measurements – Rapid Organic (n, γ) Discrimination Detector (RAM-RODD), and the Organic Scintillator Array (OSCAR). RAM-RODD is an array of eight 5.08 cm (Ø) × 5.08 cm EJ-309 organic scintillator detectors. OSCAR is a University of Michigan system and is an array of twelve 5.08 cm (Ø) × 5.08 cm stilbene detectors. Details of measurements performed with OSCAR will be discussed in a separate talk. The focus of this work is preliminary results obtained by RAM-RODD for the 8 subcritical configurations. Additional details on the measurements and on the setup and deployment of RAM-RODD will be discussed. Preliminary neutron noise analysis results including Rossi-alpha and Feynman-alpha will also be presented.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Rossi-alpha Analysis of CURIE Experiment

Critical assembly measurement and operations are crucial to the development of benchmark data to support research into criticality safety, radiation-detection development, and the overall application of nuclear technologies. Accurate nuclear data are needed for accurate predictive simulations, and validation using critical experiments is an important part of the nuclear data pipeline. The accuracy of nuclear data are improved using more robust and targeted measurements. In particular, the intermediate energy range of uranium is of great interest. LANL has successfully performed the Zeus series of experiments on the Comet assembly to investigate the intermediate energy range for HEU with various moderators. A successor to these experiments is the benchmark for the Critical Unresolved Region Integral Experiment (CURIE), designed to be sensitive to the unresolved resonance region (URR). This experiment is designed using polytetrafluoroethylene, more commonly known as Teflon, moderators. The CURIE experiment was successfully conducted at the National Criticality Experiments Research Center (NCERC). The Rossi-alpha method was used to evaluate the propensity of the CURIE configurations to sustain fission chains by estimating the prompt neutron decay constant α. This work evaluates the α at delayed critical using Rossi-alpha for different Teflon moderator thicknesses in the CURIE experiment. These results will help improve understanding of the CURIE benchmark experiments.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Critical and Subcritical Californium Source Driven Noise Analysis Experiments with Fresh PWR Fuels Pins

These experiments were performed in 1983 between August 1 and September 16 and used 35 operational days of critical facility time at the Babcock & Wilcox critical facility in Lynchburg, Va. These measurements were to assess the capability of the Cf source driven noise analysis method to measure the subcriticality of light water reactor fresh fuel configurations. This report documents the experiments of 1983 that were not reported at that time. These measurement with 2.459 wt. % 235 U enriched uranium oxide fresh fuel pins started at the delayed critical configuration of the fully assembled pressurized water reactor (PWR) core configuration with 1511 parts per million (ppm) natural boron (19.8 wt. % 10 B) in the water. This was a cylindrical configuration of 4961 fuel pins. After the initial measurements at delayed criticality, subcritical measurements by the Cf source driven noise analysis method were performed in which the number of detectors and Cf source locations were varied. Additional boron was added to the water moderator and reflector to reduce the neutron multiplication factor, with resulting boron concentrations of 1561, 1613, 1765, 1880, 2104, 2384, 2975, 3606, and 4303 ppm. After the completion of these measurements the increased, the boron concentration was returned to that at delayed critical (1511 ppm) and the reactivity was decreased by reducing the number of fuel pins in steps to 3713, 2553, 1281, 749, and 333 fuel pins and then to that (289) of a s ingle square 17 x 17 pin array, corresponding to a single PW fuel element. For all measurement that started at delayed criticality and then reduced the neutron multiplication factor to various subcritical states, inverse kinetics rod drop measurements at the higher reactivities were also performed but not reported here. At all subcritical states the break frequency noise analysis data was fitted to obtain the prompt neutron decay constant. Some data presented in this report are from notes not in the logbook. The purpose of this report is to document the experimental information for the measurements performed so that a later date someone could perform the required uncertainty and calculational analyses and documentation to use these data for an International Nuclear Criticality Safety Benchmark Program (INCSBEP) or Nuclear Energy Agency (NEA) benchmark. The data from these measurements is available from the Laboratory Records Department of Oak Ridge National Laboratory and the logbook is available from INCSBEP at Idaho National Laboratory.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Rossi-alpha Analysis of CURIE Experiment [Slides]

Critical assembly measurement and operations are crucial to the development of benchmark data. Knowledge of the prompt neutron lifetime informs on the state of the system’s neutron spectrum. Rossi-alpha analysis can give us time-dependent information on the system. Teflon was selected, via genetic algorithm, as a moderator to target the URR in uranium for CURIE. Rossi-alpha measurements of the assembly's approach to critical using He-3 detectors estimated the prompt neutron decay constant (α) at delayed critical. α values of several subcritical measurements were then used to predict the α value at delayed critical.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Subcritical Californium Source Drive Noise Analysis Measurements With Unreflected Uranium (93.15) Hydride

On July 6, 1989, subcritical californium source-driven noise analysis (CSDNA) measurements were performed with bare uranium hydride cylindrical assemblies at the Los Alamos National Laboratory Critical Experiments Facility in KIVA 1. Three configurations of ~7.5 cm radius-enriched (93.15 wt. % 235 U) uranium hydride with a density of ~10 g/cm 3 cylinders were assembled with uranium hydride heights of ~11, ~14, and ~16 cm. The uranium hydride (~2 and ~3 cm high) was in thin-welded stainless steel cans. The neutron multiplication factors obtained on-line from the measured ratios of spectral densities were 0.942 ± 0.002, 0.917 ± 0.003, and 0.867 ± 0.004 for uranium hydride heights of ~16, ~14, and ~11 cm., respectively. Neutron multiplication factors for these three configurations calculated by Los Alamos National Laboratory Monte Carlo methods were 0.952 ± 0.005, 0.922 ± 0.005, and 0.860 ± 0.005, all of which are in good agreement with the measurements. The break frequency noise analysis data could be fitted to obtain the prompt neutron decay constant at all subcritical states. Some data presented in this report are from notes that are not in the logbooks. A discussion of the two different point kinetics theories of the measurements that illustrated the deficiencies of the rigorous theory at low neutron multiplication factors (k eff < 0.80) is given in an Appendix. These measurements may be the only configuration of unreflected, highly enriched uranium hydride configuration assembled. The presence of hydrogen diluted the uranium density, decreasing the reactivity, but this is offset by slowing down the neutron energy to the energy ranges of higher-fission cross sections. Extrapolations to delayed critical indicate that adding one more 3 cm can and one more 2 cm can would result in the unreflected cylindrical system being slightly above critical with a critical mass of ~37 kg, which is considerably less than the critical mass of an unreflected and unmoderated highly enriched uranium metal sphere. An unreflected, highly enriched uranium hydride sphere would have a critical mass less than 37 kg.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Subcritical Neutron and Gamma Noise Measurements at the Seven Percent Critical Experiment (7uPCX) [Slides]

Post measurement synchronization of noise signals allowed for the investigation of previously unseen correlations. Noise of gamma, thermal and fast neutron signals performed similarly in estimating the prompt neutron decay constant at various subcritical states. The CPSD amplitude terms displayed different magnitudes. The neutron-based amplitudes suffered more from changes in detector efficiency as the number of fuel rods in the system increased. The time lag between 3 He tubes is observable using the CPSD phase angle and agreed with a simplified diffusion estimation.

3He detectors↗

Pulsed-Neutron Experiments at the Inherently Safe Subcritical Assembly

The pulsed neutron technique is a powerful, dynamic method to assay the reactivity of a multiplying system. This work presents the novel application of the pulsed neutron technique to the Inherently Safe Subcritical Assembly, an experimental configuration accepted by the International Criticality Safety Benchmark Evaluation Project Handbook. The experiments were replicated with COG11.3, a continuous-energy Monte Carlo code. The pulsed neutron data were analyzed using the Sjöstrand and Gozani area-ratio methods and by extracting the prompt neutron decay constant. Subsequent static k-eigenvalue and 𝛼-eigenvalue simulations were also performed for the same configurations. Neutron detector dead-time effects from the experiments were corrected using the Backwards Extrapolation Method and shown to have a negligible impact on the estimated reactivities. The results highlight that capturing time-dependent effects like delayed neutron precursor buildup are essential to accurately reproduce experimental results. They also highlight the importance of shielding the detectors from generator source neutrons in deeply subcritical configurations.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

On the Feynman-alpha method for reflected fissile assemblies

The Feynman-alpha method is a neutron noise technique that is used to estimate the prompt neutron period of fissile assemblies. The method and quantity are of widespread interest including in applications such as nuclear criticality safety, safeguards and nonproliferation, and stockpile stewardship; the prompt neutron period may also be used to infer the k eff multiplication factor. The Feynman-alpha method is predicated on time-correlated neutron detections that deviate from a Poisson random variable due to multiplication. Traditionally, such measurements are diagnosed with one-region point kinetics, but two-region models are required when the fissile assembly is reflected. This paper presents a derivation of the two-region point kinetics Feynman-alpha equations based on a double integration of the Rossi-alpha equations, develops novel propagation of measurement uncertainty, and validates the theory. Validation is achieved with organic scintillator measurements of weapons-grade plutonium reflected by various amounts of copper to achieve k eff values of 0.83–0.94 and prompt periods of 5–75 ns. The results demonstrate that Feynman-alpha measurements should use the two-region model instead of the one-region model. The simplified one-region model deviates from the validated two-region models by as much as 10% in the estimate of the prompt neutron period, and the two-region model reduces to the one-region model for small amounts of reflector. The Feynman-alpha estimates of the prompt neutron period are compared to those of the Rossi-alpha approach. The comparative results demonstrate that the Feynman-alpha method is more precise than the Rossi-alpha method and more accurate for k eff < 0.92, whereas the Rossi-alpha method is generally more accurate for higher multiplications. Here, the uncertainty propagation developed in this work should be used for all Feynman-alpha measurements and will therein improve fitting accuracy and appropriate precision estimates.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗