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Pulse shape discrimination plot for the organic scintillator measurement of the copper-reflected plutonium.
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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 infer...
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... to separate neutron and photon pulses since organic scintillators are sensitive to both types of radiation. A charge integration technique is used to perform PSD for discrete energy bands, for every minute, for every detector [20,21,22] and the result is the organic scintillator list of neutron detection times. A sample PSD plot is shown in Fig. 4. The NoMADs directly output their list of neutron detection times. Time differences less than a given reset time are calculated between any and all neutron detections (type-I binning [23]) and a histogram of resultant values is constructed for each configuration. The organic scintillator array uses 1-ns bin widths, whereas the NoMADs ...
Citations
... The residuals are then fit with the delayed neutron term; it is important to weight the fit (preferred, see Refs. [8,15]) or omit residual data at short/large times with large uncertainty. The total fit is shown in Fig. 7. ...
The effective delayed neutron fraction, β_eff, is a kinematic parameter describing the contribution of delayed neutrons to the effective multiplication factor, k_eff, and is of great interest to the nuclear criticality safety community and beyond. In fact, k_eff presently must be inferred (as opposed to directly measured) since variables like β_eff must be obtained from simulation, reference tables, or a dynamic or pulsed measurement where the assembly of fissile material is perturbed and not in steady state. Several recent works have proposed neutron noise techniques to estimate β_eff from static measurements (such as benchmark experiments). This work experimentally investigates an approach based on looking at late-time (up to thousands of seconds) correlated neutrons in Feynman histograms. This work utilizes measurements of weapons grade plutonium and highly enriched uranium to construct late-time Feynman histograms and investigate a proposed methodology of estimating 𝛽eff from a fit of the distribution. Data is shown from both He-3 detectors and an organic scintillator array. This work is preliminary in nature, demonstrating some experimental feasibility and proposing improvements for future investigations.
... A system based on stilbene organic scintillators (Oscar) has been developed by the University of Michigan. Oscar, shown in Fig. 5, is capable of pulse-shapediscrimination and digital acquisition and has been shown to yield accurate estimates of k eff for several subcritical special nuclear material configurations [173][174][175][176][177]. ...
Accurate nuclear data provide an essential foundation for advances in a wide range of fields, including nuclear energy, nuclear safety and security, safeguards, nuclear medicine, and planetary and space exploration. In these and other critical domains, outdated, imprecise, and incomplete nuclear data can hinder progress, limit precision, and compromise safety. Similar nuclear data needs are shared by many applications, thus prioritizing these needs is especially important and urgently needed. Many levels of analysis are required to prepare nuclear measurements for employment in end-user applications. Because research expertise is typically limited to one level, collaboration across organizations and international borders is essential. This perspective piece provides the latest advances in nuclear data for applications and describes an outlook for both near- and long-term progress in the field.
... The prompt neutron decay constant α is a combination of the fit parameters of the two-exponential fit. The uncertainty in the estimation of the prompt neutron period α −1 is determined using the sample variance method in which the entire measurement is divided into many smaller, nonoverlapping measurements, and the variance is found across the smaller measurements [10]. Table II shows that as measurement time increases, the relative uncertainty in the prompt neutron period generally decreases, suggesting that the estimation of α is more precise. ...
... The uncertainty in α can be determined through a sample method, where a long measurement (20 minutes or more) can be broken down into smaller samples (approximately 1 minute) in order to determine the bin-bybin count uncertainty by taking a bin-wise sample standard deviation. This uncertainty is used to weight the twoexponential fit, and then, through the propagation of uncertainty of the fit parameters, uncertainty in α is determined [7]. Uncertainty in α can be used to determine relative uncertainty, which is ...
... The measurements were taken over 20 minutes for the copper reflectors, and 30 minutes for the other reflectors. The measurements in this work are identical to those of references [7,8]. The data from these experiments will be used to validate our methods. ...
... 91 The Rossi-α method is also still used to provide timing information on nuclear material systems. 92,93 RTOs are configurations assembled primarily for radiation detection testing and validation. The 25 and 49 metal spherical experiments are essentially the first RTOs ever built. ...
Criticality experiments with $^{235}$U (metal and hydride) and $^{239}$Pu (metal) were performed during the Manhattan Project. Results from these experiments provided necessary information for the success of the Manhattan Project. These experiments have been previously described in compilations made after the Manhattan Project, but those works are either lacking in technical details or are not publicly available. This work aims to provide detailed information while showcasing the enduring impact of these experiments 75 years after they were performed. Furthermore, we use modern computational methods embodied in the MCNP6 code and ENDF data to analyze and interpret these historic measurements. The world's first four criticality accidents are also discussed, as lessons learned from these helped shape the field of criticality experiments.
... Further note that Equation (4.25) does not satisfy normalization requirements of a PDF, but is normalizable. Normalization is not necessary in practical implementation since only r 1 , r 2 , and the ratio ρ 1 /ρ 2 are needed to obtain α and ctd ; however, expressions have been derived in Reference [77,73] and appear in Eqn. Note that α and −1/ ctd are linear combinations of the r j exponents and, in particular, ...
... Beyond the derivation, this work develops rigorous first-order propagation of measurement uncertainty similar to Refs. [73,92]. The propagation involves weighting a fit to the ...
... Refs. [73,92]. ...
Estimating keff is of broad interest and paramount importance in the nuclear community including. A keff equal to one represents a self-sustaining and stable chain reaction and is often desirable in energy-producing reactors. An uncontrolled/accidental keff greater than one can result in criticality accidents and operator death. Therefore, it is desirable to be able to control and monitor the keff of an assembly; the value of keff can be modulated and tailored by using reflector material. A challenge is that keff cannot be directly measured; however, it can be inferred from the prompt neutron decay constant, alpha, and its negative reciprocal, the prompt neutron period. Microscopic, time-correlated, neutron noise techniques are used to measure alpha and the two most popular methods are the Rossi-alpha and Feynman-alpha approaches. This dissertation advances the two methods by addressing shortcomings in detectors, models, and uncertainty quantification. Current measurements are performed with 3He detectors that are insensitive to fast assemblies (with prompt periods shorter than a microsecond). Fast assemblies are pertinent to criticality safety applications and modern fast reactor designs, for example. The measurements of this dissertation use and validate the new organic scintillator array (OSCAR) system, which measured up to 15 kg of weapons-grade plutonium, 22 kg of highly enriched uranium, and 6 kg of neptunium (0.45 < keff < 0.95). The data analysis demonstrates that OSCAR exhibits capabilities beyond 3He systems. For instance, OSCAR is sensitive to prompt neutron periods as fast as 8 ns, whereas 3He detectors are limited to ~1 us. Furthermore, the OSCAR exhibits much less noise and can achieve desired precisions faster than competing 3He systems by factors as great as 10^2. The Rossi- and Feynman-alpha techniques were originally developed for bare cores of fissionable material and the traditional one-region point kinetics model is inadequate for reflected assemblies that requires a two-region model. Since reflectors are of interest in the application space, new theory is required. New theory is also required for uncertainty propagation and quantification from a single measurement; currently, methods are either incorrect or rely on long, repeated measurements. This dissertation extends traditional point kinetics from one-region to two-region and rigorously derives uncertainty methods for both the Rossi- and Feynman-alpha methods. The new theory is validated with the OSCAR and 3He measurements of reflected assemblies. The results demonstrate that the new theory increases the accuracy of alpha estimates by over 10% and generalizes the existing models. The two-region model introduces new variables and it is shown that the parameters can potentially be exploited as signatures of reflection. The two neutron noise techniques are compared, and it is found that the Feynman-alpha method is more precise than the Rossi-alpha method by one-to-two orders of magnitude in relative uncertainty. In terms of accuracy, the Feynman-alpha approach outperforms the Rossi-alpha approach for keff < 0.92, whereas the opposite is true for keff > 0.92. The uncertainty methods based on a single measurement are validated and can reduce measurement times by a factor of 20 or more, therein reducing measurement costs. This dissertation advances microscopic, time-correlated neutron noise techniques by demonstrating the use of a fast organic scintillator detection system that has capabilities beyond the current state-of-the-art 3He systems, developing and validating new measurement theory to account for experiments on reflected assemblies, and developing and validating quantification of measurement uncertainty.
... Beyond the derivation, this work develops rigorous firstorder propagation of measurement uncertainty similar to Refs. [13,14]. The propagation involves weighting a fit to the Feynman histogram data, which results in a more accurate fit that adequately incorporates measurement uncertainty with fit uncertainty to estimate a composite uncertainty in the fit parameters. ...
... The collective process is adapted from Refs. [13,14]. ...
... The first method of determining histogram uncertainty, called the sample method, divides a total measurement into multiple smaller measurements, calculates a histogram for each submeasurement, and then calculates the error bars by taking binby-bin standard deviations. The second method -an analytic approach -calculates the bin-by-bin standard deviation using up to the fourth factorial moment (see Eqn. (13)) and is given by [22,23] ...
The Feynman-alpha method is a neutron noise technique that is used to estimate the prompt neutron period of fissile assemblies. The quantity is 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 $k_\text{eff}$ 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 $k_\text{eff}$ values between 0.83-0.94 and prompt periods between 5-75 ns. Feynman-alpha measurements should use the two-region model, a generalization of the one-region model that deviates by more than 10% in this work, and is more accurate than the Rossi-alpha method for the range of $k_\text{eff}$ values observed in this work. 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.
... Until recently, the uncertainty quantification for either model was inadequate (inaccurate and demanded large measurement times). Measurement uncertainty quantification by sample and analytic methods was developed and validated in Ref. [7]. The purpose of this transaction is to (i) validate a new bootstrap method by comparing bin-by-bin error bar estimates and (ii) demonstrate how to choose bin widths and reset times to optimize precision and accuracy. ...
... Further comprehensive details are given in Ref. [6]. The details of the uncertainty quantification by the analytic and sample methods is similarly left to citation in Ref. [7]. In essence, both methods aim to first estimate the uncertainty in the bin counts of the histogram of time differences. ...
... Comprehensive measurement details and preprocessing steps are discussed in Refs. [7,10]. ...
The prompt neutron period (the negative reciprocal of the prompt neutron decay constant) can be estimated using the Rossi-alpha technique that is predicated on fitting Rossi-alpha histograms and of interest in nuclear criticality safety and nonproliferation [1, 2, 3]. The histograms are traditionally fit with a one-exponential model; however, recent work has proposed a two-exponential model to account for reflector-induced phenomenon [4, 5, 6]. Until recently, the uncertainty quantification for either model was inadequate (inaccurate and demanded large measurement times). Measurement uncertainty quantification by sample and analytic methods was developed and validated in Ref. [7]. The purpose of this transaction is to (i) validate a new bootstrap method by comparing bin-by-bin error bar estimates and (ii) demonstrate how to choose bin widths and reset times to optimize precision and accuracy.
... The fit to the histogram is inverse-variance weighted. Ref. [27] presents formulations and validation for estimating bin-by-bin uncertainty for Rossi-alpha histograms, including sample and quasi-analytic methods. Ref. [28] also describes a bootstrapping method and demonstrates how to optimize histogram bin width and reset time for relative uncertainty and relative error. ...
... The Jacobian matrix is used to calculate the uncertainty in the fit parameters and propagate them to final estimates of and ′ . The entire process is derived and described in Ref. [27]. All error bars shown in this work are one standard deviation, . ...
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. 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.
... Until recently, the uncertainty quantification for either model was inadequate (inaccurate and demanded large measurement times). Measurement uncertainty quantification by sample and analytic methods was developed and validated in Ref. [7]. The purpose of this transaction is to (i) validate a new bootstrap method by comparing bin-by-bin error bar estimates and (ii) demonstrate how to choose bin widths and reset times to optimize precision and accuracy. ...
... Further comprehensive details are given in Ref. [6]. The details of the uncertainty quantification by the analytic and sample methods is similarly left to citation in Ref. [7]. In essence, both methods aim to first estimate the uncertainty in the bin counts of the histogram of time differences. ...
... Comprehensive measurement details and preprocessing steps are discussed in Refs. [7,10]. ...
