Subcritical Measurements Research Articles

Dynamic mode decomposition for subcriticality measurement using measured data at single location

Dynamic mode decomposition (DMD) is an effective approach for extracting a fundamental mode eigenvalue in subcriticality measurements. According to several previous studies, data for DMD must be obtained at a sufficient number of locations. However, the number of measurement locations is typically limited owing to experimental constraints. In this study, a time-shifting augmentation technique for DMD is employed, where an augmented data matrix is constructed by stacking multiple time-shifted copies of time-series data at a single location. The proposed DMD technique is applied to numerical simulations of subcriticality measurements, such as those involving the pulsed neutron method and Rossi-α method. The fundamental mode eigenvalues of these measurements are accurately extracted via DMD using the augmented data matrix for a single location without introducing the masking time technique.

Dead time correction of Feynman sampled rates suitable for neutron coincidence counting

Neutron coincidence counting (NCC) based on shift-register logic (SRL) is extensively used by international nuclear safeguards inspectorates to verify special nuclear material inventories, particularly Pu. An alternative autocorrelation pulse counting analysis technique is founded on Feynman sampling and makes use of the well-known Feynman-Y statistic. Although the latter approach has been widely adopted by the reactor noise and sub-criticality communities it has not been used by the nonproliferation community. Both techniques may be interpreted using the same theoretical model and so should extract the same fundamental information about the detected neutron pulse train, namely the first and second reduced factorial multiplets that are determined by the joint properties of the measurement item and the surrounding external neutron detector. In the nuclear safeguards domain, a semi-empirical dead time treatment is conventionally applied to the trigger (singles) and doubles rates and, as already noted, the Feynman-Y method is not typically applied. In this article, we revisit the dead time treatment of Robba et al. (1983) for the Feynman sampling method. We show so that a dead time corrected multiplet analysis, familiar to safeguards practitioners, can be extracted. This is a first and necessary step to enabling a comparison of the relative performance of these two autocorrelation techniques on a like basis for deeply subcritical measurement items, which is the domain of concern to international nuclear safeguards inspectorates. From the analytical derivations it emerges that the Robba formalism, with minor corrections, and the commonly used NCC shift-register logic dead time correction formalism yield numerically equivalent corrections for practical purposes over the operational range of safeguards interest.

Data Assimilation Using Subcritical Measurement of Prompt Neutron Decay Constant

The prompt neutron decay constant in a steady-state subcritical system can be directly measured using a reactor noise analysis method such as the Feynman- method. To reduce the nuclear data–induced uncertainty of for a target system, this study investigates the applicability of data assimilation techniques, i.e., the bias factor method and the cross-section adjustment method, based on a subcritical measurement of conducted at Kyoto University Critical Assembly (KUCA). The sensitivity coefficients of and with respect to the nuclear data were efficiently estimated using a deterministic SN transport code with first-order perturbation theory. As a result, the a priori relative uncertainty of due to the 56-group SCALE covariance data can be reduced if there is strong correlation between the measured and the target . The experimental value of contributes to improving the nuclear data of total fission spectrum and total fission neutron number via strong correlations between and prompt and between and prompt , by utilizing the sensitivity coefficients of with respect to prompt and .

Subcriticality measurement using time-domain decomposition-based integral method for simultaneous reactivity and source changes

ABSTRACT To estimate the subcriticality in dollar units for an arbitrary state-change, the time-domain decomposition-based integral method (TDDI) is proposed using the point kinetics theory based on the fundamental mode approximation. In a general transient subcritical system, reactivity, neutron source intensity, and point kinetics parameters can vary simultaneously. Furthermore, the state-change may not necessarily be a stepwise change. For such a transient, the TDDI method can estimate the subcriticality after the transient using only the time variation of the neutron count rate. Therefore, the proposed method is useful to approximately estimate the subcriticality in a system where a detailed core configuration is unknown. To investigate the applicability of the TDDI method, transient experiments with simultaneous reactivity and source changes or to two successive safety rods dropping were performed at the Kindai University Training and Research Reactor (UTR-KINKI). By comparing with reference values using excess reactivity and control rod worth, it was validated that the subcriticality values obtained by the TDDI method better agree with the reference values than the previous integral method.

Subcriticality Measurement of Jackets with Spent FA VVER-1000 in a KhOT-1 Storage Facility Using the SKP-KhOT System

The SKP-KhOT system for measuring subcriticality, making it possible to determine Keff of jackets with spent FA VVER-1000 during normal operation as well as design basis and beyond-design basis accidents, has been installed in the KhOT-1 storage facility at the Mining and Chemical Combine. The results of its tests have been recognized as positive; the design basis subcriticality of the studied jackets falls within the confidence interval of the measured value. It is shown that Keff of a jacket does not depend on its environment.

National Criticality Experiments Research Center (NCERC) - capabilities and recent measurements

The National Criticality Experiments Research Center (NCERC) located at the Device Assembly Facility (DAF) at the Nevada National Security Site (NNSS) and operated by Los Alamos National Laboratory (LANL) is home to four critical assemblies which are used to support of range of missions, including nuclear criticality safety and nuclear nonproliferation. Additionally, subcritical systems can also be assembled at NCERC. NCERC is providing critical and subcritical experiments valuable to the nuclear data community and experiments performed at NCERC are often published as benchmarks in the International Criticality Safety Benchmark Evaluation Project (ICSBEP) Handbook. This manuscript will give a broad overview of recent experiments performed at NCERC, upcoming experiments, and why integral measurements are important and useful to the nuclear data community. The four critical assemblies are GODIVA IV, FLATTOP, COMET, and PLANET. GODIVA IV is a cylindrical metal fast burst reactor, the fourth in the GODIVA series that dates back to the 1950’s. FLATTOP is an highly enriched uranium (HEU) or Pu core reflected by natural uranium. COMET and PLANET are vertical lift assemblies, where one half of the reactor can be lifted to the upper half of the reactor to create a critical system. Some recent experiments include various critical intermediate energy assemblies with lead, and subcritical measurements of plutonium reflected by copper, tungsten, and nickel. Work is also underway to make a better measurement of the critical mass of neptunium, using a neptunium sphere surrounded by nickel shells. Additionally, measurements will be performed next year with HEU shells from Rocky Flats. These HEU shells will be stacked together to make larger systems, allowing for a large range of criticality (from subcritical to delayed critical). Other upcoming measurements include an HEU critical assembly sensitive to intermediate energy neutrons.

On Measurement of Subcriticality of Reactors with Statistical Methods

The possibility of measurement of subcriticality of reactors of nuclear power plants by statistical methods in the performance of requirements of Regulations NP-082-07 is discussed. The statistical methods, in particular, the Feynman method, make it possible to measure the subcriticality of shutdown reactors and at initial start-ups within the required range of 0.01–0.02 at the level of neutron detector counting of about one pulse per second. The Feynman method was perfected at the critical assembly of the high-temperature gas-cooled nuclear reactor PROTEUS at the Paul Scherrer Institute (Switzerland). The measurement results of subcriticality are presented. The conditions which should be ensured to obtain an acceptable result of experiment are formulated.

An impact of inherent neutron source on subcriticality measurement in a highly enriched uranium core of Kyoto University Critical Assembly

ABSTRACT In a variety of highly enriched uranium cores of Kyoto University Critical Assembly, many different subcriticality measurements have been strenuously performed. However, any influence of neutron source inherent in the highly enriched uranium fuels on these measurements has hardly been studied. This is because the influence has been expected to be negligible in the fuels. In this study, we revaluated the influence on pulsed neutron, accelerator-beam trip and rod drop measurements to reveal an unexpected impact of the weak inherent source. Especially, the inherent source was injurious to most of the beam trip and the rod drop measurements based on the integral count method. The least-squares inverse kinetics analysis also had a significant influence on the inherent source. In the area ratio analysis for a pulsed neutron measurement, a considerable number of neutrons from the inherent source was mixed into delayed-neutron area. When the influence was considered in these data analyses, the subcritical reactivity of the above measurements was in good agreement with that calculated by the continuous-energy Monte Carlo code MVP.

Experimental validation of unique combination numbers for third- and fourth-order neutron correlation factors of zero-power reactor noise

ABSTRACT Zero-power reactor noise is useful for subcriticality measurements. Based on the nuclear reactor physics and the theory of neutron detection, this paper theoretically clarifies that the third- and fourth-order neutron correlation factors and can be expressed as functions of the second-order neutron correlation factor . In particular, if the neutron-counting gate width is sufficiently large, the saturation values and are almost equal to the unique combination numbers, ‘3’ and ‘15,’ for a source-driven subcritical system, where the subcriticality is less than 10,000 pcm. These unique combination numbers, ‘3’ and ‘15,’ for and were validated using actual zero-power reactor noise measurements carried out at the Kyoto University Criticality Assembly. In this study, the estimation of statistical errors and correlations between different gate widths owing to the bunching method was achieved by the moving block bootstrap method. For a sufficiently long measured reactor noise in a steady and unperturbed state, a statistical test for the evaluation of the critical state and the absolute measurement of subcriticality can be carried out by statistically quantifying the difference between the measurement value of and the unique combination number.

Sensitivity analysis of source intensity and time bin size for the Rossi-alpha method in a numerical reactor model

Until now, various studies focusing on subcriticality measurements have been conducted using the Rossi-alpha method. However, no guidelines have been provided for the source intensity and time bin size of the Rossi-alpha analysis. In this study, sensitivity analyses were performed to determine an optimized source intensity and time bin size for a numerical reactor model. Using the MCNP6 Monte Carlo code, fission count signals in the fuel region were tallied 50 times with different random seeds in real-time mode. These signals were applied to the Rossi-alpha method as detector signals. The estimated keff values were compared to the reference keff values generated by the MCNP6 criticality calculation.As a result of the sensitivity test for the neutron source intensity, the Rossi-alpha method has errors of 200 pcm or less when the source intensity is greater than 105 s−1. It is shown that the standard deviations of 50 analyses are converged when the source intensity is greater than 105 s−1. At the same time, as a result of the sensitivity test for the time bin size, the Rossi-alpha method shows errors less than 200 pcm when the time bin size is smaller than 10−5 s. It is shown that the standard deviations of 50 analyses are converged when the time bins are smaller than 10−5 s. For the numerical reactor model in this study, the threshold time bin size was set to 10−5 s. However, it generally depends on the neutron generation time of the problem. Thus, it is recommended to set the neutron source intensity to 105 s−1 or higher and the time bins to the time of the neutron generation or less when the Rossi-alpha method is applied to subcriticality measurements in nuclear reactor cores.

Application of advanced Rossi-alpha technique to reactivity measurements at Kyoto University Critical Assembly

This study presents the first application of the advanced Rossi-alpha method (theoretically introduced by Kong et al., 2014) on the reactivity measurements in a research reactor: detector count signals at the Kyoto University Critical Assembly (KUCA) facility. The detector signals in the KUCA A-type core are analyzed by three subcriticality measurement methods: (1) Feynman-alpha (F-α) method, (2) Rossi-alpha (R-α) method, and (3) advanced Rossi-alpha (advanced R-α) method. Four cases are analyzed for two different subcritical states of the core and two different neutron source locations. Two different negative reactivity ρ values are obtained by the measurements of control rod worth and regarded as the reference reactivity values, comparing the results by the four methods.The F-α shows reactivity errors ranging between 7.1 and 7.3% due to its use of variance-to-mean ratios of detector count signals, which are not very sensitive to neutron background noise. However, the fitting uncertainties associated to the F-α results are large, ranging between 5.4 and 12.8% at one standard deviation. The R-α shows small fitting uncertainties ranging between 2.8 and 3.8%, although reactivity errors are in the range of 3.5–26.5% due to the neutron background noise. Finally, the advanced R-α that explicitly models the neutron background noise contrary to the previous methods shows the reactivity errors in the range of 1.0–11.8%, and provides the lowest uncertainties of the measured ρ in the range of 0.4–0.9%. In conclusion, among the four methods applied to the reactivity measurements at KUCA, the advanced R-α reveals the best accuracy with the lowest uncertainties.

Development of a research reactor protocol for neutron multiplication measurements

A new series of subcritical measurements has been conducted at the zero-power Walthousen Reactor Critical Facility (RCF) at Rensselaer Polytechnic Institute (RPI) using a 3He neutron multiplicity detector. The Critical and Subcritical 0-Power Experiment at Rensselaer (CaSPER) campaign establishes a protocol for advanced subcritical neutron multiplication measurements involving research reactors for validation of neutron multiplication inference techniques, Monte Carlo codes, and associated nuclear data. There has been increased attention and expanded efforts related to subcritical measurements and analyses, and this work provides yet another data set at known reactivity states that can be used in the validation of state-of-the-art Monte Carlo computer simulation tools. The diverse (mass, spatial, spectral) subcritical measurement configurations have been analyzed to produce parameters of interest such as singles rates, doubles rates, and leakage multiplication. MCNP®6.2 was used to simulate the experiment and the resulting simulated data has been compared to the measured results. Comparison of the simulated and measured observables (singles rates, doubles rates, and leakage multiplication) show good agreement. This work builds upon the previous years of collaborative subcritical experiments and outlines a protocol for future subcritical neutron multiplication inference and subcriticality monitoring measurements on pool-type reactor systems.

Experimental benchmarks on kinetic parameters in accelerator-driven system with 100 MeV protons at Kyoto University Critical Assembly

Accelerator-driven system experiments with spallation neutrons (100MeV protons and Pb-Bi target) are carried out in the 235U-fueled and Pb-Bi-zoned core at the Kyoto University Critical Assembly, under a subcritical state ranging between 1160 and 11,556pcm. In these experiments, measurement of the prompt neutron decay constant and the subcriticality is conducted by the pulsed neutron source (PNS) method and the Feynman-α method with the use of optical fiber detectors. The experimental results successfully validate the prompt neutron decay constant and the subcriticality through the deduction of kinetic parameters by both the PNS and the α-fitting methods. The detector position dependency, neutron spectrum and subcriticality measurement methods still remain, however, in these experiments. For onward studies, the experimental benchmarks obtained from these experiments are expected to be involved in the numerical verification of subcriticality on-line monitoring, in the analysis of subcriticality uncertainty and in the deterministic approach to kinetic parameters.

Sensitivity Analysis of Neutron Multiplicity Counting Statistics Using First-Order Perturbation Theory and Application to a Subcritical Plutonium Metal Benchmark

It is frequently important to estimate the uncertainty and sensitivity of measured and computed detector responses in subcritical experiments and simulations. These uncertainties arise from the physical construction of the experiment, uncertainties in the transport parameters, and counting uncertainties. Perturbation theory enables sensitivity analysis (SA) and uncertainty quantification on integral quantities like detector responses. The aim of our work is to apply SA to the statistics of subcritical neutron multiplicity counting distributions. Current SA methods have only been applied to mean detector responses and the eigenvalue. For multiplicity counting experiments, knowledge of the higher-order counting moments and their uncertainties are essential for a complete SA. We apply perturbation theory to compute the sensitivity of neutron multiplicity counting moments to arbitrarily high order. Each moment is determined by solving an adjoint transport equation with a source term that is a function of the adjoint solutions for lower-order moments. This enables moments of arbitrarily high order to be sequentially determined, and it shows that each moment is sensitive to the uncertainties of all lower-order moments. To close our SA of the moments, we derive forward transport equations that are functions of the forward flux and lower-order moment adjoint fluxes. We verify our calculations for the first three moments by comparison with multiplicity counting measurements of a subcritical plutonium metal sphere. For the first three moments, the most influential parameters are ranked, and the validity of first-order perturbation theory is demonstrated by examining the series truncation error. This enables a detailed SA of subcritical multiplicity counting measurements of fissionable material based on transport theory.

Effective delayed neutron fraction by Rossi-α method in accelerator-driven system experiments with 100 MeV protons at kyoto university critical assembly

ABSTRACTIn the accelerator-driven system (ADS), the effective delayed neutron fraction (βeff) is a requisite for converting the subcriticality from dollar units to pcm units. To evaluate the accurate βeff value in ADS, measurement of βeff complements its calculation methodology and the nuclear data on delayed neutrons. Subcriticality measurements are carried out by the pulsed neutron source method in the Kyoto University Critical Assembly, and the neutron noise analyses are conducted by the Rossi-α method with the pulsed shape of the spallation neutron source. The value of βeff is deduced with the combined use of measured subcriticality in dollar units and correction parameters by MCNP6.1 together with JENDL-4.0 and JENDL/HE-2007. A comparison between the calculated and the measured βeff represents the acceptable accuracy within the subcriticality range of around keff = 0.93 in the ADS operations. Here, the applicability of the measurement methodology based on the Rossi-α method is demonstrated by varying the subcriticality.

Sub-Criticality Measurement with Source Term for Research Reactor in Inverse Kinetics Method

In reactor physics tests, it is important to monitor sub-criticality continuously during criticality approach. Reactivity measurements by the inverse kinetics method are widely used during the operation of a nuclear reactor. This technique is successfully applied at sufficiently high power level or to a core without an external neutron source where the neutron source term in point reactor kinetics equations may be neglected. For operation at low power levels or in the sub-critical domain, the increase in the fluctuation of the neutron signal may cause difficulties in the evaluation of reactivity and the effect of direct emission from the external neutron source may not be neglected. Therefore, contribution of the neutron source must be taken into account and this implies knowledge of a quantity proportional to the source strength, which calls the source term and then it should be determined. The research work has been conducted to measure reactivity with source term using a dedicated reactivity measurement system by the Least Square Inverse Kinetics Method (LSIKM). Application to a simulator of HANARO research reactor, Korea Atomic Energy Research Institute (KAERI), with known source strength and reactivity worth has showed consistent and satisfactory agreement.

Monte Carlo Approach of Effective Delayed Neutron Fraction by k-Ratio Method with External Neutron Source

In an accelerator-driven system (ADS), the effective delayed neutron fraction βeff is required for subcriticality measurements in order to convert measured reactivity in dollar units into pcm units. Here, an alternative calculation methodology with source-dependent reaction rates is proposed to estimate the subcriticality (pcm units) with an external neutron source for the newly defined parameter. In the proposed methodology, the parameter is obtained by the k-ratio method with reaction rates considering the external neutron source (fixed-source calculation) and is compared with that obtained by the eigenvalue calculations (MCNP6.1). To investigate its applicability to the estimation of subcriticality, subcriticality measurements by the extrapolated area ratio method are carried out in the experiments in ADS at the Kyoto University Critical Assembly, with the variation of subcriticality (pcm units) and the spectrum of the external neutron source. Then, is estimated by the proposed methodology with MCNPX-2.5.0. The measured subcriticality with the use of obtained by the fixed-source calculations shows good agreement with that obtained by the different measurement methodology and MCNPX-2.5.0. Through the subcriticality estimation, the applicability of the proposed methodology is confirmed for different subcriticality levels and the spectrum of the external neutron source.

Benchmarking criticality analysis of TRIGA fuel storage racks

A criticality analysis was benchmarked to sub-criticality measurements of the hexagonal fuel storage racks at the United States Geological Survey TRIGA MARK I reactor in Denver. These racks, which hold up to 19 fuel elements each, are arranged at 0.61m (2 feet) spacings around the outer edge of the reactor. A 3-dimensional model was created of the racks using MCNP5, and the model was verified experimentally by comparison to measured subcritical multiplication data collected in an approach to critical loading of two of the racks. The validated model was then used to show that in the extreme condition where the entire circumference of the pool was lined with racks loaded with used fuel the storage array is subcritical with a k value of about 0.71; well below the regulatory limit of 0.8. A model was also constructed of the rectangular 2×10 fuel storage array used in many other TRIGA reactors to validate the technique against the original TRIGA licensing sub-critical analysis performed in 1966. The fuel used in this study was standard 20% enriched (LEU) aluminum or stainless steel clad TRIGA fuel.

Statistical error estimation of the Feynman-α method using the bootstrap method

ABSTRACTApplicability of the bootstrap method is investigated to estimate the statistical error of the Feynman-α method, which is one of the subcritical measurement techniques on the basis of reactor noise analysis. In the Feynman-α method, the statistical error can be simply estimated from multiple measurements of reactor noise, however it requires additional measurement time to repeat the multiple times of measurements. Using a resampling technique called “bootstrap method,” standard deviation and confidence interval of measurement results obtained by the Feynman-α method can be estimated as the statistical error, using only a single measurement of reactor noise. In order to validate our proposed technique, we carried out a passive measurement of reactor noise without any external source, i.e. with only inherent neutron source by spontaneous fission and (α,n) reactions in nuclear fuels at the Kyoto University Criticality Assembly. Through the actual measurement, it is confirmed that the bootstrap method is applicable to approximately estimate the statistical error of measurement results obtained by the Feynman-α method.

TRANSIENT EXPERIMENTS IN ZED-2 TO INVESTIGATE THE IMPACT OF LEAKAGE ON REACTOR PHYSICS PHENOMENA

This paper describes an experimental approach where reactor kinetics experiments are used to study reactor physics phenomena that are normally investigated using static-measurement techniques. This approach provides validation data relating to these phenomena for a range of core reactivities, rather than only providing data at critical conditions. Sub-critical and super-critical transient measurements were performed in the ZED-2 reactor. The transients were analyzed using a point kinetics model to derive the reactivity states that induced the transients. The reactor physics phenomenon of interest for the current study is Coolant Density Induced Reactivity. Initial measurements were performed using an air-cooled (i.e., voided) ZED-2 lattice; the measurements were then repeated using the same lattice cooled with light water. These measurements yielded reactivity values for both coolant conditions in the lattice for a range of super-critical and sub-critical states. This investigation avoids the inherent assumption of static-measurement analyses that the bias in predicting criticality for the two coolant conditions is identical to the bias in predicting the phenomenon of Coolant Density Induced Reactivity itself. The measured reactivity values are compared with calculations employing the 3-D stochastic neutron transport reactor code MCNP.