Neutron Multiplicity Counting Research Articles

Analysis and improvement of the influence of sample shape on Pu measurement results

ABSTRACT The analysis method of Fast Neutron Multiplicity Counting (FNMC) plays an increasingly important role in the measurement of nuclear material properties. Based on the assumption of point model, fast neutron multiplicity measurement equation is derived which can be used to measure the mass of Pu sample. However, the deviation of the simulated measurement of 1 kg Pu sample reaches 16.6% and increases with mass. Because nonpoint source samples of different shapes do not fully satify the hypothesis. To correct this deviation, a set of fast neutron multiplicity counters was built by Geant4 to simulate and study the mass attribute of Pu samples.The cylindrical sources of different shapes and different masses were simulated, the self-multiplication factor and α coefficient were corrected.And the corresponding third-order polynomial fitting equation was obtained, the goodness of fit was greater than 0.970. In the same way, the spherical and spherical shell source samples in the mass range of 0–5 kg were analyzed, the corrected mass deviation of samples was less than 10% in this interval. The results show that the combination of the fast neutron multiplicity counter and parameter correction can accurately measure the sample mass attribute.

Measurements and simulations to investigate the feasibility of neutron multiplicity counting in the current mode of fission chambers

In two earlier papers [1], [2] we investigated the possibility of extracting traditional multiplicity count rates from the cumulants of fission chamber signals in current mode. It was shown that if all neutrons emitted from the sample simultaneously are also detected simultaneously, the multiplicity rates can be retrieved from the first three cumulants of the currents of up to three detectors, but the method breaks down if the detections of neutrons of common origin take place with a time delay spread wider than the pulse shape. To remedy these shortcomings, in this work we extended the theory to two- and three-point distributions (correlations). It was found thatthe integrals of suitably chosen two- and three-point moments with respect to the time differences become independent of the probability density of the time delays of detections. With this procedure, the multiplicity rates can be retrieved from the detector currents for arbitrary time delay distributions. To demonstrate the practical applicability of the proposed method, a measurement setup was designed and built. The statistics (shape and amplitude distribution) of the detector pulse were investigated as important parameters of the theoretical model. Simulations were performed to estimate the expected value of the multiplicity rates in the built setup. Measurements were performed and two types of moments (the mean and the covariance function) of the recorded detector signals were calculated. Values of singles rates were successfully recovered.

Ability of non-destructive assay techniques to identify sophisticated material partial defects

This study explores the ability of non-destructive assay techniques to detect a partial material defect in which 100 g of plutonium are diverted from the center of a 1000 g can of PuO2 powder. Four safeguards measurements techniques: neutron multiplicity counting, calorimetry, gravimetry, and gamma ray spectroscopy are used in an attempt to detect the defect. Several materials are added to the partial defect PuO2 can to replicate signatures of the diverted material. 252Cf is used to compensate for the doubles neutron counts, 241Am is used to compensate for the decay heat, and aluminum is used to compensate for the weight. Although, the doubles and triples difference before and after diversion are statistically indistinguishable with the AWCC in fast and thermal mode, the difference in the singles counts are statistically detectable in both modes. The relatively short half-life of 252Cf leads to a decrease (three sigma uncertainty) in the doubles neutron counts after 161 days. Combining this with the precise quantity of 241Am needed (10.7 g) to mimic the heat signature and the extreme precision in 252Cf mass needed to defeat neutron multiplicity measurements gives reassurance in the International Atomic Energy Agency's ability to detect partial material defects.

Simulation of the Nondestructive Assay of 237Np Using Active Neutron Multiplicity Counting

In this work, an epithermal neutron multiplicity counter (ENMC) and an organic scintillator multiplicity counter (OSMC) are compared in the assay of 237Np, a potentially weapons-usable isotope, using active neutron multiplicity counting. In active neutron multiplicity counting, the neutron doubles and triples multiplicity rates are used to analytically calculate sample mass. To distinguish the masses of two different samples, the measured triples and doubles rates of each sample must be separated by 1σ. The time it takes each system to separate the measured triples multiplicity rates was compared using 20 metal samples of 237Np with masses logarithmically distributed between 10 and 1000 g. The results show that the OSMC can distinguish the smallest masses (10.0 and 12.7 g) beyond 1σ in 20 min and that the ENMC requires more than 400 times the measurement time to obtain the same precision. Similarly, the OSMC is at least 4.5 times faster than the ENMC in separating the doubles multiplicity rates.

High order fast neutron multiplicity measurement equations based on liquid scintillation detector

Fast neutron multiplicity counting (FNMC) analysis method is a new nondestructive analysis method for nuclear materials. It uses a fast neutron detector array to detect the neutrons emitted by the sample. The quality of plutonium in the sample is obtained by recording the neutron coincidence counting of fast neutron multiplicity. At present, the first three multiplets widely studied including singlets, doublets and triplets can no longer meet the needs of the research. In this paper, The derivation process of fast neutron multiplicity measurement equation for liquid scintillation detector is studied in detail based on the basic principle, neutron counting method, by using the methods of the factorial moments, probability generating functions and parameter estimation method, and considering the influence of scattering crosstalk. Finally, the fast neutron multiplicity measurement equation including singlets, doublets, triplets, quadruplets and pentuplets are established according to the parameter estimation method and the two kinds of solution methods of this equation are given. The work in this paper lays a theoretical and analytical foundation for the research of fast neutron multiplicity measurement system based on liquid scintillation detector.

A Note on the Nomenclature in Neutron Multiplicity Mathematics

The purpose of this technical note is to consolidate the notations used for describing parameters that pertain to neutron multiplicity mathematics relevant to various applications including nonproliferation, international safeguards, and criticality safety among others. The nomenclatures used in these techniques vary widely depending on the origin of the work and their applications. We aim to consolidate many of the previously used notations in a single document to enhance past, present, and future technical exchanges pertaining to neutron multiplicity. This will help avoid confusion in future publications and will facilitate wider application-independent advancements and utility of peer-reviewed findings. A brief introduction and history of neutron multiplicity counting is presented, followed by a summary of commonly used techniques in a variety of different applications. In each section, we present the notations used in previous publications for the reader’s reference.

Mass uncertainty in neutron multiplicity counting associated with the uncertainty on the fission multiplicity factorial moments

Passive neutron multiplicity counting relies on measurement of the spontaneous fission neutron yield, to estimate the amount of 240Pu in the tested sample. To account for additional neutron sources in the sample, typically (α,n) reactions and induced fissions in the odd fissionable isotopes, the first three sampled moments of the neutron count distribution are used in an inversion formula that quantifies the amplitude of all three neutron sources. When solving the set of equations corresponding to the inversion formula, the first three factorial moments of the fission multiplicity distribution (both the spontaneous and induced fission) are used. Thus, any uncertainty on the nuclear data and the numeric values of the neutron multiplicity moments, is bound to create a parametric uncertainty on the estimated mass. So far, most studies on the uncertainty associated with the nuclear data are experimental by nature, often focusing on a better estimation of the factorial moments and a viable uncertainty estimation on the reported values.Since the inversion formula is non-linear, the error propagation from the multiplicity moments to the mass is also non-linear, and might have a very strong dependence on the sample parameters. In the present study, we formulate mathematical formulas that describe the error propagation from the factorial moments of the fission multiplicity to the mass, and implement the formulas to quantify the uncertainty in terms of the sample characteristics. For validation, the computational results are then compared with experimental results.

Analytical error bars and RSD for neutron multiplicity counting

This paper derives the standard deviation of the moments of neutron multiplicity distributions for both random and (shift register) triggered counting gates by propagating the multinomial distribution of errors in the counting distribution. Exact and approximate analytical formulas for the singles, doubles, and triples error bars are given along with the corresponding RSD (relative standard deviation). These analytical formulas provide a simple way to analyze and predict error bars without needing empirical data or simulations. The comparison of these analytical error bars to actual measurement errors can reveal systematic errors that are not being accounted for in the modeling of the data.

Identifying neutron shielding in neutron multiplicity counting

Neutron Multiplicity Counting (NMC) and passive neutron interrogation is becoming a standard procedure in special nuclear material control and accountability, due to the relative optical transparency of other structure materials to neutron flux, making it very effective for measuring composite poorly-characterized samples. Currently, all applicable neutron multiplicity counting methods assume that both the detection efficiency and the neutron die-away time are system parameters, independent of the sample. Clearly, if the detection efficiency of the system is reduced due to neutron absorption or moderation inside the sample, the measurement will be biased. Therefore, detecting a reduction in the detection efficiency, either accidental or deliberate, is a well motivated problem. In the present study we develop, through both theory and implementation, a new method for detecting a reduced effective detection efficiency in NMC by sampling the fourth central moment of the count distribution. One of the attributes that make the proposed method appealing is that it does not require any additional operation and may be easily applied to any standard NMC counter, assuming that the data is recorded in LIST mode. The method is implemented on a set of 18 measurements, 7 of which are standard NMC measurements, and in the remaining 11 the sample is covered by a moderator, noticeably reducing the effective detection efficiency. The new method successfully discriminates between them.

Simulation study on neutron multiplicity of plutonium based on liquid scintillation detector

Fast neutron multiplicity counting (FNMC) is a new method of non-destructive analysis for nuclear materials. Using fast neutron detector array to detect the neutrons emitted from a sample, it obtains measurements according to the multiple counting method and analyzes the mass of plutonium in the sample. In this paper, A FNMC measuring device model has been constructed for simulation study in reference to the most advanced FNMC experimental device in the world. A series of typical plutonium sample models, including samples of plutonium metal and samples of plutonium oxide with different isotopic abundance and in different mass, have been designed. The correctness of the newly established fast neutron multiplicity measuring equation and the necessity of modifying the classical measuring equation have been verified by the computer simulated measurements. Compared with the calculation result from the equation developed in this paper and the calculation result from the classical NMC model, the simulated result shows that the new method is better than the classic method in result deviation.

Development of a lithium fluoride zinc sulfide based neutron multiplicity counter

The feasibility of a full-scale lithium fluoride zinc sulfide (LiF/ZnS) based neutron multiplicity counter has been demonstrated. The counter was constructed of modular neutron detecting stacks that each contain five sheets of LiF/ZnS interleaved between six sheets of wavelength shifting plastic with a photomultiplier tube on each end. Twelve such detector stacks were placed around a sample chamber in a square arrangement with lithiated high-density polyethylene blocks in the corners to reflect high-energy neutrons and capture low-energy neutrons. The final system design was optimized via modeling and small-scale test. Measuring neutrons from a 252Cf source, the counter achieved a 36% neutron detection efficiency (ϵ) and an 11.7μs neutron die-away time (τ) for a doubles figure-of-merit (ϵ2∕τ) of 109. This is the highest doubles figure-of-merit measured to-date for a 3He-free neutron multiplicity counter.

Regression analysis of coincidence measurements for determinating the neutron emission rate of <sup>252</sup>Cf spontaneous fission

The <sup>252</sup>Cf isotope sources have a recommended standard neutron spectrum of spontaneous fission, and have been widely used in scientific researches, such as the detection efficiency calibration of neutron detectors, the characterization of neutron dose equivalent meters, the active analysis of special nuclear materials, etc. However, it is often necessary to correct the neutron emission rate due to its short half-life of 2.645 years. As the source age increases the contributions from <sup>250</sup>Cf and <sup>248</sup>Cm spontaneous fission become more significant, thus the neutron emission rate cannot be calculated simply according to the <sup>252</sup>Cf decay law. In addition, the indirect measurement method by manganese bath activation needs a long period more than 8 hours; and it will have a large uncertainty while the source strength is lower than 10<sup>4</sup> n/s. In order to develop a more portable measurement method for larger suitable dynamic range, the comprehensive algorithms based on the neutron multiplicity counting are studied in this paper. On the basis of the measurement equations under the point model assumption, the neutron coincidence counting rate is correlated with the total neutron counting rate, and then the regression analyses with different coincidence gates and different source locations in the counter are performed. On the assumption that the average neutron die-away time is constant in the sensitive range of detection system, therefore the characteristic coefficient from the changing process can be extracted, and two kinds of methods of measuring the neutron strength are established, which are independent of the efficiency variation. The verification experiments are carried out by the JCC-51 neutron coincidence counter. It is shown that the values measured by the two regression methods are consistent with the corrected results of the nominal value within 2% deviation. Furthermore, the detection efficiency is inversed by dividing the total neutron counting rate with the neutron emission rate when the source is placed at the central axis, which accords with the result of Monte Carlo simulation by using the MCNPX code well. It can provide an accurate method of determining the neutron emission rate of <sup>252</sup>Cf spontaneous fission, and also an approach to calibrating the detection efficiency of neutron coincidence counter while the source strength is unknown.

Experimental evaluation of the extended Dytlewski-style dead time correction formalism for neutron multiplicity counting

Over the past few decades, neutron multiplicity counting has played an integral role in Special Nuclear Material (SNM) characterization pertaining to nuclear safeguards. Current neutron multiplicity analysis techniques use singles, doubles, and triples count rates because a methodology to extract and dead time correct higher order count rates (i.e. quads and pents) was not fully developed. This limitation is overcome by the recent extension of a popular dead time correction method developed by Dytlewski. This extended dead time correction algorithm, named Dytlewski–Croft–Favalli(DCF), is detailed in reference Croft and Favalli (2017), which gives an extensive explanation of the theory and implications of this new development. Dead time corrected results can then be used to assay SNM by inverting a set of extended point model equations which as well have only recently been formulated. The current paper discusses and presents the experimental evaluation of practical feasibility of the DCF dead time correction algorithm to demonstrate its performance and applicability in nuclear safeguards applications. In order to test the validity and effectiveness of the dead time correction for quads and pents, 252Cf and SNM sources were measured in high efficiency neutron multiplicity counters at the Los Alamos National Laboratory (LANL) and the count rates were extracted up to the fifth order and corrected for dead time. In order to assess the DCF dead time correction, the corrected data is compared to traditional dead time correction treatment within INCC. The DCF dead time correction is found to provide adequate dead time treatment for broad range of count rates available in practical applications.

Estimating the mass variance in neutron multiplicity counting—A comparison of approaches

In the standard practice of neutron multiplicity counting , the first three sampled factorial moments of the event triggered neutron count distribution are used to quantify the three main neutron source terms: the spontaneous fissile material effective mass, the relative (α,n) production and the induced fission source responsible for multiplication.This study compares three methods to quantify the statistical uncertainty of the estimated mass: the bootstrap method, propagation of variance through moments, and statistical analysis of cycle data method. Each of the three methods was implemented on a set of four different NMC measurements, held at the JRC-laboratory in Ispra, Italy, sampling four different Pu samples in a standard Plutonium Scrap Multiplicity Counter (PSMC) well counter.

Neutron Multiplicity Counting Moments for Fissile Mass Estimation in Scatter-Based Neutron Detection Systems

Neutron multiplicity counting (NMC) techniques are widely used for nuclear materials accountability and international safeguards applications to quantitatively evaluate characteristic properties pertaining to fissile material. Mathematical models for NMC moments have been previously derived for systems that use capture-based detectors; however, these models are not applicable when scatter-based detectors are used because of “neutron cross talk.” Neutron cross talk occurs when a single neutron scatters and deposits energy above threshold into multiple detectors causing spurious increase in multiplicity counts; this, in turn, has caused fissile mass to be overestimated when not treated. In this paper, we propose new mathematical models derived from point kinetics to correct for neutron cross-talk effects up to any arbitrary order N, where N denotes the maximum number of counts a single neutron can cause. The new models were used to estimate the fissile mass of plutonium metal and oxide samples with effective 240Pu mass ranging from 2.5 to 250 g. The adequacy of the models was confirmed using simulations of a conceptual scatter-based neutron multiplicity counter (e.g., organic scintillators) using MCNPX v2.7e with the PoliMi fission event generating extension. The fissile mass estimates with no correction for neutron cross-talk events yielded an average relative deviation from the true 240Pueff mass of 55.94% and 84.56% for metal and oxide samples, respectively. When neutron cross-talk events of order N = 2 are included in the model, the fissile mass estimates yielded an average relative deviation of 11.89% for metal and 13.21% for oxide samples. Accounting for neutron cross-talk events of order N = 3 resulted in fissile mass estimates with an average relative deviation of 9.58% and 10.51% for metal and oxide samples, respectively. These mass estimates were compared to a reference case (i.e., no neutron cross-talk effects) that yielded an average relative deviation of 6.81% and 4.77% for metal and oxide samples, respectively. The discrepancy between the estimates from the proposed model and the reference case is attributed to the assumed value of N, which sets a finite upper bound on the order of cross-talk events the model treats (i.e., the model for N = 3 assumes that a neutron will never cause more than three counts).

Extension of the Dytlewski-style dead time correction formalism for neutron multiplicity counting to any order

Neutron multiplicity counting using shift-register calculus is an established technique in the science of international nuclear safeguards for the identification, verification, and assay of special nuclear materials. Typically passive counting is used for Pu and mixed Pu-U items and active methods are used for U materials. Three measured counting rates, singles, doubles and triples are measured and, in combination with a simple analytical point-model, are used to calculate characteristics of the measurement item in terms of known detector and nuclear parameters. However, the measurement problem usually involves more than three quantities of interest, but even in cases where the next higher order count rate, quads, is statistically viable, it is not quantitatively applied because corrections for dead time losses are currently not available in the predominant analysis paradigm. In this work we overcome this limitation by extending the commonly used dead time correction method, developed by Dytlewski, to quads. We also give results for pents, which may be of interest for certain special investigations. Extension to still higher orders, may be accomplished by inspection based on the sequence presented. We discuss the foundations of the Dytlewski method, give limiting cases, and highlight the opportunities and implications that these new results expose. In particular there exist a number of ways in which the new results may be combined with other approaches to extract the correlated rates, and this leads to various practical implementations.

Effects of Correlated and Uncorrelated Gamma Rays on Neutron Multiplicity Counting

Neutron multiplicity counting relies on time correlation between neutron signals to assay the fissile mass, ( $\alpha $ ,n) to spontaneous fission neutron ratio, and neutron self-multiplication of samples. Gamma-ray sensitive neutron multiplicity counters may misidentify gamma rays as neutrons and therefore miscalculate sample characteristics. Time correlated and uncorrelated gamma-ray-like signals were added into gamma-ray free neutron multiplicity counter data to examine the effects of gamma-ray signals being misidentified as neutron signals on assays. Multiplicity counter measurements with and without gamma-ray-like signals were compared to determine the assay error associated with gamma-ray-like signals at various gamma-ray and neutron rates. Correlated and uncorrelated gamma-ray signals each produced consistent but different measurement errors. Correlated gamma-ray signals most strongly led to fissile mass overestimates, whereas uncorrelated gamma-ray signals most strongly lead to ( $\alpha $ ,n) neutron overestimates. Accounting for the effects of gamma rays on gamma-ray sensitive neutron multiplicity counters may allow these effects to be compensated for, thus mitigating the assay error associated with misidentified gamma rays.

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.

Characterizations of double pulsing in neutron multiplicity and coincidence counting systems

Passive neutron coincidence/multiplicity counters are subject to non-ideal behavior, such as double pulsing and dead time. It has been shown in the past that double-pulsing exhibits a distinct signature in a Rossi-alpha distribution, which is not readily noticed using traditional Multiplicity Shift Register analysis. However, it has been assumed that the use of a pre-delay in shift register analysis removes any effects of double pulsing. In this work, we use high-fidelity simulations accompanied by experimental measurements to study the effects of double pulsing on multiplicity rates. By exploiting the information from the double pulsing signature peak observable in the Rossi-alpha distribution, the double pulsing fraction can be determined. Algebraic correction factors for the multiplicity rates in terms of the double pulsing fraction have been developed. We discuss the role of these corrections across a range of scenarios.

Neutron Multiplicity Counting: Credible Regions for Reconstruction Parameters

From nuclear materials accountability to homeland security, the need for improved nuclear material detection, assay, and authentication has grown over the past decades. Starting in the 1940s, neutron multiplicity counting techniques have enabled quantitative evaluation of masses and multiplications of fissile materials. In this paper, we propose a new method to compute uncertainties on these parameters using a model-based sequential Bayesian processor, resulting in credible regions in the fissile material mass and multiplication space. These uncertainties will enable us to evaluate quantitatively proposed improvements to the theoretical fission chain model. In addition, because the processor can calculate uncertainties in real time, it is a useful tool in applications such as portal monitoring: monitoring can stop as soon as a preset confidence of nonthreat is reached.