Abstract This work presents ongoing efforts to develop a real-time program for detecting the direction and general location of a neutron source using the NoMad detector, a 15-tube He-3 array. This program is part of a larger proof-of-concept system focused on real-time neutron multiplicity monitoring, with potential applications during fuel debris removal at Fukushima Daiichi units 1, 2, and 3. The approach employs a random forest regression model, which predicts neutron source locations by learning the relationship between neutron count rates from the NoMad detector and the corresponding source positions. For real-time implementation, the system is designed to continuously collect neutron count data across all 15 tubes of the NoMad detector, feeding this data into the trained model to estimate the neutron source's location. To manage transient variations in count rates, a sliding time window approach will be applied, while optimization efforts aim for low-latency computation to support on-the-fly source localization. The random forest algorithm’s capacity to manage the non-linear relationship between neutron count rates and spatial positions is expected to address challenges from fluctuating neutron backgrounds and noise in high-radiation settings. Results for source location accuracy, latency, and resilience to background radiation fluctuations will be presented. Beyond Fukushima Daiichi, this system will have applications in nuclear nonproliferation and accident response, where its ability to provide real-time source location information will aid in critical decision-making.

For the first time, the article raises the problem of the possibility of using the high-frequency component of neutron noise to monitor the state of fuel assemblies and fuel rods during operation, since for long-time neutron noise research was limited to a frequency of 50 Hz. A brief historical summary presents the main points and stages of the development of neutron noise control, as well as the personalities of individual scientists who have made fundamental contributions to the development of neutron noise diagnostics. Using the example of data from the Novovoronezh NPP obtained during dynamic tests in 2022, the authors show the possibility of estimating the natural fluctuations of the control bodies of the control system as a function of frequency-depth of immersion in the core. This dependence makes it possible to build an alternative channel for monitoring the position of the regulatory authorities. Based on spectral estimates of high-frequency neutron noise, the possibility of detecting the boiling mode of the coolant with localization of the location by the height of the fuel assembly is substantiated. For the first time, data (frequency composition) on possible natural fluctuations of fuel rods (parts of fuel rods) measured directly during operation is presented. These values are given in the form of specific values, and not in the form of a frequency range calculated based on the results of bench tests. A critical approach to the problem of preliminary tests of fuel assembly layouts at various stands in terms of the sufficiency of information and its validity is presented. For the convenience of visualization and compression of information, a new representation of the cascade of spectra is introduced in the form of contour graphs, which makes it possible to identify common patterns on a large amount of data as efficiently as possible. The necessity of further research on neutron noise issues at existing nuclear power plants is argued in connection with the introduction of a new fuel assembly design (TVS-5), which has significant differences.

TH-NK neutron noise analysis in KWU-PWR NPP

In addition to nuclear data validation and criticality safety research, criticality experiments offer unique opportunities for investigations into fundamental reactor physics phenomena and measurement techniques. Unlike conventional light water research reactors where kinetics parameters do not significantly deviate from one reactor to another, critical experiments with neutron lifetimes from tens of nanoseconds to tens of microseconds can be constructed on vertical lift machines. Kinetics measurements of new fast reactors will be crucial for the validation of computational methods. In this work, we present the results of neutron noise measurements of a fast highly enriched uranium–fueled copper-reflected critical system constructed on the Comet vertical lift assembly at the National Criticality Experiments Research Center. Fluctuations in the system’s neutron population were analyzed in the frequency domain by 3He proportional counters and organic scintillators in order to measure the prompt neutron decay constant α at delayed critical and four subcritical states. Agreement between the extrapolated αDC values of the two detector systems was within 4%. Additionally, α values at delayed critical were examined as a function of time in the presence of small power drifts. By comparing to the linear channel, it is shown that these drifts did not cause a noticeable effect on α but did inversely vary with the signal amplitude. A consistent bias between the 3He and scintillator measurements of α and signal amplitude was observed and is believed to be caused by electronic noise or spacial effects. These measurement techniques will be essential in supporting the development and deployment of advanced fast reactor types through their ability to verify and validate computational methods.

Abstract Backgroup Energy-resolved neutron imaging is an effective method to investigate the crystal structure and stress distribution of materials. The energy-resolved neutron imaging instrument (ERNI) has been established at China Spallation Neutron Source (CSNS). An energy-resolved neutron imaging detector based on the high-speed camera TPX3Cam is used at ERNI to achieve neutron energy resolution by recording time-of-flight (ToF) of neutrons. TPX3Cam records the photon events emitted by the neutron absorption in the scintillator. An image reconstruction algorithm is needed to reconstruct the neutron events to improve the spatial and energy resolution of the detector. Purpose The data output from the TPX3Cam contains photon events that dispersion in space and time. We want to develop an image reconstruction algorithm to identify photon events produced by a single neutron and remove the gamma ray as well as the noise. Finally, better spatial resolution and energy resolution can be obtained by neutron events reconstruction. Method Image reconstruction algorithms involves photon events clustering and neutron events reconstruction. Based on the traditional two-dimensional density-based spatial clustering of applications with noise (DBSCAN) algorithm, the three-dimensional DBSCAN algorithm is developed including ToF as the third dimension of information. The precision of Bragg edge of a sample is related to the energy resolution of the detector; thus, the quality of the parameters can be evaluated by the improvement in Bragg edge precision after reconstruction. Result and conclusion The three-dimensional DBSCAN algorithm can proceed the image data effectively and identify the neutron events and noise. The precision of reconstructed Bragg edges is improved from 3.601‰ to 3.337‰, and the spatial resolution is improved from 150 $$\upmu $$ μ m/line width to 100 $$\upmu $$ μ m/line width.

Analyzing neutron noise in zero-power reactors provides information about integral parameters, such as the prompt decay constant α . This information can be used to validate codes that predict said parameters, or time-dependent behavior, particularly reactor transients. The CROCUS zero-power research reactor has been widely used for conducting noise experiments and has recently been enhanced with a new neutron detection system SAFFRON. This system includes an array of about 150 miniature neutron detectors evenly dispersed throughout the core, allowing for three-dimensional (3D) spatial detection capabilities. We conducted a neutron noise experiment using the 3D array to test this new system to determine the prompt decay constant α . Our results, derived from the Rossi- α method, aligned with the predictions from the Serpent 2 Monte Carlo code, which utilized the Lawrence Livermore National Laboratory FREYA library for fission. The agreement was within 1 σ of the estimated uncertainties. We notably observed that based on previous experiments, using all 150 detectors does not achieve the levels of detection efficiency (in counts per fission) expected to be necessary to observe the fission chain decay, yet we still observe the decay with comparatively high statistical significance. We therefore show experimentally that the spatial extent of the detection system is an important parameter in the prediction of the success of the neutron noise technique. We also explored the cross-spectral density method for different combinations of SAFFRON detectors, which gave consistent results with the Rossi- α method. In addition, uncertainty estimation methods, including the bootstrap method, were applied to SAFFRON, addressing both temporal and spatial aspects. We discuss the benefits of using bootstrap methods for estimating the uncertainty of the prompt decay constant, which we found often underestimated when using the covariance matrix from a standard nonlinear fit. The results also indicate that SAFFRON is a powerful measurement tool that can be expanded for use in active perturbation experiments, 3D flux maps, and other high-resolution reactor physics experiments.

Sensitivity analysis and uncertainty quantification of neutron noise simulations in WWER-type reactors using machine learning-based surrogate models

Power reactor noise simulation and analysis by developing Time-Domain neutron noise Simulator: iPWR case study

We present the development and implementation of a neutron event-tracking capability in OpenMC, an open-source, community-driven Monte Carlo radiation transport code. This feature can be utilized for explicit neutron noise simulations, enabling the estimation of integral kinetic parameters such as the prompt decay constant, which are important for accurate predictions of reactor transient behaviors and validation of computational tools. Experimentally, the prompt neutron decay constant ( α ) can be measured non-invasively during steady-state reactor operation via neutron noise analysis techniques such as the Rossi-alpha method. Accurately simulating these neutron noise measurements requires explicit tracking of individual neutron interactions, preserving detailed timing information essential for subsequent statistical analysis. Previously, such capabilities were primarily restricted to export-controlled software like MCNPX PoliMi or MCNP 6.3. Our open-source implementation in OpenMC offers customizable filters that discriminate and record specific neutron interactions, based on parameters such as reaction type, energy, material, and geometry. Recorded events are stored externally in either OpenMC’s native HDF5 format or the MCPL format for versatility. We demonstrate the application of this feature by employing the Rossi-alpha method for noise analysis on simulated neutron event data. Benchmarking simulations using the Godiva I geometry and a model of the CROCUS zero-power reactor, employing ENDF/B.VII.0 nuclear data, confirm the reliability of our approach through comparisons with Serpent 2 results. This development significantly expands the accessibility of neutron noise simulation capabilities. The eventtracking feature could also see use in other detection applications, such as time-of-flight experiments or radiation imaging.

We use Monte Carlo simulations to predict the responses of neutron noise experiments in zero-power Molten Salt Reactors (MSRs). As for conventional reactors, the initial testing of a newly constructed reactor often comprises zero-power tests and criticality experiments. In zero-power environments, neutron noise experiments can be part of the experimental portfolio to provide experimental data on integral kinetic parameters such as the prompt neutron decay constant or the effective delayed neutron fraction. Neutron noise experiments exploit the statistical correlations in neutron detector signals via noise analysis methods, such as the Rossi-α or PSD method. The results are then used for code validation, nuclear data feedback or safety monitoring purposes. For MSRs, the flowing fuel and the therefore flowing precursors leads to a unique dynamic behavior that could be experimentally studied with neutron noise techniques. For example, β eff depends on the fluid velocity: For higher velocities the precursors are swept out of the core and therefore might not contribute to the reactivity, and in many MSR designs β eff therefore goes down with higher flow rate. In this work, we present simulations using the MSRE model in Serpent 2 to predict neutron noise curves for different flow rates. Our approach is new in its use of explicit Monte Carlo modeling for noise experiments in MSRs, with a simplified treatment of the precursor flow. Our results indicate that noise experiments in zero-power MSRs are feasible and that noise experiments could be used to measure recirculation time and kinetic parameters.

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.

Power reactor noise refers to the small periodical variations of the neutron flux in nuclear reactor cores, induced by various perturbations. A prominent example is the vibration of fuel assemblies due to fluid-structure interactions. Although noise is generally an unwanted phenomenon, its analysis is useful for core monitoring. In this respect, several state-of-the-art deterministic or Monte Carlo solvers have been developed to solve the equations describing neutron noise. In this paper, we investigate the convergence properties of Monte Carlo methods for neutron noise analysis, within the orthodox linearization approximation. For this purpose, we establish a theoretical framework for complex-weighted Monte Carlo games and we show that convergence of such algorithms can be assessed using two sets of eigenvalues. In order to substantiate our findings, we examine a few relevant benchmark configurations for noise problems.

In the framework of an assessment of the application of neutron noise methodologies to the TAPIRO reactor, sensitivity and uncertainty analyses on impacting nuclear data for this experimental reactor have been performed using the Serpent Monte Carlo code. Integral parameters relevant to the noise analysis of TAPIRO have been investigated, namely the effective multiplication factor, the effective delayed neutron fraction, the effective generation time and the prompt neutron decay constant. The nuclear data uncertainty has been assessed using different data libraries (ENDF/B-VIII.0 and JEFF-3.3), different energy grids (ECCO-33 and XMAS-172) and different techniques (Generalised Perturbation Theory and Unscented Transform). A ranking of the most impacting nuclides ( 235 U, 63 Cu, 65 Cu and 238 U) and reactions (elastic scattering, fission, radiative capture and fission neutron yield) in terms of uncertainties has been performed, pointing out that the impact of nuclear data uncertainties on the responses is non-negligible and must be taken into account when the noise analysis of the reactor is performed. In particular, the uncertainty on the value of the prompt neutron decay constant due to effect of the nuclear data uncertainties is larger than 100%, especially when the system under study is close to criticality.

Many research staffs and groups have paid considerable attention to the issues of noise analysis and control of nuclear power plant operation parameters. This is reflected in the scientific environment in the form of numerous publications, monographs, articles, and reviews devoted to the study of noise components of various variation signals of reactor plants. However, despite the advanced theoretical works on this topic, applied research, i.e. direct reactor experiments, remains aside from the interests of both local and foreign scientists. The need of practical research is due to the complexity of interpretation of a variety of anomalies detected by noise methods, as well as the need to fine-tune various models. In addition, the spectral images of equipment can differ significantly not only between different designs of reactor plants, but also within the same-type units at one NPP. These problems cannot be solved by theoretical or computational methods alone, or by using simulation modeling. The situation is complicated by the fact that noise studies are a complex task both in terms of selecting noise data sources and interpreting the obtained information. Probably, these reasons explain the significant decrease of interest to experimental works on noise subject at various reactor plants both in the world practice and in Russia. The paper briefly discusses some possibilities of methods of neutron-noise control of cores aimed at improving the reliability and safety of NPPs. In addition, the article considers ways to reduce the labor intensity of their use for the earliest possible detection of anomalous condition of various equipment.

The degradation of clamping force in the core support barrel, which forms the internal structure of a nuclear power plant, has the potential to significantly impact the plant's safety and reliability. Previous studies have concentrated on the detection of clamping force degradation but have been constrained in their ability to identify the precise size and position. This study proposes a novel methodology for diagnosing the size and position of clamping force degradation in core support barrels, combining deep-learning techniques and dynamic time warping (DTW) algorithms. DTW is applied to the magnitude data of the ex-core neutron noise signal obtained in the frequency domain, thereby enabling the effective learning of changes in sensor data values. Moreover, autoencoder-based (AE-based) representation learning is utilized to extract features of the data, preventing overfitting and thus enhancing the robustness of the model. The experiment results demonstrate that the size and position of clamping force degradation can be accurately predicted. It is expected that this research will contribute to enhancing the precision and efficiency of internal structure monitoring in nuclear power plants.

Improvement of reactor safety through simulation and analysis of power reactor noise requires the development of the neutron noise computation codes. The aim of this study is to create a neutron noise simulator for hexagonal geometry reactors. In this research, the SD-HACNEM (Sharif Dynamic -High order Average Current Nodal Expansion Method) simulator is enhanced to solve the steady-state neutron diffusion equation and neutron noise equation in the frequency-domain for two-dimensional hexagonal geometry using the high-order nodal expansion method. Initially, calculations are carried out for the steady-state. To minimize discretization errors, the degree of flux expansion polynomials is increased from 3rd to 5th, taking into account nodes the size of a fuel assembly for both ACNEM (Average Current Nodal Expansion Method) and HACNEM (High-order Average Current Nodal Expansion Method). The validation of the ACNEM and HACNEM is performed by comparing the results with verified references for the IAEA-2D benchmark problem reactor. The steady-state numerical results show that the use of HACNEM provides more accuracy compared with ACNEM, without reducing the size of the nodes. In the main part of the present study, neutron noise calculations are performed in the frequency-domain for two types of noise sources including absorber with variable strength and ILOFAIP (Inadvertent Loading and Operation of a Fuel Assembly in an Improper Position). The results are benchmarked through simulation at zero frequency and adjoint calculations. The numerical results show that the use of the high-order nodal expansion method is effective for the simulation of neutron noise in a hexagonal reactor.

With the aging of the nuclear reactor fleet in Europe, and especially in Spain, monitoring these reactors through complex models has become of great interest to maintain the safety and operational capability of these nuclear power plants. It is of particular interest to locate the place where a possible anomaly has occurred, as well as the type, to guarantee the safety of the reactor through the analysis of neutron flux fluctuations. Therefore, we propose a deep learning framework for the deconvolution of reactor transfer functions from perturbation-induced neutron noise sources. The main objective of this work is to develop tools based on deep learning techniques to classify the type and to locate the perturbation, working with simulated data with different noise levels, and to study the number of detectors that need to be active. In particular, the data used have been simulated for the BIBLIS 2D reactor using FEMFFUSION. This work has been carried out using the Keras library based on tensor flow, managing to develop two convolutional neural networks that adapt well to the data model. High-accuracy results are obtained both when predicting the type of the perturbation and when locating the place of the perturbation, with a low error rate even when only four to eight detectors are available.

Nuclear reactor cores achieve sustained fission chain reactions through the so-called "critical state"-a subtle equilibrium between their material properties and their geometries. Observed at macroscopic scales during operations, the resulting stationary neutron field is tainted by a noise term that hinders various fluctuations occurring at smaller scales. These fluctuations are either of a stochastic nature (whenever the core is operated at low power) or related to various perturbations and vibrations within the core, even operated in its power regime. For reasons that are only partially understood using linear noise theory, incidental events have been reported, characterized by an increase of the power noise. Such events of power noise growth, sometimes up to seemingly unbounded levels, have already led in the past to voluntary scramming of reactors. In this paper, we will use a statistical field theory of critical processes to model the effects of neutron power noise. We will show that the evolution of the neutron field in a reactor is intimately connected to the dynamic of surface growths given by the Kardar-Parisi-Zhang equation. Recent numerical results emerging from renormalization-group approaches will be used to calculate a threshold in the amplitude of the reactor noise above which the core enters a new criticality state, and to estimate the critical exponents characterizing this phase transition to rough neutron fields. The theoretical model of nonlinear noise built in this paper from ab initio statistical mechanics principles will be correlated and compared to data of misunderstood reactor noise levels and reactor instabilities and will be shown to provide both qualitative and quantitative insights into this long-standing issue of reactor physics.

In response to the significant dependency on empirical judgment in measuring the prompt neutron decay constant with the traditional Rossi-alpha method and the issue of requiring an excessive number of detectors with the DMD-Rossi-alpha method, this paper introduces a calculation method for the prompt neutron decay constant based on a combination of Latin Hypercube Sampling (LHS), Dynamic Mode Decomposition (DMD), and the Rossi-alpha method. Initially, the method uses LHS to expand the sample dataset of neutron noise data to reduce the number of detectors required. It then employs the Rossi-alpha method to construct a Rossi-alpha distribution model from neutron noise data. Finally, it utilizes DMD for feature extraction from the Rossi-alpha distribution model, thereby determining the prompt neutron decay constant. Research findings demonstrate that, by simulating the KUCA facility using RMC3.5 in a near-critical state, the relative error of the α value calculated by the LHS-DMD-Rossi-alpha method model is 9% less than that calculated by the Rossi-alpha method. This approach, capable of enhancing the precision of measuring the prompt neutron decay constant with just a single detector, holds significant theoretical value and engineering significance for the advancement of reactor physics and experimental techniques.

An operating nuclear reactor is designed to maintain a sustained fission chain reaction in its core, which results from a delicate balance between neutron creations (i.e., fissions) and total absorptions. This balance is associated with random fluctuations that can have two, very different, origins. A distinction must thus be made between low-power noise, whose origin lies in the inherently stochastic nature of neutron interactions with matter, and high-power noise, whose origin lies in the particular thermomechanical constraints associated with the environment in which neutrons propagate. Modeling the behavior of this noisy neutron population with the help of stochastic differential equations, we first show how the Martin-Siggia-Rose-Janssen-De Dominicis (MSRJD) formalism, providing a field theoretical representation of the problem, reveals a convenient and adapted tool for the calculation of observable consequences of neutron noise. In particular, we show how the MSRJD approach is capable of encompassing both types of neutron noises in the same formalism. Emphasizing then on power noise, it is shown how the self-sustained chain reaction developing in a reactor core might be sensitive to noise-induced transitions. Establishing an unprecedented connection between the neutron population evolving in a reactor core and the celebrated Kardar-Parisi-Zhang (KPZ) equation, we indeed find evidence that a noisy reactor core power distribution might be subject to a process analogous to the roughening transition, well-known to occur in systems described by the KPZ equation.