Neutron Population Research Articles

Pulsed-Neutron Die-Away Experiments for Plastics and Neutron Thermal Scattering Laws

Pulsed-neutron die-away (PNDA) experiments can be useful benchmarks to validate neutron thermal scattering laws (TSLs). The experiment uses a neutron generator to impinge a short (∼10−4 s), mono-energetic neutron pulse on a target sample. After the pulse, the neutron population within the sample moderates and reaches thermal equilibrium with a fundamental spatial mode and characteristic decay-time eigenvalue. The eigenvalue can be extracted from the experimental measurements of the neutron flux and used as an integral parameter in validation. For certain materials and geometric configurations, the eigenvalue is heavily influenced by thermal neutron scattering of only the target material. For that reason, a PNDA experiment can have a higher sensitivity to TSLs than is commonly available in critical experiments. Herein, we present results for a series of new PNDA experiments conducted at Lawrence Livermore National Laboratory with plastic materials, e.g. high-density polyethylene and Lucite. We compare the experimental integral parameters to simulated results and report trends in the biases. We evaluate the bias with different Monte Carlo transport codes (MCNP6.2 and Mercury) and show no significant differences between the results of the two codes.

Measurement of delayed neutrons in a thermal nuclear reactor by means of a long run pile noise experiment in sub-critical state

The transfer function of a zero-power thermal reactor was successfully measured thanks to neutron noise techniques from 1 mHz to 160 Hz. During a month-long experimental campaign, the fluctuations of the neutron population in critical and subcritical configurations of the core were acquired using excore fission chambers and analysed through Cross-Power Spectral Density (CPSD) methodology. Firstly, the reactor’s kinetic parameters, i.e. prompt decay constant, effective delayed neutron fraction and generation time, were obtained at critical state. It required calibrating the reactor’s power, which was done by metal foil activation and measurement of the 235U fission rate. Secondly, these parameters were used to estimate the groups’ abundances of delayed neutrons from the CPSD measured in a sub-critical state. Fitting data with a point kinetic model was done with Bayesian inference - CONRAD and Stan programs were used. A very good agreement was found between experimental abundances and the ones computed with TRIPOLI-4 Monte-Carlo transport code and JEFF3.1.1 nuclear data library. Uncertainties on prior abundances between 6 % to 101 %, held mainly by nuclear data, were lowered down to 4 % to 54 %, depending on the delayed group.

New experiment for measuring the delayed neutron yields of238U fission in the range 1 MeV to 19 MeV

In nuclear reactors operating in nominal conditions, delayed neutrons (DN) drive the kinetic behavior of the neutron population. Predicting this behavior requires therefore the knowledge of the DN yield per fission, average lifetime, and kinetic of their emission, which is described by precursors groups abundances. Characterizing the uncertainties of these macroscopic data is essential, especially as they are used to design the safety margins of reactors.Even for major fissile isotopes such as235U and239Pu, discrepancies still appear between the main nuclear data library. In 2018, CEA launched the ALDEN project (Average Lifetime of DElayed Neutrons), gathering several laboratories (CEA/DES and DRF, CNRS/LPSC, LP2i and LPC Caen, ENSICAEN, and University of Caen). This collaboration aims at producing new precise DN macroscopic data for reactor applications.Three experimental campaigns were conducted in 2018, 2019 and 2021 on the thermal fission of233U,235U and239Pu at Institut Laue Langevin in Grenoble (France), giving high quality results. In February 2023, a new campaign was performed at the PTB Ion Accelerator Facility in Braunschweig (Germany), focusing on the fast fission of238U. In particular, the DN yield was measured for eight energies between 1.5 and 19 MeV. This paper presents the experimental setup, that was adapted to the new facility and neutron spectrum. The methodology of analysis is also detailed, and some preliminary delayed neutron decay curves are showed.

Percolation properties of the neutron population in nuclear reactors.

Reactor physics aims at studying the neutron population in a reactor core under the influence of feedback mechanisms, such as the Doppler temperature effect. Numerical schemes to calculate macroscopic properties emerging from such coupled stochastic systems, however, require us to define intermediate quantities (e.g., the temperature field), which are bridging the gap between the stochastic neutron field and the deterministic feedback. By interpreting the branching random walk of neutrons in fissile media under the influence of a feedback mechanism as a directed percolation process and by leveraging on the statistical field theory of birth death processes, we will build a stochastic model of neutron transport theory and of reactor physics. The critical exponents of this model, combined with the analysis of the resulting field equationinvolving a fractional Laplacian, will show that the critical diffusion equationcannot adequately describe the spatial distribution of the neutron population and shifts instead to a critical superdiffusion equation. The analysis of this equationwill reveal that nonnegligible departure from mean-field behavior might develop in reactor cores, questioning the attainable accuracy of the numerical schemes currently used by the nuclear industry.

At-power subcritical multiplication in the advanced test reactor

The degree to which a given physical subdivision of a critical reactor acts as a neutron source for other lobes is not analytically characterized for general application. ATR and ATRC both operate at power, and individual power-producing lobes rely on each other as neutron sources in order to maintain constant power, which in general requires either exactly critical multiplication within a reactor or an external neutron source. This work shows that lobe powers in ATR or ATRC can be related with subcritical multiplication theory, demonstrating that the lobes are not individually critical. This explanation is significant for ATR due to the desire to irradiate a large variety of experiments simultaneously, each having its impact on the core neutron population. This work also establishes the lack of relationship between experiment reactivity worth and cross-sections calculated from fundamental nuclear data. For any physical subdivision of any other critical reactor, it is likewise true that the subdivision undergoes only subcritical multiplication.

Radiation shielding for a nuclear fusion device with inertial electrostatic confinement

In an inertial electrostatic confinement nuclear fusion device, IECF, thermal neutron population is created near the neutron shielding that is proportional to the fast neutrons generation rate; nevertheless, this proportionality varies with the experimental arrangement. Thus, to properly measure the fast neutron generation rate by the IECF device it is necessary to previously elaborate a detailed neutron transport model between the IECF device and the radiation shield, where the neutron detector will be located. This model is elaborated using the Monte Carlo N-Particle Code and the same is used to design the required radiation shield for the safe operation of the device.

The use of an SDE model for subcritical reactor noise experiment design and its comparison to a traditional Monte Carlo computational method

Noise experiments, and the Feynman-α method in particular, are used to measure the decay rate of the neutron population in a source driven subcritical assembly, such as that of a shut down nuclear reactor core. These experiments allow for a direct measurement of the reactivity of the assembly or other kinetic parameters such as the delayed neutron fraction βeff. These experiments can take a significant amount of time to perform, as the neutron population in the system is commonly small, and thus the detection rate is low. Simulation of these experiments can be used to design the experimental setup in advance. The design space includes parameters such as the required source intensity, detector efficiency or measurement time. However, direct simulation of the branching process itself is relatively expensive, even in a point reactor model, as many particle histories must be simulated for each configuration. Previous work has shown that the branching process’ mean count rate and variance can be accurately modeled using a system of stochastic differential equations (SDEs). By solving these SDEs, one can simulate an ”experiment signal” whose mean and variance match that of the branching process, which fully simulates all the information required for a Feynman-α experiment. Using these inexpensive simulations, the variance in the extracted reactivity from many sampled detection signals is obtained for many possible experimental setups. From this analysis, we show the dependence of the relative error in one’s measurements on their setup parameters, and that for any reactivity value, there exist source intensities and detection probabilities such that any further improvement in these parameters will only have negligible impact on the error. The relationship between these two parameters for equally low relative errors is also examined. A publicly available, open source Python implementation is provided for other researchers to use in future studies.

Investigating various factors affecting neutron spectrum in the pressure tube in pressurized heavy water reactor design

The fuel bundles in the pressurized heavy water reactor design (PHWR), such as the CANDU (Canada Deuterium Uranium), are placed inside horizontal fuel channels. Each fuel channel consists of concentric tubes called the pressure tube (PT) and the calandria tube (CT). Due to continuous exposure to extreme neutronics and thermal hydraulics conditions, the PTs undergo physical deformations in both the axial and radial directions, as the reactor ages. The deformations include diametral creep, wall thinning, sag, and axial elongation. One of the contributing factors to these deformations is the neutron spectrum in the PT, especially neutrons with energy greater than 1 MeV. In this paper, the sensitivity of the neutron spectrum in the PT to various operating conditions of a PHWR is evaluated. Sensitivity assessments have been completed on several parameters namely the coolant purity, coolant temperature, moderator purity, moderator temperature, and pressure tube diametral creep (PTDC). Since the deformations are inevitable, identifying parameters that have the greatest impact on the population of neutrons with energy greater than 1 MeV in the PTs would be important for fine-tuning the operational conditions which are conducive to reducing the rate of deformation. From this study, it is concluded that the coolant temperature and PTDC are the two variables having the most impact on the fast energy neutron population in the pressure tubes.

Infiltration and Evaporation in Multiplying Porous Media and Associated Criticality Phenomena

We describe the manner and rate at which water infiltrates and/or transpires into a drum of dry uranium dioxide powder. The powder is 5% enriched and so the possibility of a critical state is possible. In view of the porous nature of the powder, it will exhibit all the characteristics of soil and hence the motion of the water will be described by the use of the methods developed over many years in the field of soil science. The basic phenomena of flow in porous media are described by Richards’ equation, which leads to the moisture concentration from which we may obtain the local density of water. This, together with the fissile cross section of the powder, will enable us to calculate the multiplication rate of the neutron population. The neutron source term arises naturally from spontaneous fission and various reactions. Several scenarios are described, but the two most important cases are (1) when water enters the drum from the top and infiltrates downward, and (2) when water leaks in from the base and capillary forces draw the water upward. Both situations can occur simultaneously depending on the damage sustained by the drum. By damage we do not necessarily mean mechanical due to impact, but also by corrosion if the drum is left unattended in a damp environment. With the space and time dependence of the water concentration available, we can solve the corresponding transport or diffusion equations for the neutron flux and hence calculate the energy produced. In this introductory paper, we do not include feedback, and so in principle, when the water reaches the boiling point our calculations must cease. However, the crucial point is whether criticality will occur, and this can be decided by the value of the multiplication factor . We use the Broadbridge and White model for the porous medium and consider the influence of the porous structure on the value of . A range of examples is considered both with infiltration and transpiration, and it is shown that the likelihood of criticality is high although less likely for transpiration.

Simulation of two-point reactor kinetics model of reflected reactors with Newtonian reactivity feedback

In this study, a non-analog dynamic Monte Carlo method, named Point Kinetics Monte Carlo (PKMC), is developed to solve the one- and two-point reactor kinetic equations for a reflected reactor with six group of delayed neutron precursors with Newtonian reactivity feedback. Dynamic weight window technique is implemented to control neutron and precursor population during the simulation. Moreover, the Stochastic differential equations for Two-Point Reactor Kinetics Model (STPRKM) is developed to determine neutron and precursor population as a function of time. Since, the random fluctuations in the population dynamics carry very often as much information as the mean value, during the derivation of STPRKM, physical nature of the model problem and inherent probabilistic mechanisms are not altered. Using the developed methods, time dependent transient problems of reflected reactors are studied and mean responses and standard deviations determined by these methods are compared with each other and available deterministic results.

SERPENT CODE POINT KINETIC PARAMETERS ANALYSIS: A NEXUS FOR NIGERIA RESEARCH REACTOR – 1 CORE CONVERSION USING ENRICHED URANIUM DIOXIDE FUEL

The International Atomic Energy Agency (IAEA) requires that all test and research reactors operating on Higher Enriched Uranium (HEU) should be converted to Low Enriched Uranium (LEU) for safety and security purposes. Nigeria having a Miniature Neutron Source Reactor (MNSR) has been long interested in fuel technological research not just to develop the area but also to meet with resolution on the nuclear treaty set out by the global nuclear regulatory body. In this study, reactor kinetic parameters such as effective delayed neutron fractions, prompt neutron lifetime as well as mean neutron generation time were analysed for Nigerian Research Reactor-1 (NIRR-1). Serpent Monte Carlo code 1.17 is used in the analysis. For delayed neutron parameters determination, we used fission probability iteration under one averaged generation time and neutron population rate.The calculated values for delayed neutron were recorded as analogue prompt and implicit prompt neutron lifetime, reproduction time and emission time are in the order of 3×10-7 (s), in agreement with the calculated data from the nuclear data libraries and some literature.The result for delay neutron fraction and other time-based parameters support the fuel core conversion for NIRR-1.The computational and pictorial results obtained from Serpent code simulation described well the transient behavior of the delayed neutron in this reactor.The analytical results also spelled out the relevance and compatibility of low enriched uranium dioxide fuel over higher enriched type.The result of this study conforms with other results obtained from similar reactors but with different Monte Carlo codes and with higher enriched uranium

Single-step Monte Carlo criticality algorithm

A single-step Monte Carlo criticality algorithm is proposed to improve the efficiency of Monte Carlo criticality calculation. This algorithm adopts the strategy of increasing neutron population cycle by cycle and achieves the highest computational efficiency through a weighted technique and mathematical optimization analysis. The inactive cycles are no longer needed, and all neutron histories contribute to the final results, so the fission source's convergence diagnosis is no longer needed. The algorithm's effectiveness is demonstrated with a single-rod model, an infinite medium problem, and the VERA benchmark problem #5 using a modified RMC code.

Symmetry Groups of the Forward Master Equation for Stochastic Neutron Populations

In this work, we apply Lie Group Theory (LGT) to aid in solving and understanding equations arising from the Forward Master Equation formulation for the neutron number distribution in a zero-dimensional setting. In particular, we focus our LGT study on a first-order hyperbolic partial differential equation satisfied by the probability generating function. We show the connection between solutions to the symmetry determining equations with established analytical solutions given by Bell and by Prinja and Souto. We derive global transformations for isolated neutron fission chains as well as neutron sources and provide a physical interpretation of the results throughout.

Pulsed plasma rocket- developing a dynamic fission process for high specific impulse and high thrust propulsion

The Pulsed Plasma Rocket (PPR) is an advanced nuclear propulsion concept that uses a fission-based nuclear power system to rapidly cause a phase change in a fuel projectile from solid to plasma during a pulsed cycle. To create the plasma bursts that provide thrust, a highly moderated Low Enriched Uranium (LEU) projectile can be used in combination with an unmoderated LEU barrel to preferentially heat the projectile. A short section of High Enriched Uranium (HEU) at the barrel base, along with a novel control drum mechanism, allows for controlled and rapid neutron population growth to transition into a plasma state in a fraction of a second. The PPR concept is intended to provide fast transit to and from locations such as Mars, with the engine capable of providing 100,000 N of thrust and 5,000s of specific impulse.The pulsed plasma rocket is a revolutionary new technology that is much more efficient than traditional rocket engines. It creates a plasma field that can be used to generate thrust, allowing spacecraft to travel much faster and farther than traditional rockets. This technology is essential for future space exploration, as it will allow us to travel to other planets and moons in the solar system.

Improved evaluation of safeguards parameters from spent fuel measurements with the Differential Die-Away (DDA) instrument

The Differential Die-Away (DDA) technique is a highly sensitive non-destructive assay method for characterizing and detecting the presence of fissile material within an item of interest. DDA utilizes a series of pulses from a neutron generator (NG) to actively interrogate an item of interest. The die-away time of the neutron population induced by this active interrogation and the integral of the total differential die-away signal can be used to characterize items such as nuclear waste drums and spent nuclear fuel assemblies. Los Alamos National Laboratory (LANL) conceptualized, designed, and fabricated a DDA instrument that was deployed for field test measurements at the Central Interim Storage Facility for Spent Nuclear Fuel (Clab) in Oskarshamn, Sweden. The instrument performed multiple static measurements at fixed locations and dynamic axial scans of 15 pressurized water reactor (PWR) and 10 boiling water reactor (BWR) spent fuel assemblies, collecting both passive and active measurement data. The static assays of the assemblies measured the differential die-away signal, die-away time, and total passive neutron emission rate to create calibration curves for the evaluation of assembly multiplication, burnup, initial enrichment, effective fissile mass, and total elemental plutonium mass. Each calibration curve was optimized by minimizing the relative root mean square error (RRMSE) of assembly assay results compared to declared assembly parameters. The same quantities were also measured with the axial scans, and the resulting data were applied in two ways: (1) in the creation of calibration curves to improve evaluation of the same safeguards parameters as static assays, and (2) for comparison to simulation. In most cases, across both PWR and BWR assemblies, axial scan data improved the estimation of the above parameters, quantified by decreasing the calibration curve RRMSE. These axial scan results demonstrate the ability of the DDA instrument and analysis method to characterize spent PWR and BWR fuel as well as, or better than, a static assay of the same assembly. Furthermore, the DDA instrument’s unique ability to obtain both active and passive data in a single, axial scan of an entire spent fuel assembly represents a more efficient and accurate way of assaying spent fuel for verification purposes. These results represent a significant advancement for characterizing spent nuclear fuel compared to current technologies.

Validation of fast neutron reactors fertile blanket depletion calculations through the analysis of the DOUBLON experiment in Phenix with TRIPOLI-4® and DARWIN3-SFR

A reliable assessment of the final inventory in the fertile blanket of a Fast Neutron Reactor is an important issue for fuel cycle physics, as it impacts safety, reprocessing and design studies. The performances of fertile blankets neutronics calculations is a long standing issue, as there as specificities in these regions that are quite challenging, especially for depletion codes.The new CEA fuel depletion calculation package is DARWIN3-SFR, which incorporates the deterministic neutronics code APOLLO3® and the depletion module MENDEL. This paper details the validation of DARWIN3-SFR for fertile blanket calculations through the re-interpretation of the DOUBLON pin-irradiation in the Phenix reactor.During this irradiation, nine pins are studied through isotopic ratios, which give us information about the depletion and, indirectly, the neutron flux calculations inside the blanket. This environment is especially challenging for neutronics codes, since there is a strong variation of the neutron energy and population over a short distance. Our recent analysis of TRAPU - which is a similar experiment, but in the core center - has proven DARWIN3-SFR to be reliable for the fuel depletion calculations of fissile subassemblies; nevertheless, its performances in the fertile blankets still require validation.We observe that, once the calculated neutron flux level has been adjusted to the experiment through the 148Nd/238U ratio, DARWIN3-SFR provides results similar to the reference stochastic code TRIPOLI-4®. However, both codes have difficulties to reproduce some of the measured isotopic ratios inside the fertile blanket. Whilst DARWIN3-SFR produces identical results for most of the isotopes analysed (234U, 235U, 236U, 238Pu, 239Pu, 240Pu), variations of the neutron spectrum lead to some disparities for the production of 241Pu and 242Pu. Indeed, the low-energy flux estimation is higher with TRIPOLI-4® than with DARWIN3-SFR in the energy range where the 240Pu has a high capture cross section, which increases the calculated production of 241Pu and 242Pu.DARWIN3-SFR and its predecessor DARWIN-2 are efficient at calculating the average neutron flux level over the entire fertile blanket. However, the results of the two codes show a strong pin-to-pin dispersion, resulting in a different shape of the neutron flux inside the blanket. With DARWIN3-SFR, the estimated neutron spectrum is softer than in DARWIN-2, which impacts the 238U capture and fission reaction rates and hence the production of plutonium.

An adjoint sensitivity analysis of the Telegrapher’s neutron kinetic equations

The work presented herein is an approach to the kinetic uncertainty analysis of the Telegrapher’s neutron kinetic equations. The adjoint sensitivity analysis framework has been resorted to meet this end. Burnup induced uncertainty in the value of the delayed neutron fraction is addressed and its impact on the neutron population (as an observable quantity by the way of flux detectors) is investigated. Results compared against those obtained through an exact forward analysis approach confirm quite satisfactory accuracy of the proposed variational method. The effect of relaxation time on the adjoint system dynamics is moreover explored.

Modification of a Dynamic Monte Carlo Technique to Simplify and Accelerate Transient Analysis with Feedback

In this paper, a simpler approach compared to the existing approaches is developed to analyze nuclear reactor dynamics based on the explicit Monte Carlo method. A new population control method is also introduced to prevent neutron population growth and consequent computer memory shortages, which also increases simulation speed. The scheme is applied for time-dependent particle tracking in three-dimensional arbitrary geometries in the presence of feedbacks through a code named MCSP-Explicit. Changes in material density, as well as geometry dimensions, are also considered during simulation. MCSP-Explicit can be run with either continuous or multigroup data libraries, and it is further boosted by parallel processing to speed up simulations. A number of benchmark problems are studied at the end to evaluate the performance of the proposed approach in various situations.

Calculation of kinetic parameters βeff and Λ with modified open source Monte Carlo code OpenMC(TD)

This work presents the methodology used to expand the capabilities of the Monte Carlo code OpenMC for the calculation of reactor kinetic parameters: effective delayed neutron fraction βeff and neutron generation time Λ. The modified code, OpenMC(Time-Dependent) or OpenMC(TD), was then used to calculate the effective delayed neutron fraction by using the prompt method, while the neutron generation time was estimated using the pulsed method, fitting Λ to the decay of the neutron population. OpenMC(TD) is intended to serve as an alternative for the estimation of kinetic parameters when licensed codes are not available. The results obtained are compared to experimental data and MCNP calculated values for 18 benchmark configurations.

Comparison of probabilistic and deterministic methods for calculation of kinetic parameters of HWZPR

The accurate calculation of kinetic parameters, including the effective delayed neutron fraction and the neutron mean generation time, is very important in the study of time dependent neutron population behavior. To calculate these parameters, it is necessary to calculate the flux and adjoint flux in the phase space. In this paper, the kinetic parameters of the new core configuration of the heavy water zero power reactor (HWZPR) are calculated using two deterministic and probabilistic methods. The quantitative and qualitative discussion is presented to illustrate the advantages and disadvantages of each method. The maximum difference between the two accounting methods was less than 3%. The effect of different energy structures on the criticality and kinetic parameters has been investigated in the deterministic approach. Additionally, the calculated kinetic parameters of the HWZPR validated experimentally with a reactivity inject response. Good consistency has been observed between different methods of computation and experimental values.