Neutron Groups Research Articles

Investigation of breakup process in 9Be(α,n)12C reaction

Neutron energies and angular distributions were measured in 9Be(α,n)12C reaction for α energies of 5.5 and 6.5 MeV. Three major neutron groups were observed in the spectrum, which correspond to the ground and first two excited states of 12C. Measured data could only be explained by the TALYS calculation if reaction at more than one location within the target is considered for a given beam energy. The preferred locations are driven by the resonance energy levels existing in 13C. Neutron yield due to the 9Be breakup process was determined which is found to be 12.6 ± 0.2% and 18.4 ± 0.5% of the total reaction cross-section for 5.5 and 6.5 MeV respectively.

A computational- experimental model of reactor kinetic for investigating the linearity response of in-core neutron detectors of a low power research reactor

In this study, the linear response of fission chamber (FC) neutron detectors in Isfahan miniature neutron source reactor (MNSR) is investigated through experiments and calculations at different powers of the reactor. The linearity of the response of the main neutron detector in the MNSR is important due to its safety functions in reactor power control. Additionally, determining the linear response region of this detector presents a linear neutron dosimetry field even outside of the reactor core, i.e. at the outlet of external beam tubes. Moreover, it is very difficult to remove and calibrate this neutron detector that has been installed in the reactor core for a long time. For this purpose, an alternative method for measuring the linearity of the response of a neutron detector is extended by investigating the kinetic behavior of reactor. The aim of this method is to calculate the delayed neutrons population in the reactor core and compare with the FC detector response. In this method, the numerical solution method is used to solve the point kinetic equation with 15 delayed neutron groups (6 delayed neutron groups and 9 photo-neutron groups) after inserting a large negative reactivity into the MNSR core by considering temperature and xenon reactivity feedbacks during a coupling procedure. To obtain the xenon reactivity feedback, xenon concentration is calculated by coupling the 135Xe and 135I production equations and the εpPFnlPTnl parameter is obtained by an experimental method. Furthermore, the value of fission cross section (Σf) is calculated using a validated model in the Dragon code. The large reactivities are inserted at two initial power of 150 W and 30 kW to investigate the response of the main FC neutron detector in a cold xenon-free condition and by considering temperature and xenon reactivity feedbacks, respectively. The results demonstrate that the response of the MNSR FC detector is linear in the neutron flux range between 5 × 107 to 1 × 1012 n.cm−2.s−1, which is equivalent to reactor power of 1.5 W to 30 kW. This innovative method can be applied to calibrate the neutron detectors in other research and power reactors.

Photonuclear reaction in 67Zn

Mono-energetic [Formula: see text]-beams ([Formula: see text][Formula: see text]eV) based on thermal neutron capture, in a nuclear reactor, using the Mn([Formula: see text]) reaction were utilized for generating a fast neutron source from Zinc, via the [Formula: see text]Zn([Formula: see text]) reaction. One of the incident [Formula: see text]-lines of the Mn source at [Formula: see text][Formula: see text]keV, photoexcites by chance a resonance level in [Formula: see text]Zn, with subsequent emission of neutrons at an energy of 191[Formula: see text]keV. The cross-section for this process was measured and found to be [Formula: see text][Formula: see text]mb with an intensity of the order of 104[Formula: see text]n/s. The angular distribution of the 191[Formula: see text]keV neutron group was also measured.

A Digital Controller for Reactivity Monitoring and Power Control

This paper introduces a controller unit for reactivity monitoring and automatic power control that was designed and constructed for the 500 kW Dalat Nuclear Research Reactor (DNRR). For power control and reactivity calculations, frequency signals from neutron measurement channels of starting and working ranges of the reactor are used. Two abovementioned independent functions were combined in an Artix-7 FPGA board for determining reactivity values by solving the point reactor kinetics equations with six delayed neutron groups and for stabilizing the reactor power at preset levels by determining the unbalance voltage signal to control the automatic control rod. With real-time calculations, the newly developed controller can monitor the reactor reactivity and control the reactor power online. The developed controller unit’s reactivity measuring and power stabilizing capabilities were assessed using the DNRR in normal operation and assumed emergency conditions and compared with those of the preexisting imported BNO-102R1 module of the DNRR control and protection system, known as ASUZ-14R. The results of the experiments show that the produced FPGA-based unit and the BNO-102R1 unit have the same technical characteristics and features, with the disparities being less than 5% and 1%, respectively, in reactivity measurement and power stabilization. The experimental data of reactivity measurements by the FPGA-based unit and the calculation results were also compared and found that the relative deviations between those are also less than 10%. The developed controller unit is capable of carrying out a variety of training and operational experiments on the DNRR.

A Novel Scheme of the ARA Transform for Solving Systems of Partial Fractional Differential Equations

In this article, a new analytical scheme of the ARA transform is introduced to solve systems of fractional partial differential equations. The principle of the proposed technique is based on combining the ARA transform with the residual power series method to create an approximate series solution for a system of partial differential equations of fractional order on the form of a rapid convergent series. To illustrate the effectiveness, accuracy, and validity of the suggested technique, an Attractive physical system, the fractional neutron diffusion equation with one delayed neutrons group, is discussed and solved. Two different neutron flux initial conditions are presented numerically to clarify various cases in order to ensure the theoretical results. The necessary Mathematica codes are run using vital nuclear reactor cross-section data, and the results for various values of time are tabulated and graphically represented.

Backstepping based model reference adaptive control for nuclear reactor with matched and unmatched uncertainties

In this work, a Backstepping Model Reference Adaptive Controller (BMRAC) is designed to control the total power of a Pressurized Water Reactor (PWR). It ensures robustness against matched and unmatched parameter uncertainties and disturbances. Reactor core dynamics based on normalized point kinetics equations with six delayed neutron groups is considered, while parametric variations in thermal feedback coefficients, control rod worth and heat transfer coefficients are considered as uncertainties. Reactivity disturbance is considered as unmatched disturbance and external disturbances that enter from control input are considered as matched disturbance. A stable reference model is designed using linear quadratic regulator (LQR) theory to generate setpoints for reactor power control. The disturbances and uncertainties are estimated by comparing reactor dynamics with a stable predictor model. Matched parameter uncertainties and disturbances are compensated with robust MRAC. To compensate for unmatched disturbance, an integrator backstepping is designed. Projection-based adaptive laws are used to provide robustness to the designed controller. The ultimate boundedness of all signals is verified through Lyapunov analysis. Efficiency of the proposed controller is demonstrated through simulation studies, controller performance is compared with conventional LQR controller and adaptive MRAC controller.

Evaluation of delayed neutron yields and time spectra from photofission of 238U induced by Bremsstrahlung photons below 9 MeV

Few data exist regarding the yields and time spectra of delayed neutrons from the photofission reaction on actinides. In this paper, we report the characteristics of both six-group and eight-group delayed neutron time models for the photofission of 238U induced by a Bremsstrahlung photon spectrum with an end-point energy at 9 MeV. This study was conducted using a 9 MeV linear electron accelerator housed at the SAPHIR platform located at CEA Paris-Saclay, France. A reference sample of depleted uranium was positioned inside a neutron detection block, previously designed and optimized by Monte Carlo simulation, made of high-density polyethylene covered by cadmium and including ten one meter-long 3He proportional counters. Based on the consistent set of half-lives proposed by Spriggs et al. as early as 1999 for neutroninduced fission, our description in eight delayed neutron groups for 238U at 9 MeV is the first published for photofission. These new results bring valuable information to the scarce data available in the literature and represent useful inputs for the development of photofission-based nuclear measurement systems as they meet a significant interest in the fields of nuclear data, radioactive waste package characterization and for security-related applications.

Analytical solutions to the coupled fractional neutron diffusion equations with delayed neutrons system using Laplace transform method

<abstract> <p>The neutron diffusion equation (NDE) is one of the most important partial differential equations (PDEs), to describe the neutron behavior in nuclear reactors and many physical phenomena. In this paper, we reformulate this problem via Caputo fractional derivative with integer-order initial conditions, whose physical meanings, in this case, are very evident by describing the whole-time domain of physical processing. The main aim of this work is to present the analytical exact solutions to the fractional neutron diffusion equation (F-NDE) with one delayed neutrons group using the Laplace transform (LT) in the sense of the Caputo operator. Moreover, the poles and residues of this problem are discussed and determined. To show the accuracy, efficiency, and applicability of our proposed technique, some numerical comparisons and graphical results for neutron flux simulations are given and tested at different values of time $ t $ and order $ \alpha $ which includes the exact solutions (when $ \alpha = 1). $ Finally, Mathematica software (Version 12) was used in this work to calculate the numerical quantities.</p> </abstract>

Beta-Ray-Bremsstrahlung Contributions to Short-Lived Delayed Photoneutron Groups in Heavy Water Reactors

Hard bremsstrahlung produced during the deceleration of fission-product beta rays in nuclear fuel is proposed as a source of delayed photoneutrons (PNs) in heavy water reactors. Electron Gamma Shower (EGS5) code simulations of coupled electron-photon transport in seven fuel element geometries immersed in an infinite heavy water medium confirm high-energy beta rays produce sufficient bremsstrahlung yields with photon energies greater than the D(γ,n)1H reaction threshold such that the beta-ray contribution to an isotopic PN yield can be comparable to or greater than yields from hard gamma rays emitted during the isomeric transition of the daughter, especially for some short-lived fission products with high-intensity direct-to-ground-state beta transitions where the beta ray and antineutrino carry away the majority of the Q-value. Some fission products that do not have hard gamma rays in their decay schemes are in fact PN precursors due to the beta-ray-bremsstrahlung contribution. The lack of evaluated nuclear data for many short-lived fission products, data reliability issues of fission products with decay scheme data, cross-section library effects, and possible decay-chain/parent-feeding phenomenon are affecting the accuracy of PN group parameters derived from a small number of legacy experiments. The reanalysis of two legacy PN experiments supports the existence of a very-short-lived direct-delayed neutron group.

Neutron Mean Free Path in the Slab Reactor Core using One-Dimensional Multi-group Diffusion Equation

Analysis of the neutron mean free path in the slab reactor core has been carried out using one-dimensional multi-group diffusion equation. This study aims to determine the neutron mean free path in the slab reactor core with the neutron diffusion coefficient calculation using macroscopic cross-section data in the nuclear fuel cell level and the neutron flux distribution. The type of reactor used in this research is a fast reactor with nuclear fuel is uranium-plutonium nitride (U-PuN). The neutron mean free path is calculated for 70 energy groups of neutron by dividing the energy groups, namely the fast energy group, the intermediate energy group and the thermal energy group. The results showed that the neutron mean free path value for U-235 and Pu-239 fuels were obtained almost the same in all energy groups, namely in the fast energy group ranging from 0.11.10-2 to 0.17.10-2 cm, in the intermediate energy group 0.16.10-2 to 1.78.10-2 cm, and in the thermal energy group 0.4.0-2 to 8.04.10-2 cm. The neutron mean free path value for U-238 fuel is much smaller than that for U-235 and Pu-239 fuel, ranging from 0.03.10-2 to 0.36.10-2 cm. These results can be confirmed, because U-238 fuel is a fertile material. Keywords: Neutron mean free path, diffusion equation, neutron flux, slab reactor core

Guidelines for collaborative development of sustainable data treatment software

Software development for data reduction and analysis at large research facilities is increasingly professionalized, and internationally coordinated. To foster software quality and sustainability, and to facilitate collaboration, representatives from software groups of European neutron and muon facilities have agreed on a set of guidelines for development practices, infrastructure, and functional and non-functional product properties. These guidelines have been derived from actual practices in software projects from the EU funded consortium ‘Science and Innovation with Neutrons in Europe in 2020’ (SINE2020), and have been enriched through extensive literature review. Besides guiding the work of the professional software engineers in our computing groups, we hope to influence scientists who are willing to contribute their own data treatment software to our community. Moreover, this work may also provide inspiration to scientific software development beyond the neutron and muon field.

On development of in-core fuel system for PWR reactors: Part I generation of macroscopic cross sections using SCALE 6.0 for use in nodal calculation

This work presents the description of the first part of a methodology applied to perform In-Core Fuel Management (ICFM) in Pressurized Water Reactor (PWR). The ICFM of a PWR reactor consists on defining the best charging or recharging pattern of fuel assemblies inside a reactor for an operational cycle. This means, finding a suitable arrangement of fuel assemblies that optimizes the performance of the reactor, which complies with all safety criteria. Genetic algorithms (GAs) are used to select the arrangements that interact with the reactor physics simulation code, holding the neutron characteristics of each fuel assembly. Therefore, a reliable and fast code was developed accordingly. The consolidated technique of coarse mesh node code that numerically solves the multigroup diffusion equation for two groups of energy, fast and thermal neutrons, in two dimensions was selected. In this type of code, it is essential that each fuel assembly is homogenized and characterized by its macroscopic cross sections, for each reactor’s burnup condition. The cross sections are generated with the support of SCALE 6.0, computational platform developed by the Reactor and Nuclear Systems Division (RNSD), from the Oak Ridge National Laboratory (ORNL). The completeness of the qualification and validation of the results obtained from the homogenization of the fuel assembly by the SCALE was performed comparing the results with actual data of a benchmark reactor. The fully documented Almaraz Nuclear Power Plant provided by the International Atomic Energy Agency (IAEA)-TECDOC-815, has been used as benchmark with successful results.

Optimized fractional-order PID controller based on nonlinear point kinetic model for VVER-1000 reactor

Abstract Nuclear reactor dynamics are nonlinear and time-varying, so the power level control is a challenging problem in nuclear power plants (NPPs) to ensure both its operation stability and efficiency. An important measure to improve the safety of the reactor core of NPP is the implementation of robust control for the core by adjusting the inserted reactivity of the control rods. Thus in the present paper, fractional-order PID (FOPID) controller is developed as it is well known for its simplicity and robustness against disturbances. A Genetic Algorithm (GA) is used to determine FOPID controller parameters to achieve the desired power level for the generation III+ reactor VVER-1000. Implementing the GA, a suitable objective function is proposed to search for the optimal FOPID parameters. The nonlinear model of the VVER-1000 nuclear reactor is presented based on the point kinetic equations with six delayed neutron groups and temperature feedback from lumped fuel and coolant temperatures. Two cases for the VVER-1000 reactor are investigated; the changes in the power loads and the control rod withdrawal that leads to reactivity disturbance. Moreover, the uncertainties that result from model parameters perturbation are added to examine the controller robustness. The simulation results show that the proposed optimized FOPID controller can track the desired power level of the VVER-1000 reactor and robustly cope with any load changes, disturbances, or any parameters uncertainties. Also, it proves the superiority of the proposed optimized FOPID controller over other PID controllers in ensuring the safe and effective operation of the VVER-1000 reactor.

Experimental Studies of Radiation-Protective Properties of a Modified Titanium Hydride

The results of experimental studies of the protective properties of titanium hydride with respect to neutron and gamma radiation in order to determine the optimal conditions for their use in the composition of the structural radiation protection of the nuclear reactor are presented. The weakening of the basic functionals in the thickness of protection, including the density of fast, intermediate and thermal neutrons, and the dose rate of gamma radiation is established. The functions of weakening the density of neutron flow and the dose rate of gamma radiation are measured in the conditions of "barrier" geometry. Determination of the protective properties of the structure was carried out when the modified titanium hydride fraction was placed in aluminum containers with a filling coefficient of a volume of container 0.63. The relaxation lengths for all neutron groups are close and on average are 9.8 cm. The functions of weakening the dose rate of gamma radiation of point sources Cs-137 and Co-60 are exponential. The weakening of radiation occurs with a constant relaxation length. For energy 0.661 MeV, the relaxation length is 7.1 cm, for energy 1.25 MeV, the relaxation length is equal to 10.1 cm. On the basis of the experimental studies, the high efficiency of the modified fraction of titanium hydride was confirmed during its use in protecting nuclear power plants.

Measurement of the spatial-energy distribution of neutrons in the irradiation channel of the critical facility

One of the basic installations of the Republican State Enterprise “Institute of Nuclear Physics” of the Ministry of Energy of the Republic of Kazakhstan is a critical assembly, which is a zero-power reactor. Desalinated water and beryllium serve as moderators and neutrons reflectors. The energy spectrum of neutrons in the core is thermal. The main purpose and area of application is the modeling and study of the neutronic characteristics of the cores of water-moderated research reactors of various types.The paper presents the results of experimental measurements of the spatial-energy distribution of neutrons in the dry, central channel of the critical assembly. Measurements of the neutron flux were carried out using activation foils for three energy groups of neutrons: thermal, epithermal, and fast.The measured thermal neutrons flux in the irradiation channel is ~ 3·108 cm‒2s‒1, and fast neutrons flux (with energies above 0.7 MeV) is ~ 8·108 cm‒2s‒1. The fraction of thermal neutrons in the integral flux was 0.23%, and the fraction of fast neutrons was 0.62%. In the axial distribution of thermal and fast neutrons, the maximum value of the neutron flux is 50 mm below the midplane of the core.

Adaptive second-order nonsingular terminal sliding mode power-level control for nuclear power plants

This paper focuses on the power-level control of nuclear power plants (NPPs) in the presence of lumped disturbances. An adaptive second-order nonsingular terminal sliding mode control (ASONTSMC) scheme is proposed by resorting to the second-order nonsingular terminal sliding mode. The pre-existing mathematical model of the nuclear reactor system is firstly described based on point-reactor kinetics equations with six delayed neutron groups. Then, a second-order sliding mode control approach is proposed by integrating a proportional-derivative sliding mode (PDSM) manifold with a nonsingular terminal sliding mode (NTSM) manifold. An adaptive mechanism is designed to estimate the unknown upper bound of a lumped uncertain term that is composed of lumped disturbances and system states real-timely. The estimated values are then added to the controller, resulting in the control system capable of compensating the adverse effects of the lumped disturbances efficiently. Since the sign function is contained in the first time derivative of the real control law, the continuous input signal is obtained after integration so that the chattering effects of the conventional sliding mode control are suppressed. The robust stability of the overall control system is demonstrated through Lyapunov stability theory. Finally, the proposed control scheme is validated through simulations and comparisons with a proportional-integral-derivative (PID) controller, a super twisting sliding mode controller (STSMC), and a disturbance observer-based adaptive sliding mode controller (DO-ASMC).

Power control of CiADS core with the intensity of the proton beam

This paper reports the control method for the core power of the China initiative Accelerator Driven System (CiADS) facility. In the CiADS facility, an intense external neutron source provided by a proton accelerator coupled to a spallation target is used to drive a sub-critical reactor. Without any control rod inside the sub-critical reactor, the core power is controlled by adjusting the proton beam intensity. In order to continuously change the beam intensity, an adjustable aperture is considered to be used at the Low Energy Beam Transport (LEBT) line of the accelerator. The aperture size is adjusted based on the Proportional Integral Derivative (PID) controllers, by comparing either the setting beam intensity or the setting core power with the measured value. To evaluate the proposed control method, a CiADS core model is built based on the point reactor kinetics model with six delayed neutron groups. The simulations based on the CiADS core model have indicated that the core power can be controlled stably by adjusting the aperture size. The response time in the adjustment of the core power depends mainly on the adjustment time of the beam intensity.

ФИЛЬТР КАЛЬМАНА В ЗАДАЧЕ ОЦЕНКИ 8-ГРУППОВЫХ СПЕКТРОВ ЗАПАЗДЫВАЮЩИХ НЕЙТРОНОВ ПРИ ДЕЛЕНИИ 235U ТЕПЛОВЫМИ НЕЙТРОНАМИ

In the present work the estimation of the 8-group delayed neutron energy spectra emitted in the fission of 235U by thermal neutrons have been done. Aggregate delayed neutron spectra that were measured with high resolution in the different time intervals after the thermal neutron irradiation of the 235U sample presented in the IAEA reference database for beta-delayed neutron emission have been used for the estimation process. Due to the lack of the uncertainties for the spectra presented in this database and the necessity of this data in the process of estimation of delayed neutron group spectra at first the estimation of uncertainties of these spectra have been done. In the estimation process the following components of uncertainty have been considered: statistical; the component due to the neutron background; component due to the distinctive features of neutron spectra restoration process measured using spectrometer filled by helium-3 and also the component appearing due to introduction of the correction on the distortion of the neutron spectra as a result of passing through the lead sheilding. Estimation of spectra have been made using the technique based on the Kalman filter that allows to take into account the uncertainties of the input data. Estimation results are shown in the numerical and graphic form.

Calculation and experimental analysis of benchmark experiments with a fast neutron spectrum and models of sodium and lead cooled fast reactors using different evaluated nuclear data libraries

The paper presents the results of a comparative analysis of criticality calculations using a Monte-Carlo code with the BNAB-93 and BNAB-RF neutron group constants, as well as with evaluated neutron data files from the Russian ROSFOND evaluated nuclear data library and other evaluated nuclear data libraries (ENDF, JEFF, JENDL) from different years. A set of integral experiments on BFS critical assemblies carried out in different years at the Institute of Physics and Power Engineering (60 different critical configurations) was analyzed. The considered integral experiments are included in the database of evaluated experimental neutronic data used to justify the neutronic performance of sodium and lead cooled fast reactors, to verify codes and nuclear data as well as to estimate uncertainties in neutronic parameters due to the nuclear data uncertainties. It has been shown that the ROSFOND evaluated nuclear data library is a library that minimizes the calculation and experimental discrepancies for the considered set of integral experiments. The paper also presents the results of criticality calculations for models of sodium and lead cooled fast reactors based on different evaluated neutron data libraries and provides estimates for the uncertainty in criticality associated with nuclear data.

Optimization algorithms based on contribution theory for broad-group energy structures in shielding calculation

To solve the Boltzmann transport equation, the discrete ordinates method was applied using multi-group cross-sections, the accuracy of which affects markedly the transport calculation. For large shielding models, using fine-group cross-sections directly in the transport calculation is inefficient. Subsequently, the multi-group cross-section generation code ARES-MACXS utilized contribution theory in selecting a broad-group structure to meet calculational requirements of engineering shielding. For different computational problems, the ARES-MACXS code generates different optimal broad-group structures and corresponding multi-group working cross-sections. The numerical results indicate that, compared with the BUGLE-B7 broad-group structure, using these optimal broad-group structures may yield transport calculation results of higher accuracy with fewer groups. On the basis of a comprehensive analysis of different shielding calculation problems, ARES-60 broad-group structure with 46 groups of neutrons, 14 groups of photons is proposed, which is suitable for AP1000 shielding calculations and other similar PWR shielding calculations.