Neutron Flux Research Articles

Development of diamond detector as fast neutron spectroscopy in the EAST tokamak

We report in this paper the development of the single crystal diamond detector as a fast neutron spectroscopy in the EAST tokamak. The diamond detector is used to detect the fast neutron directly without any neutron converter during the deuterium-deuterium fusion experiment, then the neutron energy spectrum is reconstructed from the recorded continuous scattered spectrum by using a deconvolution algorithm. The results indicate the capability of the diamond spectroscopy which can be used directly to monitor the fast neutron flux and energy spectrum in the EAST tokamak.

Diamond based neutron detector in high temperature environments of 200 °C

The stability of the neutron response function and the detection efficiency of a sCVD diamond detector in the temperature range up to 200 °C are demonstrated in this paper. A CIVIDEC neutron detector was simultaneously heated with an AmBe neutron source. This enabled the measurement of the spectrum of the deposited energy in the diamond sensor, i.e. the neutron response function of the detector and the detection rate, which in combination represents the neutron flux as a function of temperature. The measured temperature stability of the neutron response function of the detector and detection rate demonstrates the suitability of sCVD diamond detectors for harsh environments, such as encountered in geodetic applications and nuclear fusion research.

Study of circulating liquid fuel in a 1D critical system with thermal feedback

This research focuses on the description and modeling of a one-dimensional molten salt reactor (MSR), in the presence of thermal feedback. Following the example of previous works, a simple one-dimensional system is proposed, describing a molten salt reactor with a main neutron-multiplying zone called core and a recirculation loop where the salt cools down. Specific attention is paid to the precursors’ drift by modifying the neutron balance equation. Liquid nuclear fuels are characterized by a high volumetric expansion coefficient in comparison to customary solid fuels. Therefore, a strong coupling between neutronics and thermal-hydraulics is expected. As a consequence, a highly negative density coefficient characterizes the thermal feedback on the neutron reactivity. The precursor equation is here inverted analytically and combined with the neutron balance equation to obtain a generalized eigenvalue problem with the neutron flux distribution as the unknown. The balance equations are derived by finite volume integration over a discretized mesh, and the coupling between the two physical models is treated by Picard iterations. The numerical solution is finally extended to time-dependent calculations and compared to an analytical work for a one-dimensional circulating fuel reactor already existing in the literature.

Flux distribution tallies using proper orthogonal decomposition in Monte Carlo calculations

ABSTRACT In this paper, a new tallying method for a neutron flux distribution using the proper orthogonal decomposition is proposed for dimensionality reduction. The target spatial flux distribution is expanded by orthogonal basis vectors. Expansion coefficients are tallied during the random walk of the Monte Carlo calculation. The orthogonal basis vectors are extracted from the pre-calculated snapshots by the singular value decomposition. The proposed method is verified in the multi-group Monte Carlo calculation with the one-dimensional heterogeneous whole core geometry as a feasibility study. The flux distribution for each of the assemblies and energy groups is expanded by the basis vectors. The fewer basis vectors obtained from snapshots can reconstruct the target distribution well compared with the conventional Legendre polynomials used in the functional expansion tallies. The dimension of the solution in the proposed method is reduced by a factor of twenty compared with the conventional cell tally. In addition, the statistical error is reduced through dimensionality reduction thanks to the methodological feature of the proposed method. The results indicate that the proposed method has the capability of dimensionality reduction to tally the finely discretized flux distribution.

Критичність паливовмісних матеріалів в об'єкті "Укриття"

The article presents the results of the analysis of the validity of simplifications and assumptions accepted by researchers in the models of neutron-physical characteristics of fuel-containing materials (FCM) in the "Shelter" object (SO). The analysis and substantiation of the FCM nuclear safety will be one of the important issues during the SO operation for a long time, until the moment of retrieval and disposal of nuclear materials from the ChNPP Unit 4 destroyed in 1986. A significant number of nuclear materials in the SO are uncontrolled, and the geometry of their location is also little known. Therefore, the use of traditional methods of nuclear safety analysis to determine the conditions for reaching criticality in the volume of FCM can lead to significant uncertainties, depending on the assumptions and simplifications made in FCM models. In contrast to traditional nuclear facilities with design characteristics and control systems, there is no possibility to deterministically influence the FCM, and accordingly to determine their dynamic characteristics in the SO. In such conditions, it is necessary to take a responsible approach to obtain and interpret the values of FCM parameters by control systems of the SO. For example, in 1990, one of the neutron flux detectors recorded an abnormal change in the neutron pulse count rate for about 100 hours. This event is often called a “neutron incident”, and it formed the basis of some models, in which the possibility of reaching criticality in one of the FCM clusters is assumed. The article presents the results of the study on the physical possibility of the anomalous event in 1990, as well as the results of the analysis of simplifications and assumptions made in models of FCM criticality. An important result of the conducted research is the justification of the need to include in the FCM criticality model the effects of reactivity on fuel and water temperature, as well as to take into account delayed neutrons.

Neutron emission from a source moving in a gravitational field

This work is devoted to the problem of neutron field formation near elliptical orbits of space objects equipped with nuclear power plants. The high-energy part of the fission spectrum is not affected by the gravitational field. Radiation safety is ensured by the triad fair for a point source: activity-distance-time. The connection between space object orbit parameters and neutron flux density occurs for the thermal (near-thermal) part of the spectrum. The possibility of formation of a stable neutron trace in the volume of a «torus» around the orbit of a space object is considered. The paper presents theoretical and numerical evidence of the validity of the hypothesis put forward. The introduction considers the separation effect of Galileo's relativity principle in the case of rectilinear uniform motion of a point isotropic neutron source on a plane. The occurrence of angular asymmetry of the neutron distribution in a stationary coordinate system when their relative velocity is close to the transport velocity of the source is illustrated. Under these conditions, a significant velocity dispersion of initially monochromatic neutrons is also recorded. This expected fundamental kinematic effect determines the characteristic distribution of neutrons in the gravitational field when the source moves along the Kepler orbit. The solution of the problem is carried out in the velocity space. It is argued that if the distribution of neutrons in the velocity space is such that their velocities are collinear to the orbital velocity of the source, this indicates the existence of a neutron flux near the orbit. The problem is analysed on the example of one revolution of a hypothetical space station by simulation modelling. For this purpose, thermal neutron packets with isotropic angular distribution were generated at eight points of an elliptical orbit. The neutron and source velocity fluxes at the selected points of the orbit were compared in a coordinate system related to the earth. The obtained data made it possible to calculate the densities of neutron velocity fluxes to the front and rear hemispheres relative to the source orbital motion as a function of the polar angle, while the value of the determinant of the correlation matrix – an indicator of collinearity of neutron velocity vectors in the flux - was fixed. The results of the studies confirm the hypothesis put forward about the possibility of formation of a «trace» in the orbit of a thermal neutron source, which determines the need to take it into account as a significant component of radiation risk.

Using ANN for thermal neutron shield designing for BNCT treatment room

Occupational radiation protection should be applied to the design of treatment rooms for various radiation therapy techniques, including BNCT, where escaping particles from the beam port of the beam shaping assembly (BSA) may reach the walls or penetrate through the entrance door. The focus of the present study is to design an alternative shielding material, other than the conventional material of lead, that can be considered as the material used in the door and be able to effectively absorb the BSA neutrons which have slowed down to the thermal energy range of <1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$< 1$$\\end{document} eV after passing through the walls and the maze of the room. To this aim, a thermal neutron shield, composed of polymer composite and polyethylene, has been simulated using the Geant4 Monte Carlo code. The neutron flux and dose values were predicted using an artificial neural network (ANN), eliminating the need for time-consuming Monte Carlo simulations in all possible suggestions. Additionally, this technique enables simultaneous optimization of the parameters involved, which is more effective than the traditional sequential and separate optimization process. The results indicated that the optimized shielding material, chosen through ANN calculations that determined the appropriate thickness and weight percent of its compositions, can decrease the dose behind the door to lower than the allowable limit for occupational exposure. The stability of ANN was tested by considering uncertainties with the Gaussian distributions of random numbers to the testing data. The results are promising as they indicate that ANNs could be used as a reliable tool for accurately predicting the dosimetric results, providing a drastically powerful alternative approach to the time-consuming Monte Carlo simulations.

Gold content determination in small core-samples by instrumental neutron activation analysis

Application of instrumental neutron activation analysis (INAA) based on the relative method of concentration standardization was considered to determine Au content in small solid core-samples of the gold-bearing ores and rocks up to 10 g of the mass. The small core-samples about 10 mm in diameter and 22-23 mm in length were cut from the previously collected ore lumps or in-situ using a handheld drilling rig. The studied small core-samples and the polyethylene capsules of the same dimensions filled up with the corresponding certified reference material (CRM) were irradiated for 2 min by a lower density neutron flux with the help of the automated pneumatic transport system (PTS). Maximum mass and dimensions of the core-samples corresponded to the PTS design and to the conditions of its safe operation. A special device was made to fix the transport capsules in the stable counting geometry making possible to eliminate the influence of the neutron flux gradient during irradiation. Due to the substantial differences in CRM and solid sample densities, corrections for neutron self-shielding and for gamma-ray self-absorption by the core-samples were applied. The method was tried to analyze Au content in 170 small core-samples presenting different gold-bearing ores and country rocks from the Kazakhstan’s gold-barite-polymetallic deposit Maikain. This approach, rather simple methodically and requiring no unique equipment, can be used to assess gold resources together with the methods of geostatistics.

Verification of Adjoint Solution Commutativity with the New OpenNode Nodal Diffusion Code

This paper presents in-depth exploration and verification of the OpenNode nodal diffusion code, a robust tool designed for multigroup neutron diffusion simulations under steady-state conditions. Leveraging the Nodal Expansion Method with a quartic polynomial and moments weighting method, OpenNode demonstrates exceptional accuracy in approximating nodal surface fluxes, further enhanced by the Quadratic Transverse Leakage approximation. The critical concept of commutativity between adjoint and forward solutions is thoroughly investigated, serving as a benchmark for the code’s reliability in predicting system responses, determining single-point reactor kinetics parameters, and facilitating perturbation analyses. The paper meticulously details OpenNode’s methodology for adjoint neutron flux computation, unraveling its rigorous approach through transposition operations and intricate mathematical transformations. Noteworthy features, including support for second and fourth polynomial orders; versatile computation modes; different mesh points; and seamless integration with Python, PyQt5, and Blender, underscore OpenNode’s adaptability. Results from comprehensive analysis of the two-dimensional and three-dimensional International Atomic Energy Agency core benchmark problem showcase OpenNode’s prowess. The code excels in reactor geometry visualizations, benchmark parameters, and neutronic analysis, with a particular emphasis on commutativity verification against various benchmarked codes. The precision of OpenNode is further demonstrated in power distribution analyses, revealing remarkable proximity to reference values and symmetrical power distribution patterns.

Overview of fast particle experiments in the first MAST Upgrade experimental campaigns

MAST-U is equipped with on-axis and off-axis neutral beam injectors (NBI), and these external sources of super-Alfvénic deuterium fast-ions provide opportunities for studying a wide range of phenomena relevant to the physics of alpha-particles in burning plasmas. The MeV range D-D fusion product ions are also produced but are not confined. Simulations with the ASCOT code show that up to 20% of fast ions produced by NBI can be lost due to charge exchange (CX) with edge neutrals. Dedicated experiments employing low field side (LFS) gas fuelling show a significant drop in the measured neutron fluxes resulting from beam-plasma reactions, providing additional evidence of CX-induced fast-ion losses, similar to the ASCOT findings. Clear evidence of fast-ion redistribution and loss due to sawteeth (ST), fishbones (FB), long-lived modes (LLM), Toroidal Alfvén Eigenmodes (TAE), Edge Localised Modes (ELM) and neoclassical tearing modes (NTM) has been found in measurements with a Neutron Camera (NCU), a scintillator-based Fast-Ion Loss Detector (FILD), a Solid-State Neutral Particle Analyser (SSNPA) and a Fast-Ion Deuterium-α (FIDA) spectrometer. Unprecedented FILD measurements in the range of 1–2 MHz indicate that fast-ion losses can be also induced by the beam ion cyclotron resonance interaction with compressional or global Alfvén eigenmodes (CAEs or GAEs). These results show the wide variety of scenarios and the unique conditions in which fast ions can be studied in MAST-U, under conditions that are relevant for future devices like STEP or ITER.

Efficient production and purification of 32P radioisotope from sulfur by dry distillation: A practical approach with high radiochemical purity

The 32P radioisotope, with a half-life of 14.3 days and an energy level of 1.71 MeV, has diverse applications in medicine and research. Consequently, producing a carrier-free 32P radioisotope characterized by high radiochemical and radionuclide purity is imperative. Two primary methods for generating 32P radioisotopes exist: irradiating phosphorus through the nuclear reaction (n,γ) or irradiating sulfur through the nuclear reaction (n,p). Using sulfur as a target material provides several advantages. Besides the fact that the chemical element produced after irradiation (32P) differs from the irradiated element (32S), it also produces a32P radioisotope with a higher specific activity than using 31P as the target. The production of the radioisotope 32P from sulfur employs the dry distillation method, capitalizing on sulfur's easily sublimated nature. The volatility of sulfur when heated makes it easy to separate the resulting sulfur and radioisotope 32P without the need for additional reagents. This research aims to establish a practical method for producing the 32P radioisotope using the dry distillation technique. The dry distillation method utilizes a quartz ampoule containing a mixture of 32P and 35S radionuclides, a distillation tube wrapped with heating tape, and a condenser to collect the distilled sulfur. Sulfur, serving as the target material, undergoes irradiation in the reactor at the Central Irradiation Position (CIP) through the 32S(n,p)32P nuclear reaction with a fast neutron flux of 5.380 × 1013 n/cm2.sec. Separation is achieved through distillation at a temperature of 440 °C. The residual separation products are then dissolved in a 0.1 N HCl solution. The purification process involves using an AG50 WX8 cation exchange resin column, which is pre-conditioned with 0.1 N HCl. The resulting eluate contains the 32P radioisotope. The radiochemical purity of the 32P radioisotope is analyzed using thin-layer chromatography (TLC). In this analysis, a PEI Cellulose plate serves as the stationary phase, and a KH2PO4 solution acts as the mobile phase. This vacuum-free distillation method successfully separates the 32P radioisotope from sulfur, achieving a separation efficiency of 55.1 ± 9.9% (n = 7). The average activity produced after the purification process is 5.690E+10 Bq. Purifying the 32P radioisotope results in a radiochemical purity of 99.97% at Rf 0.7110, as orthophosphate, the radionuclide purity exceeds 99%.

Compact fusion blanket using plasma facing liquid Li-LiH walls and Pb pebbles

Liquid plasma facing walls allow for increased neutron-wall loading expanding the design space of fusion power-plants and experimental devices towards compact high-field reactors. This study presents the design of a compact radial build blanket for fusion devices composed of variable quantities of Lead (Pb) and Lithium-Lithium Hydride (Li-LiH). A tank-like cylindrical neutronic model of the early design of the stellarator reactor proposed by Renaissance Fusion is implemented in OpenMC (neutron transport and dose rate analyses). The reactor's radial build composition and blanket layer thicknesses are varied to fulfill the requirements on tritium breeding ratio (TBR), nuclear heat extraction, radiation shielding (for the coils, internal structures and external environment) for a stellarator-based power-plant. The analyses suggest that a radial build lower than a meter thick between the plasma and coils would be sufficient to allow for a TBR ∼ 1.60, an energy multiplication factor of ∼ 1.07, to capture ≥ 90% of the nuclear heat, limit the neutron fluence at the coils below 1019 n/cm2, and limit the structural damage on the liquid metal vessel and magnet structure. In particular, a blanket composed of 32 cm of Pb and Li-LiH, 54 cm of a heavy metal hydride such as vanadium hydride (VH2), along with a 1.3 m of concrete bioshield, would minimize the radial build of the stellarator reactor while fulfilling tritium breeding, shielding and heat extraction requirements.

Advancing Neutron Detection: Fabrication, Characterization, and Performance Evaluation of Self‐Powered PIN BGaN/GaN Superlattice‐Based Neutron Detectors

Solid state semiconductor based neutron detectors have the potential to be energy efficient and compact, making them suitable for applications where low power consumption and size constraints are important considerations. Herein, neutron detection devices based on PIN structures consisting of BGaN/GaN superlattice (SL) are demonstrated. These SL structures enable to incorporate significant boron (B) content and achieve good crystalline quality epilayers crucial for better neutron detection. Further, by leveraging the built‐in electric field generated by the PIN structure, these devices can be operated without any applied bias, simplifying overall operation and enabling a more compact size system for detection. Their performance is evaluated by measuring real‐time current response under neutron irradiation (IN) and without it (ID). The neutron induced current density (ΔJ = JN − JD) is determined, reaching an impressive value of 0.67 pA cm−2 (two times JD) under thermal neutron flux of 1.2 × 104 n cm−2 s−1 without biasing, demonstrating their self‐powered capability. They exhibit a linear response to varying thermal neutron flux levels. Additionally, the detectors successfully detect low thermal neutron fluxes down to 300 n cm−2 s−1, showcasing their potential for diverse applications, including in low neutron environments, screening nuclear warheads, and preventing illegal trafficking of radiological materials.

Aging effects in the COMPASS hybrid GEM-Micromegas pixelized detectors

Large-size hybrid and pixelized GEM-Micromegas gaseous detectors (40 × 40 cm2 active area) were developed and installed in 2014 and 2015 for the COMPASS2 physics program which started at the same time. That program involved in particular two full years of Drell-Yan studies using a high-intensity pion beam on a thick polarized target. Although the detectors were placed behind a thick absorber, they were exposed to an important flux of low energy neutrons and photons. The detectors were designed to drastically reduce the discharge rate, a major issue for non-resistive Micromegas in high hadron flux, by a factor of more than 100 compared to the former ones. A hybrid solution was chosen where a pre-amplifying GEM foil is placed 2 mm above the micromesh electrode. A pixelized readout was also added in the center of the detector, where the beam is going through, in order to track particles scattered at very low angles. The combination of the hybrid structure and the pixelized central readout allowed the detector to be operated in an environment with particle flux above 10 MHz/cm2 with very good detection efficiencies and spatial resolution. The performance has remained stable since 2015 in terms of gain and resolution, showing the interest of hybrid structures associating a GEM foil to a Micromegas board to protect gaseous detectors against discharges and aging effects.

Refueling Considerations for 99Mo Production in a CANDU Reactor

Operating CANDU reactors have the potential to produce significant quantities of molybdenum-99 (99Mo) because of their ability to be refueled online, high thermal neutron flux, and fuel design flexibility. A new molybdenum-producing fuel bundle (MPB), previously designed for CANDU reactors, has as its principal attribute that it is neutronically and thermal hydraulically equivalent to the standard 37-element fuel bundle typically used in CANDU reactors. Given that the typical irradiation time for MPBs is 20 days while the typical refueling period for a channel is on average 6 months, the refueling strategy needs to be adjusted to accommodate the shorter irradiation time of MPBs. This study evaluates a new refueling strategy suitable for employing the new MPBs in the core. A full-core, three-dimensional model is constructed in the diffusion code DONJON, and a fueling strategy for achieving the desired weekly yield of 99Mo is developed. The adequacy of the proposed refueling scheme is evaluated using a series of time-average calculations, which show that a small increase in the core reactivity (<0.4 mk) can be expected when irradiating a set of four MPBs in three different fuel channels in the inner region of the core. The small increase in the core reactivity can be managed by slightly increasing the discharge burnup in the non-MPB-bearing fuel channels, thus also improving slightly the fuel utilization in the reactor.

Development and Verification of Neutron Kinetics Parameter Calculation Program Applicable to Subcritical Systems of Long-Life Reactors

The fundamental prompt neutron delayed constant α, the effective delayed neutron fraction β eff , and the effective neutron generation time Λ eff are important for accurate measurements of keff in subcritical systems. In this paper, based on the open-source program OpenMC, a module with the function of calculating the α-eigenvalue is developed based on the k-α iterative method. Based on the nodal expansion method (NEM), an adjoint neutron flux calculation program was developed, which in turn used the idea of coupling the k-α iterative method with the NEM to obtain the neutron kinetics parameters (α, β eff , and Λ eff ) of the subcritical system and allowed for a more accurate keff under the subcritical system as compared to the traditional k-mode program. In this paper, the results of the α-eigenvalues calculated by the program are validated using the Godiva benchmark and the MUSE-4 device as computational objects. The accuracy of the results for β eff and Λ eff was verified with the KUCA (Kyoto University Critical Assembly) benchmark. The results of the keff calculations using k-mode and α-mode are compared with the ADS benchmark. The results show that the calculation program (α-mode) can obtain keff under the subcritical system more accurately, which makes up for the shortcomings of the traditional program, which cannot be calculated under the deep subcritical system. The relative error between the calculated and reference values was less than 750 pcm at deep subcriticality (keff = 0.899). The error was less than 400 pcm at the deeper subcritical system (keff = 0.952), which can satisfy the demand for neutron dynamics parameters and keff calculation in the subcritical system. The program can also continue to be upgraded in the later stage in the calculation method and other aspects.

Numerical solution of static and spatial kinetics self-adjoint angular flux neutron transport equation

This paper elucidates a comprehensive derivation of the variational formulation pertaining to the static and spatial kinetics self-adjoint angular flux (SAAF) neutron transport equation. The methodology employed for discretization of the spatial variable is the finite element method, while the energy group discretization is executed via the group method, and the directional discretization is conducted using the discrete ordinates method. Analytic expressions for the discretization to variable separation under both vacuum and reflective boundary conditions are furnished. Constructed upon the MOOSE framework, a code designated as SAAFCGSN has been developed for the resolution of the SAAF neutron transport equation. The zero-order scattering matrix within this computational framework is managed through an innovative "decoupling" method, thereby enhancing the computational efficiency significantly. The functionality and robustness of the SAAFCGSN code are corroborated through meticulous evaluation involving seven distinct steady-state scenarios as well as two transient states. Empirical outcomes verify the compatibility of the SAAFCGSN code with both structured and unstructured mesh, inclusive of their amalgamations, thus facilitating maintenance and ensuring elevated computational accuracy. In addition, a performance analysis benchmarked against IAEA standards reveals that the adoption of the scattering matrix "decoupling" method propels a computational speed increase exceeding 30 %, signifying a notable advancement in calculation efficiency.

Response of 11B enriched ZrB2 ultra-high temperature ceramic to neutron irradiation at elevated temperatures

ZrB2, an ultra-high temperature ceramic (UHTC) is being considered for use in fusion reactor first-wall structures, yet its response to irradiation remains poorly understood. This study employed scanning/transmission electron microscopy (S/TEM), synchrotron X-ray diffraction (XRD), finite element calculations, and thermal property measurements to thoroughly investigate the neutron-irradiation effects on 11B-enriched ZrB2. Neutron irradiations were conducted at 220 °C and 620 °C, with a neutron fluence of 2.2 × 1025 neutron/m2 (energy > 0.1 MeV), resulting in 3.9 dpa and 4200 appm He. The study revealed the unusual prevalence of prism loops and a > c anisotropic lattice swelling, likely linked to the low c/a ratio of ZrB2, leading to grain boundary microcracking. Reducing the grain sizes was effective in reducing intergranular cracking and macroscopic swelling. The observation of cavities in ZrB2 irradiated at 620 °C, as opposed to 220 °C, prompts questions about the temperature at which vacancies in ZrB2 become mobile, and the role of neutron absorption by 10B in elevating irradiation temperatures. Isotopic enrichment in 11B proves to be a viable strategy for mitigating helium production in transition-metal diborides, which is a critical consideration for nuclear applications. Irradiation-induced defects reduce the thermal diffusivity and conductivity of ZrB2 by a factor of 4–9, which has important implications for its role as a plasma-facing material in fusion reactors that drive high heat fluxes through first-wall materials. This comprehensive study lays the foundation for understanding ZrB2 behavior under neutron irradiation and highlights important phenomena to consider for various material applications.

Development of a diffusive simplified double P[formula omitted] approximation to the neutron transport equation

The neutron transport equation models the distribution of the neutron power inside a reactor core. The complexity of integrating this equation implies the use of some angular approximations. Discrete ordinates and spherical harmonics equations (PN equations) are commonly used to this purpose, but even when these approaches are used, the resulting set of equations requires high computational demands. An alternative is to develop simplified formulations of them, such as the simplified spherical harmonics equations (SPN equations), which provide accurate results. The spherical harmonic equations are based on the regularity of solution in terms of the angular dependence. However, in some reactor configurations, the angular fluxes can be discontinuous. For that, the double spherical harmonics equations, where angular fluxes are expanded in terms of two sets of Legendre polynomials, were studied. In this work, a simplified treatment of them is developed that leads to a diffusive set of equations, the simplified double spherical harmonics equation (SDPN equations). Numerical results show that the SDPN approximation provides faster and more accurate results than the SPN equations for some problems with strong variations of the angular neutron flux.

Delayed neutron library analysis using dynamic control rod calibration method based on results from the VR-1 reactor experiment and Serpent transient calculation

This study is focused on a comparison of experimental neutron flux data from the VR-1 reactor with results from Serpent calculation. Serpent data were calculated by the dynamic part of the code and the steady-state criticality calculation. The Serpent calculation was performed with the JEFF 3.3 and ENDF/B-VIII.0 nuclear data library. This paper expands previous work and focuses on the integral control rod worth. Comparison of the ENDF/B-VIII.0 and JEFF 3.3 nuclear data libraries with experimental data is especially valuable. The comparison shows better performance of JEFF 3.3 nuclear data instead of ENDF/B-VIII.0 for the transient calculation of the cases presented in this article. In addition, the comparison of static and dynamic reactivity provided an interesting difference, especially for small rod insertion. Moreover, the study confirms that the Serpent dynamic external source simulation mode provides an accurate description of reactor behavior, and that the shape of the integral control rod worth is close to one experimentally measured.