Spatial Distribution Of Neutron Flux Research Articles

A boundary-type algorithm based on the discrete ordinates for neutron transport equation

The spatial distribution of neutron flux in the core of a nuclear reactor plays a crucial role in ensuring nuclear safety. It can be determined by solving the neutron transport equation, where computational resource consumption is gradually receiving more attention, especially in problems with multiple reflective boundary conditions. It is common practice to assume initial boundary values in one angular direction to obtain a global solution, and then use reflective boundary conditions to solve for the other directions, iterating until convergence. However, this approach has the drawback of requiring the global solution, and each iteration necessitates storing the neutron flux values, consuming time and storage space. In order to address this issue, this paper proposes a precise and efficient boundary-type method, the Half Boundary Method (HBM). This method establishes relationships between adjacent node values through integration and mathematical deduction, ultimately obtaining the relationship among any node and the boundary values in any direction. As a result, iteration is only required for boundary values, reducing the iteration amount and thus saving time and storage space. Using the discrete ordinate (SN) method for angular discretization and HBM for spatial discretization, this paper solved the steady-state neutron transport equation for two-dimensional systems modeled with Cartesian geometry. The method is validated using several benchmark problems, including the 2D ISSA benchmark, the 2D mono-group k-eigenvalue problem and BWR rod bundle test problem. All of these problems demonstrate good results and effectively reduced computational time.

Readout Electronics for Spatial Distribution Measurement of Neutron Beam Flux in BNCT

Boron neutron capture therapy (BNCT) is a promising cancer treatment that selectively destroys tumor cells using a neutron beam. However, accurately and fast measuring the spatial distribution of neutron flux is critical to ensuring effective treatment. To address this challenge, Micromegas detectors are applied for the first time to measure the spatial distribution of neutron beam flux in BNCT. Due to the high flux, large area, and multiple components of the BNCT beam, the design of readout electronics that can handle high counting rate, large channel numbers, high integration, and discrimination of multiple beam components is challenging. This paper proposes a targeted readout electronics system to overcome this challenge. A modular readout structure based on the PCI Express (PXIe) platform is designed for 384-channel readout. A fully parallel readout structure is developed and fast shaper parameters are optimized to achieve high counting rate for each readout channel. A multi-channel high-speed, large-capacity caching technique is developed to address the high-speed data storage problem. Digital shapers are implemented in field-programmable gate array (FPGA) to achieve high integration. Tests demonstrate that each readout channel can support a counting rate of 800 kHz and achieve an excellent position resolution of 1.4 mm. Furthermore, final tests on the BNCT beam confirm that our system can successfully measure the flux spatial distribution of different neutron components.

Characterisation of neutron field in large graphite insertion in special core of the LR-0 reactor

Graphite is important reactor material used as a neutron moderator in various reactor designs. It is not only structural material used in previous reactors design but even material to which attention is focused due to the very high-temperature reactor design, which uses graphite as moderator and reflector. Due to the well-characterised cross-section of graphite, it is also a good candidate for neutron shaping experiments. In this kind of experiment, the neutron spectra are modified to the unconventional shape of neutron spectra which can be used to validate cross-section. This paper deals with validation of neutron field in graphite block surrounded by driver core arranged in large special core in LR-0 reactor. The experimentally determined shape of neutron spectra and spatial distribution of neutron flux is compared with the calculation. It is worth noting that the agreement for flux distribution is satisfactory in regions below the moderator level.

Stimulated perturbation on the neutron flux distribution in the mutually-dependent source-to-absorber geometry

The complexity of the neutron transport phenomenon throws its shadows on every physical system wherever neutron is produced or absorbed. The Monte Carlo N-Particle Transport Code (MCNP) was used to investigate the flux perturbations in the neutron field caused by an absorber. The geometry of the present experiment was designed to reach a simulation of an isotopic neutron field. The neutron source was a 241 AmBe with the production physics of neutrons being dependent only on alpha-beryllium interaction and is independent of what happened to the neutron after it was generated. The geometries have been designed to get a volume of uniform neutron densities within a spherical volume of radius 15 cm in every neutron energy group up to 10 MeV. Absorbers of different dimensions were placed within the volume to investigate the field perturbation. Different neutron absorbers were used to correlate the phenomenon to the integral cross-section of the absorber. Flux density inside and outside the absorber samples was determined, while the spatial neutron flux distribution produced by the AmBe source without an absorber was taken as a reference. This study displayed that absorbers of various dimensions perturb the neutron field in a way that is dependent on the absorption and scattering cross-sections, particularly in the neutron resonance region. Unlike the simple picture of reducing the number density of neutrons, the perturbation was found to influence the moderation of neutrons in the medium, significantly above 1 MeV.

The characterization of D–T neutron generators in precise neutron experiments

Using D–T generators as a neutron source for precise measurements requests a well-known neutron spectrum and spatial distribution of neutron flux. It is important in cross section measurements as well as in deep penetration issues. Thus, it is very important not only to validate the fluence accurately but also accurately validate the neutron spectrum in various positions. Experimental validation of two different D–T neutron generator experiments was performed using proton recoil method. Measurements performed at different angles and neutron generator voltages show relatively good agreement with the calculations. Despite the poor resolution, it was shown that stilbene is usable for the measurement of neutron energy shift due to changes in deuteron voltage.

Implementation of functional expansion tally method and order selection strategy in Monte Carlo code RMC

The spatial distribution of neutron flux or reaction rate was calculated by cell or mesh tally in traditional Monte Carlo simulation. However, either cell or mesh tally leads to the increase of memory consumption and simulation time. In this paper, the function expansion tally (FET) method was developed in Reactor Monte Carlo code RMC to solve this problem. The FET method was applied to the tallies of neutron flux distributions of uranium block and PWR fuel rod models. Legendre polynomials were used in the axial direction, while Zernike polynomials were used in the radial direction. The results of flux, calculation time and memory consumption of different expansion orders were investigated, and compared with the mesh tally. Results showed that the continuous distribution of flux can be obtained by FET method. The flux distributions were consistent with that of mesh tally, while the memory consumption and simulation time can be effectively reduced. Finally, the convergence analysis of coefficients of polynomials were performed, and the selection strategy of FET order was proposed based on the statistics uncertainty of the coefficients. The proposed method can help to determine the order of FET, which was meaningful for the efficiency and accuracy of FET method.

Preliminary Results of Neutron Transport in Blanket Module by MCNP with Profile Analysis Using Imaging Plate

Measurement of neutron flux and energy spectrum profile inside the blanket is required for fusion blanket design. An experiment using an imaging plate and activation materials (Dy, In, and Au) was performed to measure spatial distribution of neutron flux. Neutrons were generated by a discharge-type compact fusion neutron source whose neutron production rate was more than 107 n/s. A linearity between the total number of active nuclides made by neutron and photo-stimulated luminescence per area on the activation material was confirmed for three orders of magnitude. The relationships between the total number of decay of activation in the materials and the flux of the neutron in a simplified breeder assembly was measured and compared with the computation by MCNP.

Fabrication of activation foil arrays using printing techniques for evaluation of spatial distribution of neutron flux and energy

Since the activation foil and threshold detector arrays for evaluating the spatial distributions of neutron flux and energy, respectively, have traditionally been manufactured by hand, it was difficult to achieve the precise array density. In this study, a dense foil array with a precision of ≤6 µm was successfully fabricated by using a jet dispenser and printing device to arrange 100 Ag foils in an area of 16 cm2, and a complex array of Ag and Ti foils was engineered with the same precision. As the result, high-resolution spatial distributions of the flux can be measured by more dense activation foil arrays.

Demonstration of the importance of a dedicated neutron beam monitoring system for BNCT facility

The neutron beam monitoring system is indispensable to BNCT facility in order to achieve an accurate patient dose delivery. The neutron beam monitoring of a reactor-based BNCT (RB-BNCT) facility can be implemented through the instrumentation and control system of a reactor provided that the reactor power level remains constant during reactor operation. However, since the neutron flux in reactor core is highly correlative to complicated reactor kinetics resulting from such as fuel depletion, poison production, and control blade movement, some extent of variation may occur in the spatial distribution of neutron flux in reactor core. Therefore, a dedicated neutron beam monitoring system is needed to be installed in the vicinity of the beam path close to the beam exit of the RB-BNCT facility, where it can measure the BNCT beam intensity as closely as possible and be free from the influence of the objects present around the beam exit. In this study, in order to demonstrate the importance of a dedicated BNCT neutron beam monitoring system, the signals originating from the two in-core neutron detectors installed at THOR were extracted and compared with the three dedicated neutron beam monitors of the THOR BNCT facility. The correlation of the readings between the in-core neutron detectors and the BNCT neutron beam monitors was established to evaluate the improvable quality of the beam intensity measurement inferred by the in-core neutron detectors. In 29 sampled intervals within 16 days of measurement, the fluctuations in the mean value of the normalized ratios between readings of the three BNCT neutron beam monitors lay within 0.2%. However, the normalized ratios of readings of the two in-core neutron detectors to one of the BNCT neutron beam monitors show great fluctuations of 5.9% and 17.5%, respectively.

Spatial distribution of neutron flux in geological larger sample analysis at CDTN/CNEN, Brazil

Iron monitor wire was used to evaluate the neutron flux gradients inside 5 g-geological sample during irradiation. The spatial distribution for thermal flux was about 2 %/cm for radial and axial gradients and about 5 %/cm for radial and 2.5 %/cm for axial gradients for fast neutrons. The results were evaluated using reference material IAEA-SOIL-7 analysed as small and larger samples and tested with calculating E n numbers. This test pointed out that all results were consistent within a 95 % confidence interval. The contribution of the neutron flux gradients may be reduced for larger sample using the standard procedure of the k 0-instrumental neutron activation analysis.

Analytical Representation Of ZED-2 Reactor Geometry by Means of The R-Function Method

The R-function method is applied to model the geometry of the critical facility ZED-2 as an illustrative example. Each material region is represented by a real, continuous and differentiable function of spatial coordinates that is referred to as the domain function. Instead of using particular functions for individual elements, a single function is constructed to represent all spatial domains that contain the same material, for instance all fuel pins, etc. Owing to continuity and differentiability, the domain functions can be used to construct a basis for approximate solution of the related boundary-value problems. A study of the approximation ability of the domain functions is carried out using the two-group spatial neutron flux distribution in the ZED-2 facility as a model problem. The least squares method is used to determine the unknown coefficients by minimizing the discrepancy between the reference MCNP solution and a power series of domain functions. The results show that a modest number of terms in the series is able to produce a good approximation of the neutron flux distribution specified on a mesh grid of 500 x 500 points.

Solution of the isotopic depletion equations using decomposition method and analytical solutions

In this paper an analytical calculation of the isotopic depletion equations is proposed, featuring a chain of major isotopes founding a typical PWR reactor. Part of this chain allows feedback reactions of (n, 2n) type. The method is based on decoupling the equations describing feedback from the rest of the chain by using the decomposition method, with analytical solutions for the other isotopes present in the chain. The method was implemented in a PWR reactor simulation code that makes use of the nodal expansion method (NEM) to solve the neutron diffusion equation, describing the spatial distribution of neutron flux inside the reactor core. Because isotopic depletion calculation module is the most computationally intensive process within simulation systems of nuclear reactor core, it is justified to look for a method that is both efficient and fast, with the objective of evaluating a larger number of core configurations in a short amount of time.

Validation of Monte-Carlo simulations with measurements at the ICON beam-line at SINQ

ICON is the new cold neutron imaging facility at the neutron spallation source SINQ. The ICON facility is placed at beam-line S52 with direct view to the cold liquid D 2 moderator. The beam-line includes a 4.4 m long collimation section followed by a 11 m long flight path to the imaging system. The essential part of the collimation section is composed of six revolving drums and a variable aperture wheel. Depending on the investigated object, different apertures are used. Measurements have shown that each setup has a different spatial neutron flux distribution and specific beam profiles. Measured beam profiles have been used to validate results of simulations coupling the Monte-Carlo program MCNPX with the neutron ray-tracing program McStas. In a first step, MCNPX was used to calculate neutron spectra closed to the SINQ target, at the entrance of the collimation section. These results served as an input for McStas where the beam-line itself was simulated. In the present paper, experimental and theoretical results will be compared and discussed.

The effect of temperature and control rod position on the spatial neutron flux distribution in the Syrian miniature neutron source reactor

The effect on the spatial neutron flux distribution for both of water and fuel temperature increase as well as the change in the control rod position are presented in the Syrian miniature neutron source reactor (MNSR). The cross-sections of all the reactor components at different temperatures are generated using the WIMSD4 code. These group constants are used then in the CITATION code to calculate the spatial neutron flux distribution at different water and fuel temperatures and different control rod positions using four energy groups. This work shows that the increase in water and fuel temperatures during the reactor daily operating time does not affect the spatial neutron flux distribution in the reactor. The change in the control rod position does not affect as well the spatial neutron flux distribution in the reactor except in the region around the control rod position.

Three-Dimensional Radiation Shielding Analysis around the Core of BWR Plant

Radiation shielding analysis around the core of BWR plant was performed with a three-dimensional Sn code TORT to prepare detailed neutron flux distribution for the recent design needs of a BWR plant such as a life extension and a preventive maintenance. Two-dimensional R-Z, R-θ and three-dimensional R-θ-Z models, and JSSTDL cross section data based on JENDL-3 library were applied to the analysis.Consequently, detailed spatial distribution of neutron flux in the reactor pressure vessel (RPV) was obtained with the energy range of MeV to thermal neutron. The analysis method was validated by comparing the calculated results with the measured data in a surveillance test program. It was found out that both the effects of rectangular shaped geometry of the core and the neutron leakage from the upper core region are considerably high especially in the location near the core such as the shroud. In addition, the effects of the parameters; the order of P1, the number of Sn quadrature, mesh width and collapsing of cross section data on calculated results were also examined.

Measurement of eigenvalue separation by using position sensitive proportional counter

Eigenvalue separation is an important index of power reactor stability in the view of neutronics. In recent years, a long, slender Position Sensitive Proportional Counter has been developed. By using this proportional counter, the spatial neutron flux distribution of a nuclear reactor can be measured rapidly. Using these characteristics, we intend to develop the experimental method evaluating eigenvalue separation as an index for reactor stability. A method based on spatial integrals of neutron flux measured at a subcritical system with an external source is proposed. To verify this method, experiments were carried out at Kyoto University Critical Assembly. It was confirmed that eigenvalue separation can be evaluated within a relative error of 10%.

Three-Dimensional Radiation Shielding Analysis around the Core of BWR Plant.

Radiation shielding analysis around the core of BWR plant was performed with a three-dimensional Sn code TORT to prepare detailed neutron flux distribution for the recent design needs of a BWR plant such as a life extension and a preventive maintenance. Two-dimensional R-Z, R-θ and three-dimensional R-θ-Z models, and JSSTDL cross section data based on JENDL-3 library were applied to the analysis. Consequently, detailed spatial distribution of neutron flux in the reactor pressure vessel (RPV) was obtained with the energy range of MeV to thermal neutron. The analysis method was validated by comparing the calculated results with the measured data in a surveillance test program. It was found out that both the effects of rectangular shaped geometry of the core and the neutron leakage from the upper core region are considerably high especially in the location near the core such as the shroud. In addition, the effects of the parameters; the order of P1, the number of Sn quadrature, mesh width and collapsing of c...

Microtron-based neutron source for activation analysis of liquid and large volume samples

Using extracted electron beam from the 30 MeV microtron of IPP a thermal neutron source was built for activation analysis. Combined (Ta−Pb)-target is used as a gamma-neutron converter, and high-pressure polyethylene is used as a moderator. For the purpose of activation analysis special channels of different sizes were made in the moderator, with, in particular, a large pocket of about 103 cm3 in volume for irradiation of extended objects. Detailed spatial neutron flux distribution was measured, and the neutron flux density is of the order ofn·109 n·cm−2·s−1. The set up was used for detemination of Sb, As, V, Cr, Mn, Ni, Ga, Br, Re, Cd, REE content in oil, fuel oil, petrol, gaseous condensate under normal conditions. The sensitivity of noble elements determination in non-destructed loaded boards approaches 1 mg of total mass in the assembly, and equals 0.05 ppm for Au detemination in rocks and minerals.

New treatment of sodium void effect in fast reactor transient study.

A new treatment of sodium void coefficient in the fast reactor transient analysis is proposed. The method is based on the multigroup exact perturbation theory and utilizes the void reactivity map constructed by the multigroup first order perturbation theory. The change in the spatial distribution of neutron flux is corrected by the flux ratio of the fluxes in the transient and the steady states calculated with few-energy groups. The void reactivities for a homogeneous and a heterogeneous reactor are calculated by the new method with 4 and 6 energy groups and are compared with standard values obtained by the 25 group exact perturbation calculation. It is demonstrated that the new method gives almost the same values as the standard values while the ordinary calculation with 4 and 6 groups gives considerable deviation from the standard calculation. The present method has been incorporated to the two-dimensional quasi-static transient analysis code QUASAR and the code has been applied to an analysis of a control rod withdrawal accident. The results are compared with those calculated by the ordinary quasi-static method.

Sensitivities and interferences in activation analysis with cyclotron-produced fast neutrons

Fast neutrons are produced by irradiation of a thick beryllium target with deuterons from a cyclotron. The spatial neutron flux distribution was studied. Ge(Li) gamma-ray spectrometry was used to measure the radionuclides produced. Detection limits are tabulated along with the nuclear interferences.