Angular Neutron Research Articles

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.

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.

Maxwell–Boltzmann-like neutron spectrum production for Maxwellian averaged cross sections measurements

Over the years, Maxwellian Averaged Cross Sections (MACS) have been measured by neutron activation, providing a neutron energy spectrum resembling the one found inside the stars. Recently, a new method has been proposed to produce stellar spectra at different stellar temperatures (a Maxwell–Boltzmann neutron energy distribution), employing the 7Li(p,n)7Be reaction. The method is based on the idea of shaping the proton beam energy to shape the neutron beam spectrum. This method was applied to obtain a well-reproduced Maxwell–Boltzmann neutron spectrum (MBNS) at kT=28 keV. An initial proton energy of 3170 keV and an aluminum foil as a proton energy shaper were employed. Differential angular neutron energy distributions from 0 to 90 degrees in 10∘ steps were measured to obtain the 0∘–90∘ integrated neutron spectrum over a neutron flight path of 50 cm. This manuscript reports on the measurement results, confirming the method’s capability, and suggests the approach for producing a high-quality MBNS at kT=28 keV.

Estimation of Continuous Distribution of Iterated Fission Probability Using an Artificial Neural Network with Monte Carlo-Based Training Data

The Monte Carlo neutron transport method is used to accurately estimate various quantities, such as k-eigenvalue and integral neutron flux. However, in the case of estimating a distribution of a desired quantity, the Monte Carlo method does not typically provide continuous distribution. Recently, the functional expansion tally (FET) and kernel density estimation (KDE) methods have been developed to provide a continuous distribution of a Monte Carlo tally. In this paper, we propose a method to estimate a continuous distribution of a quantity in all phase-space variables using a fully connected feedforward artificial neural network (ANN) model with Monte Carlo-based training data. As a proof of concept, a continuous distribution of iterated fission probability (IFP) was estimated by ANN models in two distinct fissile systems. The ANN models were trained on the training data created using the Monte Carlo IFP method. The estimated IFP distributions by the ANN models were compared with the Monte Carlo-based data that include the training data. Additionally, the IFP distributions by the ANN models were also compared with the adjoint angular neutron flux distributions obtained with the deterministic neutron transport code PARTISN. The comparisons showed varying degrees of agreement or discrepancy; however, it was observed that the ANN models learned the general trend of the IFP distributions from the Monte Carlo-based training data.

High-Fidelity Transient Analysis with STREAM Based on the Predictor-Corrector Quasi-Static Method

The predictor-corrector quasi-static method (PCQM) is used to solve the transient problem in the STREAM code, a steady-state and transient reactor analysis code with the method of characteristics. In PCQM, the angular neutron flux undergoes a factorized split to form the product of shape and amplitude functions. The time-dependent neutron transport equation is solved to obtain the shape function whereas the amplitude function is obtained by resolving the exact point kinetics equations (EPKEs). A two-level coarse mesh finite difference technique is implemented to reduce the transient running time of the transport solution. Moreover, high-order polynomial interpolation is applied to the kinetics parameters utilized in EPKEs to reduce the error when the reactivity insertion is nonlinear. Several numerical benchmarks are solved to justify the application of the procedure, proving that the method maintains solution accuracy.

Neutronic simulations of in-vessel neutron calibrations for ITER neutron diagnostics by using simplified ITER model

The absolute calibration of the detection efficiency for the measurement of the total neutron yield in the whole plasma is one of the most important issues in neutron diagnostics. In ITER, a compact deuterium-tritium (D-T) neutron generator will be used as a neutron source for the neutron calibration prior to the D-T plasma experiments, where the neutron source will be moved in the vacuum vessel. Neutronic simulations of neutron diagnostic calibrations have been carried out for the strategy and scheduling of the calibration experiments. We have established a simplified 360° ITER model for the simulation, which includes neutron flux monitors (NFMs) in an equatorial port (EQ), micro fission chambers, diverter neutron flux monitors, and a neutron activation system. At first, angular neutron spectra of the compact D-T neutron generator have been evaluated by MCNP calculations. We evaluate the discrepancies among the detection efficiencies to be obtained by the neutron calibration experiment, those by idealistic D-T ring source, and actual detection efficiencies for the plasma neutron source. Point efficiency measurement using the compact D-T neutron generator facing NFM in EQ#1 is an effective method for the NFM calibration.

Detailed Investigation of Neutron–Neutron Angular Correlations in the Spontaneous Fission of $${}^{{252}}$$Cf

Detailed Investigation of Neutron–Neutron Angular Correlations in the Spontaneous Fission of $${}^{{252}}$$Cf

A new method to solve the neutron transport problem of spherical structure

The Boltzmann equation is an integro-differential equation representing a wide range of transport and radiative transfer problems. In this paper, we propose to use the half boundary method (HBM) in the spherical coordinate system for deriving accurate and robust numerical solutions of the Boltzmann transport equation for neutron transport problem, respectively for vacuum boundary conditions, reflection boundary conditions and multilayer dielectric materials, yielding the recursive equation of the angular neutron flux by discretizing the transport equation's space and angle variables. The relationship between any point and the boundary point is derived and the particle flux distribution is obtained. Compared to traditional discrete ordinate method, the HBM uses no inverse matrix, which increases the degree of discretion, significantly reducing the computation expenses in the solution process. Finally, the HBM results are compared to those of the Monte Carlo method, proving the proposed method's feasibility, high accuracy and applicability.

SIMULATION OF NEUTRON RESPONSE FUNCTIONS OF SILICON SENSOR APPLIED TO REAL-TIME PERSONAL ALBEDO NEUTRON DOSEMETER IN THE ENERGY RANGE BETWEEN 0.01EV AND 10KEV.

Neutron response functions of a silicon sensor, which is applied to a new real-time personal albedo neutron dosemeter, have been simulated for low energy neutrons from 0.01eV to 10keV using the Monte Carlo technique. The angular neutron response functions were obtained by multiplying simulated neutron energy spectra crossing the neutron sensor and the cross-section of the 6Li(n,t)4He reaction. The neutron response functions have been closed to the dose conversion coefficient of personal doses, Hp(10) recommended by the International Commission on Radiological Protection by selecting neutrons incident from angles of 105° to 180° with respect to an axis perpendicular to an acrylic phantom surface. From these simulation results, the neutron energy response function has been improved by shielding the sensor with cadmium box without a face toward the phantom. The neutron sensor provides a good conformance to the Hp(10) conversion coefficients within 15% for low energy neutrons.

A compact accelerator-driven deuterium–deuterium neutron source using heavy water jet target

A compact accelerator-driven deuterium–deuterium neutron source using a heavy water jet target is under development at the Institute of Nuclear Physics and Chemistry. The neutrons are generated by bombarding a 0.45 mm-thick heavy water jet target with 11 MeV/0.33 mA deuterons. The angular neutron yield between 10–14 MeV is about 6.5×1011 n/s/sr at 0 degree. The D(d,n)3 reaction is adopted to generate high energy neutrons for its relatively high angular neutron yield, outstanding forward directional characteristics and convenient for obtaining, operating and maintaining. To minimize the length of the neutron source, an IH-DTL is adopted for its high accelerating gradient, low input energy and low power consumption. The design of the deuteron accelerator, consisting of a deuteron injector, a four vane Radio-Frequency Quadrupole (RFQ) and an Interdigital H-mode Drift Tube Linac (IH-DTL), is introduced in this paper. The heavy water jet target, which suffers high deuteron beam power density, is also introduced in this paper.

OpenNTP: Implementation of the S[formula omitted] method in cartesian 2D geometry and the CP method in cylindrical and spherical 1D geometry

This paper presents the implementation of the discrete ordinates method (SN) in 2D cartesian geometry and the collision probability method (CP) in cylindrical and spherical 1D geometry in OpenNTP code (Open Neutron Transport Package). This code is a pedagogical tool for computer analysis of nuclear reactors. Its main features are as follows: a free software with an open source, it solves the neutron transport equation to a few steady-state groups on a grid structured in one or two spatial dimensions with an isotropic and anisotropic dispersion source, and any new calculation method and algorithm would be easy to implement in this proposed code. Also, the code offers the possibility to calculate the main parameters of nuclear reactors such as the multiplication factor and the distribution of the scalar and angular neutron fluxes. Additional parameters, like the reaction rates, the pin power distribution and the boundary currents are also calculated. Moreover, a graphical user interface written in Python 3 programming language has been developed to simplify the use of OpenNTP. Some applications of the OpenNTP code have been compared on the one hand with the Monte Carlo OpenMC and MCNP6.1 codes and the WIMSD-5B lattice transport code, on the other hand. Numerical results are given to illustrate the accuracy of the OpenNTP code. Program summaryProgram Title: OpenNTP, version 1.2CPC Library link to program files:https://doi.org/10.17632/gm2b6799j6.1Developer’s repository link:https://github.com/mohamedlahdour/OpenNTPLicensing provisions: GPLv2Programming language: fortran90 and Python 3External routines/libraries: NumPy, Matplotlib, PyQt5, f2pyNature of problem: Solving the steady-state multigroup neutron transport equation by different methods in one, or two spatial dimensions.Solution method: the characteristic method (MOC), the discrete ordinate (SN) method and the collision probability method (CP)

Improved MCNP Simulation Considering Neutron Angular Distribution and its Experimental Verification

Adeuterium-deuterium (DD) neutron generator has been simulated with MCNP 6.2. Two methods of simulating the emission of the neutrons created by the generator have been utilized: One with an isotropic emission of resultant neutrons and a second (anisotropic) accounting for the angular and energy distribution of resultant neutrons. The isotripic source was simulated using data generated by the DROSG-2000 program. A series of gold foils were irradiated at three different geometries around the neutron generator and the results compared to those produced from the two simulation methods.

Pharmacoscintigraphy: Techniques for Studying Drug Release And Absorption in Humans

In vivo drug release and absorption in the gastrointestinal tract are governed by a complex process subject to many variables. Extensive efforts were spent in studying the durg and manipulating the excipient and mechanical design of the formulation but little is known regarding the physiological factors that influence the release and absorptive processes. Understanding of the behavior of formulation inside the GI tract has been made by gamma scintigraphy using a single isotope. However, the technique is suffering from several limitations : (1) anatomical location of the object is difficult to determine; (2) quantification of radioactivity is difficult due to tissue attenuation and movement of isotope; (3) cannot distinguish between a radionuclide present as a solid or as a solute; (4) preparation of the radiolabeled dosage forms are problematic; and (5) neither the drug nor the excipients can be labeled with nuclide. These problems can be partly alleviated by using dual isotopic, geometric mean measurement, perturbed angular correlation, neutron activation, and pharmacokinetic techniques. Combining several scintigraphic techniques with pharmacokinetics can drastically improve the quality of the data. Thus, the term pharmacoscintigraphy was coined. The application of pharmacoscintigraphy can be further supplemented by other techniques such as stable isotope with gas chromatography-mass spectrometry, pH monitoring and gastrointestinal intubation. Those techniques can be used either independently or simultaneously with pharmacoscintigraphy to provide us with a full picture of durg release and absorption in humans.

On the account of the Moon’s gravitational field in LEND measurements

Space nuclear planetology experiments play significant role in the studies of planetary surface composition and volatiles distribution. To determine concentration of major rockforming elements and volatiles, one needs to perform model-dependent deconvolution and interpretation of experimental data. This model should completely simulate all environments and experimental conditions influencing neutron production and transport an also including finite lifetime of neutron. The existing Monte Carlo codes are extremely useful for complicated geometry simulations where time-dependent and wide-energy-range solutions are required. However, they usually do not include or include in very simplified way the gravitational field description appropriate for the simulation of neutron propagation on planetary scales. We have proposed an approach useful for surface-to-orbit transport simulations where neutron lifetime and planetary gravitational field are taken into account. The discussion how gravity force and finite neutron lifetime may influence the spectral and angular neutron distributions at different spacecraft altitudes is presented. The obtained results are implemented to the detection of hydrogen-bearing compounds in the lunar regolith. As a good example we used experimental data from LEND/LRO to evaluate how insertion of neutron finite lifetime and lunar gravitational field in numerical model of experiment may influence on the interpretation of measurements made by different LEND neutron detectors.

Air-heated solid–gas reaction setup for in situ neutron powder diffraction

The design and function of a reduction furnace, specially designed for solid–gas in situ monochromatic angular dispersive neutron powder diffraction, is presented. The functionality is demonstrated by performing a reduction experiment of CoFe2O4 nanoparticles at the instrument DMC at SINQ. Heating is provided by an air gun, allowing the sample to reach temperatures in the range of 300–973 K within less than 5 min. The setup is based on a single-crystal sapphire tube with one end closed. A φ scan of the tube reveals its single-crystal nature, through strong single-crystal reflections, while the remaining background is very low, uniform and flat. CoFe2O4 was reduced using a time resolution of 8 min and a sample volume of ∼2 cm3. By means of sequential Rietveld refinement of the in situ neutron diffraction data, a two-step reduction mechanism was discovered: CoFe2O4 → Co0.33Fe0.67O → CoFe2. The setup offers high temperatures, fast temperature stability, large sample volumes and respectable time resolution. The setup has proven to be ideal to carry out investigations of advanced materials under realistic conditions. The ability to investigate real materials in real time under realistic conditions may be a significant advantage for scientific investigations as well as for industrial applications.

Experimental study of fast-neutron production and moderation for accelerator-based BNCT system

This work aims to study the fast-neutron production and moderation for the development of a compact accelerator-based multi-port Boron Neutron Capture Therapy (AB-mBNCT) system. An initial energy distribution and the efficiency of a test moderator assembly (TMA) for fast neutrons from a tungsten (W) target bombarded with a 53 MeV proton beam were measured using organic scintillators. The experimental results were reproduced with reasonable accuracy by simulations using the PHITS code. This paper will discuss about the experimental outcome and the related benchmark calculations by PHITS code.

On an analytical solution for the two energy group neutron space-kinetic equation in heterogeneous cylindrical geometry

The present work is a continuation for the multigroup scalar neutron flux and multigroup precursor concentration model, here two energy groups and one delayed neutron precursor concentration. We determine a general solution for this problem considering cylinder geometry. The solution is determined using variable separation. The complete spectrum is analysed with respect to each variable separation and truncated such as to allow a parametrisation of the solution for the considered homogeneous problem. For a specific choice of nuclear parameter we present the three dimensional solution for the fast, the thermal angular neutron fluxes and the delayed neutron precursor concentration. Possible extensions of the model and solutions are indicated.

Calculation of the wide-angle neutron spectra from the 9Be(d, xn) reaction in a thick beryllium target * * Supported by the National Magnetic Confinement Fusion Science Program of China (2014GB104002), the National Natural Science Foundation of China (11705071, 11875155, 11675069, 21327801), NSAF (U1830102), the National Key Scientific Instrument and Equipment Development Project (2013YQ40861), and the Fundamental Research Funds for the

The multi-layer computing model is developed to calculate wide-angle neutron spectra, in the range from 0° to 180° with a 5° step, produced by bombarding a thick beryllium target with deuterons. The double-differential cross-sections (DDCSs) for the 9Be(d, xn) reaction are calculated using the TALYS-1.8 code. They are in agreement with the experimental data, and are much better than the PHITS-JQMD/GEM results at 15° , 30° , 45° and 60° neutron emission angles for deuteron energy of 10.0 MeV. In the TALYS-1.8 code, neutron contributions from direct reactions (break-up, stripping and knock-out reactions) are controlled by adjustable parameters, which describe the basic characteristics of typical direct reactions and control the relative intensity and the position of the ridgy hillock at the tail of DDCSs. It is found that the typical calculated wide-angle neutron spectra for different neutron emission angles and neutron angular distributions agree quite well with the experimental data for 13.5 MeV deuterons. The multi-layer computing model can reproduce the experimental data reasonably well by optimizing the adjustable parameters in the TALYS-1.8 code. Given the good agreement with the experimental data, the multi-layer computing model could provide better predictions of wide-angle neutron energy spectra, neutron angular distributions and neutron yields for the 9Be(d, xn) reaction neutron source.

Impact of neutron flux anisotropy from DT generator on radiation shielding effectiveness

Design of deuterium–tritium (DT) neutron generator facilities requires a careful assessment of radiation shielding. In the models of such facilities an isotropic distribution of neutron flux produced by the neutron generator is usually assumed. However, prior studies have shown that neutron flux surrounding the neutron generator can be anisotropic. This anisotropy results mostly from the design of the generator tube, as well as the angular dependence of DT fusion reaction cross section. In this work, the angular neutron flux was measured for a standard commercially available DT generator (Thermo Fisher Scientific, Model P211) using an organic scintillator and a significant degree of anisotropy was confirmed to exist. The experimentally determined flux was then used in Monte Carlo simulations to examine the impact of anisotropy on the effectiveness of radiation shielding. Although the shielding effectiveness is not considerably affected by the anisotropy, the dose rates in air around the unshielded generator can be significantly different from those predicted when an assumption of isotropic flux is made. These considerations need to be included in modeling of the dose rate around the generator in neutron generator facilities that employ typical neutron generators, which exhibit some degree of anisotropy in neutron flux.

Detailed Investigations of Neutron–Neutron Angular Correlations in Slow-Neutron-Induced Fission of 233U, 235U, and 239Pu

An experiment devoted to studying neutron–neutron angular correlations in the slow-neutroninduced fission of 233U, 235U and 239Pu nuclei was performed. The experimentally determined angular dependence of the number of neutron–neutron coincidences was compared with the results of a Monte Carlo simulation for various values of the neutron-detection threshold in the range between 490 and 2080 keV. It was found that the experimental angular distributions in question can be described well under the assumption that 2% to 5% of all prompt fission neutrons are emitted isotropically in the laboratory frame. Probably, such neutrons can be interpreted as so-called scission neutrons directly associated with the nuclear-rupture instant. Energy distributions of this component were also obtained from the present analysis.