Thermal Neutron Diffusion Research Articles

VALIDATION OF THERMAL SCATTERING LAWS FOR LIGHT WATER AT ELEVATED TEMPERATURES WITH DIFFUSION EXPERIMENTS

Light water is the most important neutron moderator in many reactor applications. Thermal neutron scattering kernels for H bound in H2O are represented by ENDF-format thermal scattering laws (TSLs) evaluated at discrete temperatures T. Nuclear data evaluations are conventionally validated utilizing a combination of critical benchmarks and experimental cross section data. Existing public critical benchmarks may be inadequate for testing water TSLs over the full range of T of interest in reactor applications, and experimental thermal scattering cross section data for water is sparse at elevated T. In this work, MC21 is used to simulate the decay of the equilibrium thermal neutron flux in light-water spheres of several radii. The fundamental-mode time eigenvalue α is calculated at 22 °C and 227 °C (at saturation pressure) for each sphere using three different H-H2O TSLs. Fitting α to a polynomial function of geometric buckling allows calculation of the thermal neutron diffusion length L. Extrapolation lengths are treated as a function of the transport mean free path and geometry. Experimental L data from 25 publications at 49 temperatures (from 10 °C to 295 °C), computed by several different time-dependent and space-dependent decay methods, is used to develop an empirical fit of L vs. T. The MC21-calculated L for the TSLs tested are within ±1% of the predicted values at 22 °C and 227 °C. This validation approach, which may be repeated at arbitrary T, constitutes an integral benchmark specific to and characterizing the detailed physics of the thermal scattering kernel applied.

Monte carlo analysis of various geometrical blankets in a fusion-fission hybrid reactor

• A dense plasma focus device design as a fusion neutron source. • Investigate the neutron diffusion equation in the cylindrical layer, the spherical layer and the frustum cone layer geometries. • Investigate the lowest probability of a neutron returning from the second blanket to the first blanket in the cylindrical layer, the spherical layer and the frustum cone layer geometries. • Investigate the neutron parameters in the One-Blanket Reactor and Two-Blanket Reactorand the ultimate energy of the hybrid reactor by MCNPX code. • To check the safety of staff and reactor facilities, the dose rate of neutrons and photons in the concrete shield is calculated by MCNPX code. Fusion - fission hybrid reactor consists of two main parts. The first part is the Dense Plasma Focus (DPF) where the fusion process is performed and the second part is the blankets which surround the DPF and the fission process is done in the blankets. The most of the fusion neutrons, near the fusion source, are directed upward, so the blanket over the DPF is designed in forms cylindrical, spherical and frustum cone of volumes 183,347 cm 3 , 136,378 cm 3 and 58,223.2 cm 3 respectively at the same effective multiplication factor. Then the thermal neutron diffusion equation, buckling and neutron parameters are studied. After selecting the first blanket, the second blanket is designed in forms cylindrical, spherical and frustum cone of volumes 4.500 × 10 6 cm 3 , 3.689 × 10 6 cm 3 and 6.441 × 10 5 cm 3 respectively. So the frustum cone is chosen for the first and second blanket. The neutron return probability in the frustum cone from the second blanket to the first blanket is low, so the first blanket's effective multiplication factor does not change and the reactor's total effective multiplication factor is stable. Also, MCNPX code has been used to checkout and select neutron multiplier and reflector cells for the most neutron yield.

Processing and application of nuclear data for low temperature criticality assessment

Until recently, criticality safety assessment codes had a minimum temperature at which calculations can be performed. Where criticality assessment has been required for lower temperatures, indirect methods, including reasoned argument or extrapolation, have been required to assess reactivity changes associated with these temperatures. The ANSWERS Software Service MONK® version 10B Monte Carlo criticality code, is capable of performing criticality calculations at any temperature, within the temperature limits of the underlying nuclear data in the BINGO continuous energy library. The temperature range of the nuclear data has been extended below the traditional lower limit of 293.6 K to 193 K in a prototype BINGO library, primarily based on JEFF-3.1.2 data. The temperature range of the thermal bound scattering data of the key moderator materials was extended by reprocessing the NJOY LEAPR inputs used to produce bound data for JEFF-3.1.2 and ENDF/B-VIII.0. To give confidence in the low temperature nuclear data, a series of MONK and MCBEND calculations have been performed and results compared against external data sources. MCBEND is a Monte Carlo code for shielding and dosimetry and shares commonalities to its sister code MONK including the BINGO nuclear data library. Good agreement has been achieved between calculated and experimental cross sections for ice, k-effective results for low temperature criticality benchmarks and calculated and experimentally determined eigenvalues for thermal neutron diffusion in ice. To quantify the differences between ice and water bound scattering data a number of MONK criticality calculations were performed for nuclear fuel transport flask configurations. The results obtained demonstrate good agreement with extrapolation methods. There is a discernible difference in the use of ice and water data.

Symmetry and Solution of Neutron Transport Equations in Nonhomogeneous Media

We propose the group-theoretical approach which enables one to generate solutions of equations of mathematical physics in nonhomogeneous media from solutions of the same problem in a homogeneous medium. The efficiency of this method is illustrated with examples of thermal neutron diffusion problems. Such problems appear in neutron physics and nuclear geophysics. The method is also applicable to nonstationary and nonintegrable in quadratures differential equations.

Porosity sensitivity study of the compensated neutron logging tool

Porosity sensitivity is an important index for determining the spacing of the neutron porosity tool, and optimized spacing can improve formation porosity resolution. Based on the neutron flux formula obtained through a double-group approach, we study the variations of fast-neutron slowing-down length and thermal-neutron diffusion length and their derivatives with formation porosities; calculate porosity sensitivity for different porosity values; and derive relationships for how the distance between the source and the near detector or the distance between the two detectors depends on porosity sensitivity. Both the theoretical analysis and the calculations show that the relationship between porosity sensitivity and the short spacing is not monotonic. For a fixed spacing interval, sensitivity increases with increasing spacing in lower porosity formations, whereas the opposite occurs in relatively higher porosity formations. The spacing has little influence on the sensitivity. For a fixed short spacing, the sensitivity is a monotonically increasing function of the spacing interval in the whole range of formation porosity.

Implementation of a tree algorithm in MCNP code for nuclear well logging applications

The goal of this paper is to develop some modeling capabilities that are missing in the current MCNP code. Those missing capabilities can greatly help for some certain nuclear tools designs, such as a nuclear lithology/mineralogy spectroscopy tool. The new capabilities to be developed in this paper include the following: zone tally, neutron interaction tally, gamma rays index tally and enhanced pulse-height tally. The patched MCNP code also can be used to compute neutron slowing-down length and thermal neutron diffusion length.

Problems of homogeneous irradiation of Si ingots more than 200 mm in diameter under neutron doping

The problem of homogeneous irradiation of Si ingots of large diameter (i.e., comparable with the thermal neutron diffusion length in silicon—20 cm) by thermal neutrons is considered. The effect of neutron absorption on the irradiation homogeneity is discussed. It is established for some usual cases of neutron doping that the neutron distribution in the irradiation zone affects the irradiation homogeneity. The results obtained can be useful for choosing and designing the irradiation zone for neutron doping of silicon.

Differential die-away analysis system response modeling and detector design

Differential die-away-analysis (DDAA) is a sensitive technique to detect presence of fissile materials such as U235 and Pu239. DDAA uses a high-energy (14MeV) pulsed neutron generator to interrogate a shipping container. The signature is a fast neutron signal hundreds of microseconds after the cessation of the neutron pulse. This fast neutron signal has decay time identical to the thermal neutron diffusion decay time of the inspected cargo. The theoretical aspects of a cargo inspection system based on the differential die-away technique are explored. A detailed mathematical model of the system is developed, and experimental results validating this model are presented.

Thermal neutron diffusion cooling in wet quartz: (Monte Carlo simulations of the pulsed neutron experiments)

The thermal neutron diffusion parameters of a rock material depend on the rock matrix itself and on the water content. The effect has been studied in quartz by Monte Carlo (MC) simulations of the variable buckling experiment for nine series of samples. A hyperbolic dependence of the density-removed diffusion cooling coefficient on the water content shows a variability of this parameter by two orders of magnitude. The function obtained for wet quartz is compared with the analogous dependence for wet dolomite.

Thermal neutron diffusion cooling in two-region small systems

The thermal neutron diffusion cooling effect is a result of the perturbation of the thermal neutron energy distribution owing to the leakage of neutrons outside a finite volume of the medium. In multi-zone systems an additional perturbation appears because of diffusion of neutrons between regions which have different diffusion cooling properties. A study of the thermal neutron diffusion cooling in two-region small cylindrical systems is presented in this paper. A Plexiglas shell (hydrogenous medium) completely surrounds the inner cylinder filled with an absorbing aqueous solution (hydrogenous medium) or with a mixture of hydrogenous and non-hydrogenous substances. The pulsed neutron technique has been used for the experimental investigation of the problem. The time decay constant of the thermal neutron flux in the two-zone systems has been measured. It has also been calculated as a function of the system geometry and neutron dynamic parameters, one of these being the diffusion cooling coefficient of the outer Plexiglas shell. From a combination of results of the calculation and the experiments, it has been found that the obtained function for the particular diffusion cooling coefficient of the Plexiglas shell is controlled by the scattering properties of the inner zone of the system.

Thermal neutron albedo and diffusion parameter measurements for monolithic and geometric voided reflectors

Experimental measurements of thermal neutron albedo ( β th ) and diffusion parameters have been carried out for monolithic as well as for water reflectors having spherical and cylindrical voids using Am–Be neutron source and BF 3 -detector. The measured saturation values of β th for monolithic water reflector has been found be 0.80 ± 0.024 , which is in good agreement with the corresponding value 0.81 quoted in the literature. In this case, the values of diffusion coefficient ( D ) and diffusion length ( L ) have been found to be 0.142 ± 0.021 and 2.57 ± 0.032 cm which are in good agreement with the standard values 0.144 and 2.755 cm, respectively. For water reflectors with spherical voids having 3.9 cm diameter, the saturation value of β th has been found to be 0.74 ± 0.018 and the values of D and L have been found to be 0.32 ± 0.043 and 4.39 ± 0.059 cm , respectively. In the case of a water reflector with cylindrical voids having diameter 2.54 cm and length 48 cm, the saturation value of β th and the values of D and L have been found, respectively, to be 0.74 ± 0.019 , 0.41 ± 0.034 , 5.79 ± 0.067 cm for parallel configuration and 0.78 ± 0.018 , 0.347 ± 0.028 , 4.22 ± 0.056 cm for the perpendicular configuration, respectively.

Design of a single moderator-type neutron spectrometer with enhanced energy resolution in the energy range from a few to 100 keV

The moderator structure for a neutron spectrometer was optimized with the Monte Carlo code MCNP-4B. The spectrometer consists of a cylindrical moderator and a position-sensitive thermal neutron detector and obtains energy spectra from thermal neutron distribution along its cylindrical axis. The structure of the moderator was improved by using a low hydrogen density material on one end and a high hydrogen density on the other, and inserting a neutron absorber that eliminates thermal neutron diffusion. This design improves the energy resolution of the spectrometer, especially for low-energy neutrons from a few to 100 keV. The designed spectrometer can be applied to the measurement of energy spectra over a neutron energy range from a few keV to 20 MeV.

Variation of the thermal neutron diffusion cooling properties of wet rock material (Monte Carlo simulations of the pulsed neutron experiments)

The water content in a rock material can significantly change the thermal neutron diffusion parameters with respect to those of the dry medium. The effect has been studied for dolomite, CaMg(CO3)2, by Monte Carlo simulations of the variable buckling experiments for 10 series of samples. The density-removed diffusion cooling coefficient CM varies hyperbolically by two orders of magnitude with water content in the range of 0–20%.

Diffusion band gaps of thermal neutron diffusion in two-dimensional structures with periodic moderators

We theoretically demonstrate thermal neutron diffusion in two-dimensional structures with periodic moderators composed of circular rods with square lattices. In such structures, damping constant regions in which thermal neutron diffusion cannot take place appear. We define these damping constant regions as diffusion band gaps. The diffusion band gaps significantly depend on the radius of the rod and the lattice constant. The moderators are assumed to be C and H2O.

Detection of explosives and illicit drugs using neutrons

A procedure developed for the determination of the flux perturbation factor required for the thermal neutron activation analysis of bulky samples of unknown composition has been extended for epithermal neutrons using hydrogenous and graphite moderators. Measurements on the diffusion and backscattering of thermal neutrons in soil components were carried out for the development of novel nuclear methods in order to speed up the humanitarian demining process. Results obtained for the diffusion length were checked by MCNP-4C calculations. In addition, the effect of the weight and density of the explosives on the observation of the anomaly in the reflected thermal neutrons was examined by using different dummy landmines.

Diffusion cooling of thermal neutrons in basic rock minerals by Monte Carlo simulation of the pulsed neutron experiments

The pulsed neutron experiment (the variable geometric buckling experiment) in spherical geometry has been simulated using the MCNP code. The time decay of the thermal neutron flux has been observed as a function of the sample size. The thermal neutron diffusion cooling coefficient C with the correction F has been determined for three basic rock minerals (quartz, calcite, dolomite) at the given specific densities. The corresponding density-removed parameters have also been obtained.

The effective absorption cross-section of thermal neutrons in a medium containing strongly or weakly absorbing centres

AbstractThe structure of a heterogeneous system influences diffusion of thermal neutrons. The thermal-neutron absorption in grained media is considered in the paper. A simple theory is presented for a two-component medium treated as grains embedded in the matrix or as a system built of two types of grains (of strongly differing absorption cross-sections). A grain parameter is defined as the ratio of the effective macroscopic absorption cross-section of the heterogeneous medium to the absorption cross-section of the corresponding homogeneous medium (consisting of the same components in the same proportions). The grain parameter depends on the ratio of the absorption cross-sections and contributions of the components and on the size of grains. The theoretical approach has been verified in experiments on prepared dedicated models which have kept required geometrical and physical conditions (silver grains distributed regularly in Plexiglas). The effective absorption cross-sections have been measured and compared with the results of calculations. A very good agreement has been observed. In certain cases the differences between the absorption in the heterogeneous and homogeneous media are very significant. A validity of an extension of the theoretical model on natural, two-component, heterogeneous mixtures has been tested experimentally. Aqueous solutions of boric acid have been used as the strongly absorbing component. Fine- and coarse-grained pure silicon has been used as the second component with well-defined thermal-neutron parameters. Small and large grains of diabase have been used as the second natural component. The theoretical predictions have been confirmed in these experiments.

A generalized interpretation of buckling experiments for thermal neutrons

The buckling experiment is a well-known pulsed measurement method used to determine the thermal neutron diffusion parameters of a medium. In the classic form of the method, a dependence between the geometric buckling B 2 (in cm −2) and the thermal neutron time decay constant λ (in s −1) are involved. In the present paper, dimensionless values for the decay constant and for the buckling are introduced. This unification offers a method to generalize the description of the buckling experiment and makes it possible to compare experiments made for different media. The application of this procedure is exemplified on results for polyethylene of two different densities (from a Monte-Carlo-simulated experiment) and for Plexiglas (from a real laboratory experiment). The conclusion is that the buckling experiment is relatively easy for interpretation in the dimensionless buckling range which does not exceed 0.2. It corresponds, for example, to the geometric buckling B 2=1.1 cm −2 for polyethylene of density 0.57 g cm −3 or to B 2=3.0 cm −2 for polyethylene of density 0.95 g cm −3 .

Monte Carlo simulation of pulsed neutron experiments on samples of variable mass density

A method is presented to facilitate the interpretation of a pulsed neutron experiment (the variable geometric buckling experiment) when the mass densities of individual samples differ. A generalisation of the classic expression, which connects the fundamental mode decay constant to the thermal neutron diffusion parameters and to the geometrical buckling, is presented. The method has been tested (on polyethylene) by means of a computer simulation of the experiments. The simulation has been based on a Monte Carlo method, using the MCNP code. The described generalised buckling method is especially recommended for experiments with bulk materials.

The diffusion cooling coefficient for thermal neutrons in Plexiglas

The thermal neutron diffusion cooling coefficient is a macroscopic material parameter which is needed for a description of the decay of the thermal neutron pulse in a medium and gives information on the diffusion cooling of the thermal neutron spectrum in a bounded volume. Experimental results from various measurements for Plexiglas (a hydrogenous substance) are overviewed in the paper. A method for a theoretical calculation of the parameter is presented. The formula used utilizes other thermal neutron parameters and a cooling function which describes the deviation of the neutron spectrum in a bounded system from the distribution in an infinite one. The energy dependence of the function is obtained numerically from relations which result from the eigenvalue problem of the scattering operator when both the decay constant and the spectrum of the thermal neutron flux are developed in powers of the geometrical buckling. The calculation utilizes Granada's synthetic scattering function. The obtained value of the diffusion cooling coefficient for Plexiglas is at the temperature of C. The uncertainty is estimated to be within the physical model of the scattering kernel used. Results obtained using the same type of kernel in other theoretical methods are also included.