Neutron Diffusion Parameters Research Articles

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 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.

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%.

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.

A method to calculate thermal neutron diffusion parameters for hydrogenous mixtures

A comprehensive method is proposed to calculate the thermal neutron diffusion parameters for homogeneous mixtures of any non-multiplying non-crystalline compounds, in particular including hydrogenous substances. The macroscopic absorption, scattering, and transport cross sections of the mixture are defined generally as functions of the incident neutron energy. The energy-averaged neutron parameters can be calculated when the energy dependence and the thermal neutron energy distribution are known. For most substances the scattering cross section can be assumed as being almost constant in the thermal neutron region (which results from the free gas model). However, serious deviations are observed for hydrogen atoms bound in molecular systems. In the paper certain effective scattering cross sections are found in this case on the basis of individual accurate data for a few hydrogenous media. The macroscopic parameters calculated are averaged over the Maxwellian energy distribution for the thermal neutron flux. Results agree well with available data.

A new idea of pulsed neutron experiments with bulk materials

Pulsed thermal neutron macroscopic parameters are density dependent. This leads to a serious difficulty in interpreting the experiments when bulk materials are investigated. A method of using the density-removed neutron diffusion parameters as well as the generalized time-decay constant and geometric buckling are presented.

Thermal neutron cross sections and diffusion parameters of diphenyl and Dowtherm-A using a synthetic scattering function

We have used a synthetic scattering function to evaluate thermal neutron cross sections and diffusion parameters for diphenyl and Dowtherm-A, over a range of temperatures of practical interest. The present formalism is based on our benzene model, which has been already validated in a previous application. Our calculated results for diphenyl are in excellent agreement with several measured quantities, whereas those for Dowtherm-A are at variance with the scarce available information.

Thermal neutron cross sections and diffusion parameters of Plexiglass

The neutron total cross section of Plexiglass has been measured for energies between 10 −3 and 10 3 eV by the transmission method with pulsed-neutron time-of-flight techniques. A calculation based on a synthetic scattering function shows a very good agreement with the measured values over the entire energy range. This model has been used to evaluate other quantities of interest in moderator design problems, including energy-transfer kernels and thermal neutron diffusion parameters. These experimental and theoretical results are compared with available data for Plexiglass.

Thermal neutron cross section and transport properties of polyethylene

We report a new measurement of the total cross section of polyethylene at room temperature, for neutrons with energies between 10 −3 and 10 eV. It is shown that a synthetic scattering function is able to produce good agreement with the measured values, as well as with other quantities of interest in moderator design problems. On this basis, thermal neutron diffusion parameters are predicted for polyethylene over a range of useful temperatures.

High-precision thermal neutron diffusion parameters for Plexiglass

The thermal neutron diffusion parameters for Plexiglass have been determined with high accuracy. The classic pulsed neutron experiment based on the concept of variable geometric buckling has been performed (the buckling B2 being from 0.036 to 1.234 cm-2). Details on the treatment of data are given. The following values of the parameters have been obtained at the temperature of 20 degrees C: v Sigma a=(4120+or-30) s-1, D0=(37312+or-100) cm2 s-1, C=(6192+or-457) cm4 s-1, F=(1203+or-400) cm6 s-1. They are compared with the values reported by other authors. The influence of experimental conditions on the final results as well as some theoretical problems concerning diffusion cooling are discussed.

Thermal neutron diffusion parameters for plexiglass

Thermal neutron diffusion and absorption parameters for plexiglass have been measured in the spherical geometry using the pulsed method. The results obtained are: νΣ a = (4120 ± 30) s −1, D 0 = (36 882 ± 314) cm 2 s −1, C = (7149 ± 615) cm 4 s −1 (at 19.5°C).

Neutron Thermalization in Graphite

The neutron thermalization and diffusion parameters in graphite were determined by pulsed technique for the neutron flux and the neutron density spectra, respectively. Measurements were performed on assemblies of geometrical bucklings between 2.26×10−3/cm2 and 15.58 × 10−3/cm2, in which, by suitable arrangement of the neutron source and detector, the higher modes of spatial harmonics were diminished. The results indicated that it was necessary to wait 1.5∼2 msec after the injection of 14 MeV neutrons, in order to let the neutron spectrum attain its asymptotic form, independent of assembly size. The thermalization and diffusion parameters for both neutron flux and neutron density spectra were in good agreement with theoretical values.

Measurement of the thermal neutron wave dispersion relations in BeO

The amplitudes and phase shifts of thermal neutron waves were measured in a block of BeO 60·96 x 60·96 x 58·42 cm 3 of average density 2·87 g cm −3 and having nominal transverse buckling of 0·0048 cm −2. The attenuation constants (α) and phase shift constants (ξ) were derived from such measurements at 18 different frequencies covering the range 52·4–506·1 Hz. The parameters α 2 - ξ 2 and 2αξ were evaluated, normalized to a reference density of 2·96 g cm −3, and corrected for the density normalized transverse buckling of 0·00513 cm −2. The normalized and corrected parameters α 2 - ξ 2 and 2αξ were fitted to polynomials in the angular frequency ω, and the resulting thermal neutron diffusion parameters were compared with those derived from a λ( B 2) experiment carried out on the same block of BeO. The parameters λ a and L determined by the two methods are in good agreement, but the diffusion coefficient and diffusion cooling constant derived from the sine wave experiment are significantly higher. The high diffusion coefficient (by ∼ 9 per cent) could be due to the effect of the sub-Bragg continuum, although the values of the parameters α and ξ appeared to be independent of the distance from the source. Agreement of the parameters α 2 - ξ 2 and 2αξ with the theoretical values is not good and reasons are advanced for the discrepancy.

Effects of buckling calculation on diffusion parameter measurements for heavy water in spheres

The neutron diffusion parameters of heavy water were determined from measurements taken in spherical aluminum shells with use of the pulsed neutron source method. The decay of the neutron population was monitored using a multichannel analyzer, with a 10 μsec channel width, and a 3He detector positioned at two locations within each sphere. The time-asymptotic decay constant for each sphere was calculated from the experimental data using the channel-dropping method. Values of the geometric buckling were calculated using the average sphere radius, with a wall-thickness correction, and two methods of calculating the extrapolation length. These methods were based on the formulations used by Dorning (method D) and Elkert (method E). This resulted in two values of the buckling for each sphere. Temperature and purity corrections were made to the decay constants, and the diffusion parameters were obtained by fitting to the customary expansion for the decay constant in the buckling. The results were as follows: For method D buckling: 1. D 0 = 2.09±0.01 × 10 5 cm 2/sec 2. C = 6.85±0.55 × 10 5 cm 4/sec 3. F = 20 ± 5 × 10 5 cm 6/sec For method E buckling: 1. D 0 = 2.02±0.01 × 10 5 cm 2/sec 2. C = 6.44±0.45 × 10 5 cm 4/sec 3. F = 24± 5 × 10 5 cm 6/sec.

Pulsed neutron measurements for beryllium in the range of large bucklings

Using the fast chopper as a pulsed neutron source the behaviour of thermal neutron flux decay in beryllium has been studied in the buckling range of 0·0838−0·285 cm −2. The measurements have been performed for cubic or near-cubic geometry. The neutron diffusion parameters have been obtained. Some problems connected with pulsed measurements in beryllium are discussed.

Measurement and Calculation of Neutron Diffusion Parameters in Water

Neutron diffusion parameters in water at a room temperature of 10°C have been measured by the pulsed neutron method for the range of geometrical buckling from 0.093 to 1.36 cm-2. The results are 205±4 μ60 for the neutron mean life time due to absorption, 34,120±610 cm2·sec-1 for the diffusion coefficient and 3,350±560 cm4·sec-1 for the diffusion cooling coefficient. The decay constant has been calculated as a function of buckling for the Nelkin and the Rad-kowsky scattering models of water on the assumption of linear anisotropic scattering. The calculated diffusion coefficients, 36,290 cm2·sec-1 for the Nelkin model and 37.610 cm2·sec-1 for the Radkowsky model, are somewhat higher than the experimental result. It is shown that the calculated diffusion coefficient approaches the experimental value if we use μ-(E), the mean value of cosine of scattering angle, obtained from the Beyster's experiment instead of that for the Nelkin model.

The Definition of Neutron Diffusion Parameters for a Uniform Reactor Lattice

Two equally valid systems of definitions are given for the neutron diffusion parameters of a reactor lattice: cell-average and cell-surface. In defining the cell-average parameters, we imagine a macroscopic flux distribution to be fixed in space while the lattice is translated with respect to it. In defining the cell-surface parameters, we work in terms of fluxes and currents on the surface of a cell having the fissile material at its center. Parameters from both systems have been used before; but until recently we have lacked complete clarity of definition and the realization that there are two valid systems of parameters that should not be mixed in the one calculation. The early formula, L2 is equal to the summation over all values of i of fiLi2, is for a cell-average thermal diffusion area; L2 = (outleakage)/B2 (absorption), applied to a cell with the fissile material at the center, is a cell-surface diffusion area and is less than the summation over all values of i of fiLi2 by ≍(lattice spacing)2/24.

A study of neutron diffusion in sintered beryllium oxide by a pulse method

BeO, which is an excellent moderator material, possesses high heat resistance, has low absorption cross section, and provides for supplementary neutron multiplication by the Be/sup 9/(n,2n) reaction, is considered a very promising material for high-temperature power reactors. In view of the contradictory data reported in the literature concerning the neutron-diffusion parameters in the sintered material, further thermal neutron-diffusion studies were undertaken using the pulsed-source method. A specimen previously used for determining the slowing-down length (Atomnaya Energ., 13: 258(1962)) was employed in this study. The values of the diffusion coefficient, diffusion length, transport length, effective transport cross section, absorption cross section, and the diffusion time were calculated and plotted. The calculated time of thermalization, 120 mu sec, was considerably lower than the value reported in the literature; this might be due to the approximating assumptions used. (TTT)

Propagation of Neutron Waves in Moderating Media

Use of a sinusoidally modulated source of neutrons is equivalent to “poisoning” a moderating medium with a 1/v poison. The inverse relaxation length of the neutron wave amplitude and the variation of the phase angle as a function of position are dependent upon the frequency of modulation and the neutron diffusion and thermalization parameters of the media in which the waves are being propagated. The neutron wave technique allows “poisoning” of solid moderators and provides a means of performing poisoning experiments for measuring nuclear properties of solid as well as liquid moderators. It should supplement the recent use of poisoning techniques in an attempt to reconcile discrepancy in the diffusion and thermalization parameters of moderators, as measured by pulsed neutron techniques. The neutron wave technique and the pulsed neutron technique are supplementary from an experimental viewpoint.