Thermal Neutron Distribution Research Articles

Simplification of the water bath method for calibrating a RaBe neutron source

The water bath method for calibrating a RaBe neutron source was simplified by introducing a fitting function for the thermal neutron distribution in water. The simplified method requires only measurement of neutrons at a single position in a comparatively small water bath.

The Angular Distribution of Thermal Neutrons at the Surfaces of Black and Grey Cylinders

Angular distributions of thermal neutrons at the surfaces of cadmium and copper cylinders were measured by activating directionally sensitive detectors. Comparisons of the experimental data with the theoretical predictions of the distributions were made by the “optical path method,” using a radial flux distribution either calculated with the THERMOS code or measured. Experimental points agree within ±3% with the predicted values given by the measured fine structure, corrected for the shadowing effect due to the collimator, and are about 10% lower than the values predicted by the THERMOS radial flux. The results give some information on the analytical form of the angular flux in the different regions of observation.

Weight optimization of reactor shielding using transmission matrix methods

In this investigation a quick and accurate method of calculating dose rates outside the primary shield of a nuclear reactor is developed. This method is then used to investigate minimum weight reactor shield configurations. The fast neutron dose at the outside of the shield is obtained by using the removal cross section concept. The thermal neutron distribution in the shield is obtained from the two group diffusion equations using fermi age theory for the slowing down of the fast neutrons. The primary and secondary gamma rays are treated by transmission matrix techniques. The optimization is carried out by determining the weight of various primary shield configurations and then searching for a minimum weight. Studies are conducted on iron-water slab shields and lead-water slab shields.

A technique for measurement of thermal neutron distributions at the surfaces of cylinders

A technique was developed for measuring the angular variation of thermal neutron flux near an absorbing cylinder placed in a moderator. A copper detector wire was encased in a cadmium sheath having a very fine collimated slot along one generatrix, so that its activation was proportional to the integrated flux in the axial plane and to the differential flux in the transverse plane. It was used, inter alia, to measure the flux near a 1.00 inch diameter copper bar and a 1.00 inch o.d., 0.75 inch i.d., copper tube. The results were found to be consistent with data calculated by usual theoretical and semi-theoretical methods.

Measurement of Fast- and Thermal-Neutron Fluxes Using a Small LiI(Eu) Crystal Detector

A crystal detector system, composed of a small LiI(Eu) crystal, highly enriched in 6Li, and a flexible light pipe, has been used to determine the fast- and thermal-neutron distributions resulting from a Pu-Be neutron source.The thermal-neutron flux is determined by the cadmium difference technique. It is found that the thermal flux thus determined agrees well with the two-group diffusion solution and with absolute foil measurement, but gamma-ray backgrounds cause serious problems in the fast flux determination by crystal. It is also found that the non-rigid light pipe offers a great deal of flexibility in the measuring process. The high efficiency in thermal-neutron measurement obtained (41%) implies that smaller crystals or longer light pipes can be used, thereby improving the accessibility of the detector. The crystal detector used is also sufficiently sensitive to follow the small change in flux magnitude with increasing temperature.

Theory of the Propagation of the Plane-Wave Disturbances in a Distribution of Thermal Neutrons

The propagation of plane-wave disturbances in a neutron gas in thermal equilibrium with a moderator is studied using the linearized Boltzmann equation. The eigenvalue spectrum of the appropriate Boltzmann transport operator is investigated for both polycrystalline and noncrystalline media, and several necessary conditions for the existence of a point spectrum (and hence for the existence of plane-wave propagation) are discussed. Techniques are presented which allow the solution of various boundary-value problems using this spectral representation.

On the existence of the fundamental mode of the neutron transport operator in a spherical assembly

We report here the results of some calculations on the existence of a fundamental discrete mode of the neutron transport operator in a spherical medium. This mode represents the asymptotic exponential decay of a thermal neutron distribution following a neutron burst. It is known that such a discrete mode does not exist for a sufficiently small medium and that the fundamental mode decay constant cannot be less than −lim [ νE( ν)] where ν is the neutron velocity and Σ is the corresponding ν → 0 total cross section. In this paper we show that if the energy domain is bounded away from zero, the discrete eigenvalue exists for any radius of a sphere; and for λ < −( νΣ) min the eigenvalue can be made to lie arbitrarily close to −( νΣ) min by choosing an appropriately small cut-off energy. It is the latter fact which is important and brings out explicitly the importance of ( νΣ) min in the approach to equilibrium even in bounded media. Although the present calculations are based on a simple thermalization model with a separable scattering kernel; the main conclusions are expected to be valid for any realistic model in any bounded geometry.

Calculating the spatial and energy distribution of thermal neutrons in a heterogeneous reactor

A method is presented for determining the spatial and energy distribution of thermal neutrons within the cells of a heterogeneous reactor. If the effect of the asymmetric part of the scattering cross section on the change in neutron energy is neglected, the problem of determining the integral parameters of a cell may, in many cases, be reduced to the solution of monoenergetic Boltzmarm equations for a certain set of energy values with a subsequent determination of the neutron energy spectrum. The possibility of using an iterative process for refining the results of the first approximation is investigated.

A new method for the exact measurement of thermal neutron distribution in an elementary cell

Exact measurement of thermal neutron density distribution in an elementary cell necessitates the knowledge of the perturbations involved in the cell by the measuring device. A method has been developed in which a special stress is made to evaluate these perturbations by measuring the response from the perturbations introduced in the elementary cell. The unperturbed distribution was obtained by extrapolation to zero perturbation. The final distributions for different lattice pitches were compared with a thermos-type calculation and as a pleasing fact a very good agreement has been reached.

Flame-Temperature Measurement by Thermal Neutron Probe

Thermal neutrons from the CP‐5 reactor at Argonne National Laboratory were scattered from an oxyhydrogen flame. Simple analysis shows that the energy distribution of the scattered neutrons depends on the translational motion temperature of the flame nuclei. The energy distribution was calculated assuming Maxwell‐Boltzmann statistics in the flame and averaging over the energy distribution of the incident thermal neutrons. The measured transmission of the scattered neutrons by thin cadmium foils plotted versus foil thickness (0.001–0.015 in.) is compared with calculated plots yielding the translational motion temperature. The temperature determined in this way for a flame at ambient pressures from 20 to 30 Torr is 2800 ± 400°K.

Energy distribution of thermal neutrons in semi-infinite and finite blocks of beryllium oxide assembly

Energy distributions of thermal neutrons in semi-infinite and finite blocks of beryllium oxide assembly have been studied by solving the Boltzmann equation in the diffusion approximation by numerical iteration. In the steady-state problem a constant source of thermal neutrons in contact with the free face of the semi-infinite block has been assumed. Different absorptions of the medium have been considered. For pure beryllium oxide moderator, the value of diffusion length obtained is in good agreement with the experimental results. The decay rates of neutrons in assemblies of different sizes are calculated by using two different scattering kernels. Placzek kernel is found to give higher values of decay constant A. The value of the diffusion constant D agrees well with the experimental results but the diffusion cooling constant C comes out to be about twice the experimentally observed value.

Spatial energy distribution of thermal neutrons in a heterogeneous reactor

The spatial energy distribution of the thermal neutrons in a heterogeneous reactor has been determined in the heavy gas model approximation. It is assumed that the moderator is non-absorbing and that the fuel slugs do not moderate the neutrons. To describe the energy dependence of the solution it turns out that as well as the ordinary Laguerre polynomials the functions witociated with them are also very convenient. Possible ways of improving the accuracy of the results are discussed.

Borehole Models for Nuclear Logging

Abstract Borehole models used in the study of nuclear well logging are reviewed and the merit of heterogeneous vs homogeneous formation simulation is discussed. A heterogeneous model for simulating sandstone formations of variable porosity is described. Simulation adequacy was checked by steady-state and pulsed-neutron measurements. Introduction In the course of developing new methods of nuclear well logging, the problem of testing new logging instruments under controlled conditions always arises. This testing is usually done in wells of known lithology, porosity and fluid saturation, or in laboratory test facilities which simulate the borehole environment. Although the former approach is possibly more satisfying, it is frequently difficult or inconvenient to find wells with enough variation in the cited parameters for a truly comprehensive study. On the other hand, laboratory test facilities can simulate a wide variety of formation and borehole conditions if care is exercised to maintain adequate simulation under all conditions. Workers concerned with the development of nuclear well logging methods have reported several types of research facilities in the past. Tittle, et al used cubical tanks filled with Ottawa silica sand to study the steady-state behavior of thermal and epithermal neutrons in simulated sandstone logging environments. In addition to the effects of fresh vs salt water, a Wide variety of casing sizes and compositions were investigated. Tittman also used a large tank of Ottawa sand to measure the slowing down length of SiO2; for making the same measurement in CaCO3, however, an assembly of solid Vermont marble blocks was used. More recently a very useful and carefully planned test pit for nuclear logs was constructed under the auspices of the API. This facility consists of three massive limestone sections, each 6-ft thick and more than 5 ft in diameter. The blocks are buried, one on top of the other, in a concrete- lined pit having a total depth of 24 ft. Each section is made of a different limestone to achieve porosity variation, the selection being Carthage (2 per cent), Indiana (19 per cent) and Austin (26 per cent). The blocks are traversed by a 7 7/8-in. diameter borehole and are saturated with fresh water. Great care was taken to insure total saturation of the stone. Homogeneous mixtures and materials have not been used exclusively for simulating earth formations. Tittle, et al 4 showed that a heterogeneous lattice of water and graphite could be used to simulate liquid furfural with very little effect or measured thermal and epithermal neutron distributions. Subsequently, a lattice-type model for simulating limestone earth formations was designed and built by Berry. This limestone model was constructed of 7/8- x 7/8- x 36-in. marble rods glued together with a plastic resin m form a 36-x 42- x 45-in. cube. The cube was honeycombed vertically with 7/8- x 7/8- x 36-in. holes for porosity and had a 11 1/2-in. diameter hole in the center to serve as the borehole. Lower porosities were simulated by placing marble rods in the square holes. The finished cube was used with the borehole vertical and set in a tank to hold liquid for filling the holes in the rock matrix. A second type of heterogeneous borehole model has been proposed by Kukharenko, et al. In this concept the model is composed entirely of solid material. The hydrogen equivalent of formation fluids is simulated by making the model of alternating layers of dense rock and celluloid. Additional hydrogen is included by drilling vertical holes in the rock sections and filling them with solid forms of hydrogeneous material. The volume of the holes is equal to the volume of the celluloid layers, so an axial and radial dispersion of the hydrogeneous material is thus obtained.one such model was composed of alternate 50 mm-thick sand layers and 2 mm-thick celluloid sheets. Approximately 200 appropriately spaced plastic tubes were used in each sand section. The plastic tubes were filled with paraffin for additional hydrogen concentration. This arrangement yielded a model with a water-equivalent hydrogen concentration of 10 per cent. SPEJ P. 109ˆ

Measurement of the Angular Distribution of Thermal Neutrons at the Surfaces of Cadmium Rods

Measurement of the Angular Distribution of Thermal Neutrons at the Surfaces of Cadmium Rods

Measurement of Thermal Utilization Factor in a Square Cell of UO2-H20 Lattice

Thermal neutron distribution in a square lattice of water moderated UO2 (enriched to 2.596 w/0 in 235U) was measured with dysprosium micro-foils. Diameters of the fuel pellet and the aluminum cladding tube were 12.5mm and 14.12mm respectively. The pitch of the square lattice was 19.56mm, and the water to fuel volume ratio 1.844. To obtain the integrated flux in the fuel and moderator regions, the solution for the P-1 diffusion equation was used. A disadvantage factor of 1.27±0.02 and a thermal utilization factor of 0.891±0.002 were obtained. The theoretical value of the disadvantage factor obtained by the 30 group integral transport theory in a square call is 1.341 and is larger than the experimental value by a discrepancy exceeding the experimental error. The result is also compared with some approximate calculations.

Space-energy distribution of thermal neutrons in a homogeneous reactor

The space-energy distribution of thermal neutrons in a heterogeneous reactor is determined in a heavy gas model approximation. The moderator is assumed to be nonabsorbing and the fuel sings are assumed to be nonmoderating to neutrons. In order to describe the energy dependence of the solution, adjoint functions are included in addition to the Laguerre polynomials normally used, and which is shown to be very suitable. Possible methods of refining the results are discussed.

A Paraffin-Moderated 4π-Neutron Detector

A flat response 4π-neutron detector has been constructed by arranging BF3 counters in multiple concentric rings in a cylindrical paraffin moderator. The sensitivity is flat within ±5% for neutrons between 50 keV and 700 KeV. The absolute efficiency is 2.24% for 50 to 700 keV neutrons and 1.76 % for RaD–Be neutrons in the standard counter arrangement. This efficiency can be increased by mounting more BF3 counters but the relation is not linear because of the mutual interference effect in BF3 counters. The dependence of the counting efficiency on the angular distribution of neutron source was investigated by measurements of thermal neutron distributions in the moderator, and it has proved to be quite small (<1.5%) even for the T3(p, n) He3 reaction in its threshold region.

Methods for calculating slow neutron spectra

Formulas are given for the zeroth and first angular variable moments of the thermal neutron scattering kernel for a monatomic gas model as well as for a model which includes molecular and crystal binding. A method is presented for calculating the space-energy distribution of thermal neutrons which accounts for thermalization in multizone cylindrical lattice cells by means of the Ps approximation of the spherical harmonic method. Experimental results are compared with results of the calculations.

Thermal neutron diffusion parameters of heavy water

The decay of the asymptotic thermal neutron distribution was measured by the pulsed technique in D 20(99·82 mol per cent, δ = 22°C) within a rather large range of geometrical buckling (00013 cm −2 < B 2 < 0·0470 cm −2). In the lower buckling region (B 2 < 0·0060 cm −2) we employed a modal analysis method outlined in a previous paper ( Meister, 1963). From the experimental decay constant α plotted against B 2 we obtained the diffusion constant D 0 = (2000 ± 0·0009) × 105 cm 2/sec and the diffusion cooling constant C = (525 ± 025) × 105 cm 4/sec in a fairly good agreement with earlier experimental data ( Sjöstrand, 1958; Ganguly and Waltner, 1961; Waltner and Westfall, 1962).

Asymptotic solutions of the transport equation for thermal neutrons

Synopsis The eigenvalue problem defining the exponential time decay of a thermal neutron distribution is investigated. It is found that the decay constant is bounded whenever the neutron transit time is unbounded. For the particular case of spherical geometry, isotropic scattering and a simple thermalization model, the fundamental mode decay constant reaches its upper bound for a finite sphere radius. This implies that there are no discrete eigenvalues of the thermal neutron transport operator for a sufficiently small sphere. This is in contrast to the result for mono-energetic neutrons obtained by Jorgens. The problem is first illustrated by reviewing the results for mono-energetic neutrons for a single fourier component in an infinite medium, for a slab and for a sphere. Only the last of these has a bounded neutron transit time, and this also becomes unbounded when the possibility of zero velocity neutrons in a thermal neutron velocity distribution is considered. It is indicated, but not proved, that the conclusions drawn from the special model studied apply to more realistic models of slow neutron interaction with matter. The relevance to pulsed neutron experiments in small moderating samples is discussed.