Neutron Wave Propagation Research Articles

Neutron Wave Propagation Across an Absorption Discontinuity

Two-group calculations of the propagation of neutron waves across an absorption discontinuity in beryllium are reported. The first slab is assumed to be of finite width, while the second is taken to be of infinite dimensions. It is found that in the first slab, the effect of the interface is felt earlier for lower frequencies.

Generator of Reactivity Functions

Time-dependent reactivities of many kinds are useful for the analysis of neutron kinetics, such as the study of reactor parameters, neutron wave propagation, or any other specific evolution of the ...

Generator of Reactivity Functions

Time-dependent reactivities of many kinds are useful for the analysis of neutron kinetics, such as the study of reactor parameters, neutron wave propagation, or any other specific evolution of the reactor in time. This is done by imposing the time function directly on a cadmium rod and measuring the neutron flux. Two experiments were performed: In the first one, the reactivity function required for a sinusoidal output was generated with all its parameters in agreement with the previous calculation. In the second experiment, a parameter was slightly altered. Both cases were analyzed, and their results agreed with calculations based on the point reactor model.

Influence of transverse stack dimensions on neutron wave propagation in graphite

Measurements have been made of neutron pulse propagation in three graphite assemblies of Bperpendicular to 2=(1.07, 1.78 and 3.55)*10-3 cm-2. It has been found that a pseudo-discrete mode can be observed over a substantial range of frequencies and throughout a considerable volume of each assembly. For a given frequency, the volume associated with an observable dominant pseudo-mode decreases as the transverse buckling increases. Measurements taken in this region led to values of diffusion and thermalization parameters which were independent of transverse buckling. The dispersion relations have shown that asymptotic reactor theory can be used with confidence for frequencies up to 500 Hz. The existence of interference between the cold and thermal neutron waves has been broadly confirmed.

Neutron Wave Propagation Across a Temperature Discontinuity

Propagation of neutron waves across a temperature discontinuity in an infinite graphite assembly is investigated using a two-group approach. The first slab is assumed to be of finite width and the second is taken to be infinite. It is seen that the presence of the second medium is felt in the first medium at a larger distance from the interface for waves of smaller frequencies. In the second medium, equilibrium is established at a distance that depends on the frequency of the wave. It increases with the approach of critical frequency, becomes very large for frequencies greater than the critical frequency, and decreases with further increase in the frequency.

Neutron wave propagation in multiplying assemblies with and without control rods

In this work the dispersion law is expanded in a power series of the frequency up to the third order; for this, two-group diffusion theory is used. In this manner the nuclear parameters of this approximation can be related with the experimental observables in a closed and definite form. Also a model is developed that predicts the existance of an asymptotic progagation mode even in the presence of control rods; this model permits one to calculate the wave front and the dispersion law. The models are compared with experiments done in a highly compact system with 90% 235U enriched uranium fuel and H 2O moderator.

Neutron wave propagation in beryllium

The propagation of thermal neutron waves has been studied in four beryllium parallelepipeds. The transverse bucklings of these parallepipeds ranged from 0·0497 to 0·2572 cm −2, values which are greater than the critical buckling (0·00116 cm −2). From the space-time profiles, the dispersion law for beryllium was deduced over the frequency range 0 < ω < 1000 Hz. For the larger systems good agreement was found with calculations based on thermalization theory at frequencies less than 600 Hz. The effect of continuum contamination was apparent in all the systems but in the larger blocks this contamination had about the same magnitude and attenuation as the discrete modes. For the smaller systems, the continuum contamination was associated with neutrons having energies below the Bragg cut-off and was manifested by oscillations in the complex inverse relaxation lengths at the higher frequencies.

Pseudo-mode analysis of neutron wave propagation in polycrystalline moderators

Neutron wave propagation in a polycrystalline prism is analysed via a velocity-dependent transport equation with a simple scattering kernel. Particular attention is devoted to examining the behaviour of sub-Bragg neutrons, and the effects of temperature and transverse buckling on the neutron waves. The contribution from the sub-Bragg continuum (pseudo-mode) is made possible to compute by the use of the analytical continuation of the dispersion function in the case of 1/v-form cross sections. Numerical results of the energy spectrum and detector response of neutron waves are presented for beryllium and graphite. The interference phenomenon between the discrete modes and pseudo-modes is also demonstrated for various temperatures and transverse bucklings.

〔55〕動的測定法と炉物理

A number of workers in Japan have undertaken neutronic kinetic experiments in reactor physics during the past decade, and the theoretical background for these experiments has been established. Many of the important reports related to these studies have appeared in the Journal of Nuclear Science & Technology.The present survey briefly reviews the work covered by outstanding papers published in this Journal, as well as some particularly noteworthy reports that have appeared in foreign journals in the same period.Pulsed neutron experiments in multiplying and non-multiplying systems are discussed separately for thermal reactor physics and fast reactor physics. Statistical correlation methods are covered in such forms as Rossi-α, Feynman-α, zero-count probability, polarity correlation and reactivity determination problems. Progress in neutron wave propagation studies is reviewed in respect of both theoretical and experimental aspects.

Neutron wave propagation in finite assemblies of graphite

Neutron-wave propagation in graphite assemblies of finite transverse dimensions has been studied in the diffusion theory approximation using multigroup (30 groups) approach and energy dependent boundary conditions. Frequency dependence of the thirty eigenvalues is discussed. It is shown that the critical frequency f ∗ depends upon transverse size. For infinite transverse size ∗ is nearly equal to 130 Hz whereas for some critical transverse dimensions (in the present case it lies between 80 × 80 cm 2 and 70 × 70 cm 2) ∗ becomes zero. The existence of a pseudo-discrete mode in the continuum is discussed. Strong interference between the cold neutron density and the ’epicold‘ neutron density is predicted at some specific distance from the source. The position and intensity of interference is found to depend upon the frequency of the wave, the transverse size of the assembly, the energy spectrum of the source neutrons and the temperature of moderator. Neutron wave propagation in finite assemblies of graphite at 200°K and 150°K is also discussed.

Study of neutron wave propagation through a subcritical assembly

We report here the results of a series of calculations on the propagation of neutron waves in multiplying media using multigroup diffusion theory. For a heavy-water natural uranium subcritical assembly (taking into account the slowing down of fission neutrons), the variation of the attennuation constant α and phase lag ξ with frequency have been studied and compared with the available esperimental data. It is found that the multigroup theory gives satisfactory agreement with the experimental data. The striking feature of the multigroup theory is that it gives the correct frequency dependence of α and ξ not only at low frequencies but also at high frequencies. On the other hand, the two group theory results totally fail at high frequencies. The multigroup theory is also better than the Fermi-age theory because the latter, though gives a correct behaviour of the dispersion curve, shows a general disagreement with the experimental data for all frequencies.

Interference Phenomena of Neutron Waves in Heterogeneous Multiplying Systems

An experimental and theoretical study has been conducted on two interference effects of neutron waves in heterogeneous multiplying systems—the interference between elementary waves having greatly different characteristics of propagation and the interference due to lattice effect, taking as example a plate-type system consisting of natural uranium and graphite. The experiments on neutron wave propagation were performed with external modulated sources. The effects examined on the neutron waves covered the multiplicity of system, the direction of propagation and the source spectrum. Analyses by fission expansion method have proved the existence of the first-mentioned form of interference in the source transient region. The second form of interference effect on the dispersion law with account taken of heterogeneity, is discussed numerically in comparison with the homogeneous multiplying system.

Effect of lateral leakage on neutron waves in polycrystalline media

Abstract The reduced three-dimensional transport equation for neutron wave propagation is solved in the velocity-dependent case with a separable scattering kernel by the eigenfunction-expansion method. The full-and half-range orthogonalities for the eigenfunctions are derived. The former is applied to solve the transport equation in an infinite system. In the case of a discontinuous total cross section, the contribution from the two-dimensional continuum in the spectral plane is reduced to an integral along the branch cut by applying the analytical continuation of the dispersion function. The effects of transverse buckling on the discrete and pseudo modes are examined by numerical calculations of the solution for beryllium and graphite.

Neutron Wave Milne Problem in Polycrystalline Media

The Milne problem of neutron wave propagation in polycrystalline media is solved by using the half-range orthogonality for the complete set of eigenfunctions derived in a previous paper. The emergent distribution at the free surface exhibits a singularity when the discrete space eigenvalue attains the continuums in the spectral plane. This resonance phenomenon is demonstrated by numerical calculations for beryllium and graphite. The deformation of the energy spectrum in the directions parallel and perpendicular to the free surface are also shown for various oscillation frequencies.

Neutron Diffusion as a Random Walk Problem

The one-dimensional random walk problem has been generalized to allow for absorption at lattice sites, and then this technique has been used to study one velocity neutron diffusion. We show that most of the results that are normally obtained by solving the diffusion equation under appropriate boundary conditions, can be obtained directly. Various special cases have been considered, including leakage from a finite lattice and neutron-wave propagation in an infinite lattice.

Transport Theory of Neutron Wave Propagation by Eigenfunction Expansion Method

Transport Theory of Neutron Wave Propagation by Eigenfunction Expansion Method

Effect of Cold Neutrons on the Neutron Pulse and Wave Propagations in Crystalline Media

With the view to contributing information on the effect of cold neutrons on neutron pulse propagation and on die-away phenomena and phenomena related to neutron wave propagation, measurements of propagating pulse shapes in graphite and lead prisms were carried out with 300°K water moderated and 77°K ice moderated sources. Corresponding theoretical analyses were also performed, with use made of the successive iteration method, and a coupled two- group theory based on the distributed source diffusion equation was developed. As a result, it was established that: (a) infiltrating cold neutrons below Bragg-cut-off energy, which has a sharply peaked pulse head, produce peculiarly shaped pulse propagation responses from detector; (b) the resonance phenomena observed in wave propagation can be fairly well explained as due to the interference between the thermal neutron group and the infiltrating cold neutron group, the cold neutrons in question being those below the Bragg cutoff energy in the case of graphite, an...

Transport Theory of Neutron Wave Propagation by Eigenfunction Expansion Method

An eigenfunction expansion method is developed for the neutron wave propagation theory with a cut off cross section. The full and half range orthogonality relations for the eigenfunctions are derived, which are respectively applied to obtain an infinite space solution and the space eigenvalue formula. The formula is tried on some actual evaluations, and found to reduce considerably the laborious procedure required hitherto. The existence of marked interference phenomena between the discrete and the pseudo modes is demonstrated by numerical calculations performed on the solutions for graphite and beryllium.

Complete-backs cattering effects in neutron wave propagation problem

Abstract Using the Fourier transform technique, the neutron-wave-propagation problem has been studied in the presence of complete backscattering plus isotropic scattering of neutrons. The discrete and continuum solutions have been obtained in one-speed transport theory as well as in multi-velocity transport theory. A one-term degenerate kernel has been used for carrying out the analysis.

Some comments on the propagation of temperature waves in insulators

The theory developed by Englman for the propagation of temperature waves in insulators has been extended and some of his results obtained in simpler form. By analogy with problems already met in sound wave and neutron wave propagation, a method is described which enables the concept of a normal mode wave to be extended to a wider frequency range than was hitherto possible.