Neutron Wave Propagation Research Articles

Ultracold neutrons and the interaction of waves with moving matter

The present review is focused on the problem of interaction of neutron waves with moving matter. The validity of the 1/v law for ultracold neutrons and the possibility to characterize the interaction of neutrons with matter using the effective potential were verified in the so-called null Fizeau experiments. A neutron wave in such experiments propagates through a flat sample that moves parallel to its edges. The observation of effects caused by this motion provides evidence that the concept of constant effective potential is not correct. The second part of the review deals with the prediction and the first observation of the accelerated matter effect (a change in the energy of neutrons in passing through a refractive sample that moves with an acceleration directed along or opposite the direction of neutron propagation). The characteristic features of this phenomenon in the case of birefringent material are considered. In conclusion, the problem of propagation of neutron waves in matter moving with giant acceleration is discussed.

Monte Carlo analysis of the propagation of fusion neutrons in a high enriched uranium system

Monte Carlo methods were used to calculate experimental observables related to the propagation of pulses of fusion neutrons in a compact and highly enriched (90%) subcritical system. These observables are the amplitude and phase of the Fourier transform of the detection rate of a 3He moving detector, they correspond to the propagation of neutron waves excited by a sinusoidal neutron source. The MCNP code was used to model in great details all the heterogeneities of the experimental set up allowing in particular to have a good model of the neutron leakage in the direction perpendicular to the propagation.The very good results of the comparison with the experimental results contrast with previous comparisons with diffusion and transport theory models. The Monte Carlo modeling allows a full analysis of neutron wave experiment in space, time and energy allowing to define asymptotic regions where global complex wave vector exists. We propose to use the extensive literature of neutron wave experiments for further benchmark of MCNP.

Propagation of neutron spherical waves through a thick, vibrating Ge single crystal

The results of experimental and theoretical studies into the influence of ultrasound on the propagation of neutron waves in a thick Ge crystal are presented. The neutron intensity profiles were measured for the case of Laue diffraction inside the Borrmann fan. At low amplitudes of ultrasonic waves interference effects (diffraction intensity beatings) were observed. The observations were possible because of the uniform acoustic-field distribution through the whole bulk of the crystal. As distinct from the classical Shull experiments, wide analysing slits or position-sensitive detectors were used. To explain the results obtained, a modified theory for the spatial distribution of neutron diffraction intensities in the presence of acoustic excitation of the crystal is proposed. A good agreement between experiment and theory is obtained. At high amplitudes of ultrasonic waves the transition to kinematic scattering was not observed, despite the large strains in the crystalline lattice created by ultrasound. This could be connected with the formation of a superlattice having a standing wave period. A strong rise in the diffraction intensity and a sharp constriction of the neutron beam at the centre of the Borrmann fan were observed. This new effect could be used for the creation of ultrasound-controlled monochromators.

New test of the weak equivalence principle for neutrons

We describe a neutron gravity quantum experiment of a new type. The gain in kinetic energy of free-falling neutrons is compensated by a quantum of energy ℏ Ω , due to phase modulation of the neutron wave. As phase modulator a grating was used moving perpendicular with respect to the direction of the neutron wave propagation. As a result, monochromatic neutrons will have exactly the same energy after falling as before the free fall. The weak equivalence principle was tested to an accuracy of 2×10 −3. A possible future experiment of more improved accuracy is discussed as well.

Cylindrical IEC neutron source design for driven research reactor operation

A resurgence in nuclear power use is now underway worldwide. However, due many university research reactors shutdown, they must rely on using sub-critical assemblies which employs a cylindrical Inertial Electrostatic Confinement (IEC) device to provide a fusion neutron source. The source is inserted in a fuel element position, with its power input controlled externally at a control panel. This feature opens the way to use of the critical assembly for a number of transient experiments such as sub-critical pulsing and neutron wave propagation. That in turn adds important new insights and excitement for the student teaching laboratory.

Coherent neutron wave propagation through a substance

The present work studies propagation of neutrons through an inhomogeneous crystal medium with density fluctuations. The well-known formulas of multiple scattering theory are a starting point of calculations. The optical model within the framework of which the Lipman–Schwinger equation with the effective potential is considered is applied for a description of multiple scattering in the inhomogenous medium. The optical potential allows the scattered neutron wave intensity to be calculated.

Neutron standing waves in layered systems

A theory of propagation of neutron waves in multilayer magnetic and nonmagnetic systems is presented. It is shown how a system forms the wave function of a neutron, how the wave function formed can be controlled, and how this function can be used to investigate materials. The results of experimental investigations of the neutron reflection from multilayer systems with simultaneous measurement of different types of secondary radiation are reported.

Applications of Monte Carlo Simulations of Thermalization Processes to the Nondestructive Assay of Graphite

This work originated because of the need to measure (in situ and nondestructively) the degree of purity of the graphite of the Swiss critical facility Proteus. The comparison between measured and calculated values of the decay constant of a pulse of neutrons λ was the chosen technique. The decay constant (in the absence of fissile materials) depends, mainly, on the purity of the graphite (via the absorption process) and leakage. The leakage factor depends on the thermalization process and the geometry of the system. Because it is very difficult to calculate in complex geometries like the Proteus cavity, Monte Carlo simulations of the behavior of a pulse of neutrons were made with the MCNP code. Despite all the sophistication of MCNP, the ultimate accuracy of the calculations is dependent upon the quality of the nuclear data that describe the thermalization process in the graphite. A recent review of these data shows that very little has changed in the last 30 yr in the ENDF/B evaluation of the double-differential scattering cross section. We decided then to benchmark the current state of the art to compute kinetics experiments in graphite (the MCNP code and the ENDF/B-VI cross-section set) against experimental data and other theoretical results for the analysis of the thermalization problem. Two classes of experiments were analyzed: (a) neutron wave propagation, where the observable is the complex relaxation length, and (b) pulsed neutron decay, where λ is measured as a function of the dimensions of the graphite. Once the bias of the calculational technique was known, it was used to calculate the neutron decay constant of the Proteus cavity as a function of the 10B equivalent impurity concentration. A comparison with pulsed neutron decay experiments made at Proteus allowed the determination of the degree of purity of the graphite. In this last part, we took full advantage of the sophistication of the MCNP code to model many details of the facility quite accurately including room return effects.

Time-dependent boundary source term for advanced nodal diffusion theory

An extension to nodal diffusion theory was developed to deal with time-dependent boundary source terms. It is shown that this extension is easily introduced in advanced, full-functional diffusion theory by means of Dirac's delta spatially-dependent functions at the nodal boundaries, and allows the evaluation of reactor transients showing the propagation of neutron waves or the effects of pulsed neutron sources. A model problem with exact solutions for both the diffusion and the P 1 (telegrapher's) equations was developed to test the capabilities of the theoretical extension. The larger discrepancies occur at the earliest times computed showing, at t=50 μs, mean-square deviations between the exact diffusion solution and the numerical approximations of 2.95, 1.72, 0.32, and 0.16% for the fourth, sixth, eighth, and tenth polynomial expansion order, respectively. The availability of the exact telegrapher's solution, however, demonstrates that improved accuracy is meaningless since the mean-square deviation between the exact diffusion and exact telegrapher's solution is very similar to the mean-square deviation between the exact diffusion and the poorer (fourth-order) diffusion approximation.

Application of a new integral representation of the Ko Bessel function

The analysis of either the noise signatures of boiling water reactors or the homogeneous equivalence of a nuclear reactor fuel cell require the analysis of the propagation of neutron waves along the fuel rods embedded in a moderator. During the course of our work, we have found a convenient integral representation of the K o Bessel function that allowed us to find the relaxation length of the neutron waves.

A method to measure the thermal neutron scattering properties of a sample by neutron wave propagation

For the determination of the thermal neutron diffusion coefficient for samples of limited size, it is proposed to use the neutron wave or pulse propagation method. A thin slab of the material under investigation is then placed between two blocks of a medium with known properties. Numerical calculations have been performed on such a system. It is found that, for a certain frequency and some specified conditions, the phase shift in the outer medium will be the same as if the sample had the same properties as the outer medium. This fact may be used for a measurement of the diffusion coefficient of the sample.

The asymptotic behavior of neutron waves in small systems and its application to the investigation of solutions of the neutron transport equation

The neutron wave propagation method has been applied in small graphite blocks to study the axial propagation of the neutron disturbance and the transverse wave propagation. No evidence of non-asymptotic behavior within the limits of the wave frequencies investigated was found, and an effect of transverse wave propagation which points to a frequency-dependent complex transverse buckling has been demonstrated for the first time.

A space and angle dependent study of neutron wave propagation in beryllium

Using transport theory, the authors have studied the problem of neutron wave propagation in beryllium. Space and angle dependent neutron wave propagation parameters have been calculated inside an assembly of dimensions 59.2*61.7*94.0 cm3 for different frequencies. Some of the calculated results are compared with the observed results of Miles et al. (1974) and the diffusion theory results of Kumar et al. (1978).

A novel approach to dynamical neutron diffraction by a deformed crystal

The propagation of neutron waves in a deformed crystal is considered from the point of view of quantum mechanics. Instead of solving the Takagi-Taupin equations the probability of transitions, induced by the variation of the interaction potential, between quantum states corresponding to the two sheets of the dispersion surface is calculated. In this way transmission and reflection coefficients for an incident plane wave are obtained after a simple analytical calculation for a wide class of crystal deformations. The predictions of this theory are found to be in agreement with direct solutions of the Takagi-Taupin equations as well as with the experimental results.

Neutron Noise Transmission Characteristics of Multiplying Media and Neutron Noise Source Localization in Liquid-Metal Fast Breeder Reactors by Using the Neutron Wave Propagation Technique

The results of a theoretical study of noise transmission characteristics of multiplying media and neutron noise source localization in liquid-metal fast breeder reactors (LMFBRs) by using the neutr...

A Study of the Neutron Noise Transmission Characteristics of Nonmultiplying Media in Liquid-Metal Fast Breeder Reactors by Neutron Wave Propagation Technique

In this paper, an attempt has been made to investigate the noise transmission characteristics of nonmultiplying media of liquid-metal fast breeder reactors (LMFBRs) and study its implications on the detection of malfunctions in LMFBR cores by using out-of-core detectors and noise analysis methods. Neutron wave propagation technique has been used to study the problem by employing different approximations such as infinite and finite medium, one- and two-group diffusion theory, and multiregion and multigroup diffusion theory approximations. It has been found that reactor core noise will be transmitted to the out-of-core detectors with equal attenuation for all frequencies, ω < (ωΣt)min where Υ is the speed of neutrons and Σt is the total macroscopic removal cross section of the medium. For normal in-reactor vessel nonmultiplying media, (ΥΣt)min is of the order of 1 kHz. However, for materials like graphite if used as a moderator surrounding the out-of-core detectors, the limit (ΥΣt)min can be as low as 10 Hz. Reactor noise of malfunctions due to thermal events inside the reactor core such as sodium boiling lies in the frequency range of 2 to 15 Hz for integral boiling and goes up to 1 kHz for local boiling. Noise due to mechanical events is also a high frequency phenomenon. Therefore for detecting the malfunctions due to thermal and mechanical events in LMFBR cores by out-of-core detectors and noise analysis methods, one has to keep in mind that for moderating materials like graphite used in the surroundings of detectors, a band limited noise in reactor may be transmitted to detector locations in a distorted way and since high frequency noise is likely to be attenuated more, it will pose a problem in detecting the malfunction in its incipient stage.

Neutron Wave Propagation in Heterogeneous Media and the Interpretation of Neutron Noise in Boiling Water Reactors

For a heterogeneous multiplying system, a one-group diffusion model is shown to exhibit two spatial eigenvalues (inverse relaxation lengths). In this paper, a one-group neutron diffusion model that accounts explicitly for heterogeneities of the system is applied. The existence of a short-range relaxation length is shown to be a direct consequence of the physical properties of a heterogeneous multiplying system. The existence of these two eigenvalues is relevant to interpretation of neutron noise measurements in boiling water reactors. 21 refs.

Neutron Wave Propagation Across a Temperature Discontinuity—Multigroup Approach

Calculations of neutron wave propagation across a temperature discontinuity in graphite using a multigroup approach are reported. Diffusion, as well as thermalization properties of the medium, are investigated near the interface. As the interface is crossed from the higher to the lower temperature region, a depletion of sub-Bragg neutrons is observed. There is a buildup of neutrons as one crosses the interface from the lower to the higher temperature side.

A space and angle dependent study of neutron wave propagation in beryllium oxide

Using the multigroup discrete-ordinate form of the transport equation, the authors have studied in detail the problem of neutron wave propagation in beryllium oxide. The transfer-scattering matrix method has been employed to solve the transport equation numerically. Space and angle dependent neutron wave propagation parameters have been calculated for different frequencies of the source. Some of the calculated results are compared with earlier diffusion theory results as well as with the observed results of Ritchie and Whittleston (1972, 1973). For the first time, a reasonable agreement between the calculated space dependence of wave propagation parameters and the observed results has been obtained at all frequencies.

Neutron Wave Propagation in Heavy Water

We report here some results of our study of neutron wave propagation in heavy water using the scattering kernel proposed by Bansal et al. Calculations have been made both by including and by neglecting the contribution of molecular modes. We find better agreement with the experimental results of Perez et al. when contribution of molecular modes is included in the scattering kernel. This study also reveals the importance of including the chemical binding effects in the scattering kernel.