Dependence Of Reflection Coefficient Research Articles

Modelling of particle beams

The two-dimensional relativistic electromagnetic current-line code “POISSON 2” was used for numerical modelling of the behaviour of a relativistic electron beam (REB) in external and internal electromagnetic fields under various boundary conditions. The calculations confirmed that the generated beam is homogeneous and monoenergetic in a broad central region. In the case of cylindrical diode the mixing of electron trajectories was only observed in a narrow peripheral beam region. The formation of a virtual cathode (VC) by the REB propagating through the terminating foil into a vacuum region was also investigated. The dependencies of reflection coefficient of scattered beam by created VC on total beam current, beam energy, external magnetic field and on the length of vacuum drift tube were determined. Such data might be useful for additional plasma heating generated via a two-stream instability in our experimental REBEX devices.

Body‐wave radiation patterns and AVO in transversely isotropic media

The angular dependence of reflection coefficients may be significantly distorted in the presence of elastic anisotropy. However, the influence of anisotropy on amplitude variation with offset (AVO) analysis is not limited to reflection coefficients. AVO signatures (e.g., AVO gradient) in anisotropic media are also distorted by the redistribution of energy along the wavefront of the wave traveling down to the reflector and back up to the surface. Significant anisotropy above the target horizon may be rather typical of sand‐shale sequences commonly encountered in AVO analysis. Here, I examine the influence of P‐ and S‐wave radiation patterns on AVO in the most common anisotropic model—transversely isotropic media. A concise analytic solution, obtained in the weak‐anisotropy approximation, provides a convenient way to estimate the impact of the distortions of the radiation patterns on AVO results. It is shown that the shape of the P‐wave radiation pattern in the range of angles most important to AVO analysis (0–40°) is primarily dependent on the difference between Thomsen parameters ε and δ. For media with ε − δ > 0 (the most common case), the P‐wave amplitude may drop substantially over the first 25–40° from vertical. There is no simple correlation between the strength of velocity anisotropy and angular amplitude variations. For instance, for models with a fixed positive ε − δ the amplitude distortions are less pronounced for larger values of ε and δ. The distortions of the SV‐wave radiation pattern are usually much more significant than those for the P‐wave. The anisotropic directivity factor for the incident wave may be of equal or greater importance for AVO than the influence of anisotropy on the reflection coefficient. Therefore, interpretation of AVO anomalies in the presence of anisotropy requires an integrated approach that takes into account not only the reflection coefficient but also the wave propagation above the reflector.

Dispersion limitations to short pulse generation with the parametric nonlinear mirror

We show that due to the dispersion of phase-compensation plate (necessary element of nonlinear mirror) the wavelength dependence of reflection coefficient has a form of several maxima. The distances between maxima is inversely proportional to the plate thickness. Besides, the wave reflected from the mirror gains intensity dependent phase shift. In the processes of ultra short pulse reflection these properties of the mirror limit the pulse duration and introduce nonlinear delay.

On the use of Schrödinger’s equation in the analytic determination of horn reflectance

The flaring horn has traditionally been modeled in one dimension using piecewise conical or cylindrical elements. Acoustic properties within each element are known, and scattering between the elements is computed. Under the piecewise model, a shape for the wavefront of the acoustic disturbance within the horn is implicitly assumed (planar for cylindrical elements, spherical for conical elements). For horns of significant flare, the true wavefront shape will be neither planar nor spherical. A more general model is thus desirable. Here an alternate model is presented: The flaring horn is modeled according to Webster’s equation. A change of variables transforms the equation into the form of the Schrödinger wave equation using in one-dimensional particle scattering. Boundary conditions can be derived directly from the physical dimensions of the horn, and the solution of the equation gives estimates of acoustic properties in terms of frequency dependent reflection and transmission coefficients. Here, Webster’s equation is solved along the entire length of the horn, with no lumped scattering. Advantages over piecewise modeling techniques include the ability to specify arbitrary axisymmetric wavefront shapes for the acoustic disturbance within the horn. Under appropriate assumptions for wavefront shapes, results converge to those obtained with traditional piecewise models.

X-ray standing waves on the surface of the crystal with the uniform strain gradient

The results of theoretical investigation of X-ray Standing Waves (XSW) on the surface of the crystal with the Uniform Strain Gradient (USG) are presented. Bent crystals are the typical examples of the crystals with the USG. The proposed theory is based on the Takagi-Taupin theory of X-ray propagation in a weakly deformed crystal. This theory is applied for calculation of the angular dependencies of reflection coefficient and XSW on the surface of the crystal with USG for the specific case of Si(400) thick crystal, CuKa radiation. The behaviour of the XSW with the different position of adsorbed atoms (different values of the phase shift) are analyzed

A method for predicting the reflection and refraction of spherical waves across a planar interface

An approximate method is presented to find the magnitude of the reflected and refracted waves that result when a spherical wave encounters a planar interface separating two elastic solids. This method relies on: a multipole field solution for spherical waves to describe the compressional and shear waves that emerge from the interface upon reflection and refraction, virtual sources to locate the reflected and refracted wave origins above and below the interface, and a discrete, ray-based approach to solve the complex system of equations that result from the boundary conditions imposed. In addition to the elastic constants, the reflection and refraction coefficients are found to depend on the boundary conditions at the interface, the wavefront curvature, and source frequency. The dependence of reflection coefficients on boundary conditions is significant and has important implications for brittle materials subjected to impulsive (shock) loading, such as a turbine blade containment structure or ballistic ceramic armor. It is shown that a good impedance match between two solids is not sufficient to prevent fragmentation due to a reflected wave. Shear coupling of the interface is necessary to minimize damage. The Matrix Algebra for Reflective/Refractive Systems computer program has been developed to solve the resulting system of equations and illustrate these results.

Effects of water and melt on seismic velocities and their application to characterization of seismic reflectors

The effects of a silicate melt and water on seismic velocities are compared at relatively small fluid fraction (less than 20 vol.%) on the basis of a theoretical model of composite materials, to show that the two fluids are clearly characterized by the velocity ratio Vp/Vs. For a silicate melt, Vp/Vs increases with increasing fluid fraction. When a significant reflection is expected, Vp/Vs becomes much larger than 2. For water, Vp/Vs decreases as the fluid fraction increases to 10 vol.% then it increases. But it remains similar to a solid state value (about 1.8), unless the amount of water exceeds 15 vol.%. This will be a good measure to distinguish between two candidates for seismic reflectors: partially molten rocks and rocks containing free water. If a reflector can be treated as a thin low velocity layer, the velocity ratio in it can be estimated from the frequency dependence of reflection coefficient.

E(k) above the Vacuum Level from Low Energy Electron Reflection. ΓK Line of Cu and Ni

Incidence angle dependent electron reflection coefficient curves R(E) measured in the 0 to 30 eV range on Cu(111) and Ni(111) surfaces are analysed. With incidence scanning in ΓK azimuth, some extrema of the dR/dE curves are shown to manifest bands along the ΓK line of the Brillouin zone. Comparing the experimental angular dispersion of these extrema with its calculated counterpart, bands along ΓK are mapped. Experimental technique and details of calculation are briefly discussed. [Russian Text Ignored].

A computer implementation of 2.5-D common‐shot inversion

The computer implementation of a two‐and‐one‐half dimensional (2.5-D) constant density prestack inversion formalism with laterally and depth‐dependent background propagation speed is a Kirchhoff‐type inversion, summing data from a line of receivers over traveltime curves in the depth‐dependent background medium with weights determined from Born/Kirchhoff inversion theory. This theory predicts that the output will be a reflector map with peak amplitudes on each reflector being in known proportion to the angularly dependent geometrical optics reflection coefficient. The 2.5-D feature provides for out‐of‐plane spreading correction consistent with the prescribed background medium. The method is applied to a synthetic data set and to a physically modeled data set generated at the Seismic Acoustic Laboratory. The graphical output demonstrates the validity of the formalism as a Kirchhoff migration. Parameter estimation for the synthetic data confirmed the theory. Parameter estimation for the experimental data was less successful, partially due to problems with amplitude control in the original experiment and partially due to the limited aperture of the common‐shot data, thereby suggesting that a common‐offset inversion might be more useful for parameter estimation.

Reflection of a plane wave from a fluid layer with continuously varying density and sound speed

This paper considers the transmission of an acoustic plane wave through a horizontally stratified fluid layer whose density and sound speed both vary continuously with depth. The stratified layer is of finite thickness and lies between two semi-infinite homogeneous fluids. The situation modeled is intended to be representative of an inhomogeneous marine sediment overlying a uniform substrate. Exact solutions of the Helmholtz equation, valid in the stratified layer, are derived for a class of density profiles and a number of classes of sound-speed profile. These include profiles that closely resemble measured density and sound speed variation in marine sediments. The solutions in the stratified layer are matched with solutions in the homogeneous upper and lower layers, to derive analytical expressions for the reflection coefficient of a plane wave, incident from the upper medium. Internal losses are modeled in both the substrate and the sediment layer. The solutions enable assessments to be made of the dependence of reflection coefficient on wavenumber and grazing angle for different shapes of density and sound speed profile in the sediment. The limiting cases of very low and very high frequency are examined, and both limits are shown to give reflection coefficients independent of the shape of the density or sound speed profile in the sediment layer. A number of numerical results are presented, and comparison is made with computed results from a general propagation model.

The fluctuation model of a mode-locked laser using a mirror with intensity-dependent reflection coefficient

A fluctuation model is presented for a mode-locked laser incorporating a mirror with intensity dependent reflection coefficient. Computer simulation with this model is executed for some nonlinear crystals and for varied parameters. The optimum parameters and conditions under which good mode-locking will be achieved is predicted according to the simulation calculation.

Reflection of plane acoustic waves from a layer of varying density

Analytical solutions of the Helmholtz equation are derived for the reflection of plane acoustic waves from a layer of varying density between two homogeneous media. The solutions show that the reflection coefficient is dependent on dimensionless vertical wavenumber and on the shape of the density profile in the intermediate layer. The most general case considered is one in which a step change in density is followed by a continuously varying density profile in a transition layer of finite thickness. Results are presented illustrating the dependence of reflection coefficient on wavenumber and on the structure of the transition layer. It is demonstrated that, in the limit of very low wavenumber or grazing incidence, the reflection coefficient tends to the Rayleigh coefficient appropriate to the overall density change between upper and lower media, while, in the high wavenumber limit, the reflection is given by the Rayleigh coefficient for the step change only.

THEORETICAL CALCULATION OF A NEW METHOD OF MODE-LOCKING FOR LASERS

A fluctuation model is suggested in this paper for the mode-locked laser incorporating a nonlinear mirror with intensity dependent reflection coefficient. Computer simulation with this model is conducted for varied parameters of Nd: YAG lasers and for two kinds of nonlinear crystal (KTP and KDP). The optimum parameters and conditions under which perfect mode-locking will be achieved are predicted according to the simulation calculation.

Surface Electromagnetic Waves in Quasiperiodic Superlattices

AbstractDispersion equations are obtained and the conditions of existence are considered for surface electromagnetic waves in quasiperiodic dielectric superlattices with layers arranged according to the recurrent Fibonacci rule. It is shown that in the quasiperiodic superlattices an immense number of surface modes exists approximately proportional to the number of layers in the structure. Excitation of surface waves is studied in quasiperiodic superlattices using attenuated total reflection (ATR) technique. Angular and frequency dependences of reflection coefficient for ATR technique are of fractal character.

Modelocking using mirrors with intensity dependent reflection coefficients

The steady state modelocking of a laser incorporating a mirror with an intensity dependent reflection coefficient is analysed. The pulse length is determined by the balance between pulse stretching due to gain narrowing and pulse shortening due to the nonlinear mirror. The final pulse length can approach the limit set by the gain bandwidth of the active medium.

Detection of smooth bondings of polymer coatings by ultrasonic spectroscopy

Calculations of reflection coefficients for a steel substrate with a polymer coating were made with different boundary conditions at an interface between the coating and the substrate. PET film was taken as an example of the polymer coatings. At incident angles 20–40°, frequency dependences of reflection coefficients were quite different for perfect and smooth bondings. Experimental observations of spectra of ultrasonic waves with incident angles θ≈25–27° reflected at steel substrates with coatings of PET films showed a tendency that double dips in the spectrum became single dips when the bonding became smooth.

INCOMING AND OUTGOING WAVE INTERACTIONS ON BEACHES

A technique to decompose colocated random field measurements of wave elevation and current velocity into incoming (shoreward propagating) and outgoing (seaward propagating) components is presented. This decomposition technique, which is less sensitive to noise, enables us to determine the frequency dependent reflection coefficients and also the relative phase between the incoming and outgoing waves. The method is applied to C2S2 and NSTS data sets, from beaches with wide ranging characteristics and wave regimes. The results demonstrate the selective nature of beach absorption/reflection characteristics but are inconclusive in terms of a proper parameterization of reflections on natural beaches

Prestack Kirchhoff inversion of common‐offset data

In trying to resolve complex geologic structures, the pitfalls in employing the CDP method become evident. Additionally, stacking multioffset traces corrupts the amplitudes necessary for stratigraphic analysis. In order to preserve whatever structural and amplitude information is in the data, prestack processing should be performed. Given common‐offset data and the velocity above a reflector, prestack acoustic Kirchhoff inversion resolves the location of the interface. When amplitude information has been preserved in the data, the method additionally calculates the reflection coefficient at each interface point. For band‐limited seismic data, the inversion operator produces a sinc‐like picture of the reflector, with the peak amplitude of this band‐limited singular function equal to the angularly dependent reflection coefficient. The inversion development is based upon high‐frequency Kirchhoff data which are inserted into a general 3-D inversion operator. Asymptotically evaluating the four resulting integrals by the method of four‐dimensional stationary phase permits an inversion amplitude function to be chosen so that the inversion operator produces a singular function of support on the reflector, weighted by the reflection coefficient. Specializing the three‐dimensional inversion operator to two and one‐half dimensions allows for processing of single lines of common‐offset data. Synthetic examples illustrate the accuracy of the method for constant‐velocity Kirchhoff data, as well as the problems in applying constant‐velocity data to multivelocity models.

Surface impedance method for the analysis of phased arrays with a lossy ground plane

An approximate method for the analysis of phased arrays of waveguide apertures in a lossy surface is developed. The procedure uses a surface impedance boundary condition in place of modal expansions in the lossy region. The method is validated in the two‐dimensional case by comparing numerical results with those obtained by using modal expansions both in the feed waveguide and the lossy medium. The accuracy of the method improves as the magnitude of the lossy dielectric constant increases. The location of the blind spot when the lossy region is backed with a conductor is accurately predicted by the surface impedance method. Calculations of scan dependent matched reflection coefficient, element power gain and power loss to the surface are presented. Salient features of the effects of loss are discussed. The results of the paper permit an extrapolation of the surface impedance method to arrays of realistic waveguide phased array elements with lossy ground.

Analysis of the introduction and removal of glycerol in rabbit kidneys using a Krogh cylinder model

In 1982, Rubinsky and Cravalho described a Krogh cylinder model for the analysis of cryoprotectant transport in a perfused organ. By application of the Kedem-Katchalsky equations, changes in tissue volume caused by movements of water and solute were used to predict changes in capillary radius ( Cryobiology 19, 70–82, 1982). We have now measured the changes in vascular resistance that are produced when sucrose or glycerol is introduced into the perfusate flowing through rabbit kidneys at 10 °C, and have analyzed these data by means of the Rubinsky-Cravalho semiempirical model. The sucrose data provided an estimate of hydraulic conductivity and the dimensions of the Krogh tissue units. Three rates of addition of glycerol, 10, 30, and 90 m M/min to a final concentration of 3 M, were studied. The vascular resistance fell to ~40% of its initial value (radius ~128% of initial value) with all three rates of addition, and then returned toward its normal value while the glycerol concentration was still increasing. This behavior could be explained either by a sudden change in solute permeability at that capillary radius, or by an inverse dependence of reflection coefficient upon solute concentration. Evidence is presented that favors the latter interpretation. The best fits for the apparent hydraulic conductivity and apparent solute permeability for glycerol are 1 × 10 −6 cm/sec atm and 6 × 10 −8 cm/sec, respectively, with the reflection coefficient falling from 1.0 when the glycerol concentration is zero to 0.1 when it is 3 M. The model is used to predict tissue concentrations of glycerol throughout each experiment.