Showing papers on "Plane wave published in 1972"

Nonlinear Modulation of Gravity Waves

Abstract: Slow modulation of gravity waves on water layer with uniform depth is investigated by using singular perturbation methods. It is found, to the lowest order of perturbation, that the complicated system of equations governing such modulation can be reduced to a simple nonlinear Schrodinger equation. A nonlinear plane wave solution to this equation is found to correspond to the so-called Stokes wave. The linear stability of this plane wave solution is essentially determined by the sign of the product of two coefficients in this equation, yielding Benjamin and Whitham's criterion. The same equation is found to give a weak cnoidal wave derived from the Korteweg-de Vries equation in the shallow-water limit.

Use of the three‐dimensional covariance matrix in analyzing the polarization properties of plane waves

Abstract: A technique for analyzing the polarization properties of plane waves that offers a number of advantages over methods currently used in the analysis of both ground and satellite observations of waves is developed. This technique reduces the computations required to find the wave normal vector, is less sensitive to common noise sources, and is amenable to analog implementation. The technique here is applied specifically to the analysis of a proton whistler, but it can also be used in most studies of ULF, ELF, and VLF magnetic-wave phenomena.

Nonlinear Frequency Shift of an Electron Plasma Wave

Abstract: The shift in the complex frequency of a large-amplitude electron plasma wave is formulated in terms of a new subtraction procedure which reproduces the damping coefficient of Mazitov and of O'Neil directly from Poisson's equation. A time-dependent frequency shift is obtained which produces a phase shift that should be amenable to experimental observation. The results are interpretated in terms of simultaneous conservation of momentum and energy in the wave frame.

Group-theoretical analysis of elementary particles in an external electromagnetic field

Abstract: We consider the symmetry properties of a particle interacting with an electromagnetic circularly polarized plane wave. The classical and quantum analysis of the stability group of the plane wave exhibits the origin of the mass shift of the particle. The Chakrabarti’s dynamical representation of the Poincare group is rederived and its physical meaning is given.

On non-linear theory of instability of a mono-energetic electron beam in plasma"

Abstract: The excitation of a monochromatic plasma wave by a 'cold' electron beam is investigated. The solution obtained describes the transition from the exponential growth of the wave amplitude in the linear stage to the amplitude oscillations associated with trapping of the beam in the potential well created by the wave. The maximum amplitude and its oscillation period are found. Both non-relativistic and relativistic beams are investigated.

Acoustic abatement method and apparatus

Abstract: An acoustic receiver, amplifier and transmitter generate an anti wave which is in-phase and of mirror symmetry with respect to a propagating acoustic wave. Coherent propagation means such as an acoustic duct of particular dimensions redirects and/or converts the acoustic wave and the anti wave, which otherwise propagate with incremental wavefronts at different vectors, into plane waves which are superimposed to create wave interference which itself propagates. For noise of high sound pressure level such as created by a gas turbine engine, the acoustic transmitter comprises a modulated gas flow speaker coupled to one or more bleed ports which supply gas at one or more pressures offset from ambient pressure.

Analytical studies of some acoustic problems of jet engines

Abstract: This thesis presents analytical studies of internal noise generation and transmission in jet engines and its radiation from the duct ends. The propagation and generation of acoustic waves in a choked nozzle is considered first. Pressure and entropy fluctuations caused by gas stream non-uniformities like "hot spots," are incident on the nozzle entrance. A novel noise-generation mechanism is uncovered where acoustic waves are produced by a distribution of sources of strength proportional to the entrance entropy fluctuation and local gradient of the mean flow velocity. The propagation of acoustic waves in a moving medium in the presence of semi-infinite or finite boundaries is then considered. A transformation is introduced which relates the solutions of such problems to the solutions of associated problems in a stationary medium. The method is described by discussing the Sommerfeld problem of diffraction of a plane wave by a half plane immersed in a subsonically moving medium. When the plane has a trailing edge, it is shown that both reflection and shadow regions expand; while the opposite occurs for a leading edge,in which circumstance an additional diffracted wave also appears. In the supersonic case, all the diffraction problems are related to a single reference problem, solved by Fourier transform methods. A decomposition of the pressure field in a "geometrical optics" field and a diffracted field is given, showing some remarkable similarities with the subsonic case solution. The radiation of acoustic modes from a duct immersed in a subsonically moving medium is treated by a similar transform method. The presence of the uniform flow has roughly the same effect as an increase in frequency of the incident wave, at constant mode number. The effect of acoustical lining on the radiation pattern is examined, and side radiation is shown to be greatly reduced for the lower order modes. The transmission and reflection of acoustic waves incident on a blade row is analyzed by the transform method,and the transmission and reflection coefficients for the blade row immersed in a moving medium are expressed in terms of the basic acoustic characteristics of the blade row in a stationary medium.

A Lagrangian theory for nonlinear wave packets in a collisionless plasma

Abstract: A Lagrangian, for the slowly varying complex amplitude of an almost monochromatic electrostatic plasma wave in an unmagnetized plasma, is derived The method is a variant of the averaged Lagrangian technique of Whitham, adapted for use in plasma physics by employing Low's Lagrangian, together with certain elimination procedures to simplify the Lagrangian to usable form The expansion in powers of the wave amplitude is carried out to quartic terms, and non-adiabatic terms are also retained Variations with respect to the amplitude lead to a nonlinear Schrodinger equation for the amplitude, while variations of the particle trajectories lead to a modified Vlasov equation, which includes the nonlinear reaction of the wave on the average trajectories It is assumed that there are no resonant particles These equations are coupled through the nonlinear frequency shift It is found that the particle aspect of the plasma has a profound effect on the stability of the system, due to resonance of the wave envelope with particles moving at the group velocity This effect, nonlinear Landau damping, is always destabilizing, leading to growth of modulations In terms of the nonlinear Schrodinger equation, the effect changes the equation from a Hartree-Fock equation with a delta-function interaction to one with a non-momentum-conserving, non-local interaction In the limit of fairly small wavelength, of the modulations, it is shown that the growth rate approaches that expected from plasma kinetic theory

Fourth Moment of a Wave Propagating in a Random Medium

Abstract: The fourth statistical moment of a scalar wave propagating in a random medium is investigated. Starting with a partial differential equation obtained by various authors in a multiple-scattering approximation, we discuss the general properties of the fourth moment of an initially plane wave and then present numerical results for a two-dimensional plane wave. Results are presented for the variance and covariance of irradiance scintillations. Both results are shown to agree well with experiment. In particular, the variance exhibits the experimentally observed saturation phenomenon, and the covariance results indicate that the correlation length for irradiance scintillations is not proportional to (λz)12 in the saturation region and that the aperture-averaging effect is less than that predicted by results based on the Born or Rytov approximations.

The Principle of Complementarity

Abstract: The wave-particle duality of photons and electrons was thoroughly discussed at a conference held at the Solvay Institute in October 1927, where Albert Einstein and Niels Bohr were the most prominent participants. From the beginning Einstein manifested great hesitation in accepting the renunciation of causal description of physical phenomena introduced by quantum theory. He clearly demonstrated his basic attitude by discussing the example of an atomic object (electron or photon) impinging upon a screen with a single slit (see figure 4). To the left of the screen the object is supposed to have a precisely defined momentum p and hence it is represented as a plane, harmonic wave. When passing through the slit, the plane wave is scattered into a cylindrical wave with an opening angle determined by the wavelength and the slit aperture. Einstein’s problem consisted of the fact that as soon as the object is detected at some point A on a photographic plate placed to the right of the screen, the object-wavecannot be detected in any other part of space whatever, which is directly contradictory to any wave phenomenon in classical physics. But the object-wave cannot be detected in any other part of space whatever, which is directly contradictory to any wave phenomenon is classical physics. But the object-wave just cannot be a classical wave phenomenon because this would imply the possibility of knowing the dynamical state of the object far more precisely than is compatible with the indeterminacy relations.

A method of numerical analysis of wave propagation application to wave diffraction and refraction

Abstract: A method is presented to obtain numerically wave patterns in the region of arbitrary shape. The principle is to solve the linearized wave equations under given boundary conditions from a certain initial state. In this paper, two principal applications of our method of numerical analysis are presented in the fundamental fashion. The first application of our method is related to wave diffraction. The distribution of wave height along a semi-infinite breakwater and a detached breakwater is calculated and compared with that obtained from the conventional analytic solutions to confirm the validity of our numerical method. Three examples of application are presented to the wave height distribution along breakwaters of arbitrary shape and of arbitrary reflecting power and to wave force upon a large isolated vertical structure. The second application is to wave refraction. In particular, this method of numerical analysis is applicable to the analysis of wave propagation in the region of ray intersections which are indicated by the conventional geo-optic wave refraction theory. An example of application to a submerged shoal with concentric circular contours where a cusped caustics is formed is presented and the calculated wave height distribution around the shoal is compared with that obtained from hydraulic model experiments. Our method of numerical analysis might be applied to the calculation of wave height distribution in the region of more realistic bottom topography and it is possible to include vertical boundaries of arbitrary shape.

Ionospheric propagation of oblique hydromagnetic plane waves at micropulsation frequencies

Abstract: In this paper we consider the high-latitude transmission and reflection properties of the ionosphere for oblique hydromagnetic plane waves in the Pc 1 frequency regime. Transmission and reflection coefficients for the upper and lower ionosphere are obtained for daytime and nighttime conditions. The results are compared with those obtained for a vertically incident plane wave.

Acoustic Radiation Pressure in a Traveling Plane Wave

Abstract: A theory is developed for acoustic radiation pressure exerted by a plane wave on a perfect absorber, using Euler's momentum theorem. For the case of an open vessel, the radiation pressure P equals the mean energy density E even when nonlinearities of the medium and distortion of wave form are taken into account. For a closed vessel P equals [1 + 12(B/A)]E. The term B/A describes the non-linearity in the pressure-density relation for the medium and equals γ−1 for the case of an ideal gas under adiabatic conditions.

Spectral resolution of breakwater reflected waves

Abstract: A means of resolving incident and reflected wave heights for a partial standing wave through the use of two fixed wave sensors is demonstrated. Field studies were conducted in which the waves incident to the permeable rubblemound breakwater located in Monterey Harbor, CA, are spectrally resolved into incident, reflected and transmitted wave components. Power-spectra and cross-spectra are calculated for various characteristic sea states. Amplitude and phase are determined for the spectral wave components compromising the partial standing wave phenomena and reflection and transmission coefficients determined. The reflection coefficients vary between 0.3 and 0.7 and the transmission coefficients between 0.1 and 0.2. The transmission and reflection coefficients are shown to be dependent on the frequency and amplitude of the incident waves and the tidal stage.

A study of charge density in beryllium

Abstract: The x-ray structure amplitudes for the 27 lowest-angle Bragg reflections of beryllium metal have been measured on an absolute scale. These can be used to deduce the charge density. The measured structure amplitudes are compared with those predicted both by the free atom Hartree-Foch wave functions and by a free electron orthogonalized plane wave model. For both models the predicted value for the lowest angle reflection is close to that observed, but the structure amplitudes of subsequent reflections given by the models are significantly greater than those observed. To account for these discrepancies a model of beryllium involving 2p-like tight binding functions is proposed.

Wave propagation and dispersion in space-time periodic media

Abstract: The dispersion characteristics of electromagnetic fields are examined for waves propagating in a medium with a permittivity which is modulated periodically with respect to time and one spatial co-ordinate. By taking a guided-wave approach, which expresses the fields of arbitrary sources in terms of a superposition of modal solutions, it is shown that many properties of the individual modes may be inferred by means of wavenumber diagrams. These diagrams are easily constructed for the special case of a vanishingly small periodic modulation. By using coupled-mode consideration, this special case is extended to serve as a good approximation for finite modulation amplitudes. In addition to yielding information on the dispersion character of modal fields, it is shown that the wavenumber diagrams may be employed to extract the modal constituents of a plane wave scattered by a layer containing a space-time periodic medium. The principal far-field components of waves excited by a localised arbitrary source embedded in such a medium may also easily be obtained from the wavenumber diagrams. The guided-wave approach, together with its associated wavenumber diagrams, is thus shown to serve as a powerful tool in analysing and understanding a large class of phenomena, which includes the diffraction of light by sound and parametric effects in nonlinear media, as well as other aspects of wave interactions in material bodies.

On diffraction and focusing in anisotropic crystals

Abstract: This paper discusses various aspects of diffraction and focusing for waves in anisotropic crystals, and the concepts are applicable to electromagnetic, ultrasonic bulk, or ultrasonic surface waves in homogeneous but arbitrarily anisotropic crystals. A numerical technique based on an angular spectrum of plane waves representation is shown to produce theoretical intensity profiles in good agreement with acoustooptic probe measurements of the diffraction field of a slit-type ultrasonic transducer launching quasi-longitudinal and quasi-shear waves in quartz along on axis of extreme anisotropy where the wave normal and the direction of energy flow are separated by angles greater than 20°. A theoretical study of two-dimensional focusing structures for use in anisotropic crystals reveals that a launching transducer fabricated in the shape of the relevant group-velocity surface can be far superior in producing a well-defined focus to a structure having the shape of a circular arc. The computation techniques can be applied to obtain the diffraction field of any arbitrary aperture function and the examples described, theoretical and experimental, concern acoustic waves in crystals demonstrating extreme elastic anisotropies, in fact much more extreme than would be encountered in analogous cases of optical diffraction. Because of current relevance to device research, emphasis in the latter sections of the paper is placed on ultrasonic surface waves.

Radio Wave Propagation in Stratified Media with Nonuniform Boundaries and Varying Electromagnetic Parameters: Full Wave Analysis

Abstract: Full wave solutions are derived to the problem of radio wave propagation in stratified media with non-uniform boundaries and varying electromagnetic parameters. The analysis employs a complete set of forward and backward travelling waves. The continuous parts of the wavenumber spectrum constitute the radiation field and the lateral waves, and the discrete part of the spectrum is identified as the surface wave term. The solutions are not restricted by the approximate surface impedance concept and the source and receiver can be situated on opposite sides of the interface. Exact boundary conditions are imposed and the solutions are shown to be consistent with the reciprocity relationships.

Measurement of vibrational amplitude by modulation of projected fringes.

Abstract: A full-field, variable sensitivity technique for mapping the vibrational amplitude of a diffuse surface is demonstrated. The surface under study is placed in an optical field consisting of two mutually coherent plane waves which propagate in different angular directions. At any instant of time the interference of these waves causes a fringe pattern to be formed on the surface under study. The time average, over one or more vibrational periods, of the intensity pattern on the surface can be obtained in real time by utilizing visual persistance or by making a time-average recording of an image of the surface. The visibility of the fringe pattern thus obtained is found to be modulated by a function of the local amplitude of vibration. This modulation can be observed directly or a photograph of the pattern can be optically processed to yield fringes that are loci of constant vibrational amplitude.

Computation of Dispersion Curves for a Hot Magnetoplasma with Application to the Upper‐Hybrid and Cyclotron Frequencies

Abstract: Rapid calculations of the dispersion relation can be made for a hot, Maxwellian electron magnetoplasma, with collisions and for any angle β between the wave normal and static magnetic field without using the low-temperature or the quasi-static approximations. The dispersion equations of Lewis and Keller [1962] are discussed and interpreted for the purpose of computer programming; these equations are valid for a Vlasov-Maxwellian plasma and contain a particle-preserving collision term. Examples of dispersion curves for homogeneous plane waves show: (1) protrusions from some refractive-index surfaces and (2) the usual multiplicity of solutions for a Maxwellian plasma when the real and imaginary components of the refractive index are of similar magnitude. For a wave frequency 1.11 times the plasma frequency and about 1.78 times the gyrofrequency, a minimum is found in the collisionless damping at β = 0° and a maximum is found at about β = 14°. Three alternatives for the gyroresonance observations on topside ionograms can be found from a study of the dispersion curves near the gyrofrequency: (1) an energy transfer between the highly damped whistler mode and electrons in the vicinity of the sounder, (2) the field resulting from the multiplicity of solutions mentioned above, and (3) an evanescent field.

Physical Parameters in Microwave Heating Processes

Abstract: The physical parameters involved in microwave heating processes of heterogeneous materials containing water are considered. On the basis of a general equation, which determines the increase of temperature when the body is exposed to microwave electromagnetic field, we analyze the interaction of the thermal, mechanical, and electromagnetic parameters of the body and the heating process. The analogy with scattering of waves by bodies of various shapes is explored and illustrated analytically for the simple model of a plane wave incident on a half space filled with lossy dielectric.

A study of microwave leakage through perforated flat plates.

Abstract: A simple formula useful for predicting leakage through a circular hole array in a metallic flat plate is presented. A correction is given for plate thickness. The formula is applicable to arrays having either a 60-deg (staggered) or 90-deg (square) hole pattern, but is restricted to the case of (1) an obliquely incident plane wave with the E field polarized normal to the plane of incidence, and (2) large transmission loss. When theoretical values were compared to experimental data obtained on test samples having transmission losses greater than 20 dB, the agreement between theory and experiment was typically better than 1 dB at S band and 2 dB at X band.

Time domain radiation and scattering by thin wires

Abstract: Direct time domain solutions for radiation from and scattering by thin conducting wires are considered. The problem is formulated in terms of two coupled integrodifferential equations derived from the retarded potentials, the continuity equation, and the boundary conditions for the wire. Solution of these equations is effected using the method of moments resulting in a set of simultaneous time iterative matrix equations. A time domain reciprocity theorem suitable for thin wire objects is also presented. The theorem demonstrates the relationship between reciprocity and the adjoint operator for the problem. Two moment solutions are presented for straight wires: (1) a point tested solution, and (2) a pulse tested solution. The radiation field is found by direct application of the reciprocity theorem. All solutions are presented as algorithms suitable for computation. The algorithms are time iterative by nature, and inexpensive in terms of computer time. Computed results are presented for the straight wire scatterer excited by a plane wave with unit step time dependence. The “end fire” effects predicted by traveling wave theory are observed in the scattered field results. The source of these effects is shown to be the end of the wire last intercepted by the incident field. Additional results are presented for the straight wire antenna excited by a unit step voltage applied at an arbitrary driving point. The computed driving point current is compared to the results derived for the case of an infinite wire antenna over the time interval that the comparison is valid.

Propagation and absorption of ion hybrid waves in a weakly inhomogeneous plasma laser. I

Abstract: The problem of electromagnetic wave propagation and absorption in weakly inhomogeneous plasma layer (in the geometrical optics approximation) is solved. The plasma density increases in the direction perpendicular to the magnetic field. The excitation of the waves occurs in the low density region. It is shown that deceleration of the wave along the magnetic field is necessary for its propagation into the plasma layer. As the wave penetrates the plasma layer its phase velocity reduces and at a certain plasma density the electromagnetic wave transforms into a plasma wave. The conditions for such a transformation of electromagnetic wave into plasma wave have been calculated in the hydrodynamic approximation.

Choice of the model of atmospheric turbulence.

Abstract: The concept of equivalent models of turbulence is introduced in order to investigate how the theoretical behavior of the structure function of an electromagnetic wave propagating in a given turbulent medium depends on the turbulence model. It is shown that equivalent models may give rise to substantially different structure functions of a wave parameter. On the other hand, the experimental structure function of the phase of a plane wave can be well fitted by the theoretical curves derived from different models, with suitable choices of the turbulence parameters appearing in the models. However, such models turn out not to be equivalent. When experimental data on the turbulence are not available, simultaneous measurements of the structure functions of more than one wave parameter are suggested, for the choice of the model.

A Study of Microwave Leakage through Perforated Flat Plates (Short Papers)

Abstract: A simple formula useful for predicting leakage through a circular hole array in a metallic flat plate is presented. A correction is given for plate thickness. The formula is applicable to arrays having either a 60/spl deg/ (staggered) or 90/spl deg/ (square) hole pattern, but is restricted to the case of 1) an obliquely incident plane wave with the E field polarized normal to the plane of incidence, and 2) large transmission loss. When theoretical values were compared to experimental data obtained on test samples having transmission losses greater than 20 dB, the agreement between theory and experiment was typically better than 1 dB at S band and 2 dB at X band.

Propagation of Plane Waves in Biaxially Anisotropic Layered Media

Abstract: This paper is concerned with the general theory of wave propagation in layered biaxially anisotropic media. Details are presented for the calculation of the induced waves that are due to an arbitrarily polarized and obliquely incident wave impinging on a three-layer structure. The total numbers of partial waves with their respective phase velocities, direction of phase propagation, and polarization are determined by the use of the Fresnel equation and Snell’s law applied to each layer. The vector amplitudes of the partial waves are found by proper matching of the field components at the interfaces. The expressions thus found are shown to reduce to known results for a uniaxial three-layer structure. An extension of this theory to an arbitrary number of layers is also presented.