Showing papers on "Wave propagation published in 1974"

A theory of long-period magnetic pulsations: 1. Steady state excitation of field line resonance

Abstract: A theory of long-period (Pc 3 to Pc 5) magnetic pulsations is presented based on the idea of a steady state oscillation of a resonant local field line that is excited by a monochromatic surface wave at the magnetosphere. A coupled wave equation between the shear Alfven wave representing the field line oscillation and the surface wave is derived and solved for the dipole coordinates. The theory gives the frequency, the sense of polarizations, orientation angle of the major axis, and the ellipticity as a function of magnetospheric parameters. It also clarifies some of the contradicting ideas and observations in relation to the sense of polarization and excitation mechanism. At lower latitude it is shown that the orientation angle rather than the sense of rotation is a more critical parameter in finding the direction of wave propagation in the azimuthal coordinate and hence in finding the evidence of wave excitation at the magnetospheric surface by the solar wind.

Acoustic‐gravity waves in the upper atmosphere

Abstract: In this paper we review the theory of acoustic-gravity waves, the interaction of such waves with the ionosphere, the experimental support for the existence of such waves in the upper atmosphere, and the role played by acoustic-gravity waves in thermospheric dynamics. After a thorough discussion on the properties of acoustic-gravity waves in an ideal isothermal atmosphere, the effects produced by horizontal winds, sharp boundary discontinuities, and dissipative processes are discussed. The generation of these waves by stationary or moving sources is then treated. It is shown that the atmospheric response to a stationary impulse source can be described by the emission of three waves: acoustic, buoyancy, and gravity. These discussions are then followed by reviewing propagation effects in a realistic atmosphere for both free waves and guided waves. Recent numerical results are given. When acoustic-gravity waves propagate through the ionosphere, interaction between the wave and the ionosphere will take place. The physical processes involved in such an interaction are examined.

Raman and Brillouin scattering of electromagnetic waves in inhomogeneous plasmas

Abstract: Raman and Brillouin scattering of an electromagnetic wave in an inhomogeneous, expanding plasma are studied. Application to laser‐pellet irradiation is considered.

On the propagation of sound waves in cylindrical tubes

Abstract: It is shown that the two main parameters governing the propagation of sound waves in gases contained in rigid cylindrical tubes, are the shear wave number, s = R ρ s ω / μ , and the reduced frequency, k = ωR/a 0 . It appears possible to rewrite the most significant analytical solutions for the propagation constant, Γ, as given in the literature, as simple expressions in terms of these two parameters. With the aid of these expressions the various solutions are put in perspective and their ranges of applicability are indicated. It is demonstrated that most of the analytical solutions are dependent only on the shear wave number, s , and that they are covered completely by the solution obtained for the first time by Zwikker and Kosten (1949) . The full solution of the problem has been obtained by Kirchhoff (1868) in the form of a complicated, complex transcendental equation. In the present paper this equation is rewritten in terms of the mentioned basic parameters and brought in the attractive form F =0, which is solved numerically by using the Newton-Raphson procedure. As first estimate in this procedure the value ofaccording to the solution of Zwikker and Kosten is taken. Results are presented for a wide range of s and k values.

On the incipient breaking of small scale waves

Abstract: It is shown that the surface wind drift in the ocean substantially reduces the maximum wave height ξx and wave orbital velocity that can be attained before breaking. If q is the magnitude of the surface drift at the point where the wave profile crosses the mean water level and c is the wave speed, then \[ \zeta_{\max} = \frac{c^2}{2g}\bigg(1-\frac{q}{c}\bigg)^2. \] Incipient breaking in a steady wave train is characterized by the occurrence of stagnation points at wave crests, but not necessarily by discontinuities in slope. After breaking, there is in the mean flow a stagnation point relative to the wave profile near the crest of the broken wave, on one side of which the water tumbles forward and behind which it recedes more smoothly to the rear. Some simple flow visualization studies indicate the general extent of the wake behind the breaking region.

Synthetic microseismograms; logging in porous formations

Abstract: Biot’s theory of wave propagation in a fluid‐filled porous elastic solid takes account of energy dissipation due to relative motion between viscous pore fluid and solid matrix. This theory has been applied to a numerical study of sound pulses propagating along a cylindrical borehole and along a plane interface. It is found that properties such as permeability affect the attenuation of the signal only at high frequencies. For the plane interface, the effect on the P-arrival is small; on the S-arrival it is moderate; and on the Stoneley‐wave it is large, but only if source and detector are close to the interface and the flow of fluid across the interface is relatively unrestricted. With a wide‐band signal, the low‐frequency pseudo‐Rayleigh wave can partially mask the S-arrival. Similar conclusions hold for the logging tool centered in the borehole, and arrivals other than the first P may be difficult to pick, especially for narrow‐band signals. The amplitude of the wave train arriving with approximately the...

Principles of distributed feedback and distributed Bragg-reflector lasers

Abstract: Wave propagation in periodic waveguides is analyzed by decomposing the eigen Bloch waves into traveling-wave components. It is shown that the principal components consist of a primary forward wave, a primary backward wave, and their Bragg-scattered secondary waves. One important parameter is the coupling constant s due to Bragg scattering, which relates the secondary wave to the respective primary wave. Laser threshold condition is then obtained by applying the continuity of tangential E and H at the two boundaries. The results thus obtained are general and applicable to thin-film lasers with various waveguide structures. The laser threshold condition of thin-film Bragg lasers is expressed in terms of two effective reflection coefficients for easy comparison with conventional lasers. For appreciable reflection, a significant change either in the propagation constant or in the coupling constant is required. Two basic types of thin-film Bragg lasers are distributed-feedback (DFB) lasers in which Bragg scattering is confined to the active medium and distributed-Bragg-reflector (DBR) lasers in which Bragg scattering is limited to regions beyond the active medium. The threshold gain, frequency control, and mode selectivity for both types are analyzed and the analyses are applied to GaAs and Nd lasers. It is shown that DBR lasers should have a lower threshold gain and a better mode selectivity than DFB lasers. For distributed-feedback effect to play a significant role in thin-film Bragg lasers, the product kL int must be greater than unity where K is the distributed-feedback coefficient and L int is the interaction length. Advantages for having periodic structures outside the active medium so as to relax constraints on k and L int are also discussed.

Thermal Self-Focusing of Electromagnetic Waves in Plasmas

Abstract: An intense electromagnetic wave propagating in a collisional plasma is found to be unstable to a thermal self-focusing instability by a self-consistent solution of the hydrodynamic, heat conductivity, and wave propagation equations. The results are applied to ionospheric modifications and proposed power transmission experiments, and to laser-plasma interactions.

Instabilities in continuous-wave light propagation in absorbing media

Abstract: The stability of a monochromatic constant-intensity laser beam propagating through a resonant medium is considered. It is found that many absorbers should exhibit a region of negative conductivity and, consequently, amplify perturbations. The associated gain is dependent on a number of variable parameters, such as laser-beam intensity, perturbation frequency, relaxation times, degeneracy, transverse mode, inhomogeneous broadening, etc. Putting absorbers inside Fabry-Perot interferometers allows the construction of plane-wave devices with a bistable output.

Experimental study of internal waves over a slope

Abstract: Internal waves of the fundamental mode propagating into a shoaling region have been studied experimentally in a continuously stratified fluid. The waves divide into three classes depending upon the ratio of the bottom slope γ to the wave-characteristic slope c. For γ/c 1, the waves are inhomogeneous and have complex spatial dependence.

Geometrical optical approach for electromagnetic wave propagation in rectangular mine tunnels

Abstract: Electromagnetic wave propagation inside an empty rectangular mine tunnel with imperfect walls is considered. The modal expansion of the fields is complicated by the coupling of the basic modes by the imperfect walls. To avoid this difficulty, and in view of the large guide dimensions relative to the free space wavelength, a geometrical ray approach is proposed. To provide a theoretical foundation for the method, we first consider an idealized waveguide model with two perfectly reflecting side walls. The modal field expansion for this prototype model is fully analyzed to provide a satisfactory comparison between the modal and the geometrical ray sums. The proposed general ray method is then applied to the rectangular waveguide when all four walls are imperfectly conducting. Finally, the influence of wall roughness is considered by a relatively simple method.

Whistler waves observed upstream from collisionless shocks

Abstract: Waves in the frequency range 0.5 - 4 Hz were studied in the region upstream of the earth's bow shock using data from the fluxgate magnetic field experiment on IMP-6. Analysis of 150 examples of these waves during a three month interval indicates that amplitudes are generally less than 1 or 2 gammas and propagation directions generally make angles of between 20 and 40 degrees with the field direction. The waves as measured in the spacecraft frame of reference are either left or right hand polarized with respect to the average field direction. It is concluded that the observed waves are right handed waves in the plasma frame of reference with wavelengths of approximately 100 km propagating upstream in the whistler mode. Doppler shifting reduces the observed frequencies in the spacecraft frame and reverses the observed polarization for those waves propagating more directly upstream. Similar waves are seen ahead of most interplanetary shocks.

Nonlinear evolution of parallel‐propagating hydromagnetic waves

Abstract: The nonlinear evolution of plane hydromagnetic fluctuations propagating along the unperturbed magnetic field direction is considered. From an expansion of the ideal magnetohydrodynamic equations and the hydromagnetic shock jump conditions, it is shown that a wave in which the magnitude of the magnetic field is nonconstant steepens into a shock and subsequently evolves toward a purely Alfvenic fluctuations of lower mean energy density. Explicit expressions are derived for the asymptotic state and for the characteristic lines which describe the evolution toward that state. A class of fluctuations which includes linearly polarized waves is shown to evolve into rotational discontinuities. The results are applied to observations of hydromagnetic fluctuations in the solar wind.

Krylov‐Bogoliubov‐Mitropolsky method for nonlinear wave modulation

Abstract: The Krylov‐Bogoliubov‐Mitropolsky perturbation method is applied to systems of nonlinear dispersive waves including plasma waves such as ion‐acoustic, magneto‐acoustic, and electron plasma waves. It is found that long time slow modulation of the complex wave amplitude can be described by the nonlinear Schrodinger equation for a very wide class of nonlinear dispersive waves.

A theory of medium-scale traveling ionospheric disturbances

Abstract: Analysis of the excitation of atmospheric gravity waves leads to a hypothesis concerning the nature of medium-scale traveling ionospheric disturbances (TID's) and their relation to large-scale TID's Stationary phase techniques are used to derive the asymptotic fluctuations of velocity and electron density generated by a line source (eg, the auroral electrojet) Dissipation by viscosity and thermal conductivity is included in an approximate manner The gravity wave response includes a discrete spectrum of upper-atmospheric guided modes and a continuous spectrum of freely propagating waves; these two classes of waves can be associated with large-scale and medium-scale TID's, respectively The medium-scale TID's, in turn, are primarily composed of two families of waves: those that propagate obliquely upward from the source and reach the F region directly and those that propagate initially downward and reach the F region only after reflection from the earth For an E region source the earth-reflected waves appear as nearly monochromatic wave packets, whereas the direct waves appear for the most part as single pulses; this qualitative difference corresponds to J E Titheridge's observational distinction between periodic and nonperiodic TID's It is suggested that this dichotomy may imply the dominance of upper-atmospheric (as opposed to tropospheric) sources In this connection the average fluctuations of the auroral electrojet are shown to be sufficient to generate sizable medium-scale TID's that propagate to large horizontal distances with no loss of amplitude despite the absence of ducting mechanisms Such propagation is possible because amplitude attenuation due to cylindrical spreading is counteracted by the fact that the lower-frequency waves, which reach the F region at the greater horizontal distances, are generated with larger amplitudes Several properties of the calculated response, including the linear increase of period and wavelength with distance from the source, might be useful in future observational studies designed to identify the sources of medium-scale TID's

Behavior of the flare-produced coronal MHD wavefront and the occurrence of type II radio bursts

Abstract: The propagation of the weak MHD fast-mode shock emitted into the corona by flares at their explosive phase is computer-simulated. It is shown as the result that the shock wave is refracted towards the low Alfven velocity regions pre-existing in the corona, and the strength of the shock, which is otherwise weak, is drastically enhanced on encountering low- V A regions due to the focussing effect by refraction and also due to the lowered propagation velocity of the shock in such regions. It is expected that electron acceleration takes place in such a drastic strengthening of the shock, leading to the local excitation of plasma waves and eventually to the occurrence of radio bursts at such locations. Such locations of shock strength enhancement, when computed by using HAO realistic models of coronal density and magnetic field of the day of certain type II burst events, actually coincide roughly with the observed positions of type II bursts. Peculiar configurations of type II burst sources as well as their occurrence even beyond the horizon of the responsible flare are explained consistently by the large scale refraction and the local enhancement of the shock due to the global and local distribution of Alfven velocity in the corona. A unified interpretation is given for the occurrence of type II bursts and Moreton's wave phenomena, and also the relation of our MHD fast-mode disturbance with other flare-associated dynamical phenomena is discussed.

Theory of parametric instability near the lower‐hybrid frequency

Abstract: The dispersion relation for parametric instabilities near the lower‐hybrid frequency is derived and analyzed. It is found that for propagation angles cos2θ(mi/me) < 1 resonant decay into ion acoustic (ion‐cyclotron) waves does not occur; rather, decay into nonresonant quasi‐ion modes and lower‐hybrid waves occurs. The driving mechanism for this instability is shown to be analogous to nonlinear Landau damping in perturbation theory. The large amplitude dispersion relation is analyzed numerically for a number of typical experimental regimes, and growth rates and thresholds are obtained for both the purely growing mode and the newly found quasi‐ion modes.

Excitation of edge waves by waves incident on a beach

Abstract: It is shown theoretically that surface waves incident on a beach from deep water can excite edge waves. In particular, a standing wave normally incident on a beach of constant gentle slope is found to transfer energy to edge waves through a weak resonant interaction resulting from an instability of the incident wave with respect to perturbation by edge waves. The analysis is based on the shallow water approximation and ignores the earth's rotation and consequently applies only to relatively low-mode, high-frequency waves. Coupling coefficients, frequencies, and longshore wave numbers of the excited waves are given. In accordance with Hasselmann's (1967) rule, only edge waves with frequencies lower than the frequency of the incident wave are excited by this mechanism. Viscous effects suggest that an edge wave with a frequency one-half that of the incident wave is preferentially excited.

The stability of planetary waves on an infinite beta‐plane

Abstract: The stability of a planetary wave on an infinite s‐plane is examined. There are two parameters in the problem, (a) ? = Uκ2/β where U is the velocity amplitude of the planetary wave and κ its wavenumber, and (b) the direction of the wavenumber of the planetary wave. For large M, the problem reduces to the Rayleigh problem for a sinusoidal velocity distribution. The growth rate of the most unstable wave is 0.27 Uκ. 38 % of the energy lost by this wave is transferred to wavenumber 0.59 κ and 61 % is transferred to wavenumber 1.16 κ. As ? decreases and β effects become more important, there are fewer unstable waves, but unstable waves can always be found. For small M, the disturbance comprises two waves which form a resonantly interacting triad with the primary wave. Some geophysical applications are discussed. It is shown, for instance, that for strong currents like the Gulf Stream, this type of instability is much more important than inertial instability. Also, observations indicate that the dominant eddies...

Intense Coherent Cherenkov Radiation Due to the Interaction of a Relativistic Electron Beam with a Slow-Wave Structure

Abstract: Extremely high-power microwave emission is generated when a pulsed relativistic electron beam propagates down the axis of a corrugated-wall wave guide. The radiation occurs at a frequency such that the phase velocities of the negative-energy space charge wave on the beam and a low-order TM mode in the wave guide are equal. Power levels of 500 MW are generated. The conversion efficiency of electron energy into electromagnetic energy radiation is 17%.

Amplification and absorption of electromagnetic waves in overdense plasmas

Abstract: The spatial variation of the amplitude of electromagnetic radiation propagating into an inhomogeneous plasma is discussed in reference to nonlinear interaction of HCN laser radiation with plasmas and to experiments on r.f. heating of the ionosphere. Previous results on the ordinary wave and on the extraordinary wave at normal incidence are reviewed with emphasis on the physical processes affecting the amplitude behaviour. New numerical results are obtained starting from an integral representation of the solution of the wave equation for waves in a cold, inhomogeneous, magnetized plasma slab. Resonance absorption is discussed for the cases of normal incidence in the presence of a magnetic field (the Budden problem) and oblique incidence in the absence of a magnetic field.

On the propulsion of micro-organisms near solid boundaries

Abstract: In this paper an infinite waving sheet is used to model a micro-organism swimming either parallel to a single plane wall, or along a channel formed by two such walls. The sheet surface, which undergoes small amplitude waves, can represent either a single flagellum or the envelope of the tips of numerous cilia. Two different solutions of the equations of motion are presented, depending upon whether or not the wave amplitude is small compared with the separation distances between the sheet and walls. It is found that the velocity of propulsion is bounded by the velocity of wave propagation by the sheet. Both the propulsive velocity and rate of working by the sheet increase as the separation distances decrease. However, it is demonstrated that suitable alterations in wave speed or wave shape can fix the rate of working while still causing increases in propulsive velocity. Reductions in propagated wave speed, i.e. beat frequency, are particularly effective in this regard.

Standing waves on beaches

Abstract: Simultaneous measurements of run-up spectra and nearshore wave spectra associated with standing waves have been made on a natural beach. Digital wave staffs and bottom-mounted pressure sensors were placed in a line at various distances offshore from a digital run-up meter. The run-up meter, which measured the position of the edge of the water, consisted of a series of electrical contacts suspended above the beach face and spaced 30 cm apart. Because of the possible influence of nonlinear interactions on the spectra, bicoherence was estimated, and the frequency range appropriate to a linearized model was defined. In this low-frequency region of the spectrum the cross-spectra phase angles between data records had values near 0 or π at frequencies of high coherence. The energy spectrum levels and the observed phase differences between records were in good agreement with the linear shallow water wave theory (Lamb, 1932) for standing waves on a plane beach. The general reflection coefficient for the data, estimated from the disagreement between data and standing wave theory, was found to be approximately 0.7. This result indicates that the theory of Miche (1944) for reflection from a plane beach predicts a reflection coefficient that is too high by a factor of approximately 1.5.

On a variety of wave phenomena in chemical reactions

Abstract: A variety of wave phenomena are analyzed and discussed for systems in which chemical reactions and transport take place. Certain families of wave solutions of reaction‐transport equations arise owing to the weak stability of a reference state to a class of perturbations. We consider both wave induction by heterogeneities and autonomous waves and seek perturbation solutions which provide the dispersion relation and the wave vector dependence of the amplitude for one‐parameter families of waves characterized by the wave vector. For the case of an arbitrary reaction mechanism possessing a homogeneous steady state we derive, by use of bifurcation theory and frequency renormalization, small amplitude autonomous plane waves and standing and rotating waves. We find solutions corresponding to long wavelength waves, static structures, and phenomena existing only at intermediate frequencies and wavelengths. The theory is found to have a nonuniformity in convergence in the core region of pacemaker and spiral‐like so...

Propagation and mode conversion of lower-hybrid waves generated by a finite source

Abstract: The propagation of electrostatic plasma waves, and their subsequent conversion into hot plasma waves at the lower hybrid frequency is calculated for realistic density profiles and finite rf sources in a slab geometry. A finite length slow wave source having a potential distribution phi ~ cosk0z is found to generate spatial oscillations having a well-defined wavelength. These oscillations are confined to regions bounded by conical curves originating at the ends of the source. The axial distance of rf energy propagation to the lower hybrid layer is found to be greater than the radial distance of propagation by a factor of the order (mi/me)1/2. The conversion at the lower hybrid layer of the electrostatic cold plasma waves excited by a finite source into propagating hot plasma waves is calculated. It is shown that collisional damping at the lower hybrid layer may predominate over mode conversion even for relatively low collision frequencies.

Elastic waves in a fiber-reinforced composite

Abstract: T he propagation of time-harmonic elastic waves in a fiber-reinforced composite is studied. The circular fibers are assumed to be parallel to each other and randomly distributed with a statistically uniform distribution. The direction of propagation and the associated particle motion are considered to be normal to the fibers. It is shown that the average waves in the composite separate into compressional and shear types. General formulae for the complex wave number giving the phase velocity and the damping are obtained. It is shown that these formulae lead to the Hashin-Rosen expressions for the transverse bulk modulus and the lower bound for the transverse rigidity, if the correlation in the positions of the fibers can be ignored. The correlation terms, for exponential correlation, are shown to have a significant effect on the damping property of the composite, especially at high frequencies and concentrations.