Showing papers on "Wave propagation published in 1971"

ALFVÉNIC Wave Pressures and the Solar Wind

Abstract: Outwardly propagating coronal Alfven waves pressure exertion on solar wind, using one fluid polytrope model

Propagation of a Finite Optical Beam in an Inhomogeneous Medium

Abstract: The first part of this paper is devoted to extending the Huygens-Fresnel principle to a medium that exhibits a spatial (but not temporal) variation in index of refraction. Utilizing a reciprocity theorem for a monochromatic disturbance in a weakly inhomogeneous medium, it is shown that the secondary wavefront will be determined by the envelope of spherical wavelets from the primary wavefront, as in the vacuum problem, but that each wavelet is now determined by the propagation of a spherical wave in the refractive medium. In the second part, the above development is applied to the case in which the index of refraction is a random variable; a further application of the reciprocity theorem results in a formula for the mean intensity distribution from a finite aperture in terms of the complex disturbance in the aperture and the modulation transfer function (MTF) for a spherical wave in the medium. The results are applicable for an arbitrary complex disturbance in the transmitting aperture in both the Fresnel and Fraunhofer regions of the aperture. Using a Kolmogorov spectrum for the index of refraction fluctuations and a second-order expression for the MTF, the formula is used to calculate the mean intensity distribution for a plane wave diffracting from a circular aperture and to give approximate expressions for the beam spreading at various ranges.

Parallel Propagation of Nonlinear Low‐Frequency Waves in High‐β Plasma

Abstract: A pair of coupled, nonlinear, partial differential equations which describe the evolution of low‐frequency, large‐scale‐length perturbations propagating parallel, or nearly parallel, to the equilibrium magnetic field in high‐β plasma have been obtained. The equations account for irreversible resonant particle effects. In the regime of small but finite propagation angles, the pair of equations collapses into a single Korteweg‐de Vries equation (neglecting irreversible terms) which agrees with known results.

Nonlinear waves in the pitaevskii--gross equation.

Abstract: Nonlinear waves, solitary and periodic, are studied exactly in the Pitaevskii-Gross equation for the wave function of the condensate of a superfluid. We also study the relationship between these two waves and Bogoliubov's phonon, and the energies associated with these waves. The creation energy of a solitary wave with amplitudeA is proportional toA3/2. Solitary waves show interesting behavior on their collision due to their localized character. The effect of collision on solitary waves can be described by the phase shift. We give a formula of the phase shift on a collision of two solitary waves. We further discuss the decay of an arbitrary initial disturbance into solitary waves.

Weak turbulence of capillary waves

Abstract: In recent years the theory of weak turbulence, i.e. the stochastic theory of nonlinear waves [I, 9], has been intensively developed. In the theory of weak turbulence nonlinearity of waves is assumed to be small; this enables us, using the hypothesis of the random nature of the phases of individual waves, to obtain the kinetic equation for the mean squares of the wave aplitudes.

Quantization of Evanescent Electromagnetic Waves

Abstract: The problem of the quantization of evanescent waves, which appear in the angular spectrum representation of the electromagnetic field in a half-space, is discussed. Although evanescent waves are associated with material sources, scatterers, etc., we are able to treat the electromagnetic field, including the evanescent waves, effectively as a free field, by making use of the idea of the refractive index of a passive, macroscopically continuous medium. We consider a space which is filled with a homogeneous dielectric to the left of the plane $z=0$, and is empty to the right of the plane. Triplets of incident, reflected, and transmitted waves at the interface form the fundamental orthogonal modes of the space. By expanding the field in terms of these triplet modes, we show that the field Hamiltonian reduces to the sum of independent harmonic-oscillator Hamiltonians. The quantization is therefore straightforward. We introduce the creation and annihilation operators for the triplet wave modes, and encounter Fock states, coherent states, etc., for a field having evanescent wave components. The field commutator at two space-time points in the right half-space is shown to have an explicit contribution from evanescent waves, characterized by an exponential decay to the right and a propagation parallel to the interface. We also examine the problem of atomic excitation by quantized evanescent waves, and show that the results are of the form given by semiclassical treatments.

On the generation of long waves

Abstract: For relatively long waves generated by a piston-type wave maker, the classical linear wave-maker theory is extended to second order accuracy. Within the limits of validity of the theory, this agrees well with experimental results for the motion generated by a sinusoidally moving wave maker, and shows that secondary waves are associated with the existence of a second harmonic free wave. By giving the wave maker a motion that consists of a first and a second harmonic, it is shown that this free second harmonic wave may be eliminated, so that the generated wave is virtually of permanent form.

Transmission of electromagnetic waves into time-varying media

Abstract: Expressions are obtained for the electromagnetic fields transmitted into the time-varying medium when a plane wave is incident upon either a dielectric or dispersive half-space. Solutions are obtained for the case when the medium is changed in a stepwise fashion, and also for the case when the medium varies slowly and continuously.

Density fluctuations driven by Alfvén waves

Abstract: The equations for a linearly polarized Alfven wave, propagating parallel to the direction of the average magnetic field in a perfectly conducting fluid, are solved to second order in the wave quanities for cases where the fluid obeys single adiabatic or double adiabatic equations of state. To this order, we find no change in the wave magnetic field or transverse wave velocity, but longitudinal wave velocity and density fluctuations appear, driven by gradients in the wave magnetic-field pressure. This is in contrast to the common belief that even large-amplitude Alfven waves remain purely transverse. The density fluctuations can become quite large when the Alfven speed is close to the ion sound speed in the fluid; this condition may at times exist in the solar wind at 1 AU. We suggest that part of the density fluctuations observed in the solar wind by satellites and interplanetary scintillation may be associated with large-amplitude Alfven waves. Heating of the solar wind might result if the ion sound waves, which are driven by the Alfven waves, are appreciably damped.

Theory of triggered VLF emissions

Abstract: A theory is presented to explain the origin of triggered discrete VLF emissions that is more complete than earlier theories, in that it is not restricted to the discussion of kinematical relations but evaluates the dynamics of the problem. Resonant electrons are phase correlated with the wave magnetic field by a finite length whistler train moving in the opposite direction. The time for phase correlation is of the order of the period of oscillation of a particle in the effective ‘potential well’ of the wave. It is recognized that the wave acceleration due to the inhomogeneous magnetic field of the earth must be small enough for the particle to stay trapped in the potential well. The phase-correlated electrons are subject to an instability in the form of an emitted whistler with a growth rate γ/ω ∼ (n/no)2/5(υ⊥/c)2/5 (ωp/Ω)2/5, where (n/no) is the fractional density of the resonant particles, υ⊥ is their mean transverse velocity, and ωp and Ω are local cold plasma and gyrofrequencies. The emitted frequency varies according to ω = k(ω)υ∥ − Ω, where υ∥ is the zero order longitudinal velocity of the resonant electron, and the wave vector k is a function of frequency ω through the whistler dispersion relation. The theory is in good agreement with observation.

Ionization disturbances caused by gravity waves in the presence of an electrostatic field and background wind

Abstract: Internal gravity waves in the neutral air propagating through the ionosphere cause a corresponding disturbance in the ionization. This note discusses additional effects that arise owing to the presence of an electrostatic field and background wind and in particular the possibility of a ‘spatial resonance’ when the natural drift of ionization irregularities equals the phase velocity of the gravity wave. The electrostatic field may be the one associated with the tidal motions that drive the Sq current system. It is shown that short-period (τ<30 min) disturbances in the F region may be appreciably affected by spatial resonance, if the component of E×B/B2 drift in the wave normal direction is equal to the phase velocity of the wave. In the E region a similar coincidence between the ion drift velocity and the wave phase velocity may cause intense patches of sporadic E to drift almost with the background wind at the sporadic E height.

Group rays of internal gravity waves in a wind‐stratified atmosphere

Abstract: The propagation of internal gravity waves in a model atmosphere with stratified neutral winds is studied. The waves are subjected to a ray-tracing analysis and, as a result, are grouped into three types: (1) those that penetrate the F region of the ionosphere, (2) those that are reflected, and (3) those that nearly reach the critical-layer condition and are absorbed. Examples of the three types of ray paths are shown. The traveling waves observed in the ionosphere are excited by the propagating acoustic-gravity waves launched at lower levels in the atmosphere. The characteristics of the waves, such as period and velocity, are dependent on atmospheric conditions, as well as on the nature of the source. Extensive computations show that neutral winds provide a directional filter effect as depicted in several contour plots. From Faraday rotation data taken during the summer of 1968, the characteristics of 13 traveling waves that were observed fit into the calculated contours reasonably well.

Wave Propagation in a One-Dimensional Random Medium

Abstract: Wave propagation in a slab of random medium is considered. The index of refraction is assumed to fluctuate randomly about a mean value, the fluctuations being small. Using a recent result of Hashminskii we give a description of the statistical characteristics of the reflection and transmission coefficients.

Conversion of Electrostatic Plasma Waves into Electromagnetic Waves: Numerical Calculation of the Dispersion Relation for All Wavelengths

Abstract: The dispersion curves have been computed for a wide range of wavelengths from electromagnetic waves to electrostatic waves in a magnetoactive warm plasma with a Maxwellian velocity distribution function. The computation was carried out mainly for the perpendicular propagation mode. The upper hybrid resonance is the connection point of the electrostatic waves and the electromagnetic waves. The electrostatic waves not associated with the upper hybrid resonance are subjected to electron cyclotron damping when the wavelength becomes long. Oblique propagation is allowed for the electrostatic waves in a frequency range from the plasma frequency to the upper hybrid resonance frequency in the long-wavelength region where Landau damping can be neglected and where the electrostatic mode smoothly connects to the electromagnetic X-mode. In a slightly inhomogeneous plasma, the Bernstein-mode electrostatic wave can escape by being converted into the O-mode electromagnetic wave; two reflections take place during this escape process.

Laminar wave train structure of collisionless magnetic slow shocks

Abstract: The laminar wave-train structure of collisionless magnetic slow shocks is investigated using two-fluid hydromagnetics with ion-cyclotron-radius dispersion. For shock strengths less than the maximally strong switch-off shock, in the shock-leading edge, dispersive steepening forms a magnetic-field gradient, while in the downstream flow dispersive propagation forms a trailing wave train; dispersion scale lengths are the ion inerrial length if β > 1 and the ion cyclotron radius if β > 1. In the switch-off slow-shock leading edge, dispersion only produces rotations of the magnetic-field direction; the gradient of the magnetic-field magnitude, and hence the shock-steepening length, is determined solely by resistive diffusion. The switch-off shock structure consists of a long trailing train of magnetic rotations which are gradually damped by resistivity. The low-6 parallel fast switch-on shock has a similar wave-train structure with the magnitude of the field rotations gradually increasing toward the downstream flow.

Optical Guided Wave Mode Conversion by an Acoustic Surface Wave

Abstract: The experimental observation of efficient (55%) mode conversion of thin‐film optical guided waves by a collinear interaction with a surface acoustic wave is reported. The effects of waveguide dispersion and finite geometry are discussed.

Transmission and Reflection of Plane Waves at an Elastic-Viscoelastic Interface

Abstract: Summary The reflected and transmitted waves due to an elastic plane sinusoidal P or SV wave impinging on the plane interface between an elastic and a linearly viscoelastic medium are found analytically for any type of viscoelastic behaviour. The properties of these waves depend both on the frequency of the incident wave and the angle of incidence of the impinging wave. Some general properties of the transmitted waves are that both the dilatational and equivoluminal waves in the viscoelastic media have refraction angles less than 90°, the displacement trajectories of material points in the viscoelastic media are ellipses, and the waves attenuate with increasing distance from the interface.

Run-up distributions of waves breaking on slopes

Abstract: Run-up of irregular waves which break on a slope is calculated by assuming that on the average the run-up of each wave with a given height and period equals the run-up of a periodic wave train of the same height and period. General expressions are derived for the distributions of the run-up and the wave steepness as functionals of an arbitrary joint distribution of the wave height and the square of the period. Explicit results are obtained for the case when these variates are jointly Rayleigh distributed with arbitrary degree of correlation. Some of the assumptions are verified by a comparison of the analytical results with previous experimental data.

Wave Propagation in Nematic Liquid Crystals

Abstract: Basic laws of motion of micropolar continuum are presented, and the adequacy of applying micropolar theory to liquid crystals is indicated. A set of constitutive equations is derived for nematic liquid crystals. Wave propagation problems are solved, and it is shown that the theoretical analysis is in good agreement with the experimental data, which indicates the isotropy of the phase velocity of the longitudinal wave and the anisotropy of the damping coefficient. The coupling, although small, is shown to exist between longitudinal and rotational waves.

Collisionless Damping of a Large Amplitude Whistler Wave

Abstract: Nonlinear damping of electromagnetic waves propagating along a uniform magnetic field has been calculated by computing nonlinear trajectories for trapped and resonant untrapped particles while using linear theory to describe the rest. This procedure parallels O'Neil's calculation for electrostatic modes, and the results are qualitatively similar. After an initial linear damping, amplitude oscillations set in and the amplitude quickly approaches a finite constant value. The frequency of the amplitude oscillations is temperature dependent. Phase mixing results from the spread in both parallel and perpendicular velocities, giving rise to a more rapid approach to the asymptotic amplitude than for electrostatic modes.

An Analytical Study of Tropospheric Structure as Seen by High-Resolution Radar

Abstract: In the present paper, atmospheric structure revealed by a high-resolution FM/CW radar sounder is compared with hypothetical models of internal wave structure and convection. Special attention is given to the distribution of Richardson's number in trapped and untrapped gravity waves. It is concluded that the multiple layers result from untrapped internal gravity waves, whose propagation vector is directed newly vertically, within very stable height regions. In contrast to the convective instability proposed by Orlanski and Bryan, it is concluded that the layers are caused by Kelvin-Helmholtz instability resulting from the reduction in the Richardson's number due to growth of the amplitude-to-wavelength ratio as the waves propagate into thermally stable height regions of the atmosphere.

Velocity shear and low-frequency plasma instabilities

Abstract: The effects of transverse velocity shear on the low‐frequency stability of a plasma are examined theoretically for a low‐β resistive plasma in a uniform magnetic field. Cylindrical geometry is used and the velocity shear is introduced by a nonuniform E × B rotation. Both numerical and analytic methods are used. The principal analytic result is a dispersion relation for instabilities caused by a thin velocity shear layer. This dispersion relation describes the Q machine edge oscillation, which is identified either as a Kelvin‐Helmholtz instability or as a velocity‐shear analog of the resistive drift wave, depending on the parallel wavelength. The numerical results show that properties of instabilities observed in several experiments agree reasonably well with theory. The effect of velocity shear on the drift instability is to make it into either a local or nonlocal type of normal mode.

Diffraction in crystals at high energies

Abstract: By means of several distinct stages of approximation, the way in which wave propagation in a lattice becomes classical at high energies is analysed. First, the principle that deflection angles (whether caused by 'quantum' or 'classical' processes) are small at high energies is used to derive a simplified wave equation involving the lattice potential averaged along the direction of the incident beam. Next, the many-beam solution of this equation for the case of systematic reflections is presented in a form which emphasises the spatial variation of the potential, rather than its Fourier components. Third, approximate analytical expressions for the Boch eigenvalues and eigenfunctions, and for the amplitudes of the diffracted beams, are derived by means of the WKB method; this leads to easily calculable expressions for the number of diffracted beams expected in a given situation, as well as for the number of Bloch waves contributing to these beams.

Wave propagation in random media

Abstract: This paper discusses a general theory of wave propagation through a random medium whose random inhomogeneities are confined to small deviations from the mean. The theory is initially worked out in detail for the propagation of transverse waves along an infinite stretched string whose density is a random function of position. The manner in which the mean wave profile is modified by scattering from the density inhomogeneities is discussed in great detail, with particular emphasis on physical interpretation. The general theory of wave propagation in arbitrary dispersive or non-dispersive media is then discussed, and it is shown how the theory may be extended to wave propagation problems involving scattering from rough boundaries.

Semidispersive wave systems

Abstract: The statistical initial-value problem for a class of weakly coupled waves whose linear dispersion relation is ω ∞ ± | k | is examined. It is found that in two and higher dimensions a natural asymptotic closure is possible. The redistribution of energy is achieved by means of two mechanisms; the first by a resonance between collinear wave vectors; the second by a local transfer between adjacent rays. The entropy functional is ∫ log n ( k ) d k and corresponds to particles obeying Bose–Einstein statistics.