A Note on Second Harmonics Generated by a Surface Wave on a Warm Plasma Half-Space

A part of the second harmonics generated through the self-interaction of a surface wave on a warm plasma half-space is shown not to have a surface wave character but represents a wave propagating obliquely away from the plasma-vacuum interface into the bulk of the plasma.     

Reflection of a plasma wave from the flat boundary of a degenerate plasma

The linearized problem of reflection of a plasma wave from the boundary of a degenerate collisional plasma occupying the half-space is stated and analytically solved for the first time. As the boundary conditions, both mirror and diffuse reflections of electrons are applied. The reflection coefficient is found as a function of the input parameters. The long-wave limit is analyzed.     

The effect of ion motion on the reflection of an electromagnetic wave from plasma

An electromagnetic wave with electric vector parallel to the plasma boundary falls from a vacuum on a half-space filled with magnetoactive plasma and bounded by a particle-reflecting wall. A comparison is made of the effect of thermal motion of electrons and ions on the boundary, on the coefficient of reflection and on the absorbed energy.     

Trapping of an electromagnetic wave by the boundary of created plasma

We discuss a new phenomenon of the electrodynamics of transient media, the trapping of electromagnetic radiation by the boundary of a transient plasma due to the conversion of the radiation into surface waves localized at the boundary. Calculations are done for an initial plane wave and for a beam of finite width in conditions where the boundary of the suddenly created (because of ionization) plasma half-space is perpendicular to the initial wavefront. Two frequency down-shifted surface waves traveling along the boundary in opposite directions are shown to be excited, as well as frequency up-shifted outgoing radiation and a time-independent mode in the form of a spatially inhomogeneous structure of dc currents and a magnetic field within the plasma half-space. We study the associated kinematic, amplitude, and energy relations. Finally, we establish that the most efficient trapping (up to 40% in energy) can be achieved with the forward (with respect to the direction of the initial wave propagation) surface mode and that the trapping is accompanied by concentration of electromagnetic energy at the plasma boundary. Zh. éksp. Teor. Fiz. 113, 1277–1288 (April 1998)     

Nonlinear theory of surface-helical instability of a semiconductor plasma. II. Calculation of linear parameters

A numerical analysis is made of the threshold characteristics of the helical instability of a semiconductor plasma which fills a half-space; these are the threshold electric field, the threshold frequency of the oscillations, the optimal wave vector, and the optimal angle of propagation of a wave. The characteristic dependences for these quantities are presented and explained qualitatively.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 79–84, April, 1980.     

Dust-Lower-Hybrid Surface Waves in Classical and Degenerate Plasmas

The dispersion relation for general dust low frequency electrostatic surface waves propagating on an interface between a magnetized dusty plasma region and a vacuum is derived by using specular reflection boundary conditions both in classical and quantum regimes. The frequency limit ω«ω_ci«ω_ce is considered and the dispersion relation for the Dust-Lower-Hybrid Surface Waves (DLHSW's) is derived for both classical and quantum plasma half-space and analyzed numerically. It is shown that the wave behavior changes as the quantum nature of the problem is considered.     

Reflection of spin and spin-elastic waves at the interface of a ferromagnetic half-space

This paper considers the reflection of pure spin and spin-elastic (or magneto-elastic) waves at the interface of a ferromagnetic half-space and a vacuum. For pure spin waves two cases are considered, with exchange effects, and without. It is shown that when exchange effects are taken into account, volume spin waves in the ferromagnetic half space incident at the boundary with the vacuum generate a reflected volume spin wave, and an accompanying compound surface wave propagating along the boundary and consisting of two partial inhomogeneous spin waves in the ferromagnetic half-space and a partial magneto-static inhomogeneous surface wave in the vacuum. When exchange effects are neglected the incident wave generates only a reflected volume wave in the ferromagnetic half-space.

Reflection and transmission of spin-elastic (or magneto-elastic) waves has been considered only in the case of the absence of exchange effects. An incident volume wave generates a volume spin-elastic reflected wave and one inhomogeneous magneto-static accompanying surface wave.

Excitations of the magnetic field are not transmitted into the vacuum in both cases when the exchange effect is neglected. In all cases the reflection of a spin wave has the character of a full internal reflection.     

Investigation of statistical characteristics of waves in layered media with regular and random inhomogeneities based on the invariant imbedding method

We consider a model of a stationary problem of wave propagation in a layered half-space with regular and random inhomogeneities. The choice of regular perturbation corresponds to a linear profile of the wave velocity. Random inhomogeneities are simulated in the framework of the white noise model. We analyse the influence of inhomogeneities on the probability distribution of the reflection-coefficient phase and the imaginary value of the average wavefield at the boundary of the half-space.     

On reflection from a suddenly created plasma half-space: transientsolution

The reflection by a suddenly created plasma half-space of a time-harmonic plane electromagnetic wave propagating in free space is considered. The problem involves a temporal discontinuity, a spatial discontinuity, and a dispersive medium. The steady-state solution is obtained by considering the basic features of the scattering processes due to each of the discontinuities in terms of analogous transmission-line models. The electric field of the reflected wave consists of two components. One component (called component A) is of the same frequency as the incident wave frequency and is due to the spatial discontinuity. The other component (called component B) is of a different frequency and arises because of the temporal discontinuity. The B component is damped out even if the plasma is only slightly lossy. The damping rate of the B component is calculated. The transient solution is obtained through the use of Laplace transforms. The solution is given in terms of Bessel-like functions. The limiting value of this solution is shown to agree with the steady-state solution. Numerical results illustrating the transient effects are for two typical cases     

Boundary graphene layer effect on surface plasmon oscillations in a quantum plasma half-space

The effect of graphene on unique features of surface plasmon-polariton excitations near the interface of vacuum and quantum plasma half-space is explored using a quantum hydrodynamic model including the Fermi electron temperature and the quantum Bohm potential together with the full set of Maxwell equations.It is found that graphene as a conductive layer significantly modifies the propagation properties of surface waves by making a change on the corresponding wave dispersion relation.It is shown that the presence of graphene layer on the interface of vacuum and plasma leads to a blue-shift in the surface Plasmon frequency.The results of present study must be contributed to the modern electronic investigations.     

Transition from transient response to steady state for a layered medium

The transition from transient response to steady-state for a layered medium subjected to antiplane loadings is studied. The steady-state formula for a layered medium is derived and the solutions for a layered half-space are then expressed explicitly in the form of wave number integrals. The transient response solutions for a layered half-space are obtained by the convolution of time harmonic loading function with transient response formula derived analytically from an effective matrix method. Two layered half-spaces with different ratios of wave velocities in the layer and half-space are considered and investigated by means of extensive numerical results to show their quite different transition behavior. The numerical results indicate that transient responses will approach steady state after certain characteristic times when the transient effects die away. The transition phenomena and characteristic times are investigated in detail through the responses from near field to far field as well as from low frequency to high frequency.     

Scattering of a Rayleigh surface acoustic wave by a small-size inhomogeneity in a solid half-space

We use the Born approximation of the perturbation method to solve the problem of scattering of a harmonic Rayleigh surface acoustic wave by a weak-contrast inhomogeneity that is small compared with the wavelength and is located in a solid half-space near its boundary. The material of the inhomogeneity differs from the material of the half-space only in its density. The Rayleigh wave incident on the inhomogeneity is excited by a monochromatic surface force source acting normally to the half-space boundary. We derive expressions for the displacement fields in the scattered spherical compressional and shear (SV- and SH-polarized) waves. Scattering of the Rayleigh wave into a Rayleigh wave is studied in detail. We find expressions for the vertical and horizontal components of the displacement vector in the scattered Rayleigh wave as well as its radiated power. It is shown that the field of the scattered surface wave is mainly formed by vertical oscillations of the inhomogeneity in the field of the incident wave. In this case, the radiated power for the scattered Rayleigh wave formed by vertical motion of the inhomogeneity in the incident-wave field depends on the depth of the inhomogeneity as the fourth power of the function describing the well-known depth dependence of the vertical displacements in the Rayleigh surface wave. Correspondingly, the dependence of the radiated power for the scattered Rayleigh wave formed by horizontal motion of the inhomogeneity depends on its location depth as the fourth power of the depth dependence of the horizontal displacements in the Rayleigh surface wave. We perform calculations of the ratio between the powers of the scattered and incident Rayleigh waves for different ratios between the velocities of the compressional and shear waves in a solid. It is shown that the radiated power for the scattered surface wave decreases sharply with increasing depth of the subsurface-inhomogeneity location. Thus, the scattering of a Rayleigh wave into a Rayleigh wave is fairly efficient only when the location depth of the inhomogeneity does not exceed about one-third of the wavelength of the shear wave in an elastic medium.     

一种计算分层半空间上方导线瞬态响应的新方法

提出了一种将时域积分方程(time domain integral equation, TDIE)方法和时域有限差分(finite differnce time domain, FDTD)方法相结合计算分层有耗半空间上方导线瞬态电磁响应的新方法.其中,一维FDTD方法用于计算入射电磁波经分层半空间反射的时域波形.TDIE用于求解细导线在加入两个激励源(直接入射电磁波和经分层半空间反射的电磁波)时的瞬态响应.相关计算理论和数值模拟结果说明了本文方法是一种解决了分层有耗介质上方水平放置导线瞬态响应的高效解决方案. 关键词： 时域积分方程 时域有限差分 细导线 分层半空间     

Rayleigh wave and detection of low-velocity layers in a stratified half-space

The excitation and propagation of the guided waves in a stratified half-space and a Rayleigh wave exploration method in shallow engineering seismic exploration are studied in this paper. All the modes of the guided waves are calculated by the bisection method in the case where the low velocity layers are contained in a stratified half-space. Cases when the formation shear wave velocity gradually decreases from the top to the bottom layers are also studied. The dispersion curves obtained in actual Rayleigh wave exploration are usually noncontinual zigzag curves, but the dispersion curves given by the elastic theory for given modes of the guided waves are smooth and continual curves. In this paper, the mechanism of zigzag dispersion curves in Rayleigh wave exploration is investigated and analyzed thoroughly. The zigzag dispersion curves can give not only the possible positions of the low-velocity layers but also the other information on the formation structure (fractures, oil, gas, etc.). It is found that the zigzag dispersion curves of the Rayleigh wave are the result of the leap of the modes and the existence of low velocity layers in a stratified half-space. The effects of the compressional wave velocity, shear wave velocity, and density of each layer on zigzag dispersion curves and the relationship of the low velocity layers to zigzag dispersion curves are also investigated in detail. Finally, the exploration depth of the Rayleigh wave is discussed. The exploration depth of the Rayleigh wave is equal to the wavelength multiplied by a coefficient that is variable and usually given by the work experience and the formation properties of the local work area.     

Viscosity and Diffusion Effects at the Boundary Surface of Viscous Fluid and Thermoelastic Diffusive Solid Medium

This paper concentrates on the wave motion at the interface of viscous compressible fluid half-space and homogeneous isotropic, generalized thermoelastic diffusive half-space. The wave solutions in both the fluid and thermoelastic diffusive half-spaces have been investigated; and the complex dispersion equation of leaky Rayleigh wave motion have been derived. The phase velocity and attenuation coefficient of leaky Rayleigh waves have been computed from the complex dispersion equation by using the Muller's method. The amplitudes of displacements, temperature change and concentration have been obtained. The effects of viscosity and diffusion on phase velocity and attenuation coefficient of leaky Rayleigh waves motion for different theories of thermoelastic diffusion have been depicted graphically. The magnitude of heat and mass diffusion flux vectors for different theories of thermoelastic diffusion have also been computed and represented graphically.     

Semi-analytical analysis of the isolation to moving-load induced ground vibrations by trenches on a poroelastic half-space

A semi-analytical model is proposed to investigate the screening efficiency of trenches to moving-load induced ground vibrations. The ground is modeled as a fully saturated poroelastic half-space governed by Biot's dynamic poroelastic theory. The trenches are obtained by placing three rectangular elastic layers with appropriate width upon the poroelastic half-space. By Helmholtz decomposition, the displacement fields of the elastic layers are decomposed into three scalar potentials. Analytical solutions are obtained based on Fourier transform and Fourier series in the transformed domain. The time-domain results are obtained by the fast Fourier transform (FFT). The different performances of trenches on a saturated poroelastic half-space and a single-phase elastic half-space to the moving load-induced ground vibration are identified. It is found that the discrepancy of the screening efficiencies between the two models becomes significant when the load speed approaches the Rayleigh wave speed of the ground surface. Also, some parametric studies for the screening efficiency of the trench on the poroelastic half-space are presented.     

Plasmons and polaritons in a semi-infinite plasma and a plasma slab

Plasmon and polariton modes are derived for an ideal semi-infinite (half-space) plasma and an ideal plasma slab by using a general, unifying procedure, based on equations of motion, Maxwell's equations and suitable boundary conditions. Known results are re-obtained in much a more direct manner and new ones are derived. The approach consists of representing the charge disturbances by a displacement field in the positions of the moving particles (electrons). The dielectric response and the electron energy loss are computed. The surface contribution to the energy loss exhibits an oscillatory behaviour in the transient regime near the surfaces. The propagation of an electromagnetic wave in these plasmas is treated by using the retarded electromagnetic potentials. The resulting integral equations are solved and the reflected and refracted waves are computed, as well as the reflection coefficient. For the slab we compute also the transmitted wave and the transmission coefficient. Generalized Fresnel's relations are thereby obtained for any incidence angle and polarization. Bulk and surface plasmon-polariton modes are identified. As it is well known, the field inside the plasma is either damped (evanescent) or propagating (transparency regime), and the reflection coefficient for a semi-infinite plasma exhibits an abrupt enhancement on passing from the propagating regime to the damped one (total reflection). Similarly, apart from characteristic oscillations, the reflection and transmission coefficients for a plasma slab exhibit an appreciable enhancement in the damped regime.     

Reflection and refraction of the electromagnetic field in a semi-infinite plasma

We compute the reflected and refracted electromagnetic fields for an ideal semi-infinite (half-space) plasma, as well as the reflection coefficient, by using a general procedure based on equations of motion and electromagnetic potentials. The approach consists of representing the charge disturbances by a displacement field in the positions of the moving particles (electrons). The propagation of an electromagnetic wave in plasma is treated by means of the retarded electromagnetic potentials, and the resulting integral equations are solved. Generalized Fresnel’s relations are thereby obtained for any incidence angle and polarization and the angles of total polarization and total reflection are derived. Bulk and surface plasmon-polariton modes are identified. As it is well known, the field inside the plasma is either damped (evanescent) or propagating (transparency regime), and the reflection coefficient exhibits an abrupt enhancement on passing from the propagating regime to the damped one (total reflection).     

Parametric scattering of high-frequency elastic waves by a small spherical cavity oscillating under the action of a Rayleigh wave

Scattering of high-frequency transverse and longitudinal plane waves incident on a spherical cavity located at a small depth under the surface of a half-space is considered. The cavity oscillates as a whole in the field of a low-frequency Rayleigh surface wave, the oscillation vectors of the longitudinal, transverse, and surface waves being coplanar. The cavity radius is assumed to be small compared to the wavelengths of the sounding wave and the pumping surface wave. The scattered compression and shear waves at the combination frequencies ω±Ω are calculated in the dipole approximation. Expressions obtained describe the qualitative behavior of the combination-frequency signal levels produced at the outputs of horizontally and vertically oriented geophones moving over the free surface of the elastic half-space.     

Electromagnetic field induced by shock compression of a current-carrying conductor

The electromagnetic field induced by shock compression of a current-carrying conductor is shown to consist of two current waves. One propagates in the uncompressed material at the shock-wave velocity. The other is due to current inward diffusion. As the shock wave propagates, the current passes from the first wave to the second. At large observation periods, the situation resembles conventional current diffusion into a conducting half-space. Control parameters for electrodynamic problems with shock waves are found. Their physical meaning is the ratio between the times of field convection and diffusion in different regions. In specific cases, the problem is reduced to the motion of the surface of a current-carrying half-space and to shock metallization of an insulator.