Showing papers on "Dispersion relation published in 1986"

P-SV wave propagation in heterogeneous media: Velocity‐stress finite‐difference method

Abstract: I present a finite-difference method for modeling P-SV wave propagation in heterogeneous media This is an extension of the method I previously proposed for modeling SH-wave propagation by using velocity and stress in a discrete grid The two components of the velocity cannot be defined at the same node for a complete staggered grid: the stability condition and the P-wave phase velocity dispersion curve do not depend on the Poisson's ratio, while the S-wave phase velocity dispersion curve behavior is rather insensitive to the Poisson's ratio Therefore, the same code used for elastic media can be used for liquid media, where S-wave velocity goes to zero, and no special treatment is needed for a liquid-solid interface Typical physical phenomena arising with P-SV modeling, such as surface waves, are in agreement with analytical results The weathered-layer and corner-edge models show in seismograms the same converted phases obtained by previous authors This method gives stable results for step discontinuities, as shown for a liquid layer above an elastic half-space The head wave preserves the correct amplitude Finally, the corner-edge model illustrates a more complex geometry for the liquid-solid interface As the Poisson's ratio v increases from 025 to 05, the shear converted phases are removed from seismograms and from the time section of the wave field

Numerical simulation of nonoscillatory mirror waves at the Earth's magnetosheath

Abstract: The generation of nonoscillatory mirror waves is studied using a one-dimensional periodic hybrid electromagnetic simulation. The ion dynamics are treated exactly; the electrons are approximated as a finite pressure, massless fluid. Compression of the flux tubes in the magnetosheath causes a large pressure anisotropy, and it has been proposed that this anisotropy drives a mirror instability. The mirror waves have been identified by large amplitude fluctuations of the magnetic field, anticorrelated with pressure fluctuations. The simulations are initiated in a homogeneous high beta (beta = 2.5) plasma with the ambient magnetic field at various angles to the simulation axis. It is found that ion cyclotron waves are also driven by the pressure anisotropy, in competition with the nonoscillatory mirror waves. Simulations indicate that in a pure ¹H+ plasma the much faster growing ion cyclotron waves absorb the free energy in the anisotropy to the extent that mirror waves should not be observed. Analysis of the dispersion relations of mirror waves and ion cyclotron waves in the multi-component plasma indicates that 4He2+ and 16O6+ ions in the solar wind should stabilize the ion cyclotron waves sufficiently that the mirror waves become the dominant instability.

Resonances of two-dimensional particle gratings in surface-enhanced Raman scattering

Abstract: Dipolar interactions between silver particles arranged on a square two-dimensional grating give rise to characteristic features in the wavelength dependence of surface-enhanced Raman scattering from adsorbed molecules. The interactions produce two pronounced effects: first, they shift and broaden the plasmon resonance corresponding to the isolated particle, and second, they induce an additional sharp resonance feature at lower energy. The two enhancement maxima are separated by a minimum (cusp), which corresponds to the wavelength at which a grating order changes from radiating to evanescent in character. Dispersion relations describing the grating-induced resonances are presented. The consequences of the simultaneous enhancement of both the input and output electric fields are discussed, and the effects of imperfections in the particle shape are considered. The wavelength dependence of Raman scattering from p-nitrobenzoic acid adsorbed on a 380-nm-period two-dimensional array of silver spheroids was measured by means of an internal standard. Close agreement between experimental results and theoretical predictions was obtained.

Parametric instabilities of circularly polarized Alfvén waves including dispersion

Abstract: A class of parametric instabilities of large-amplitude, circularly polarized Alfven waves is considered in which finite frequency (dispersive) effects are included. The dispersion equation governing the instabilities is a sixth-order polynomial which is solved numerically. As a function of K identically equal to k/k-sub-0 (where k-sub-0 and k are the wave number of the 'pump' wave and unstable sound wave, respectively), there are three regionals of instability: a modulation instability at K less than 1, a decay instability at K greater than 1, and a relatively weak and narrow instability at K close to squared divided by v-sub-A squared (where c-sub-s and v-sub-A are the sound and Alfven speeds respectively), the modulational instability occurs when beta is less than 1 (more than 1) for left-hand (right-hand) pump waves, in agreement with the previous results of Sakai and Sonnerup (1983). The growth rate of the decay instability of left-hand waves is greater than the modulational instability at all values of beta. Applications to large-amplitude wave observed in the solar wind, in computer simulations, and in the vicinity of planetary and interplanetary collisionless shocks are discussed.

Magneto-optical ellipsometry

Abstract: Through the extension of the Yeh's formalism (Surf. Sci.96 (1980) 41) to magnetic crystalline media the formulas of the magneto-optic ellipsometry and the dispersion relations for wave-guiding in multilayer magnetic crystalline structures are obtained. The theory covers most of the situations considered so far in the magneto-optics in which the optical response of the structures is linear in the amplitude of the incident wave. It is capable of treating the interfaces between two magnetic media and the structures containing such interfaces with no restrictions on the orientation of the magnetizations and crystalline axes at an arbitrary angle of incidence. The polar, longitudinal and transversal magnetizations in the structures are considered as special cases. Possible applications of the theory are in the analysis of the planar multilayer magneto-optic systems in the integrated optics and magneto-optic memory technology, in the study of profiles of magnetic surfaces subjected to mechanical wear, ion implantation, etc.

Modulation instability of circularly polarized Alfvén waves

Abstract: The stability of a finite amplitude circularly polarized Alfven wave of wave number k0 is studied by using the two-fluid isentropic equations. Linear perturbation analysis, involving two sideband transverse waves having wave numbers k0 ± k and a longitudinal wave with wave number k, is used to find the exact sixth-order dispersion relation. The analysis is then limited to the case where k ≪ k0. The resulting fourth-order dispersion relation is examined analytically and numerically, and a surface is found that separates stable and unstable regions in parameter space. This surface describes the boundary between stable and unstable regions not only for k ≪ k0 but for the entire branch of the dispersion relation which extends to k = 0. We refer to this branch as the modulation branch and the corresponding instability as a modulation instability. A sufficient condition for modulation stability is found to be υϕ0 cs for right-hand polarized waves, where υϕ0 and cs are the phase velocity of the unperturbed wave and the unperturbed sound speed, respectively. Modulation wave amplitudes and growth rates are given.

Low-frequency waves in a high-beta collisionless plasma: polarization, compressibility and helicity

Abstract: This paper considers the linear theory of waves near and below the ion cyclotron frequency in an isothermal electron-ion Vlasov plasma which is isotropic, homogeneous and magnetized. Numerical solutions of the full dispersion equation for the magnetosonic/whistler and Alfven/ion cyclotron modes at beta(i) = 1.0 are presented, and the polarizations, compressibilities, helicities, ion Alfven ratios and ion cross-helicities are exhibited and compared. At sufficiently large beta(i) and theta, the angle of propagation with respect to the magnetic field, the real part of the polarization of the Alfven/ion cyclotron wave changes sign, so that, for such parameters, this mode is no longer left-hand polarized. The Alfven/ion cyclotron mode becomes more compressive as the wavenumber increases, whereas the magnetosonic/whistler becomes more compressive with increasing theta.

Longitudinal polar optical modes in semiconductor quantum wells

Abstract: A continuum theory is employed for investigating the longitudinal optical (LO) modes in polar semiconductor heterostructures. Particular emphasis is laid on the symmetric double heterostructure (DHS) such as occurs in a semiconductor quantum well. The existence of two-dimensional (2D) bulk-type double-interface-type and guided-type LO modes is examined for this case and their characteristic dispersion relations derived. It is shown with reference to a typical GaAs quantum well that the presence of at most two double-interface modes and a finite number of guided LO modes depends on the difference between the squares of the limiting bulk LO frequencies of the two materials. The implications of the results for light scattering experiments and for the properties of electrons confined in quantum wells are pointed out and discussed.

Direct and inverse scattering in the time domain for a dissipative wave equation. II. Simultaneous reconstruction of dissipation and phase velocity profiles

Abstract: The one‐dimensional inverse scattering problem for inhomogeneous lossy media is considered. The model problem involves electromagnetic wave propagation in a medium of unknown thickness with spatially varying conductivity and permittivity. Two inversion algorithms are developed in the time domain using data obtained from normally incident plane waves. These algorithms utilize reflection data from both sides of the medium, and one of them also uses transmission data. These algorithms are implemented numerically on several examples, one of which includes the effects of noisy data. The possibility of using one‐sided reflection data and no transmission data is reviewed and analyzed.

Longitudinal wave propagation in a generalized thermoelastic cylinder

Abstract: In this paper the longitudinal wave propagation in a circular infinite cylinder is studied. The infinite circular cylinder is assumed to be made of a generalized thermoelastic material. The dispersion relation is obtained for the case in which the temperature is kept constant on the surface of the cylinder. Because of the complexity of the dispersion relation, the numerical solutions are given. For various values of parameters appearing in the field equations, some dispersion, attenuation, and phase velocity diagrams are presented

Stability of nonlinear stationary waves guided by a thin film bounded by nonlinear media

Abstract: The stability of stationary, TE0‐type, nonlinear, thin‐film guided waves was investigated numerically for both symmetric and asymmetric planar waveguides with nonlinear cladding and substrate layers. It is found that large regions of the dispersion curves are unstable at high powers.

Electron‐cyclotron maser instability in relativistic plasmas

Abstract: The electron-cyclotron maser instability is studied for the case of an anisotropic electron velocity distribution in the regime where the relativistic corrections to the wave dispersion are significant. Solution of the linear dispersion relation reveals that when the plasma frequency-gyrofrequency ratio is less than v(te)/c, the instability is localized just below k(perpendicular)c/Omega(e) = 1. The growth rate is then strongly peaked for emission at 90 deg to the magnetic field and is considerably larger than would be the case if the cold-plasma dispersion theory were valid. These features are confirmed by EM particle simulations.

Theory for resonant ion acceleration by nonlinear magnetosonic fast and slow waves in finite beta plasmas

Abstract: A Korteweg–de Vries equation that is applicable to both the nonlinear magnetosonic fast and slow waves is derived from a two‐fluid model with finite ion and electron pressures. As in the cold plasma theory, the fast wave has a critical angle θc. For propagation angles greater than θc (quasiperpendicular propagation), the fast wave has a positive soliton, whereas for angles smaller than θc, it has a negative soliton. Finite β effects decrease the value of θc. The slow wave has a positive soliton for all angles of propagation. The magnitude of resonant ion acceleration (the vp×B acceleration) by the nonlinear fast and slow waves is evaluated. In the fast wave, the electron pressure makes the acceleration stronger for all propagation angles. The decrease in θc resulting from finite β effects results in broadening of the region of strong acceleration. It is also found that fairly strong ion acceleration can occur in the nonlinear slow wave in high β plasmas. The possibility of unlimited acceleration of ion...

Relativistic plasma dispersion functions

Abstract: The known properties of plasma dispersion functions (PDF’s) for waves in weakly relativistic, magnetized, thermal plasmas are reviewed and a large number of new results are presented. The PDF’s required for the description of waves with small wave number perpendicular to the magnetic field (Dnestrovskii and Shkarofsky functions) are considered in detail; these functions also arise in certain quantum electrodynamical calculations involving strongly magnetized plasmas. Series, asymptotic series, recursion relations, integral forms, derivatives, differential equations, and approximations for these functions are discussed as are their analytic properties and connections with standard transcendental functions. In addition a more general class of PDF’s relevant to waves of arbitrary perpendicular wave number is introduced and a range of properties of these functions are derived.

First-principles calculation of surface phonons on the Al(110) surface.

Abstract: The surface-phonon dispersion curves of Al(110) have been calculated with force constants determined from first-principles self-consistent total-energy calculations. Relaxation of the surface layers produces changes in the surface force constants which have a significant influence on the surface-phonon frequencies near the zone boundary.

Systematic study of the lattice dynamics of the uranium rocksalt-structure compounds.

Abstract: The phonon-dispersion relations of USe and UTe have been determined by the inelastic scattering of thermal neutrons. All existing phonon measurements for the UX series, viz., UC, UN, UAs, USb, US, USe, and UTe, have been fitted to the rigid-ion and shell models and dispersion relations have been predicted for UP. The U-X force constants dominate the lattice dynamics and are nearly constant for the series, whereas the U-U force constants vary systematically from being large and positive for the compounds with the smallest lattice parameter to being negative for the chalcogenide series. The negative U-U force constant is identified with destabilizing f-d interactions. Elastic constants, derived from the slopes of the dispersion relations and from ultrasound velocity measurements, have been determined. The bulk modulus decreases unusually rapidly as the lattice parameter increases and is in fair agreement with band-structure calculations.

Technique of surface‐wave scattering and calibration with simple liquids

Abstract: Heterodyne detection of light scattered from capillary waves is used to study the surface properties of the air–liquid interface. A diffraction grating is employed to select a precise ripplon wave vector k and to provide a stable local oscillator field. The optics are designed to form a real image of the grating on the surface, thus allowing the measurements to be reproducible within 5%. The power spectrum detected in frequency domain is well fitted by a Lorentzian profile for the range of ripplon wave vectors 260≤k≤390 cm−1. The shape of the scattered spectra at each wave vector is corrected for the incident beam profile by effecting a convolution of the Lorentzian and Gaussian functional forms. The surface tensions and the kinematic viscosities of water, anisole, and ethanol are deduced from the ripplon dispersion relation corrected to the first order in damping, and found to be within 5% of the literature values. Thus we confirm the validity of approximations made for the instrumental function and the dispersion relation.

Fabrication of planar optical waveguides by K + -ion exchange in BK7 and Pyrex glass

Abstract: Planar graded index optical waveguides have been formed by K+ ion exchange in BK7 optical glass and Pyrex glass. Measurements of the mode indexes have been made and are well described by the WKB dispersion relation with a complementary error function refractive index profile for both glass types with refractive index changes ( \Delta n ) of 0.0094 and 0.0073 for BK7 and Pyrex, respectively. A linear relation was found between the diffusion depth and the square root of the diffusion time for both materials, and effective diffusion coefficients were calculated. Diffusion times necessary to achieve a desired number of modes and diffusion depths have also been established.

The evolution of nonlinear Alfven waves subject to growth and damping

Abstract: Results of a numerical study of Alfven waves are presented subject to nonlinearity, dispersion, growth, and damping. The model presented is the derivative nonlinear Schrodinger equation, modified to include linear growth and damping processes. The processes that are considered are wave amplification by streaming particle distributions, and damping resulting from ion‐cyclotron resonance absorption. These growth and damping mechanisms are dominant in different portions of wavenumber space. The primary role of nonlinearity is the transfer of wave energy from growing or amplified wavenumbers to those which are damped. A nonlinear saturation mechanism thereby results, in which instability of low wavenumber modes may be quenched. A simple phenomenological model is developed, which accounts for many of the salient features of the numerical calculations. The application of these results to observations of Alfven waves upstream of the Earth’s bow shock is briefly considered. It is suggested that the short wavelength ‘‘shocklet’’ structures resemble the soliton‐like pulses that emerge from the driven derivative nonlinear Schrodinger equation. However, the nonlinear effects discussed in this paper do not seem responsible for limiting the amplitude of the ‘‘low‐frequency’’ waves in the foreshock region.

Solitary vortices in a rotating plasma

Abstract: Nonlinear equations describing the flute dynamics of rotating plasma are derived and solitary vortex solutions are obtained. The solution takes the form of a shielded dipole vortex, similar to that found for nonlinear Rossby waves. The nonlinear dispersion relation, relating propagation speed to vortex radius, is obtained. Vortex speeds are shown to take values complementary to the phase velocities of the linear modes of the system. The E×B circulation velocity of the plasma trapped in the vortex is comparable to the diamagnetic drift velocity in the equilibrium plasma.