Showing papers on "Dispersion relation published in 1999"

Convectively Coupled Equatorial Waves: Analysis of Clouds and Temperature in the Wavenumber–Frequency Domain

Abstract: A wavenumber-frequency spectrum analysis is performed for all longitudes in the domain 158S‐158N using a long (;18 years) twice-daily record of satellite-observed outgoing longwave radiation (OLR), a good proxy for deep tropical convection. The broad nature of the spectrum is red in both zonal wavenumber and frequency. By removing an estimated background spectrum, numerous statistically significant spectral peaks are isolated. Some of the peaks correspond quite well to the dispersion relations of the equatorially trapped wave modes of shallow water theory with implied equivalent depths in the range of 12‐50 m. Cross-spectrum analysis with the satellite-based microwave sounding unit deep-layer temperature data shows that these spectral peaks in the OLR are ‘‘coupled’’ with this dynamical field. The equivalent depths of the convectively coupled waves are shallower than those typical of equatorial waves uncoupled with convection. Such a small equivalent depth is thought to be a result of the interaction between convection and the dynamics. The convectively coupled equatorial waves identified correspond to the Kelvin, n 5 1 equatorial Rossby, mixed Rossby-gravity, n 5 0 eastward inertiogravity, n 5 1 westward inertio-gravity (WIG), and n 5 2 WIG waves. Additionally, the Madden‐Julian oscillation and tropical depression-type disturbances are present in the OLR spectra. These latter two features are unlike the convectively coupled equatorial waves due to their location away from the equatorial wave dispersion curves in the wavenumber-frequency domain. Extraction of the different convectively coupled disturbances in the time‐longitude domain is performed by filtering the OLR dataset for very specific zonal wavenumbers and frequencies. The geographical distribution of the variance of these filtered data gives further evidence that some of the spectral peaks correspond to particular equatorial wave modes. The results have implications for the cumulus parameterization problem, for the excitation of equatorial waves in the lower stratosphere, and for extended-range forecasting in the Tropics.

Numerical simulation of ion cyclotron waves in tokamak plasmas

Abstract: Introduction. The code TORIC [1] solves Maxwell equations in the Ion Cyclotron (IC) range of frequencies in toroidal axisymmetric plasmas. To make possible selfconsistent simulations of IC experiments in tokamaks, TORIC has been coupled with SSFPQL [2], which solves the quasilinear Fokker-Planck (QLFP) equation for ions. The TORIC-SSFPQL package has been described in some details in [3]. Here we will briefly recall the physics included in the codes, and discuss some features of the model related to specifically toroidal effects. Use of this package for parametric studies of IC heating scenarios in ASDEX Upgrade is illustrated in a companion contribution to this Conference [4]. TORIC. The model implemented in TORIC includes propagation and damping of the externally excited fast wave (FW), and of Ion Bernstein (IBW) and Ion Cyclotron (ICW) waves which can be excited by linear mode conversion (LMC) near ion-ion resonances. The absorption channels are fundamental and first harmonic IC heating of ions, and Landau and Transit Time damping by electrons. Optionally, damping of the FW at higher IC harmonics can be simulated, although not simultaneously with mode conversion [5]. The wave equations are derived from Vlasov equation by expanding the e.m. fields in Fourier modes in the toroidal and poloidal angles [6]. While for the FW an expansion to second order in the Larmor radius is adequate, large Larmor radius effects are taken into account to describe IBWs [7], in such a way that the local dispersion relation of the wave equations solved by TORIC is everywhere a good approximation of the full hot-plasma dispersion relation. As a stand-alone, TORIC assumes local thermal equilibrium; for iteration with SSFPQL the coefficients of the wave equations are evaluated (to all orders in the Larmor radius) using the distributions predicted by the quasilinear kinetic equation as explained in [3]. The spectral representation of the hf field allows a rigorous definition of the local wavevec

Dispersive properties of finite, one-dimensional photonic band gap structures : applications to nonlinear quadratic interactions

Abstract: We discuss the linear dispersive properties of finite one-dimensional photonic band-gap structures. We introduce the concept of a complex effective index for structures of finite length, derived from a generalized dispersion equation that identically satisfies the Kramers-Kronig relations. We then address the conditions necessary for optimal, phase-matched, resonant second harmonic generation. The combination of enhanced density of modes, field localization, and exact phase matching near the band edge conspire to yield conversion efficiencies orders of magnitude higher than quasi-phase-matched structures of similar lengths. We also discuss an unusual and interesting effect: counterpropagating waves can simultaneously travel with different phase velocities, pointing to the existence of two dispersion relations for structures of finite length.

Kinetic Alfven wave revisited.

Abstract: We develop a series of new analytical expressions describing the physical properties of the kinetic Alfven wave. The wave becomes strongly compressive when is of the order of the ion inertial length. Thus, in a low-β plasma, the kinetic Alfven wave can be compressive at values of k⊥ for which the dispersion relation departs only slightly from that of the usual MHD Alfven wave. The compression is accompanied by a magnetic field fluctuation δB‖ such that the total pressure perturbation δptot ≈ 0. Thus the wave undergoes transit-time damping as well as Landau damping; the two effects are comparable if the ion thermal speed is of the order of the Alfven speed. We find that the transverse electric field is elliptically polarized but rotating in the electron sense; this surprising behavior of the polarization of the Alfven branch was discovered numerically by Gary [1986]. We derive a new dispersion relation which explicitly shows how the kinetic Alfven wave takes on some properties of the large-k⊥ limit of the slow mode. We also derive approximate dispersion relations valid for a multi-ion plasma with differential streaming. We suggest that the kinetic Alfven wave may be responsible for the flattening of density fluctuation spectra observed at large wavenumbers in the corona and in the solar wind. We also find that our derived properties of the kinetic Alfven wave are consistent with its presence in the dissipation range of MHD turbulence [Leamon et al., 1998a, b].

The conductivity of dense molecular gas

Abstract: We evaluate the conductivity tensor for molecular gas at densities ranging from 104 to 1015 cm-3 for a variety of grain models. The Hall contribution to the conductivity has generally been neglected in treatments of the dynamics of molecular gas. We find that it is not important if only 0.1-μm grains are considered, but for a Mathis--Rumpl--Nordsieck grain-size distribution (with or without PAHs) it becomes important for densities between 107 and 1011 cm-3. If PAHs are included, this range is reduced to 109-- 1010 m cm-3. The consequences for the magnetic field evolution and dynamics of dense molecular gas are profound. To illustrate this, we consider the propagation of Alfven waves under these conditions. A linear analysis yields a dispersion relation valid for frequencies below the neutral collision frequencies of the charged species. The dispersion relation shows that there is a pair of circularly polarized modes with distinct propagation speeds and damping rates. We note that the gravitational collapse of dense cloud cores may be substantially modified by the Hall term.

Dimensionality Dependence of the Conductivity Dispersion in Ionic Materials

Abstract: The dielectric response of many materials exhibits universal behavior in the form of a power law frequency dependence of the ac conductivity. This response is seen in all types of structures both crystalline and amorphous and for all types of polarizing species including dipoles and ions. Here I demonstrate that for ionic materials the power law exponent decreases with decreasing dimensionality of the ion conduction pathways. Although percolation concepts such as random walks on a self-similar fractal lattice provide a qualitative explanation, experimental findings instead indicate that the dispersion is the result of localized ion motion occurring on an atomic length scale. {copyright} {ital 1999} {ital The American Physical Society }

Phonon group velocity and thermal conduction in superlattices

Abstract: With the use of a face-centered cubic model of lattice dynamics we calculate the group velocity of acoustic phonons in the growth direction of periodic superlattices. Comparing with the case of bulk solids, this component of the phonon group velocity is reduced due to the flattening of the dispersion curves associated with Brillouin-zone folding. The results are used to estimate semiquantitatively the effects on the lattice thermal conductivity in Si/Ge and GaAs/AlAs superlattices. For a Si/Ge superlattice an order of magnitude reduction is predicted in the ratio of superlattice thermal conductivity to phonon relaxation time [consistent with the results of P. Hyldgaard and G. D. Mahan, Phys. Rev. B 56, 10 754 (1997)]. For a GaAs/AlAs superlattice the corresponding reduction is rather small, i.e., a factor of 2--3. These effects are larger for the superlattices with larger unit period, contrary to the recent measurements of thermal conductivity in superlattices.

Diffusion, localization and dispersion relations on "small-world" lattices

Abstract: The spectral properties of the Laplacian operator on “small-world” lattices, that is mixtures of unidimensional chains and random graphs structures are investigated numerically and analytically. A transfer matrix formalism including a self-consistent potential a la Edwards is introduced. In the extended region of the spectrum, an effective medium calculation provides the density of states and pseudo relations of dispersion for the eigenmodes in close agreement with the simulations. Localization effects, which are due to connectivity fluctuations of the sites are shown to be quantitatively described by the single defect approximation recently introduced for random graphs.

One-Dimensional Electronic Structure and Suppression of d-Wave Node State in (La1.28Nd0.6Sr0.12)CuO4

Abstract: Angle-resolved photoemission spectroscopy was carried out on (La1.28Nd0.6Sr0.12)CuO4, a model system of the charge- and spin-ordered state, or stripe phase. The electronic structure contains characteristic features consistent with other cuprates, such as the flat band at low energy near the Brillouin zone face. However, the low-energy excitation near the expected d -wave node region is strongly suppressed. The frequency-integrated spectral weight is confined inside one-dimensional segments in the momentum space (defined by horizontal momenta | kx | = π/4 and vertical momenta | ky | = π/4), deviating strongly from the more rounded Fermi surface expected from band calculations. This departure from the two-dimensional Fermi surface persists to a very high energy scale. These results provide important information for establishing a theory to understand the charge and spin ordering in cuprates and their relation with high-temperature superconductivity.

Experimental measurement of group velocity dispersion in photonic crystal fibre

Abstract: The authors report measurements of group velocity dispersion in photonic crystal fibre using low coherence techniques. The results confirm theoretical predictions that photonic crystal fibre, unlike conventional step-index fibre, can exhibit anomalous waveguide dispersion while remaining singlemode. This allows the design of singlemode fibres with zero dispersion points at wavelengths much shorter than is possible in standard fibre.

Large Dispersive Effects near the Band Edges of Photonic Crystals

Abstract: We have used phase-sensitive ultrashort-pulse interferometry to study the modification of optical pulse propagation near the photonic band edges in colloidal crystals consisting of polystyrene spheres in water. A strong suppression of the group velocity is found at frequencies near the $L$ gap of the fcc lattice. The group velocity dispersion diverges at the band edges and shows branches of both normal dispersion and anomalous dispersion, which can be interpreted as large changes in the effective mass, both positive and negative. We obtain excellent agreement with the dynamical diffraction theory.

Experimental demonstration of photonic crystal based waveguides

Abstract: We report the experimental demonstration of waveguides built around layer-by-layer photonic crystals. An air gap introduced between two photonic crystal walls was used as the waveguide. We observed full (100%) transmission of the electromagnetic (EM) waves through these planar waveguide structures within the frequency range of the photonic band gap. The dispersion relations obtained from the experiment were in good agreement with the predictions of our waveguide model. We also observed 35% transmission for the EM waves traveling through a sharp bend in an L-shaped waveguide carved inside the photonic crystal.

Waves in Twisted Magnetic Flux Tubes

Abstract: The modes of oscillation of a twisted magnetic flux tube in an incompressible medium are investigated analytically. An exact dispersion relation for the case of uniform twist is obtained. In contrast to the case of an untwisted incompressible tube, body, surface, and hybrid (surface-body) modes arise.

Global high-resolution phase velocity distributions of overtone and fundamental-mode surface waves determined by mode branch stripping

Abstract: SUMMARY We apply the mode branch stripping (MBS) technique of van Heijst & Woodhouse (1997) to approximately 110 000 three-component seismograms.We select high-quality data with the reliability estimate of van Heijst & Woodhouse (1997). We assess the in£uence of diierent selection criteria and remove outliers using smooth degree-12 phase velocity maps. We present ¢nal results in terms of Rayleigh- and Love-wave fundamental-mode and overtone global high-resolution (l~40) phase velocity maps. We determine the optimum damping of the high-resolution maps with a method based on cross-validation. Our fundamental-mode phase velocity maps are generally in good agreement with previous studies, especially with Ekstro« m et al. (1997). They do, however, contain more short-wavelength structure than previous studies as we apply relatively little damping. The Rayleigh wave overtone phase velocity measurements made with MBS are of high quality in broad frequency ranges. The measurements are generally well explained by phase velocity maps, and variance reductions for some modes, after rejecting outliers, are as high as 85 per cent. We compare our global phase velocity distributions to the previous results of Stutzmann & Montagner (1994) and to phase velocity maps predicted by 3-D tomographic mantle models. Agreement of the model predictions with our Rayleigh wave phase velocity maps, in terms of both amplitude and observed structures, is good. For Love waves, the qualityof the measurements made with MBS is not as high as for Rayleigh waves.The variance reductions achieved are lower and the agreement between model predictions and our phase velocity maps is less, especially in the frequency ranges where interference between diierent mode branches is strong. Finally, as an additional check on the quality of our overtone measurements, we present a comparison of the fundamental-mode Rayleigh phase velocity distribution at 40 s and our fourth Rayleigh wave overtone phase velocity distribution at 62 s. These two modes are similarly sensitive to velocity anomalies in the top of the upper mantle. We show that the two phase velocity maps are in very close agreement.

Non parabolic band transport in semiconductors: closure of the moment equations

Abstract: The problem of the closure of the moment equations of the semiconductor Boltzmann equation is studied in the framework of the Kane dispersion relation (therefore avoiding the limitations of the parabolic band approximation). By using the maximum entropy ansatz for the closure one obtains, in the limit of small anisotropy, explicit constitutive relations for the stress tensor and the flux of energy flux tensor. The results obtained are in remarkable agreement with those arising from Monte Carlo simulations.

Direct evidence for R- rotons having antiparallel momentum and velocity

Abstract: Experimental evidence is presented that shows that the momentum of a R- roton (a particle-like excitation in liquid helium-4) is antiparallel to its velocity. Although this is anticipated from the negative slope of the dispersion curve for these excitations, it has only been possible to test since the development of a source of ballistic R- rotons. The backward refraction of the quantum evaporation process, which is the signature of antiparallel momentum and velocity, is observed.

Acoustic stop bands of surface and bulk modes in two-dimensional phononic lattices consisting of aluminum and a polymer

Abstract: Spatial and frequency distributions of forbidden bands of both surface and bulk acoustic waves are studied theoretically for two-dimensional (2D) periodic elastic structures consisting of aluminum and polymer. The surface is perpendicular to the 2D periodic arrays of circular cylinders embedded in a background material. The dispersion relations of the surface and bulk modes with wave vectors parallel to the surface are calculated for triangular lattices, and the stop band distributions are plotted in a form relevant to the comparison with ultrasound imaging experiments.

Analysis of quasi-linear diffusion coefficients

Abstract: This paper considers the quasi-linear treatment of either electrons or protons cyclotron-resonant with either whistler or ion cyclotron waves. The dispersion relation used does not yield a simple, explicit expression for the resonant frequency ω. Detailed analysis is made of the conditions determining the resonant frequencies ω for a given wave normal angle θ; there may be up to three values of ω(θ). Criteria are derived which identify the frequencies and indicate when they are outside specified frequency cutoffs. From this analysis, much unnecessary computational effort to evaluate the diffusion coefficients may be avoided. For electron-whistler interactions in the radiation belts, the sensitivity of the local results to the parameters of the wave distribution is considered. It is shown how parameter-independent calculations may be used to analyze the dependence on the parameter values. This approach is extended to the bounce-averaged coefficients, which determine estimates of the pitch angle distribution and corresponding time to pitch angle scatter into the loss cone. Numerical results are obtained using recently reported parameters for whistler waves due to hiss, lightning, and VLF transmitters, as well as perturbations to these values.

FDTD dispersion revisited: faster-than-light propagation

Abstract: The numerical dispersion relation that governs the propagation of fields in a finite-difference time-domain (FDTD) grid was derived several years ago. In this work a different interpretation is given for the governing equation. It is shown that the dispersion relation predicts faster-than-light propagation for coarsely resolved fields. Additionally, some spectral components that were previously believed to have zero phase velocity are shown to propagate, albeit with exponential decay.

Resonant acceleration and heating of solar wind ions by dispersive ion cyclotron waves

Abstract: We investigate the preferential acceleration and heating of solar wind alpha particles by the resonant cyclotron interaction with parallel-propagating left-hand-polarized ion cyclotron waves. The Alfven wave spectrum equation is generalized to multi-ion plasmas and a Kolmogorov type of cascade effect is introduced to transfer energy from the low-frequency Alfven waves to the high-frequency ion cyclotron waves, which are assumed to be entirely dissipated by the wave-particle interaction. In order to distribute the dissipated wave energy among the alphas and protons, the quasi-linear theory of the wave-particle interaction is used along with the cold plasma dispersion relation, and a power law spectrum of the ion cyclotron waves is assumed, with the spectral index as a free parameter of the model. The set of three-fluid solar wind equations and the Alfven wave spectrum equation are then solved in order to find fast solar wind solutions. It is found that the effect of the alpha particles on the dispersion relation, omitted in most previous wave-driven solar wind models, has a significant influence on the preferential acceleration and heating of the alphas, especially in the region close to the Sun. With this effect included, the alpha particles can be accelerated to a bulk flow speed faster than the protons by a few hundred kilometers per second and heated by the resonant cyclotron interaction to more than mass-proportional temperature values at several solar radii. However, this mechanism does not yield a differential speed of the order of an Alfven speed and a mass-proportional temperature for the alphas beyond 0.3 AU, as observed, which confirms the same conclusion reached previously by Isenberg and Hollweg [1983] for nondispersive ion cyclotron waves.

Axisymmetric propagating vortices in the flow between a stationary and a rotating disk enclosed by a cylinder

Abstract: The destabilization of the stationary basic flow occurring between two disks enclosed by a cylinder is studied experimentally when the radius of the disks is large compared to the spacing. In the explored range of the cell aspect ratio, when one disk only is rotating, circular vortices propagating to the centre are observed above a critical angular velocity. These structures occur naturally but can also be forced by small modulations of the angular velocity of the disk. For each rotation rate the dispersion relation of the instability is experimentally reconstructed from visualizations and it is shown that this dispersion relation can be scaled by the boundary layer thickness measured over the disk at rest. The bifurcation is found to be of supercritical nature. The effect of the forcing amplitude is in favour of a linear convective nature of this instability of the non-parallel inward flow existing above the stationary disk. The most unstable temporal frequency is found to be about four times the frequency of the rotating disk. The evolution of the threshold of this primary instability is described for different aspect ratios of the cell. Finally, two sets of experiments made under transient conditions are presented: one in order to investigate further a possible convective/absolute transition for the instability, and the other to compare with the impulsive spin-down-to-rest experiments of Savas (1983).

Exact treatment of the dispersion and beam interaction impedance of a thin tape helix surrounded by a radially stratified dielectric

Abstract: An exact dispersion relation is obtained for electromagnetic waves propagating on a thin metallic tape helix of arbitrary width, supported by a radially stratified dielectric layer and enclosed by a metallic shell. By expanding the surface currents on the tape in a series of Chebyshev polynomials, the unquantifiable assumptions made in all previously published analyzes of the tape helix regarding the forms of the surface current on the tape, or the electric fields at the radius of the tape, are avoided. The power flow and interaction impedance are exactly computed. The dispersion relation is solved numerically for slow waves and the resulting phase velocity and interaction impedance are compared to those computed using the frequently made assumptions of constant current along the tape and zero current across the tape. It is found that for wide tapes significant errors are made in both the phase velocity and interaction impedance when neglecting the transverse variation of the longitudinal current and neglecting the transverse current. For narrow tapes, the two approaches agree to good accuracy. Plots of the surface currents for wide and narrow tapes are presented. The longitudinal current shows a significant variation across the tape. An example is given showing the existence of an optimum tape width, at which the on-axis interaction impedance is maximized. It is separately shown how an approximate, but useful model of metallic vanes may be incorporated in the analysis by the modification of certain boundary conditions. In all cases, computations of phase velocity and impedance across a wide frequency band take well under a minute on a modern workstation.

Bogoliubov dispersion relation and the possibility of superfluidity for weakly interacting photons in a two-dimensional photon fluid

Abstract: The Bogoliubov dispersion relation for the elementary excitations of the weakly interacting Bose gas is shown to hold for the case of the weakly interacting photon gas (the ``photon fluid'') in a nonlinear Fabry-Perot cavity. The chemical potential of a photon in the two-dimensional photon fluid does not vanish. The Bogoliubov relation, which is also derived by means of a linearized fluctuation analysis in classical nonlinear optics, implies the possibility of a new, superfluid state of light. The theory underlying an experiment in progress to observe sound waves in the photon fluid is described, and another experiment to measure the critical velocity of this superfluid is proposed.

A kinetic‐fluid model

Abstract: A nonlinear kinetic-fluid model for high β plasmas with multiple ion species which can be applied to multiscale phenomena is presented. The model embeds important kinetic effects due to finite ion Larmor radius (FLR), wave-particle resonances, magnetic particle trapping, etc., in the framework of simple fluid descriptions. When further restricted to low-frequency phenomena, with frequencies less than the ion cyclotron frequency, the kinetic-fluid model takes a simpler form in which the fluid equations of multiple ion species collapse into one-fluid density and momentum equations and a low-frequency generalized Ohm's law. The kinetic effects are introduced via plasma pressure tensors for ions and electrons which are computed from particle distribution functions that are governed by the Vlasov equation or simplified plasma dynamics equations such as the gyrokinetic equation. The ion FLR effects provide a finite parallel electric field, a perpendicular velocity that modifies the E × B drift, and a gyroviscosity tensor, all of which are neglected in the usual one-fluid MHD description. Eigenmode equations are derived, which include magnetosphere-ionosphere coupling effects for low-frequency waves (e.g., kinetic/inertial Alfven waves and ballooning-mirror instabilities).

Measurement of semiconductor laser gain and dispersion curves utilizing Fourier transforms of the emission spectra

Abstract: A new technique for the measurement of semiconductor laser gain and dispersion spectra is presented. The technique is based on an analysis of the subthreshold emission spectrum by Fourier transforms. Applications of this method to AlGaInP-based interband laser diodes and mid-infrared intersubband quantum cascade lasers are discussed. A good agreement between the measured dispersion of the refractive index and tabulated values in the literature was found.

Temperature dependence of collective modes in liquid sodium

Abstract: We present results for the purely coherent dynamic structure factor of liquid sodium obtained from inelastic X-ray scattering experiments. Measurements were carried out at four temperatures between 388 and 1173 K. The dispersion relations for longitudinal collective excitations in the liquid could be determined for each temperature. It is found that the adiabatic sound velocity given as the slope of the dispersion at lower Q is increased compared to the bulk value. This `positive dispersion' still exists even at the highest temperatures attained in this experiment. From the data an estimate is given for the shear modulus of the liquid along the temperature range covered by our experiment.

Reflectance and emission spectra of excitonic polaritons in GaN

Abstract: High-resolution reflectance and emission spectra have been measured for high-quality free-standing GaN nearly free from residual strains and impurities. They have been analyzed based on a model exciton-polariton picture in which free A, B, and C excitons couple simultaneously to an electromagnetic wave, where the effective-mass anisotropy and the optical anisotropy are taken into account. Taking account of the free-exciton damping, we have calculated not only the dispersion relations but also the energy dependence of the imaginary part of the wave vectors for the excitonic polaritons. Furthermore, the lifetime of each polariton branch has been calculated combining the imaginary part of the polariton wave vectors and the group velocity obtained from the polariton dispersion relations. It is demonstrated that information on the polariton lifetime is indispensable for interpreting the emission spectra. A brief discussion will be given on obtained values for some physical parameters, including hole parameters.