Showing papers on "Dispersion relation published in 1982"
TL;DR: In this article, the authors introduce the concept of the local wavenumber and frequency spectral density, which can be estimated using spatially fixed, point data sources (fixed probe pairs).
Abstract: We introduce the concept of the local wavenumber and frequency spectral density, which can be estimated using spatially fixed, point data sources (’’fixed probe pairs’’), and discuss the relationship of this spectral density to the conventional wavenumber and frequency spectral density and the cross‐power spectral density. The local wavenumber and frequency spectral density is shown to be equivalent to the conventional wavenumber and frequency spectral density when the fluctuation is stationary and homogeneous and consists of a superposition of wave packets; such a fluctuation is the basic model used in many turbulence theories. A digital method for estimating the local wavenumber spectrum is described and applied to the study of drift‐wave turbulence in an rf‐excited discharge. The statistical dispersion relation and wavenumber spectral width, computed from the local wavenumber and frequency spectrum of the drift‐wave turbulence, are compared with the conventional spectral moments computed using the correlation method of Iwama and Tsukishima; good agreement is found over a wide range of frequency. A frequency‐integrated wavenumber spectrum is computed; both frequency and wavenumber spectral indices are found independently. The local wavenumber and frequency spectrum is a completely new approach to the use of fixed‐probe data, and we believe it can greatly extend the quantity of information available from fixed probes, which are the principle tools in many, if not most, fluctuation experiments.
392 citations
TL;DR: In this paper, a ray tracing study of ULF waves below FH+, the proton gyrofrequency is presented, where the dispersion relation of the ULF wave is split into three branches, and the ray paths for these three branches are studied.
Abstract: Intense ultralow-frequency waves are commonly observed on GEOS 1 and 2 spacecraft, around FHe+, the helium gyrofrequency. These waves were identified as ion cyclotron waves (ICW's) by Young et al. (1981), who showed their close connection with a sufficient amount of He+ in the magnetospheric plasma. Motivated by these observations, we present a ray tracing study of ULF waves below FH+, the proton gyrofrequency. In the presence of He+ the dispersion relation of ULF waves is split into three branches, and we have studied the ray paths for these three branches. Of particular interest is the ion cyclotron branch, which is left handed above the new crossover frequency Fcr introduced by the presence of He+ ions. This mode is amplified, in the equatorial region, by anisotropic (T⊥ > T∥) energetic protons. It is well guided along field lines, suffers a polarization reversal when F = Fcr locally, and continues to be guided up to the point where F = Fbi, the bi-ion hybrid frequency. Then it is reflected and returns to the equator, where it is amplified again. Thus such waves undergo several bounces through the amplifying region without significant drift, either azimuthal or radial. This mirroring effect, which can only occur when minor ions, such as He+, are present, is believed to be crucial for ICW amplification. We also show that for each such equatorial crossing the parallel wave number is conserved while the perpendicular one progressively increases. As a consequence, ICW's become quasi-electrostatic, which enables them to acquire a small but finite parallel electric field; it is suggested that this electric field can in turn accelerate thermal electrons parallel to B.
279 citations
TL;DR: In this article, a review of the experiments done since then on these waves are critically reviewed and analysed in terms of appropriate models and corresponding dispersion relations. Discrepancies and unresolved issues are identified and discussed.
Abstract: Plasma surface waves were discovered in 1958. The experiments done since then on these waves are critically reviewed and analysed in terms of appropriate models and corresponding dispersion relations. Discrepancies and unresolved issues are identified and discussed. Wave damping experiments and analysis, and results of more recent works on nonlinear aspects of these waves, are also reported.
254 citations
TL;DR: In this paper, the effect of a uniform static external magnetic field oriented normal to the two-dimensional layers, on the collective-mode spectrum was discussed with the use of the self-consistent field and hydrodynamic approximations.
Abstract: Electronic collective modes of a system of large numbers of equally spaced, parallel two-dimensional electron layers are discussed within a self-consistent-field approach. Plasmon dispersion relations for the finite system as well as for the infinite periodic system are obtained. It is shown that the optical-plasmon frequency of the periodic system goes into the known two- or three-dimensional limit, respectively, depending on whether $\mathrm{qa}\ensuremath{\gg}1$ or $\mathrm{qa}\ensuremath{\ll}1$, where $q$ is the wave number in the two-dimensional plane and $a$ is the layer spacing. Effect of a uniform static external magnetic field oriented normal to the two-dimensional layers, on the collective-mode spectrum, is discussed with the use of the self-consistent-field and hydrodynamic approximations. It is shown that magnetoplasmons, helicon, and Alfv\'en waves can all exist in such a periodic system under suitable conditions. The theory is generalized to a system where the alternate layers are electrons and holes. The relevance of these results to semiconductor superlattice systems (both types I and II) is pointed out.
237 citations
TL;DR: In this paper, the amplitude of the superconducting gap propagates as an undamped collective mode with a finite frequency and the dispersion and damping of this mode are calculated.
Abstract: At low temperature the long-wavelength perturbations of the amplitude of the superconducting gap propagate as an undamped collective mode with a finite frequency. The dispersion and damping of this mode are calculated. The phase or the Bogoliubov modes of a superconductor are strongly affected by Coulomb interactions and rendered indistinguishable from plasmons. By contrast, the amplitude modes are shown not to perturb the charge density thus remaining unaffected by the Coulomb interactions. Under certain conditions long-wavelength phonons couple to this mode. This coupling is derived and the observation of the amplitude mode through Raman scattering experiments in the charge-density-wave compound Nb${\mathrm{Se}}_{2}$ are quantitatively explained.
217 citations
TL;DR: In this article, a linearized kinetic model for heating of tokamak plasmas by Alfven waves is studied by using a sheet current of single helicity and frequency ω, located between the plasma edge and a conducting wall.
Abstract: Heating of tokamak plasmas by Alfven waves is studied by means of a linearized kinetic model which takes into account electron inertia and Landau damping, finite ion gyroradius, the equilibrium current, and magnetic shear. In cylindrical geometry, a fourth‐order set of differential equations in r for the perturbed fields E r and E ⊥ is solved numerically for modes driven by a sheet current of single helicity and frequency ω, located between the plasma edge and a conducting wall. Realistic profiles of density, temperature, and safety factor are employed. The energy deposition and density fluctuations as functions of r and the total impedance to be expected in experiments on the p r e t e x t tokamak are computed, and optimum conditions for heating are investigated. Mode conversion to the kinetic Alfven wave and its damping are observed in the computed solutions. The plasma impedance is sensitive to the profiles and mode numbers chosen, and, with two exceptions, is consistent with previous work based on magnetohydrodynamics. Kinetic effects can produce ’’high Q’’ resonant absorption, both for frequencies below the Alfven continuum (corresponding to discrete stable kink modes) and for frequencies such that the Alfven resonance approaches the plasma edge (corresponding to normal modes of the kinetic shear wave in cold plasma).
204 citations
TL;DR: In this paper, the dispersion of the plasma frequency of layered electron gases in GaAs-(AlGa) As heterostructures was determined by inelastic light scattering, and the measured dispersions differ from that in two-and three-dimensional plasmas.
Abstract: The dispersion of the plasma frequency of layered electron gases in GaAs-(AlGa) As heterostructures was determined by inelastic light scattering. The measured dispersions differ from that in two- and three-dimensional plasmas. They are linear in the in-plane component of the wave vector. This observation confirms predictions of theoretical models.
198 citations
TL;DR: In this article, it was shown that the Si(111)-(2 x 1) surface can be formed easily in the cleavage process without increasing the total energy by more than 0.03 eV/(surface atom).
Abstract: Pseudopotential total-energy calculations show that the ..pi..-bonded chain reconstruction of the Si(111)-(2 x 1) surface can be reached from the ideally bonded surface without increasing the total energy by more than 0.03 eV/(surface atom). Hence, the chain surface can be formed easily in the cleavage process. The minimum-energy chain geometry is determined, and the corresponding surface-state dispersion is in remarkable agreement with recent angle-resolved photoemission experiments.
164 citations
TL;DR: In this article, the status of experimental and theoretical investigations of kaon-nucleon and kaonnucleus interactions and suggest areas likely to be of interest as the field of Kaon-nuclear physics develops.
159 citations
TL;DR: In this paper, the invariant isospin-even πN amplitude D+(ν2,t) to the Cheng-Dashen point, ν=0, t=2μ.
Abstract: Dispersion relations in the (ν2,t) plane along hyperbolas are used in order to extrapolate the invariant isospin-even πN amplitude D+(ν2,t) to the Cheng-Dashen point, ν=0, t=2μ. The fluctuation of the results obtained with different hyperbolas gives a realistic estimate of the errors, except for errors of the partial wave solution and of the ππ
$$ - N\bar N$$
amplitudes assumed at t < 4μ2 —If our ππ
$$ - N\bar N$$
partial waves are used, which are based on the ππs-wave scattering length a
0
0
=0.28 μ-1, the result for the sigma term is 64±8 MeV, in agreement with earlier determinations.—The discrepancy with the theoretical prediction σπN≈ 30 MeV is smaller by only 8 MeV, if our
$$ - N\bar N$$
amplitudes are modified in such a way that the threshold behaviour of the ππs-wave agrees with Weinberg's prediction a
0
0
=0.16 μ-1. Further progress depends on new accurate experimental π±p scattering data in the Coulomb interference region at low energies.
115 citations
TL;DR: In this paper, a modified version of the dispersion relation was proposed to predict a modified dispersion law in which the sound travel time across the cavity is a function of the ratio of the temporal frequency to the horizontal wavenumber.
Abstract: The simple model of p-mode solar oscillations of Liebacher and Stein (1981), in which the acoustic vibrations are trapped in a resonant cavity taking the form of a spherical shell below the solar surface, is compared with Doppler shift observations of vertical velocities. The model is shown to predict a modified dispersion law in which the sound travel time across the cavity is a function of the ratio of the temporal frequency to the horizontal wavenumber, resulting in a single curve when the temporal frequency is plotted against the wavenumber. Frequencies derived from a two-dimensional power spectrum of velocity observations are found to conform to a modified version of the dispersion relation, and that only when the fundamental mode is excluded. Results thus suggest that all modes with the same frequency/wavenumber ratio are trapped in an identical cavity, or, more plausibly, that the difference in upper boundary conditions for different modes has minimal effect on the resulting frequencies.
TL;DR: In this article, it was shown that phonon dispersion curves of crystals can be calculated from first principles within the local density functional formalism using atomic numbers and masses of constituent elements and crystal structures as the only input information.
Abstract: We demonstrate that by using atomic numbers and masses of constituent elements and crystal structures as the only input information, phonon dispersion curves of crystals can be calculated from first principles within the local-density-functional formalism. As shown by an exemplary calculation for the [001]-direction phonon dispersion curves of Si, the agreement with experiment is excellent. The calculation is carried out using the ab initio pseudopotential method and the Hellmann-Feynman theorem.
TL;DR: In this paper, a Langevin treatment of the lattice dynamics, based on harmonic potentials and a theory of hydrodynamic interactions, is presented, which is exact to lowest order in sphere volume fraction and includes important unsteady flow effects.
Abstract: Photon correlation spectroscopy was performed on a dilute bcc colloidal crystal in a thin-film cell to measure its response to thermal fluctuations with wave vectors along lattice symmetry directions. The phonon dispersion curves show a definite harmonic-lattice behavior for longitudinal and transverse modes. We present a Langevin treatment of the lattice dynamics, based on harmonic potentials and a theory of hydrodynamic interactions which is exact to lowest order in sphere volume fraction and includes important unsteady flow effects. The model takes into consideration the discreteness of the lattice, which is important near the Brillouin-zone boundary, and has the correct behavior for long-wavelength fluctuations as well (underdamped transverse modes, overdamped longitudinal modes). The mass renormalization of propagating transverse lattice modes is discussed, along with the effects of the thin-film configuration on their propagation. The role of backflow in overdamping longitudinal modes is made clear. From the measured dispersion curves for longitudinal wave vectors, we obtained the following elastic constants: ${c}_{11}=6.96$ dyn/${\mathrm{cm}}^{2}$ and ${c}_{12}={c}_{44}=2.43$ dyn/${\mathrm{cm}}^{2}$.
TL;DR: In this article, the stability of one-dimensional solitary vortex structures in the electron phase space (electron holes) is investigated and a linear eigenvalue problem is derived in the fluid limit.
Abstract: The stability of one-dimensional, solitary vortex structures in the electron phase space (electron holes) is investigated. A linear eigenvalue problem is derived in the fluid limit and solved exactly, assuming that the normal mode is well represented by the lowest eigenstate of a properly chosen field operator. A new dispersion relation is obtained which exhibits purely growing solutions in two dimensions but only marginally stable solutions in one dimension. This explains the numerically well-known fact that vortex structures disappear in going from one to two dimensions.
TL;DR: In this paper, the results of molecular dynamics calculations of the two-dimensional one-component plasma with logarithmic interactions between the particles are reported, and a solid-fluid transition is observed for Γ = q 2 kT ≈ 135.
Abstract: We report the results of molecular dynamics calculations of the two-dimensional one-component plasma with logarithmic interactions between the particles. A solid-fluid transition is observed for Γ = q 2 kT ≈ 135 . The hysteresis observed on traversing the transition region indicates that the transition is first order. The velocity autocorrelation function shows marked oscillations in the strong coupling region, with a frequency, almost independent of Γ, close to the plasma frequency.
TL;DR: In this article, the role of relativistic mass variation on wave absorption in the electron cyclotron range of frequencies is investigated and the validity of the nonrelativistic linear dispersion relation for a Maxwellian plasma is restricted by the conditions N2∥≫Te/mc2 and N2 ∥≖1−ω2c/ω2
Abstract: The role of the relativistic mass variation on wave absorption in the electron cyclotron range of frequencies is investigated. It is first shown that the validity of the nonrelastivistic linear dispersion relation for a Maxwellian plasma is restricted by the conditions N2∥≫Te/mc2 and N2∥≫‖1−ω2c/ω2‖. A numerical investigation of wave damping in a plasma slab located in an inhomogeneous tokamak‐like magnetic field shows that for most angles of practical interest the latter condition is easily violated and, therefore, the nonrelativistic dispersion relation yields inaccurate results. The problem of the validity of the nonrelativistic quasilinear equation for oblique propagation is also discussed. Using a quasilinear model equation, it is shown that the inclusion of the relativistic mass variation in the diffusion coefficient results in a basic change of the wave–particle selective interaction compared to the nonrelativistic approximation for any value of Te or N∥.
TL;DR: In this paper, the cold plasma dispersion relation for ωR, k, and θ is solved for R-X waves with large, positive growth rates and small group velocities, implying a very small convective growth length ∼10 m.
Abstract: Auroral kilometric radiation (AKR) has a peak intensity at 250 kHz and is associated with discrete aurora in regions where ωp/ωc 0 because of the magnetic mirroring force, and diffusion of trapped electrons in the upgoing loss cone with R-X waves are toward decreasing energies, so that wave growth is possible. To determine which frequency and wave vector (k, θ) is associated with each resonant contour, we solve the cold plasma dispersion relation for ωR, k, and θ, where ωR > ωx, the right-hand cutoff frequency. Growing waves will be associated with those contours that pass through regions of velocity space where ∂f/∂υ⊥ > 0 is large. A simple criterion is given to show which R-X waves will have large positive growth rates. Finally, we calculate the group velocity of R-X waves and show that R-X waves with large, positive growth rates also have small group velocities (Vg/c ≪ 1), implying a very small convective growth length ∼10 m. The intense wave generation should occur at wave frequencies just above the right-hand cutoff frequency and have wave normal angles 75° 0 is large) associated with either the upgoing loss cone or the downgoing precipitating electrons that are undergoing mirroring.
TL;DR: In this paper, the scattering of low-energy atoms on metal surfaces is investigated theoretically, assuming that the adatom motion is coupled to surface phonons, and the trajectory approximation is used.
Journal Article•
TL;DR: In this paper, a new method was proposed for finding the dispersion laws of collective excitations in systems described by non-Abelian gauge theories, based on an expansion of the polarization and mass operators at high temperatures.
Abstract: A new method is proposed for finding the dispersion laws of collective excitations in systems described by non-Abelian gauge theories. The method is based on an expansion of the polarization and mass operators at high temperatures. By means of the method, the dispersion laws of collective Bose and Fermi excitations in a hot quark-gluon plasma are found explicitly. Without being inconsistent with the gauge and chiral symmetries, all the dispersion laws have an optical nature. Possible experimental consequences of the obtained results are briefly discussed.
TL;DR: In this paper, a study of the asymptotic behavior of the gravity modes of an incompressible spherical oceanic layer, surrounding a rigid Earth, as its radius goes to infinity is conducted.
TL;DR: In this article, the dispersion relations of acoustic phonons of the orthorhombic black phosphorus have been measured at room temperature and atmospheric pressure, and very anisotropic dispersion surfaces were observed along the three principal directions.
TL;DR: In this article, a minimum-phase function was derived using the Hilbert transform, which was incorporated into a tissue model which has a causal impulse response and from which accurate estimates of the slope of attenuation times path length can be extracted.
TL;DR: In this article, the propagation velocity and damping of surface plasmons on sinusoidally modulated gold and silver surfaces with different grating constants were measured at wavelengths of 6471 A and 5682 A as function of the amplitude of the grating (up to ca. 300 A).
TL;DR: In this article, a closed algebraic dispersion relation for the eigenfrequency ω and the axial wave number k is obtained for arbitrary azimuthal harmonic number.
Abstract: Properties of the electromagnetic waves propagating through a helix‐loaded waveguide are investigated, including the important influence of the outer conducting wall on the dispersion properties. A closed algebraic dispersion relation for the eigenfrequency ω and the axial wave number k is obtained for arbitrary azimuthal harmonic number. It is shown that in the limiting case, where the outer conducting wall approaches close to the helix, this dispersion relation is reduced to three distinctive modes. These are the transverse electric mode, the transverse magnetic mode, and the helix mode, which can be further simplified to straight lines in the (ω, k) parameter space. Numerical investigation of the dispersion relation is also presented.
TL;DR: In this article, the dispersion relation for an anisotropic medium with arbitrary tensor permittivity and permeability is derived for the case of layered media, and applications to layered media are discussed.
Abstract: The dispersion relation is derived for an anisotropic medium with arbitrary tensor permittivity and permeability. Particular cases and applications to layered media are discussed.
TL;DR: In this article, the dispersion relation for k/sub parallel/ = 0 modes excited by warm ion rings in velocity space was studied and it was shown that waves are excited with real frequencies near the lower hybrid frequency and with growth rates ranging from approx.0.01 to 1 times the ion cyclotron frequency.
Abstract: Discrete emissions at the lower hybrid frequency are often seen on the S3-3 satellite. Simultaneous observation of perpendicularly heated ions suggests that ions may provide the free energy necessary to drive the instability. Studies of the dispersion relation for k/sub parallel/ = 0 modes excited by warm ion rings in velocity space show that waves are excited with real frequencies near the lower hybrid frequency and with growth rates ranging from approx.0.01 to 1 times the ion cyclotron frequency. Numerical results are therefore consistent with the possibility that the observed ions are the free energy source for the observed waves.
01 Nov 1982
TL;DR: In this article, a dispersion equation which describes the linear, hydrodynamic stability of an interfacially perturbed, thin (O(10-100 nm)), planar, uncharged, transversely isotropic, viscoelastic film bounded by electrolytic Newtonian fluids is developed for the case in which the film interfaces are tangentially immobile.
Abstract: A dispersion equation which describes the linear, hydrodynamic stability of an interfacially perturbed, thin (O(10–100 nm)), planar, uncharged, transversely isotropic, viscoelastic film bounded by electrolytic Newtonian fluids is developed for the case in which the film interfaces are tangentially immobile. The linear viscoelastic rheology of the film is described by a Boltzmann superposition in which the stress relaxation tensor is formulated by utilizing Kelvin models. The influence of the electrical interactions of the film system on the linear dynamics is derived explicitly by integrating the normal mode electrostatic field equations. An investigation of the adjoint properties of the normal mode mechanical field relations indicates that for a certain class of films, (i) the principle of exchange of stabilities is valid, (ii) instability is nonoscillatory, and (iii) oscillatory states decay. A simplified dispersion equation for a symmetric film system is deduced, and it is shown that this equation describes squeezing and stretching eigenmodes.
TL;DR: In this article, the dispersion relations for the acoustic and optic phonons in HgTe and HgSe were determined by neutron inelastic scattering in three high symmetry directions.
Abstract: The dispersion relations for the acoustic and optic phonons in HgTe and for the acoustic phonons in HgSe were determined by neutron inelastic scattering in three high symmetry directions The effect of the free-carrier screening of the long-range electric field of LO phonons in HgTe was observed The formalism of the rigid ion model is used for numerical calculations of the phonon dispersion relations and the phonon densities of states in HgTe and HgSe