Showing papers on "Dispersion relation published in 1998"
15 Dec 1998-Philosophical transactions - Royal Society. Mathematical, physical and engineering sciences
TL;DR: In this article, Boussinesq-type equations of higher order in dispersion as well as in nonlinearity are derived for waves and wave-current interaction over an uneven bottom.
Abstract: Boussinesq–type equations of higher order in dispersion as well as in nonlinearity are derived for waves (and wave–current interaction) over an uneven bottom. Formulations are given in terms of various velocity variables such as the depth–averaged velocity and the particle velocity at the still water level, and at an arbitrary vertical location. The equations are enhanced and analysed with emphasis on linear dispersion, shoaling and nonlinear properties for large wave numbers.
As a starting point the velocity potential is expanded as a power series in the vertical coordinate measured from the still water level (SWL). Substituting this expansion into the Laplace equation leads to a velocity field expressed in terms of spatial derivatives of the vertical velocity ŵ and the horizontal velocity vector u at the SWL. The series expressions are given to infinite order in the dispersion parameter, μ. Satisfying the kinematic bottom boundary condition defines an implicit relation between ŵ and u, which is recast as an explicit recursive expression for ŵ in terms of u under the assumption that μ ≪ 1. Boussinesq equations are then derived from the dynamic and kinematic boundary conditions at the free surface. In this process the infinite series solutions are truncated at O (μ6), while all orders of the nonlinearity parameter, ϵ are included to that order in dispersion. This leads to a set of higher–order Boussinesq equations in terms of the surface elevation η and the horizontal velocity vector u at the SWL.
The equations are recast in terms of the depth–averaged velocity, U leaving out O (ϵ2μ4, which corresponds to assuming ϵ =O(μ). This formulation turns out to include singularities in linear dispersion as well as in nonlinearity. Next, the technique introduced by Madsen and others in 1991and Schaffer & Madsen in 1995 is invoked, and this results in aset of enhanced equations formulated in U and including O (μ4,ϵμ4)terms. These equations contain no singularities and the embedded linear and nonlinear properties are shown to be significantly improved. To quantify the accuracy, Stokes's third–order theory is used as reference and Fourier analyses of the new equations are carried out to third order (in nonlinearity) for regular waves on a constant depth and to first order for shoaling characteristics. Furthermore, analyses are carried out to second order for bichromatic waves and to first order for waves in ambient currents. These analyses are not restricted to small values of the linear dispersion parameter, μ. In conclusion, the new equations are shown to have linear dispersion characteristics corresponding to a Pade [4,4] expansion in k′h′ (wave number times depth) of the squared celerity according to Stokes's linear theory. This corresponds to a quite high accuracy in linear dispersion up to approximately k′h′ = 6. The high quality of dispersion is also achieved for the Doppler shift in connection with wave–current interaction and it allows for a study of wave blocking due to opposing currents. Also, the linear shoaling characteristics are shown to be excellent, and the accuracy of nonlinear transfer of energy to sub– and super–harmonics is found to be superior to previous formulations.
The equations are then recast in terms of the particle velocity, ũ, at an arbitrary vertical location including O μ4,ϵ5μ4)terms. This formulation includes, as special subsets, Boussinesq equations in terms of the bottom velocity or the surface velocity. Furthermore, the arbitrary location of the velocity variable can be used to optimize the embedded linear and nonlinear characteristics. A Fourier analysis is again carried out to third order (in ϵ) for regular waves. It turns out that Pade [4,4] linear dispersion characteristics can not be achieved for any choice of the location of the velocity variable. However, for an optimized location we achieve fairly good linear characteristics and very good nonlinear characteristics.
Finally, the formulation in terms of ũ is modified by introducing the technique of dispersion enhancement while retaining only O (μ4,ϵ5μ4) terms. Now the resulting set of equations do show Pade [4,4] dispersion characteristics in the case of pure waves as well as in connection with ambient currents, and again the nonlinear properties (such as second– and third–order transfer functions and amplitude dispersion) are shown to be superior to those of existing formulations of Boussinesq–type equations.
328 citations
TL;DR: In this article, the influence of strong correlations on low frequency collective modes in a dusty plasma is investigated, and it is shown that strong correlations lead to new dispersive corrections, an overall reduction of the frequency and phase velocity and the existence of parameter regions where ∆/∆k < 0.
Abstract: The influence of strong correlations on low frequency collective modes in a dusty plasma is investigated. The dust dynamics is modeled by the generalized hydrodynamics description. For the well known dust acoustic mode, strong correlations lead to new dispersive corrections, an overall reduction of the frequency and phase velocity and the existence of parameter regions where ∂ω/∂k<0. A novel result is the possibility of sustaining a low frequency transverse mode—a dust shear mode—in which the correlation energy acts as an effective bulk modulus. The influence of ion streaming and collisional interaction with a background of neutrals on the modes are also studied and it is shown that the longitudinal modes may be driven unstable by ion streaming.
325 citations
Dissertation•
01 May 1998
TL;DR: In this article, the authors present the simultaneous inverse inversion of Rayleigh Phase Velocity and Attenuation for Near-Surface Site at a near-surface site at the Georgia Institute of Technology.
Abstract: Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Simultaneous Inversion of Rayleigh Phase Velocity and Attenuation for Near-Surface Site
228 citations
Book•
01 Jan 1998
TL;DR: In this article, the Sellmeier Coefficients for Refractive index were derived from nonlinear optical laser devices and applied to noncritical optical Parametric Oscillators (NPOO) and optical fiber communication systems.
Abstract: Preface. Introduction. Refractive Index: Introduction. Measurement. Dispersion Relations for Refractive Index. Derivation of the Sellmeier Coefficients. Sellmeier Coefficients. Comparison of Refractive Indexes. References. Thermo-Optic Coefficients: Definition. Measurement. Dispersion Relations. Derivation of the Sellmeier Coefficients: Nonlinear Crystals. Other Oxide and Laser Crystals. Halide Crystals/Glasses. Semiconductors. Optical Fiber/Optical Glasses. References. Applications: Nonlinear Optical Laser Devices: Noncritically Phase-Matched Second Harmonic Generations. Noncritical Optical Parametric Oscillators. Sum Frequency Generation. Optical Fiber Communication Systems: Chromatic Dispersion and Zero-Dispersion Wavelength. Thermo-Optic Switch. Optical Fiber Temperature Sensor. Thermo-Optic Modulators. References. Future Technology. Subject Index.
220 citations
TL;DR: In this article, the authors show that the probability distribution for the formation of a freak wave is universal, that is, it does not depend on the statistics of the current, but only on a single distance scale parameter, provided that this parameter is finite and non-zero.
Abstract: When deep-water surface gravity waves traverse an area with a curved or otherwise variable current, the current can act analogously to an optical lens, to focus wave action into a caustic region. In this region, waves of surprisingly large size, alternatively called freak, rogue, or giant waves are produced. We show how this mechanism produces freak waves at random locations when ocean swell traverses an area of random current. When the current has a constant (possibly zero) mean with small random fluctuations, we show that the probability distribution for the formation of a freak wave is universal, that is, it does not depend on the statistics of the current, but only on a single distance scale parameter, provided that this parameter is finite and non-zero. Our numerical simulations show excellent agreement with the theory, even for current standard deviation as large as 1.0 m s−1. Since many of these results are derived for arbitrary dispersion relations with certain general properties, they include as a special case previously published work on caustics in geometrical optics.
211 citations
TL;DR: In this paper, the dependence on size distribution of the Raman line shape of optical vibron modes in CdSe dots was examined, and a detailed comparison with the theory of electron-hole correlated Raman scattering in spherical quantum dots, which includes LO-confined modes, was carried out.
Abstract: We examine the dependence on size distribution of the Raman line shape of optical vibron modes in CdSe dots. A detailed comparison with the theory of electron-hole correlated Raman scattering in spherical quantum dots, which includes LO-confined modes, is carried out. The obtained CdSe vibron frequencies are found to map well on the ab initio calculated LO phonon dispersion relations of wurtzite CdSe along the [001] direction of the Brillouin zone.
195 citations
TL;DR: Results suggest that this d-wave-like dispersion of the insulator is the underlying reason for the pseudo gap in the underdoped regime.
Abstract: An angle-resolved photoemission study is reported on Ca2CuO2Cl2, a parent compound of high-Tc superconductors. Analysis of the electron occupation probability, n(k), from the spectra shows a steep drop in spectral intensity across a contour that is close to the Fermi surface predicted by the band calculation. This analysis reveals a Fermi surface remnant, even though Ca2CuO2Cl2 is a Mott insulator. The lowest energy peak exhibits a dispersion with approximately the |coskxa – coskya| form along this remnant Fermi surface. Together with the data from Dy-doped Bi2Sr2CaCu2O8+δ, these results suggest that this d-wave–like dispersion of the insulator is the underlying reason for the pseudo gap in the underdoped regime.
187 citations
TL;DR: Olendraru et al. as discussed by the authors determined the absolute/convective instability properties of the Batchelor vortex by direct numerical simulation of the linear impulse response and applied a novel decomposition procedure to the computed wavepacket in order to retrieve the complex wavenumber and frequency prevailing along each spatio-temporal ray.
Abstract: The absolute/convective instability properties of the Batchelor vortex are determined by direct numerical simulation of the linear impulse response. A novel decomposition procedure is applied to the computed wavepacket in order to retrieve the complex wavenumber and frequency prevailing along each spatio-temporal ray. In particular, the absolute wavenumber and frequency observed in the laboratory frame are determined as a function of swirl parameter and external flow. The introduction of a moderate amount of swirl is found to strongly promote absolute instability. In the case of wakes, the transitional helical mode that first undergoes a switch-over to absolute instability is found to be m=−1 without requiring any external counterflow. In the case of jets, the transitional helical mode is very sensitive to swirl and varies in the range −5[les ]m[les ]−1. Only a slight amount of external counterflow (1.5% of centreline velocity) is then necessary to trigger absolute instability. The results of this numerical procedure are in good qualitative and quantitative agreement with those obtained by direct application of the Briggs–Bers criterion to the inviscid dispersion relation (Olendraru et al. 1996). Implications for the dynamics of swirling jets and wakes are discussed.
177 citations
TL;DR: In this paper, the authors considered a two-dimensional circular annulus as a waveguide and derived the dispersion equation analytically and numerical examples for the frequency dispersion curves.
Abstract: A two-dimensional circular annulus is considered in this paper as a waveguide. The guided steady-state time-harmonic waves propagating in the circumferential direction are studied. It is found that the guided circumferential waves are dispersive. The dispersion equation is derived analytically and numerical examples are presented for the frequency dispersion curves. The displacement profiles across the wall thickness of the annulus are also obtained for the first five propagating modes. In addition, the analogy between a flat plate and an annulus in the asymptotic limit of infinite radius of curvature is discussed to reveal some interesting wave phenomena intrinsic to curved waveguides.
156 citations
TL;DR: In this paper, the effect of swirl on jets and wakes is investigated by analyzing the inviscid spatiotemporal instability of the Rankine vortex with superimposed plug flow axial velocity profile.
Abstract: The effect of swirl on jets and wakes is investigated by analyzing the inviscid spatiotemporal instability of the Rankine vortex with superimposed plug flow axial velocity profile. The linear dispersion relation is derived analytically as a function of two nondimensional control parameters: the swirl ratio S and the external axial flow parameter a (a>−0.5 for jets, a<−0.5 for wakes). For each azimuthal wave number m, there exists a single unstable Kelvin–Helmholtz mode and an infinite number of neutrally stable inertial waveguide modes. Swirl decreases the temporal growth rate of the axisymmetric Kelvin–Helmholtz mode (m=0), which nonetheless remains unstable for all axial wave numbers. For helical modes (m≠0), small amounts of swirl lead to the widespread occurrence of direct resonances between the unstable Kelvin–Helmholtz mode and the inertial waveguide modes. Such interactions generate, in the low wave number range, neutrally stable wave number bands separated by bubbles of instability. As S increases...
142 citations
TL;DR: In this paper, the spectrum of black hole radiation of a scalar field satisfying a wave equation with high frequency dispersion was computed using a combination of Laplace transform and WKB techniques for finding approximate solutions to ordinary differential equations.
Abstract: We present a method for computing the spectrum of black hole radiation of a scalar field satisfying a wave equation with high frequency dispersion. The method involves a combination of Laplace transform and WKB techniques for finding approximate solutions to ordinary differential equations. The modified wave equation is obtained by adding a higher order derivative term suppressed by powers of a fundamental momentum scale $k_0$ to the ordinary wave equation. Depending on the sign of this new term, high frequency modes propagate either superluminally or subluminally. We show that the resulting spectrum of created particles is thermal at the Hawking temperature, and further that the out-state is a thermal state at the Hawking temperature, to leading order in $k_0$, for either modification.
TL;DR: In this article, an improved analysis technique based on the quantity |δE/(δn/n)| versus frequency and applied to the Freja plasma wave measurements is presented, which can be used to infer the dispersion relation for the measured emission as well as give estimates of the thermal plasma temperatures.
Abstract: High-resolution measurements by the Freja spacecraft of broadband extremely low frequency (BB-ELF) emission from dc up to the lower hybrid frequency (a few kHz) are reported from regions of transverse ion acceleration (TAI) and broad-energy suprathermal electron bursts (STEB) occuring in the topside ionospheric auroral regions. A gradual transition of the broadband emission occurs near the local O+ cyclotron frequency (ƒO+ ≈ 25 Hz) from predominantly electromagnetic below this frequency to mostly electrostatic above this frequency. The emission below 200 Hz often reach amplitudes up to several hundred mV/m and density perturbations (δn/n) of tens of %. An improved analysis technique is presented, based on the quantity |δE/(δn/n)| versus frequency and applied to the Freja plasma wave measurements. The method can be used to infer the dispersion relation for the measured emission as well as give estimates of the thermal plasma temperatures. The BB-ELF emission is found to consist partly of plasma waves with an ion Boltzmann response, which is interpreted as originating from the so-called slow ion acoustic wave mode (SIA). This emission is associated with large bulk ion (O+) temperatures of up to 30 eV and low electron temperatures (1–2 eV) and therefore occurs during conditions when Te/Ti ≪ 1. The BB-ELF emissions also contain other wave mode components, which are not equally easy to identify, even though it is reasonably certain that ion acoustic/cyclotron waves are measured. The ion Boltzmann component is characterized by a dominantly perpendicular polarization with respect to the Earth's magnetic field direction and a small magnetic component with amplitudes around 0.1–1 nT. The ion Boltzmann component dominates the lower-frequency part (30–400 Hz) of the BB-ELF emissions. The BB-ELF emission have often an enhanced spectral power when certain waveform signatures, interpreted as solitary kinetic Alfven waves (SKAW), or when large-amplitude electric fields, possibly related to black aurora, are encountered in regions often associated with large-scale auroral density depletions. A scenario where the SKAW provides the original free energy and via the BB-ELF emission causes intense transverse ion heating (TAI) is suggested.
TL;DR: In this article, the dispersion relation of a two-dimensional dust plasma crystal has been measured experimentally in a parallel plate rf discharge, and agreement is found with dust lattice waves, whereas deviations from dust acoustic waves exist.
TL;DR: In this article, the free parameters were determined by a fit to the most recent data for π + and π 0 production on the proton and the neutron, in the energy range 160 MeV ⊽ E γ ⩽ 420 MeV, and the position of the resonance pole was obtained in exellent agreement with pion-nucleon scattering.
TL;DR: In this article, the authors derived coherent frequencies and stability properties of anisotropic or ''nonequipartitioned'' beams with different focusing constants and emittances in the two transverse directions.
Abstract: Based on self-consistent Vlasov-Poisson equations, we derive coherent frequencies and stability properties of anisotropic or ``nonequipartitioned'' beams with different focusing constants and emittances in the two transverse directions The thus obtained dispersion relations of transverse multipole oscillations with quadrupolar, sextupolar, and octupolar symmetries are solved numerically We find that for sufficiently large energy anisotropy some of the eigenmodes become unstable in the space-charge-dominated regime Applying our results to high-current linear accelerators, we find that ``nonequipartitioned'' beams may exist in relatively large regions of parameter space under stable conditions It is only in beams with strongly space-charge-depressed betatron tunes that harmful instabilities leading to emittance exchange should be expected
TL;DR: In this paper, the general structure of the cross section of the scattering with polarized photon and/or nucleon in initial or final state is systematically described and exposed through invariant amplitudes.
Abstract: The general structure of the cross section of $\ensuremath{\gamma}N$ scattering with polarized photon and/or nucleon in initial and/or final state is systematically described and exposed through invariant amplitudes. A low-energy expansion of the cross section up to and including the order $\mathcal{O}({\ensuremath{\omega}}^{4})$ is given that involves ten structure parameters of the nucleon (dipole, quadrupole, dispersion, and spin polarizabilities). Their physical meaning is discussed in detail. Using fixed-$t$ dispersion relations, predictions for these parameters are obtained and compared with results of chiral perturbation theory. It is emphasized that Compton scattering experiments at large angles can fix the most uncertain of these structure parameters. Predictions for the cross section and double-polarization asymmetries are given and the convergence of the expansion is investigated. The feasibility of the experimental determination of some of the structure parameters is discussed.
TL;DR: In this article, the out-of-plane angular dependence of the ferromagnetic resonance linewidth, ΔH, has been measured for thin magnetic films coupled to NiO and for uncoupled control films.
Abstract: The out-of-plane angular dependence of the ferromagnetic resonance linewidth, ΔH, has been measured for thin magnetic films coupled to NiO and for uncoupled control films. In the control films, ΔH is described by nearly angle-independent damping parameters. In the NiO-coupled films, however, the damping was found to depend strongly on magnetization orientation, with linewidth values comparable to the control samples at normal orientation, but several times larger when the magnetization lies in plane. The additional linewidth in the NiO-coupled films follows the angular dependence of the number of nearly degenerate spin wave modes, in agreement with the predictions of a two-magnon scattering model of damping which incorporates a spin wave dispersion relation suitable for ultrathin films.
TL;DR: In this paper, a method based on a dispersion relation for propagation of sound waves through a bubbly liquid is developed, which is used to relate the attenuation and phase velocity of a sound wave to the bubble population.
Abstract: A nuclei size measurement technique is developed, based on a dispersion relation for propagation of sound waves through a bubbly liquid. This is used to relate the attenuation and phase velocity of a sound wave to the bubble population, leading to two integral equations. These equations are ill posed, and require special treatment for solution. Algorithms based on a minimization method that imposes a number of physical constraints on the solution, rendering the equation well posed, are developed. The procedure is first tested on analytical data with varying artificial noise added, and found to be successful in recovering the bubble density function, and to perform much better than other published solution techniques. Then, bubbles were generated using electrolysis and air injection through porous tubes, and bubble populations measured. Short monochromatic bursts of sound at different frequencies were emitted and received using hydrophones. The received signals were then processed and analyzed to obtain the attenuation and phase velocity. The void fraction and known experimental errors were also obtained and were fed as constraints to the inverse problem solution procedure. This resulted in bubble populations which compare favorably to those obtained by microphotography.
TL;DR: In this paper, the phonon density of states of a bulk GaN powder was measured by time-of-flight neutron spectroscopy and the dispersion curves, lattice specific heat, and Debye temperature were calculated from fitting the data with a rigid-ion model.
Abstract: We report the measured phonon density of states of a bulk GaN powder by time-of-flight neutron spectroscopy. The observed one-phonon excitation spectrum consists of two broad bands centered at about 23 and 39 meV corresponding to the acoustic and the first group of optical phonons; two sharp bands of upper optic modes at about 75 and 86 meV; and a gap of 45–65 meV. The phonon dispersion curves, lattice specific heat, and Debye temperature are calculated from fitting the data with a rigid-ion model.
TL;DR: In this paper, the free energy source for electrostatic ion cyclotron (EIC) waves was examined for a single nightside auroral zone crossing and it was shown that the electron drift can drive low frequency (<∼50 Hz) waves unstable.
Abstract: FAST particle and wave data for a single nightside auroral zone crossing are utilized to examine the free energy source for electrostatic ion cyclotron (EIC) waves. Comparisons of the unstable wave modes, obtained by an electrostatic linear dispersion relation solver, to the observed waves for two intervals with upflowing ion beams and two with upflowing electron beams are consistent with the conclusion that the observed waves near the cyclotron frequencies are EIC which are driven by the electron drift both in the upgoing ion beam regions and in the upgoing electron regions. A limitation is that the drifting bi-Maxwellian model used in the dispersion relation is not a good match to the observed upflowing electron distributions. The observed ion beams do not drive EIC waves; however, the relative drift of the various ion species comprising the ion beam can drive low frequency (<∼50 Hz) waves unstable. The electron drift, during some intervals, also destabilizes electron acoustic waves.
TL;DR: In this paper, the linear versus nonlinear convective/absolute instability of a family of plane wake profiles at low Reynolds number is investigated by numerically comparing the linearized and the fully nonlinear impulse responses.
Abstract: The linear versus nonlinear convective/absolute instability of a family of plane wake profiles at low Reynolds number is investigated by numerically comparing the linearized and the fully nonlinear impulse responses. Through an analysis of the linear flow response obtained by direct numerical simulation (DNS), the linear temporal and spatiotemporal instability properties are retrieved, in excellent agreement with the properties obtained by Monkewitz [Phys. Fluids 31, 3000 (1994)] from the study of the associated viscous dispersion relation. Nonlinear terms are then shown to limit the amplitude to a saturation level within the response wave packet, while leaving the trailing and leading edges unaffected. For this family of open shear flows, the velocities of the fronts, formed between the trailing or leading edge and the central saturated region, are thus selected according to the linear Dee and Langer criterion [Phys. Rev. Lett. 50, 383 (1983)], whereas the front solutions are fully nonlinear. This proper...
TL;DR: In this paper, the relativistic dynamics of an electron submitted to the three-dimensional field of a focused, ultra-high-intensity laser pulse are studied numerically and boundary conditions for this problem are defined.
Abstract: The relativistic dynamics of an electron submitted to the three-dimensional field of a focused, ultrahigh-intensity laser pulse are studied numerically. The diffracting field in vacuum is modeled by the paraxial propagator and exactly satisfies the Lorentz gauge condition everywhere. In rectangular coordinates, the electromagnetic field is Fourier transformed into transverse and longitudinal wave packets, and diffraction is described through the different phase shifts accumulated by the various Fourier components, as constrained by the dispersion relation. In cylindrical geometry, the radial dependence of the focusing wave is described as a continuous spectrum of Bessel functions and can be obtained by using Hankel's integral theorem. To define the boundary conditions for this problem, the beam profile is matched to a Gaussian-Hermite distribution at focus, where the wave front is planar. Plane-wave dynamics are verified for large f numbers, including canonical momentum invariance, while high-energy scattering is predicted for smaller values of f at relativistic laser intensities.
TL;DR: The dispersion equation for Love wave propagation in a layer lying over a half-space is derived in this article, where both media are assumed to be transversely isotropic fluid-saturated poroelastic solids with principal axes perpendicular to the surface.
Abstract: The dispersion equation for Love wave propagation in a layer lying over a half-space is derived. Both media are assumed to be transversely isotropic fluid-saturated poroelastic solids with principal axes perpendicular to the surface. The analysis is based on the Biot’s theory. The dissipation due to fluid viscosity is considered and therefore the dispersion equation is complex and intractable analytically. An iterative procedure is developed to solve this equation. Two situations are discussed in detail: (i) an elastic layer overlying a poroelastic half-space and (ii) a poroelastic layer lying over an elastic half-space. Dispersion curves and attenuation curves of Love waves are plotted for these two cases. In addition, the upper and lower bounds of Love wave speeds are also explored.
TL;DR: In this paper, it was shown that the ratio of the electric to magnetic field is not always equal to the velocity of the kinetic Alfven wave, especially for structures that are very narrow in the direction perpendicular to the magnetic field.
Abstract: Auroral satellites and sounding rockets frequently observe large electric fields perpendicular to the magnetic field that have a narrow scale length perpendicular to the magnetic field if they are interpreted as spatial structures. These fields have been variously attributed to electrostatic shock structures or to kinetic Alfven waves. These two models can be distinguished by considering the ratio of the magnetic field perturbation to the electric field. This ratio is calculated within the context of the electrostatic approximation, the fully kinetic Alfven wave dispersion relation considered by Lysak and Lotko [1996], and the cold fluid model including ionospheric reflection presented by Lysak [1991, 1993]. Results for this model show that the ratio of the electric to magnetic field is not always equal to the Alfven speed, especially for structures that are very narrow in the direction perpendicular to the magnetic field. These narrow structures have electric fields that are enhanced with respect to the Alfvenic value, and thus may appear as electrostatic.
TL;DR: In this paper, a helical wiggler free-electron laser with ion-channel guiding is presented, and the growth rate of the ion channel is analyzed. But the authors only consider the single particle dynamics and regimes of orbit stability.
Abstract: A theory of a helical wiggler free-electron laser with ion-channel guiding is presented. Electron motion has been analyzed using single particle dynamics and regimes of orbit stability have been discussed. With the help of these trajectories, source currents have been obtained and the linear dispersion equation showing coupling of electromagnetic and space-charge waves by the wiggler field has been set up for a monoenergetic electron beam. Growth rates have been obtained for different ion-channel frequencies. The variation of resonant frequencies and peak growth rates with ion-channel frequency has been illustrated. Substantial enhancement in peak growth rate is obtained as the ion-channel frequency approaches the wiggler frequency.
TL;DR: In this article, the properties of low-frequency waves in a relativistic electron-positron plasma in a strong external magnetic field typical of pulsar magnetospheres are discussed.
Abstract: The properties of low-frequency waves in a one-dimensional, relativistic electron-positron plasma in a strong external magnetic field typical of pulsar magnetospheres are discussed. Approximate dispersion relations are derived for a broad class of distribution functions that have an intrinsically relativistic spread in energies. The effects of the non-neutrality, associated with rotation, and of the relative motion of the plasma species are discussed briefly. In the plasma rest frame only three wave modes need be considered. The magnetosonic $(t)$ mode becomes firehose unstable as the magnetic field weakens, and this occurs in the wind zone of the pulsar. The Alfv\'en $(A)$ mode exists only below a maximum frequency, and is weakly damped only for sufficiently strong magnetic fields. The Langmuir-$O$ mode is approximately longitudinal near its cutoff frequency, and approximately transverse at high frequencies. We argue that the emission zone is within $\ensuremath{\sim}{10}^{2}$ pulsar radii, and that only $t,$ $A,$ and Langmuir waves may participate in the formation of the observed radio spectrum.
TL;DR: In this article, the authors derived new evolution equations for nonlinear acoustic waves in micro-inhomogeneous media, which take into account relaxation processes, and provided the description of such physical effects such as frequency-dependent nonlinear absorption of sound, nonlinearity of its velocity dispersion, and dispersion of the non-linear acoustic parameters of micro inhomogeneous materials.
Abstract: New evolution equations for nonlinear acoustic waves in micro-inhomogeneous media, which take into account relaxation processes, are derived. The proposed theory provides the description of such physical effects as frequency-dependent nonlinear absorption of sound, nonlinearity of its velocity dispersion, and dispersion of the nonlinear acoustic parameters of micro-inhomogeneous materials. The theory predicts that, depending on the ratio of the characteristic relaxation time to the wave period, nonlinearity can grow or diminish with increasing frequency, while an increase in wave amplitude can lead to a rise or fall of the propagation velocity. In the limiting cases where the relaxation processes are instantaneous or quasi-frozen, analytical solutions of the nonlinear equations are found and analyzed.
TL;DR: In this paper, an exact solution of free harmonic wave propagation in a composite laminated cylindrical shell is presented within the framework of the theory of three-dimensional cylindrically anisotropic elasticity.
Book•
30 Nov 1998
TL;DR: Theoretical dispersion relations in linear and nonlinear optics have been studied in this article, where the maximum entropy method has been used for analysis of optical spectra and the sum rules have been applied.
Abstract: Classical dispersion theory.- Dispersion relations in linear optics.- Dispersion relations in nonlinear optics.- Conformal mappings in analysis of optical spectra.- Maximum entropy method.- Sum rules.
TL;DR: In this article, the complex refractive index n =n+ik and the dielectric function e =e1+ie2 at room temperature of AlxGa1−xSb films with 0⩽x⌽05, grown by molecular beam epitaxy on a GaSb substrate, were determined from 002 to 6 eV by using the complementary data from fast Fourier transform far-infrared, dispersive, and ellipsometric spectrometry.
Abstract: The complex refractive index n=n+ik and the dielectric function e=e1+ie2 at room temperature of AlxGa1−xSb films with 0⩽x⩽05, grown by molecular beam epitaxy on a GaSb substrate, were determined from 002 to 6 eV by using the complementary data from fast Fourier transform far-infrared, dispersive, and ellipsometric spectrometry The effect of the native oxide was accounted for and the self-consistency of the optical functions was checked in the framework of the Kramers–Kronig causality relations In the restrahlen region the dielectric function was well fitted by classical Lorentz oscillators; in the transparent region below the fundamental gap E0, the refractive index was modeled by a Sellmeier dispersion relation, and in the interband region the dielectric function near the critical points was analyzed through standard line shapes Interpolating the fitting parameters or the interband dielectric spectra, it was possible to obtain the optical functions for any concentration x between 00 and 05