Showing papers on "Dispersion relation published in 1983"
TL;DR: In this paper, the effect of the electromagnetic terms and the stability boundaries in both low and high-beta plasmas were examined. And the authors derived an approximate dispersion relation showing the relation of this mode to the whistler and compared the solutions of it with those obtained from the exact dispersion relations.
Abstract: In a high‐beta plasma the so‐called modified‐two‐stream instability, which results from strongly magnetized electrons drifting relative to unmagnetized ions across a homogeneous magnetic field, is misnamed because the mode is highly kinetic, particularly when the relative streaming velocity exceeds the Alfven speed of the plasma. This kinetic cross‐field streaming instability is investigated in detail, examining the effect of the electromagnetic terms and the stability boundaries in both low‐ and high‐beta plasmas. An approximate dispersion relation showing the relation of this mode to the whistler is derived and solutions of it are compared with those obtained from the exact dispersion relation. The kinetic mode, unlike the usual modified‐two‐stream instability, is not stabilized by electromagnetic effects when the relative electron–ion drift speed exceeds the Alfven speed.
146 citations
TL;DR: In this article, a technique for the numerical modelling of stress wave propagation in pressure bars, using the theoretical dispersion relations, is described and applied to remove the effects of dispersion from experimental records, and pulses which show a moderate amount of dispersive distortion can be processed successfully.
Abstract: Describes a technique for the numerical modelling of stress wave propagation in pressure bars, using the theoretical dispersion relations. The method is applied to remove the effects of dispersion from experimental records, and pulses which show a moderate amount of dispersive distortion can be processed successfully. The technique is simple and comparatively rapid, and can be applied on a routine basis to correct the results from split Hopkinson bar tests and similar high strain rate and impact stress measurements.
137 citations
TL;DR: In this article, high-resolution time-of-flight measurements of 17-meV He atoms scattered from an Ag(111) surface along the $112 and $110 azimuths are reported.
Abstract: High-resolution time-of-flight measurements of 17-meV He atoms scattered from an Ag(111) surface along the $〈112〉$ and $〈110〉$ azimuths are reported. Most of the spectra reveal two sharp peaks and from their locations dispersion curves have been determined out to the zone boundary. The agreement of the lower-frequency mode with the theoretical Rayleigh dispersion curve is excellent. The other mode is significantly lower (35%) than the calculated longitudinally polarized surface mode.
133 citations
TL;DR: In this article, the authors considered the dispersion of a pulse of solute in a capillary tube undergoing irreversible, heterogeneous reaction or reversible adsorption at the tube wall.
111 citations
TL;DR: In this article, the authors show that the shape of the dispersion curve resembles that of solid argon except for a wave-length region where the oscillation frequency vanished as predicted by kinetic theory.
Abstract: Neutron scattering experiments on liquid argon show evidence for the existence of well defined though strongly damped sound waves with wavelengths comparable to the size of the atoms. The dynamic structure factor can be described in terms of Rayleigh and Brillouin lines. The sound oscillation frequency shows an anomaly consistent with the mode-coupling theory. The shape of the dispersion curve resembles that of solid argon except for a wave-length region where the oscillation frequency vanished as predicted by kinetic theory.
103 citations
TL;DR: The dispersion relation for Rayleigh waves propagating across a grating, on the surface of a semi-infinite, nondissipative, isotropic elastic medium was recently calculated by Rayleigh's method and equivalently by a formally exact method based on Green's theorem as mentioned in this paper.
Abstract: The dispersion relation for Rayleigh waves propagating across a grating, on the surface of a semi‐infinite, nondissipative, isotropic elastic medium was recently calculated by Rayleigh’s method and equivalently by a formally exact method based on Green’s theorem. Now, using a complex wave‐vector k or complex frequency ω in the present work, we continue the solutions of the dispersion relation into the radiative region of the kω‐plane (i.e., above the bulk transverse sound line) and into the first frequency‐gap on the boundary of the Brillouin zone caused by the grating periodicity. Here the solutions for the surface waves have components that radiate outwardly into the bulk. The acoustic attenuation for the Rayleigh waves, calculated from the imaginary part of complex k, agrees very well with experiment: all the observed peaks, including those missed by previous perturbation scattering theories, are found. Moreover, a branch is found in the dispersion relation, to which a corresponding complex solution is...
100 citations
93 citations
TL;DR: Surface-plasmon polaritons guided by thin, lossy metallic films bounded by dissimilar dielectric media are investigated, and new solutions to the dispersion relation are found, representing waves that are leaky in one of the dielectrics.
Abstract: Surface-plasmon polaritons guided by thin, lossy metallic films bounded by dissimilar dielectric media are investigated. New solutions to the dispersion relation are found, representing waves that are leaky (radiative) in one of the dielectrics. The new waves are interpreted in terms of the coupling of a damped surface plasmon at one interface with continuum modes at the other. Their excitation by end-fire coupling techniques is suggested.
91 citations
TL;DR: In this paper, a more general dispersion relation is obtained to determine the effects of rotation, relaxation time and the external magnetic field on the phase velocity of the plane harmonic waves in an infinite conducting thermo-elastic solid permeated by a primary uniform magnetic field when the entire elastic medium is rotating with a uniform angular velocity.
76 citations
TL;DR: In this article, a nonlinear dispersion relation for Type I irregularities is obtained which predicts: isotropy of the Doppler shift with elevation, limiting phase velocity equal to ion acoustic speed, and saturation amplitude which is maximum for horizontally propagating waves and decreases with elevation.
Abstract: By taking into account the effect of wave electric fields on electron orbits, a nonlinear dispersion relation for Type I irregularities is obtained which predicts: (1) isotropy of the Doppler shift with elevation, (2) limiting phase velocity equal to ion acoustic speed, and (3) saturation amplitude which is maximum for horizontally propagating waves and decreases with elevation.
74 citations
TL;DR: In this article, the dispersion relations and field structure of TE-polarized guided waves travelling along an asymmetric dielectric slab surrounded by two different nonlinear media are considered.
Abstract: We consider dispersion relations and field structure of TE-polarized guided waves travelling along an asymmetric dielectric slab surrounded by two different nonlinear media. For a given configuration there are four types of guided waves. Three of this four types possess at least one field maximum outside the slab region and have no counterpart in linear waveguide optics. The solutions of the dispersion relations depend now on an additional parameter making them more flexible with respect to the linear limit.
TL;DR: In this paper, the authors used the properties of the dispersion relation in the neighborhood of the mode conversion point to construct differential equations for the mode amplitudes, in a well defined way, which give energy conservation in the absence of damping.
Abstract: Many radio‐frequency heating methods involve conversion of an incoming wave to another mode which only propagates within the plasma and is ultimately damped. A method previously used to consider electron cyclotron heating by the O mode is extended to other mode conversion phenomena.From the properties of the dispersion relation in the neighborhood of the mode conversion point, differential equations for the mode amplitudes are constructed, in a well‐defined way, which give energy conservation in the absence of damping. An analytic solution gives the transmission and conversion coefficients in terms of parameters defining the local behavior of the dispersion relation. The technique is applied to a number of problems, showing that they can all be solved by elementary algebraic manipulations of the local dispersion relation. The phenomenon of electron cyclotron emission also falls rather naturally into this mode conversion picture. It is also suggested that the method of dealing with cyclotron emission may have some relevance to the more general problem of energy transport across a magnetic field. The technique, therefore, brings together into a unified theory a number of problems which have been treated by diverse, and usually more complicated, mathematical techniques in the existing literature.
TL;DR: In this article, a self-consistent theory of the free-electron laser is derived in the collective regime which includes all transverse variations in the wiggler field as well as the effects of a finite waveguide geometry.
Abstract: A fully self-consistent theory of the free-electron laser is derived in the collective regime which includes all transverse variations in the wiggler field as well as the effects of a finite waveguide geometry. A general orbit theory is derived by perturbation about the steady-state trajectories in a configuration which consists of an axial guide field in addition to the helical wiggler field, and used to obtain the source current and charge density for the Maxwell-Poisson equations. By this means, a set of coupled differential equations is found which describes an arbitrary radial beam profile. A dispersion equation is obtained under the assumption of a thin monoenergetic beam, and solved numerically for the growth rates of the TE/sub 11/ and TM/sub 11/ modes in a cylindrical waveguide. A selection rule is found by which the TE/sub l/m or TM/sub l/m modes are resonant at the lth free-electron-laser Doppler upshift.
TL;DR: In this paper, the conditions for the existence of global Alfven eigenmodes below the continuum were investigated and an analytical dispersion relation describing the modes was obtained, where the curvature together with gradients of the equilibrium current (magnetic shear), and finite ω/ωci effects are responsible for these modes which could play an important part in Alfven wave heating of tokamak plasmas.
Abstract: The conditions for the existence of global Alfven eigenmodes below the continuum are investigated, and an analytical dispersion relation describing the modes is obtained. In cylindrical geometry, the curvature together with gradients of the equilibrium current (magnetic shear), and finite ω/ωci effects are responsible for these modes which could play an important part in Alfven wave heating of tokamak plasmas.
TL;DR: In this paper, the angular distribution and time-of-flight spectra were measured for the collisions of 20-meV He atoms with a NaCl(001) surface in the 100g direction.
Abstract: Angular distributions and time-of-flight spectra have been measured for the collisions of 20-meV He atoms with a NaCl(001) surface in the 100g direction. Structures in the angular distribution and in the time-of-flight spectra due to elastic and inelastic scattering are measured and used to extract (1) a corrugation parameter of the rigid-atom surface potential ${\ensuremath{\zeta}}_{0}=0.34$ \AA{}, (2) three bound-state energies of the He-surface potential, and (3) a surface-phonon Rayleigh dispersion curve out to the edge of the Brillouin zone. Furthermore, we were able to demonstrate that by rotating the crystal about the surface normal it is possible to unambiguously identify kinematical focusing features in the angular distributions. These features were then used to determine a surface-phonon dispersion curve in good agreement with that obtained from the time-of-flight experiments.
TL;DR: In this article, the authors examined the conductivity of ion waves in plasmas and found that the reduction in conductivity is independent of the wave amplitude, thus differing from the reduction due to saturation found recently by numerical solution of the Fokker-Planck equation.
Abstract: Electron energy transport in plasmas is examined in the context of ion waves which are intermediate between collisionless isothermal ion acoustic waves and collisional adiabatic sound waves. The conductivity is found to be much less than the Spitzer‐Harm result for wavelengths less than 1000 electron mean free paths. This is expected to be relevant to laser‐produced ablating plasmas in which the temperature can vary considerably over a distance of 10 to 100 mean free paths. The reduction in conductivity is independent of the wave amplitude thus differing from the reduction due to saturation found recently by numerical solution of the Fokker–Planck equation. At short wavelengths the heat flow approaches an upper limit which depends on the phase velocity of the wave. Diffusive ion wave damping is strong over a large range of wavelengths.
TL;DR: In this article, it was shown that in the ion cyclotron range of frequencies omega less than or equal to 4..cap omega../sub i/, with modest ion temperatures, the finite-Larmor-radius effect removes the wave singularity at lower-hybrid resonance layer, enabling an externally initiated electron plasma wave to transform continuously into an ion Bernstein wave.
Abstract: Ion Bernstein wave excitation and propagation via finite ion-Larmor-radium mode-transformation are investigated theoretically and experimentally. It is shown that in the ion cyclotron range of frequencies omega less than or equal to 4..cap omega../sub i/, with modest ion temperatures (T/sub i/ less than or equal to 10 eV), the finite-Larmor-radius effect removes the wave singularity at lower-hybrid resonance layer, enabling an externally initiated electron plasma wave to transform continuously into an ion Bernstein wave. In an ACT-1 hydrogen plasma (T/sub e/ approx. = 2.5 eV, T/sub i/ less than or equal to 2.0 eV), externally excited ion Bernstein waves have been observed for omega less than or equal to 2..cap omega../sub i/ as well as for omega less than or equal to 3..cap omega../sub i/. The finite ion-Larmor-radius mode transformation process resulting in strong ion Bernstein wave excitation has been experimentally verified. Detailed measurements of the wave dispersion relation and of the wave-packet trajectory show excellent agreement with theory. The dependence of the excited ion Bernstein wave on the antenna phasing, the plasma density, and on the neutral pressure (T/sub i/) is also investigated.
TL;DR: In this paper, the authors used wave formulae derived from the dispersion relation for linear waves to find an analytical solution to the problem of wave height variation on a simple topography; i.e. topographies with incrementally constant slope and straight parallel contours.
TL;DR: In this article, the authors showed that the energy dependence of the $4 ε-band expected for a single-particle system is transferred into $k$-dependent intensity variations of the quasiparticle excitation and the intense satellite line.
Abstract: Photoelectron spectra from ordered CO on Cu(111) exhibit anomalously small $4\ensuremath{\sigma}$ band dispersion compared to all other CO adsorption systems previously studied. The bonding $5\ensuremath{\sigma}$ band displays normal one-electron dispersion. It is shown that the energy dependence of the $4\ensuremath{\sigma}$ band expected for a single-particle system is transferred into $k$-dependent intensity variations of the quasiparticle excitation and the intense satellite line \ensuremath{\sim}2 eV lower in energy. The first moment of the spectral weight function over this energy range recovers the anticipated one-electron band dispersion.
TL;DR: In this article, the general dispersion relation of electromagnetic surface waves propagating at the interface of certain types of nonlinear media can be obtained exactly without first solving for the field profiles across the boundary.
Abstract: It is shown that the general dispersion relation of electromagnetic surface waves propagating at the interface of certain types of nonlinear media can be obtained exactly without first solving for the field profiles across the boundary.
TL;DR: In this paper, a general theory of the light propagation in periodic structures characterized by a uniform rotation of the dielectric tensor about a given axis is presented, which can be used to calculate the wave vectors as a function of the mean and the incidence angle.
Abstract: A general theory of the light propagation in periodic structures characterized by a uniform rotation of the dielectric tensor about a given axis is presented. Starting from a fundamental approach of Dreher and Meier, which is mostly numerical, an analytical solution of the characteristic equation has been found which can be used to calculate the wave vectors as a function of $\ensuremath{\omega}$ and of the incidence angle ${\ensuremath{\theta}}_{i}$. The electromagnetic wave is described as a superposition of elementary modes having the form of Bloch waves. Each elementary mode is represented by a sum of plane waves elliptically polarized, whose wave vectors are the roots of the characteristic equation. The analysis of the solutions of such an equation allows us to draw a more complete map of the stability and instability regions for light propagation in helical structures than the ones currently available in the literature. The coexistence of two distinct modes, with different polarization states, determines the shape of the stability map. Each mode presents a series of Bragg instabilities. Between the two Bragg instabilities of the same order a further instability exists which is common to both modes and does not satisfy the Bragg conditions. All instability bands, with the exception of only one of the first order, vanish at normal incidence. This occurs for any value of the optical anisotropy and is a peculiarity of perfectly ordered helical structures. The bandwidth increases with ${\ensuremath{\theta}}_{i}$, and overlapping may occur. Typical plots of dispersion curves and attenuation constants are reported. Finally, we compute the intensity and the polarization state of the light reflected from a thin film, in order to clarify the controversial point about the structure\char22{}doublet or triplet\char22{}of the higher-order reflection bands.
01 Jan 1983
TL;DR: In this article, the relativistic effects of Doppler broadening on the dispersion of electromagnetic waves in relativistically Maxwellian plasmas were investigated. But the authors did not consider the effect of broadening with respect to wave dispersion.
Abstract: The propagation and absorption of electromagnetic waves in a relativistic Maxwellian plasma are investigated by solving the uniform plasma dispersion relation. Both the Hermitian and the anti‐Hermitian parts of the plasma conductivity tensor σ are calculated relativistically. The Bessel functions occurring in σ are not expanded, and many cyclotron harmonic terms are included at high temperatures. The dispersion relation is solved numerically for perpendicular propagation, k∥ =0, where the relativistic effects are maximum and are not masked by Doppler broadening, which has been more thoroughly investigated. It is found that relativistic broadening has a substantial effect on wave dispersion, shifting the extraordinary mode right‐hand cutoff and the upper‐hybrid resonance to higher magnetic field with increasing temperature. Above a critical temperature, the cutoff disappears entirely. There is a broad range of temperatures, 20 keV≤Te ≤500 keV, for which the wavenumber k⊥ differs significantly from both the cold‐plasma value and the vacuum value. This has important implications for ray tracing in relativistic plasmas. Wave damping rates are calculated and compared to results from a previous formulation using the Poynting theorem, in which only the Hermitian part of σ is calculated relativistically.
TL;DR: In this article, the absorption and emission properties of a magnetized plasma in the electron cyclotron range of frequencies are simply and exactly expressed in terms of the Z function, which gives a useful working form to the dielectric tensor, for any wave vector and harmonic number.
Abstract: In order to study the absorption and emission properties of a magnetized plasma in the electron cyclotron range of frequencies, the weakly relativistic (Shkarofsky) plasma dispersion functions are simply and exactly expressed in terms of the Z function. This gives a useful working form to the dielectric tensor, for any wave vector and harmonic number, covering also the case of electron Maxwellian distributions drifting along the magnetic field.
TL;DR: In this article, the wavenumber-dependent vibrational spectra for longitudinal and transverse excitations in a two-component metallic glass are calculated based on pseudopotential-derived interatomic forces, a novel variant of the cluster-relaxation technique for the determination of the equilibrium static structure and density, and on the recursion method for the computation of the vibrational spectrum.
Abstract: The wavenumber-dependent vibrational spectra for longitudinal and for transverse excitations in a two-component metallic glass are calculated. The calculation is based on pseudopotential-derived interatomic forces, a novel variant of the cluster-relaxation technique for the determination of the equilibrium static structure and density, and on the recursion method for the computation of the vibrational spectra. For both longitudinal and transverse vibrations the dispersion relations for two distinct modes-corresponding to the acoustic and optic modes in a crystal-could be determined. At very long wavelength these modes correspond to collective density and concentration fluctuations, at short wavelength they can be identified with the incoherent vibrations of the two atomic species. For longitudinal excitations the results can be compared with recent neutron inelastic scattering experiments and good agreement is found.
TL;DR: In this article, the authors use eikonal theory to investigate the induced diffusion interaction in the ocean between small-scale internal waves and a much larger scale internal wave field and find that diffusion occurs in σ − z space, and a simple “mean first passage” calculation allows to derive an expression for the probability density of critical layers.
TL;DR: In this paper, an electromagnetic linear stability analysis of transverse magnetic waves propagating along the direction of electron drift in a planar system described by a relativistic laminar flow equilibrium is presented.
Abstract: The stability of the electron flow in magnetically insulated transmission lines and diodes, and in microwave devices is an important issue. Presented in this paper are the results of an electromagnetic, linear stability analysis of transverse magnetic waves propagating along the direction of electron drift in a planar system described by a relativistic laminar flow equilibrium. In general, this equilibrium features cold electrons executing E×B drifts in self‐consistently calculated electromagnetic fields. For this paper, a class of laminar flow equilibria in which the relativistic plasma and cyclotron frequencies are multiples of one another was chosen, and the electrons were taken to be confined to a layer placed in a vacuum gap between two conductors. This configuration is driven unstable by two separate mechanisms which tap the free energy associated with the sheared velocity field of the layer. At long wavelengths, the interaction of positive and negative energy surface waves results in the diocotron instability. At shorter wavelengths, the interaction of surface waves and sheets of electrons resonant at the local Doppler‐shifted cyclotron frequencies leads to a pair of unstable branches of the dispersion relation which are referred to collectively as the magnetron instability. The scaling of the growth rates with equilibrium parameters and the relative importance of the two instabilities are discussed.
TL;DR: In this article, the evaluation of auroral radar measurements in terms of the Farley-Buneman instability is reviewed and adjusted to recent observational (Te > Ti) and theoretical (propagation not exactly perpendicular to the magnetic field, high growth rates of the unstable waves) evidence that applies for the high-latitude E region.
Abstract: The evaluation of auroral radar measurements in terms of the Farley-Buneman instability is reviewed and adjusted to recent observational (Te > Ti) and theoretical (propagation not exactly perpendicular to the magnetic field, high growth rates of the unstable waves) evidence that applies for the high-latitude E region. The kinetic dispersion relation of the instability is studied in detail for a wavelength of 1 m in order to facilitate comparisons with the STARE auroral radar. The results of this new approach are compared with the results obtained with the simple dispersion relation which has so far been used to evaluate auroral radar experiments. It is shown that the new method results in considerably higher electron drift velocities in the case of strong convection. This means that with the former simple dispersion relation the electron drift velocities and electric fields have often been underestimated.
TL;DR: In this paper, the linear stability of zonal, parallel shear flow on a beta-plane is discussed, where the localized shear region supports unstable waves, while the far-field can support Rossby waves because of the ambient potential-vorticity gradient.
Abstract: The linear stability of zonal, parallel shear flow on a beta-plane is discussed. While the localized shear region supports unstable waves, the far-field can support Rossby waves because of the ambient potential-vorticity gradient. An infinite zonal flow with a continuous cross-stream velocity gradient is approximated with segments of uniform flow, joined together by segments of uniform potential vorticity. This simplification allows an exact dispersion relation to be found. There are two classes of linearly unstable solutions. One type is trapped to the source of energy and has large growth rates. The second type is weaker instabilities which excite Rossby waves in the far-field: the influence of these weaker instabilities extends far beyond that of the most unstable waves.
TL;DR: In this paper, the adaptation of surface acoustic wave resonator technology to a ZnO-on-Si layered medium is presented. And a technique for temperature compensating the devices by use of a thermal SiO2 layer is discussed.
Abstract: The adaptation of surface acoustic wave resonator technology to a ZnO‐on‐Si layered medium is presented. Several distributed reflector schemes are considered, including shorted and isolated metallic strips, as well as grooves etched in the ZnO layer. In the case of etched groove reflectors, a first‐order velocity perturbation arises due to the dispersive nature of the layered medium. Unique resonator design considerations result from the reflector array velocity and reflectivity characteristics. Transverse mode resonances are characterized and their effect on resonator response eliminated by a novel transducer design. A technique for temperature compensating the devices by use of a thermal SiO2 layer is discussed.
TL;DR: In this paper, the linear combination of atomic orbitals method is applied to clusters of 365 atoms, which are constructed to model the pair distribution functions of liquid and amorphous Fe.
Abstract: The linear combination of atomic orbitals method is applied to clusters of 365 atoms, which are constructed to model the pair distribution functions of liquid and amorphous Fe. From these models the authors compute densities of states, spectral functions and electrical conductivities. Densities of states are quite similar in both models. Some evidence of residual E-k dispersion relations is found in the peaks of the spectral functions, but no evidence is found for any negatively sloped portion of the E-k curve. Although s states are found to be more mobile than d states, the conductivity is dominated by d states because of their much greater density.