Showing papers on "Dispersion relation published in 1996"

Dispersion of Plasma Dust Acoustic Waves in the Strong-Coupling Regime

Abstract: Low-frequency compressional waves were observed in a suspension of strongly coupled $9.4\ensuremath{\mu}\mathrm{m}$ spheres in an rf Kr plasma. Both parts of the complex wave number were measured to determine the dispersion relation, which agreed with a theoretical model of damped dust acoustic waves, ignoring strong coupling, but not with a strongly coupled dust-lattice wave model. The results yield experimental values for the dust plasma frequency, charge, Debye length, and damping rate, and support the applicability of fluid-based dispersion relations to strongly coupled dusty plasmas, which has been a controversy.

Lattice waves in dust plasma crystals

Abstract: Techniques previously known from solid state physics are used to look at linear and weak non‐linear wave propagation in dust lattices. These expansion techniques include only electrostatic interactions between neighbor particles in addition to assuming small vibrations in the dust lattice. As a simple model for the dust lattice, a one‐dimensional Bravais lattice is considered. For this particular lattice, expressions for the linear phase velocity are compared to a quasi‐particle simulation. The word quasi here means that only the dust particles are represented as diffuse objects, while the plasma is treated as a fluid. The simulation is also used to study the breakdown of the analytical theory and to investigate non‐linear dust lattice waves. A very good agreement is found between the analytical expressions and the particle simulations, for cases where the average dust separation a is of the order of or larger than the plasma Debye length λD. This is a condition which very often applies to dust crystal in...

On the kinetic dispersion relation for shear Alfvén waves

Abstract: Kinetic Alfven waves have been invoked is association with auroral currents and particle acceleration since the pioneering work of Hasegawa. However, to date, no work has considered the dispersion relation including the full kinetic effects for both electrons and ions. Results from such a calculation are presented, with emphasis on the role of Landua damping in dissipating Alfven waves which propogate from the warm plasma of the outer magnetosphere to the cold plasma present in the ionosphere. It is found that the Landua damping is not important when the perpendicular wavelength is larger than the ion acoustic gyroradius and the electron inertial length. In addition, ion gyroradius effects lead to a reduction in the Landua damping by raising the parallel phase velocity of the wave above the electron thermal speed in the short perpendicular wavelength regime. These results indicate that low-frequency Alfven waves with perpendicular wavelengths greater than the order of 10 km when mapped to the ionosphere will not be significantly affected by Landau damping. While these results based on the local dispersion relation, are strictly valid only for short parallel wavelength Alfven waves, they do give an indication of the importance of Landua damping for longer parallel wavelengthmore » waves such as field line resonances. 26 refs., 5 fig.« less

Unconventional ferromagnetic transition in La1-xCaxMnO3.

Abstract: Neutron scattering has been used to study the magnetic correlations and long wavelength spin dynamics of ${\mathrm{La}}_{1\ensuremath{-}x}{\mathrm{Ca}}_{x}{\mathrm{MnO}}_{3}$ in the ferromagnetic regime $(0\ensuremath{\le}xl\frac{1}{2})$. For $x\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\frac{1}{3}$ $({T}_{C}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}250\mathrm{K})$ where the magnetoresistance effects are largest the system behaves as an ideal isotropic ferromagnet at low $T$, with a gapless $(l0.04\mathrm{meV})$ dispersion relation ${E\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}Dq}^{2}$ and ${D}_{T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0}\ensuremath{\approx}170\mathrm{meV}{\AA{}}^{2}$. However, an anomalous strongly field-dependent diffusive component develops above $\ensuremath{\sim}200\mathrm{K}$ and dominates the fluctuation spectrum as $T\ensuremath{\rightarrow}{T}_{C}$. This component is not present at lower $x$.

Kinetic theory of low-frequency Alfvén modes in tokamaks

Abstract: The kinetic theory of low-frequency Alfven modes in tokamaks is presented. The inclusion of both diamagnetic effects and finite core-plasma ion compressibility generalizes previous theoretical analyses (Tsai S T and Chen L 1993 Phys. Fluids B 5 3284) of kinetic ballooning modes and clarifies their strong connection to beta-induced Alfven eigenmodes. The derivation of an analytic mode dispersion relation allows us to study the linear stability of both types of modes as a function of the parameters characterizing the local plasma equilibrium and to demonstrate that the most unstable regime corresponds to a strong coupling between the two branches due to the finite thermal ion temperature gradient. In addition, we also show that, under certain circumstances, non-collective modes may be present in the plasma, formed as a superposition of local oscillations which are quasi-exponentially growing in time.

Velocity Dispersions and X-Ray Temperatures of Galaxy Clusters

Abstract: Using a large and well-controlled sample of clusters of galaxies, we investigate the relation between cluster velocity dispersions and X-ray temperatures of intra-cluster gas. In order to obtain a reliable estimate of the total velocity dispersion of a cluster, independent of the level of anisotropies in galaxy orbits, we analyze the integrated velocity dispersion profiles over increasing distances from the cluster centers. Distortions in the velocity fields, the effect of close clusters, the presence of substructures, and the presence of a population of (spiral) galaxies not in virial equilibrium with the cluster potential are taken into account. Using our final sample of 37 clusters, for which a reliable estimate of the velocity dispersion could be obtained, we derive a relation between the velocity dispersions and the X-ray temperatures, with a scatter reduced by more than 30 % with respect to previous works. A chi square fit to the temperature-velocity dispersion relation does not exclude the hypothesis that the ratio between galaxy and gas energy density (the so-called spectral beta) is a constant for all clusters. In particular, the value of beta=1, corresponding to energy equipartition, is acceptable.

Complex spiral wave dynamics in a spatially distributed ionic model of cardiac electrical activity

Abstract: This study presents computations and analysis of the dynamics of reentrant spiral waves in a realistic model of cardiac electrical activity, incorporating the Beeler–Reuter equations into a two‐dimensional cable model. In this medium, spiral waves spontaneously break up, but may be stabilized by shortening the excitation pulse duration through an acceleration of the dynamics of the calcium current. We describe the breakup of reentrant waves based on the presence of slow recovery fronts within the medium. This concept is introduced using examples from pulse circulation around a ring and extended to two‐dimensional propagation. We define properties of the restitution and dispersion relations that are associated with slow recovery fronts and promote spiral breakup. The role of slow recovery fronts is illustrated with concrete examples from numerical simulations.

Evidence of High Frequency Propagating Modes in Vitreous Silica.

Abstract: The detailed understanding of the dynamical properties of topologically disordered systems, like glasses, is still an open question. At low momentum transfer (Q) values, the existence of propagating collective excitations is demonstrated by the sharp Brillouin lines observable in light-scattering experiments. This is straightforward from an intuitive point of view since at low Q’s one samples particle-particle correlations on a long time and large space scales with respect to interatomic motions and distances. In the mesoscopic time-space domain the situation is more complicated, and the existence of collective dynamics is doubted. The evidence of modes in glasses in the mesoscopic region comes from incoherent neutron scattering and light scattering studies [1], where a broad band is found around 2 to 10 meV, almost independently from the material. This band has been named boson peak because its intensity scales with temperature approximately according to the Bose-Einstein statistics. The relaxational or vibrational character of the excitations giving rise to the boson peak is highly debated [1], especially in view of the fact that the extrapolation of the dispersion relation found at small Q to the mesoscopic Q region would give excitation energies similar to those of the boson peak. In this region, the experimental determination of the dynamical structure factor SsQ, Ed became only recently possible, thanks to the development of inelastic x-rays scattering (IXS) with meV energy resolution. It was shown for some “intermediate” [2] and “fragile” [3] glasses that propagating excitations exist up to energies comparable to that of the boson peak. Similar determinations have not been attempted yet on “strong” network-forming glasses. Among them, vitreous silica, y-SiO2, is probably the archetype [4]. In this Letter we present the measurement of the SsQ, Ed of y-SiO2 at T › 1050 K, in the 1 6 nm 21 momentum transfer range. We report the existence of collective modes in the whole investigated Q range. These modes are found to propagate with a velocity of sound y › 5800 6 200 my su p to Q ›3.5 nm 21 and E 13 meV. Hence, the energies spanned by these excitations cover the boson peak region [5], thus indicating that they must contribute to its origin. Moreover, the comparison of the present data with light-scattering data at T › 300 K shows that the linewidth of these excitations is temperature independent, suggesting that the peaks broadening is not associated with dynamical processes, but to the ill-definition of Q as a good quantum number. The experiment was carried out at the new very high energy resolution inelastic x-ray scattering beam line (BL21ID16) at the European Synchrotron Radiation Facility. This instrument is based on backscattering from high order reflections in perfect silicon crystals, and in this work we used the Si(999) reflection at 17.794 keV. The total instrumental resolution function was measured using a Plexiglas scatterer at the maximum of its static structure factor where the scattering is dominated by the elastic component; the energy resolution, full width at half maximum (FWHM), was 2.8 6 0.2 meV. The momentum transfer, Q › 2k0 sinsusy2d (where k0 and us are the wave vector of the incident photon and the scattering angle, respectively), was selected between 1 and 6 nm 21 . The Q resolution was set to 0.3 nm 21 by an aperture in front of the analyzer crystal. Energy scans were performed by varying the relative temperature between the monochromator and analyzer crystals. Each scan took about 120 min, and each Q point was obtained by typically averaging four scans. The data were normalized to the intensity of the incident beam. Further details on the beam line are reported elsewhere [2,6‐ 9]. The SiO2 suprasil sample, purchased from Goodfellow, was a 2 mm diameter rod. Its dimension was comparable to the x-ray photoabsorption length and gave negligible multiple scattering. A preliminary experiment performed at room temperature on y-SiO2 showed very weak IXS intensity, strongly merged into the tails of the central peak, thus not allowing a determination of the spectral shape with the necessary accuracy [10]. To increase the expected inelastic scattering signal we performed the measurements at about 1000 K. This gave an enhancement of the excitations with E 10 meV by a factor of 3.5. The y-SiO2 rod was placed inside a graphite tube ( 20 mm in length,

Spin Waves throughout the Brillouin Zone of a Double-Exchange Ferromagnet.

Abstract: We use inelastic neutron scattering to measure the spin wave dispersion throughout the Brillouin zone of the double-exchange ferromagnet La0.7Pb0.3MnO3. Magnons with energies as high as 95 meV are directly observed and an unexpectedly simple Heisenberg Hamiltonian, with solely a nearest-neighbor coupling of 8.79 +/- 0.21 meV, accounts for the entire dispersion relation. The calculated Curie temperature for this local moment Hamiltonian overestimates the measured Curie point (355 K) by only 15%. Raising temperature yields unusual broadening of the high frequency spin waves, even within the ferromagnetic phase.

Determination of velocity and attenuation of shear waves using ultrasonic spectroscopy

Abstract: The ultrasonic spectroscopy (broadband pulse) technique was applied to simultaneously measure phase velocity and attenuation coefficient of shear waves in a solid at frequencies ranging from 2.2 to 7.6 MHz. This technique is an extension of the ultrasonic spectropy technique currently used in determining dispersion of longitudinal waves.

Spin Excitation Spectrum of La$_{1-x}A_x$MnO$_3$

Abstract: As an effective model to describe perovskite-type manganates (La,$A$)MnO$_3$, the double-exchange model on a cubic lattice is investigated. Spin excitation spectrum of the model in the ground state is studied using the spin wave approximation. Spin wave dispersion relation observed in the inelastic neutron scattering experiment of La$_{0.7}$Pb$_{0.3}$MnO$_3$ is reproduced. Effective values for the electron bandwidth as well as Hund's coupling is estimated from the data.

Two-dimensional planar ferromagnetic coupling in LaMnO3

Abstract: Neutron-scattering experiments have been performed on a LaMnO 3 single crystal. The spin waves exhibit two-dimensional anisotropic dispersion, that is, strong planar ferromagnetic coupling and weak antiferromagnetic interplane coupling with a finite gap. The critical exponent β of the order parameter is 0.25 ±0.01, which is much smaller than values obtained for the three-dimensional Ising (0.326) and Heisenberg (0.367) models. Ferromagnetic spin-wave-like dispersion remains for ω> 10 meV at T c ≈140 K, though the spectrum near the zone center is entirely overdamped around ω= 0.

Dynamical response of a one-dimensional quantum-wire electron system.

Abstract: We provide a self-contained theoretical analysis of the dynamical response of a one-dimensional electron system, as confined in a semiconductor quantum wire, within the random-phase approximation. We carry out a detailed comparison with the corresponding two- and three-dimensional situations, and discuss the peculiarities arising in the one-dimensional linear response from the nonexistence of low energy single-particle excitations and from the linear nature of the long wavelength plasmon mode. We provide a critical discussion of the analytic properties of the complex dielectric function in the complex frequency plane. We investigate the zeros of the complex dielectric function, and calculate the plasmon dispersion, damping, and plasmon spectral weight in one dimension. We consider finite temperature and impurity scattering effects on one-dimensional plasmon dispersion and damping. \textcopyright{} 1996 The American Physical Society.

Pattern formation in a vibrated two-dimensional granular layer.

Abstract: We report experiments on a vibrated bidimensional granular layer showing peak pattern formation. We measure the dispersion relation and observe two regimes of pattern selection: at low frequency, a parametric excitation of vertical shearing waves, and at high frequency, a crossover to a pattern selection with a constant wavelength. The amplitude of the patterns is proportional to the amplitude of vibration. We study the instability onset at high frequency and we find evidence of burst waves taking place in a subcritical region defined by two acceleration values. \textcopyright{} 1996 The American Physical Society.

Dispersive properties of a magnetized plasma with a field‐aligned drift and inhomogeneous transverse flow

Abstract: Electrostatic fluctuations driven by the combination of a magnetic‐field‐aligned electron current and a localized transverse electric field are investigated. Characteristic parameters, such as scale length and magnitude of the sheared E×B velocity, magnitude of the magnetic‐field‐aligned current, and temperature ratio τ≡Ti/Te are varied to include conditions associated with electrostatic waves driven entirely by magnetic‐field‐aligned current, driven entirely by transverse electric field, and driven by a combination of magnetic‐field‐aligned current and transverse electric field. It is shown that, in contrast to the homogeneous case of current‐driven modes, the modes in the presence of a transverse‐velocity shear can be unstable in a wider range of temperature ratio τ and they are broadband in frequency. Using a simplified model, numerical solutions of the nonlocal dispersion relation, and physical arguments, cases of stabilization and destabilization due to the inhomogeneous energy‐density driven instabi...

A dispersive analysis of bispherical pickup ion distributions

Abstract: We investigate the properties of a bispherical shell distribution of pickup ions when dispersion of the resonant waves is taken into account. We also extend the method of Johnstone et al. [1991] and Huddleston and Johnstone [1992] for determining the spectra of the quasi-linear self-generated waves to include dispersion. Our specific results assume that all waves propagate along the average magnetic field, and that the waves satisfy the cold electron-proton dispersion relation. The major effect of including dispersion in the analysis is that the particles in a bispherical distribution retain more of their initial energy than in the nondispersive treatment, so the resulting wave spectra are less intense than predicted when dispersion is neglected. The dispersive analysis also encounters the well-known gap in the cyclotron resonance with fast-mode waves which is absent in the nondispersive picture. We present detailed results for pickup protons in the two extreme configurations of magnetic field perpendicular to, and parallel to, the solar wind flow for a range of values of VA/VSW. We find that when pickup protons are scattered to a bispherical distribution with VA/VSW = 0.1, typical of conditions in the solar wind, the discrepancy in the total energy density of the self-generated waves between the dispersive and nondispersive results amounts to 18% in the perpendicular configuration. This discrepancy falls between 9% and 73% in the parallel configuration, depending on the extent of the particle transport through the resonance gap. These discrepancies are substantially larger for larger values of VA/VSW. These results indicate that dispersive effects can be important in the correct modeling of the quasi-linear resonant wave-particle interaction between pickup ions and self-generated waves in the solar wind.

MHD waves generated by the Kelvin-Helmholtz instability in a nonuniform magnetosphere

Abstract: A linear analysis of the Kelvin-Helmholtz instability is performed by assuming that one of the plasma regimes (magnetosphere) separated by a velocity shear layer of zero thickness is spatially nonuniform. The previous theories based on the semi-infinite uniform model with infinitesimally thin magnetopause showed that wave growth due to the Kelvin-Helmholtz instability exhibits monotonic increase for shorter frequency. This finding implies that no monochromatic waves whose spatial scales are as large as the magnetospheric size are generated by the Kelvin-Helmholtz instability. In contrast, the present analysis reveals that the Kelvin-Helmholtz instability generates global-scale monochromatic waves when the magnetosphere is nonuniform and the magnetosheath flow speed is quite fast. The wave number is given through the dispersion relation of the Kelvin-Helmholtz unstable wave.

The attenuation and dispersion of sound in water containing multiply interacting air bubbles

Abstract: The classic theory of linear acoustic propagation in bubbly water inaccurately represents the physical behavior of dense populations of resonating bubbles. It assumes the bubbles always oscillate independently, while they may actually be strongly coupled by acoustic radiation, especially when uniformly sized. Sound propagation can be properly understood only in terms of the collective action of the medium, which is dominated by the ‘‘symmetric’’ normal mode. In this work, the propagational characteristics of bubbly water are determined by averaging the ensemble behavior of the symmetric mode over distributions of bubble radii and locations. The method includes all orders of multiple scattering, and incorporates ‘‘shielding’’ effects in the medium. New theoretical expressions for the phase speed and attenuation are obtained, and compared to experimental data by integrating multiple scattering effects over a ‘‘region of collective interaction’’ around each bubble. For uniform bubbles and volume fractions β ...

Photonic band structure of guided bloch modes in high index films fully etched through with periodic microstructure

Abstract: By adapting the well-known 'zigzag' ray model for use with a periodic waveguide (i.e. replacing the plane wave rays with Bloch wave rays), we show that thin films of high refractive index, supported by a low index substrate and fully etched through with a periodic pattern, can support guided modes. From the dispersion relation of these guided Bloch modes, it is shown that the in-plane modal group velocity can be zero, suggesting applications in enhanced dipole-field interactions and control of spontaneous emission in waveguide lasers.

On travelling waves and double-periodic structures in two-dimensional sine - Gordon systems

Abstract: Exact travelling-wave solutions of the (2 + 1)-dimensional sine - Gordon equation possessing a velocity smaller than the velocity of the linear waves in the correspondent model system are obtained. The dependence of their dispersion relations and allowed areas for the wave parameters on the wave amplitude are discussed. The obtained waves contain as particular cases static structures consisting of elementary cells with zero topological charge. The self-consistent parameters of one static structure are calculated. The obtained structures require minima spatial system sizes for their existence. As an illustration the obtained results are applied for a description of structures in spin systems with an anisotropy created by a magnetic field or by a crystal anisotropy field.

On the transient non-Fickian dispersion theory

Abstract: The Fickian dispersion equation is the basic relationship used to describe the nonconvective mass flux of a solute in a porous medium. This equation prescribes a linear relationship between the dispersive mass flux and the concentration gradient. An important characteristic of the Fickian relationship is that it is independent of the history of dispersion (e.g. the time rate of change of the dispersion flux). Also, the dispersivities are supposed to be medium constants and invariant with temporal and spatial scales of observation. It is believed that in general these restrictions do not hold. A number of authors have proposed various alternative relationships. For example, differential equations have been employed that prescribe a relationship between the dispersion flux and its time and space derivatives. Also, stochastic theories result in integro-differential equations in which dispersion tensor grow asymptotically with time or distance. In this work, three different approaches, which lead to three different non-Fickian equations with a transient character, are discussed and their primary features and differences are highlighted. It is shown that an effective dispersion tensor defined in the framework of the transient non-Fickian theory, grows asymptotically with time and distance; a result which also follows from stochastic theories. Next, principles of continuum mechanics are employed to provide a solid theoretical basis for the non-Fickian transient dispersion theory. The equation of motion of a solute in a porous medium is used to provide a rigorous derivation of various dispersion relationships valid under different conditions. Under various simplifying assumptions, the generalized theory is found to agree with the conventional Fickian theory as well as several other non-Fickian relationships found in the literature. Moreover, it is shown that for nonconservative solutes, the traditional dispersion tensor is affected by the rate of mass exchange of the solute.

Enhanced frequency agility of high-power relativistic backward wave oscillators

Abstract: This paper describes how finite length effects in high-power backward wave oscillators can be exploited in a controlled manner to achieve enhanced frequency agility. Experiments were performed using a Sinus-6 high-power relativistic repetitively pulsed electron beam accelerator. A uniform slow wave structure was used in these studies and its parameters were fixed. Sections of smooth-walled circular waveguide of varying lengths were inserted both before and after the slow wave structure. Variations in the length of smooth-walled waveguide on the order of a quarter-wavelength of the generated electromagnetic radiation were found to significantly affect both microwave frequency and radiation efficiency in a periodic-like manner. The experimental results were reproduced in TWOQUICK electromagnetic particle-in-cell simulations. A bandwidth of about 500 MHz centered around 9.5 GHz at hundreds of MW power levels has been achieved with constant beam and slow wave structure parameters.

On the seasonal dependence of medium‐scale atmospheric gravity waves in the upper atmosphere at high latitudes

Abstract: Seasonal dependence of medium-scale atmospheric gravity waves is examined in SuperDARN HF radar data and through analysis of the gravity wave dispersion relation. We found that the probability of gravity wave observation in the HF radar data is highest in winter months and lowest in summer months. The winter probability of observation in a given 2-hour period with sufficient amounts of ground backscatter peaks at about 0.8, while in the summer the probability remains near 0.4. Examination of the dispersion relation shows that there is a seasonal dependence to the altitude profile of the gravity wave's vertical wavelength that may lead to a seasonally dependent reflection of the waves resulting from the mesospheric temperature gradient. The dispersion relation predicts that for waves of a given horizontal wavelength, the minimum wave period that may be transmitted through the mesosphere is longer in the summer than in the winter; the longer the wavelength, the longer the minimum period. Thus some waves that are transmitted through the mesosphere in the winter may not be transmitted in the summer. This seasonal dependence predicted from the dispersion relation is consistent with the HF radar observations.

Experimental wavelet analysis of flexural waves in beams

Abstract: The wavelet transform (WT) is applied to the time-frequency analysis of flexural waves in beams. The WT with the Gabor wavelet decomposes a dispersive wave into each frequency component in the time domain, which enables one to determine the traveling time of a wave along the beam at each frequency. By utilizing this fact, a method is developed to identify the dispersion relation and impact site of beams.

Temperature‐dependent dispersion relation of ferroelectric lithium tantalate

Abstract: The temperature‐dependent dispersion equation is derived to predict the ordinary and extraordinary refractive indices of lithium tantalate in the region of 0.4–4 μm and for a temperature range of 25 °C–300 °C. The Sellmeier equation is compared with the measured data.

Acceleration and heating of heavy ions by circularly polarized Alfvén waves

Abstract: We study the dispersion relation of left-hand-polarized Alfven waves in multicomponent plasmas. If initially the plasma components are not drifting relative to each other, the Alfven waves propagate until they meet the gyrofrequency of the species with the largest Ml = ml/zlmp value (ml is the ion mass, zl is the degree of ionization, and mp is the proton mass). As a result of resonance absorption, these ions are heated and accelerated by quasi-linear resonant interaction. When these ions reach a given velocity, the dispersion relation of the Alfven waves changes drastically. The Alfven branch of the dispersion relations no longer goes to the gyrofrequency of the ion species with the largest Ml value, but it goes to the gyrofrequency of the species with the second largest Ml value. In this way, more and more channels open up. We apply these results to high-speed solar wind streams, and we argue that Alfven waves generated in coronal holes or in nearby regions can heat and accelerate heavy ions.