Showing papers on "Dispersion relation published in 1969"
TL;DR: In this article, the system of equations for the magneto-acoustic wave propagating along a critical direction is reduced to a simple dispersive equation similar to the Korteweg-de Vries equation except that the third order derivative (the dispersion term) is replaced by the fifth order one.
Abstract: The hydromagnetic waves with small but finite amplitude in a cold collision-free plasma are investigated by using a nonlinear perturbation method. In the lowest order of perturbation, we can show that the system of equations for the magneto-acoustic wave propagating along a `critical' direction is reduced to a simple dispersive equation similar to the Korteweg-de Vries equation except that the third order derivative (the dispersion term) is replaced by the fifth order one. An extension of the problem to more general dispersive system is also made. On the other hand, the system of equations for the Alfven wave is reduced to a modified Korteweg-de Vries equation in the sense that the non-linear term f ∂ f /∂ξ in the Korteweg-de Vries equation is replaced by f 2 ∂/∂ξ. In the case of steady propagation this equation can be integrated to give a solution in closed form, which exhibits a solitary wave. Two kinds of solitary wave (both compressive and rarefied) are found to be possible.
363 citations
TL;DR: In this paper, the authors discuss digital moving window analysis of group and phase velocity and use of time variable filters for surface wave study techniques, and discuss the use of a time variable filter.
Abstract: Surface wave study techniques, discussing digital moving window analysis of group and phase velocity and use of time variable filters
203 citations
TL;DR: In this article, a systematic account of the infinitely many solutions of Landau's dispersion relation verifies that there is always a least-damped wave provided the wavenumber is real and not zero.
Abstract: A systematic account of the infinitely many solutions of Landau's dispersion relation verifies that there is always a least‐damped wave provided the wavenumber is real and not zero. This no longer holds when the frequency is real; yet, the mode originally considered by Landau predominates in a limited range. Strong “coupling” is found between this wave and higher‐order modes at complex frequencies, or when collisions are taken into account. However this coupling does not give rise to resonances other than at the plasma frequency. Short tables of Landau poles and singular points of the dispersion relation conclude this account.
123 citations
TL;DR: In this paper, two types of low-frequency oscillations are found: the usual drift wave localized to the region of large density gradient, and a higher frequency wave localized on the radial boundary.
Abstract: In thermally ionized alkali‐metal plasmas (Q machines), two types of low‐frequency oscillations are found: the usual drift wave localized to the region of large‐density gradient, and a higher‐frequency wave localized to the region of the radial boundary. The latter “edge” oscillation is shown to be a Kelvin‐Helmholtz instability driven by the large shear in plasma rotational velocity at the boundary. An analytic solution of the finite‐Larmor‐radius dispersion equation for the unstable wave is found by making the simplifying assumption that the rotational velocity jumps discontinuously. The results agree reasonably well with experimental measurements.
107 citations
TL;DR: The complete phonon dispersion relation for the symmetry directions in silver at room temperature has been measured by triple-axis neutron spectrometry as mentioned in this paper, but there is some disagreement with the time-of-flight results of Drexel et al.
105 citations
TL;DR: In this paper, a simple method of calculating effects of various boundaries around the helix on the dispersion relation and the interaction impedance is presented, based on the use of equivalent circuit parameters derived from rigorous field analyses.
Abstract: A simple method of calculating effects of various boundaries around the helix on the dispersion relation and the interaction impedance is presented. The analytical technique is based on the use of equivalent circuit parameters derived from rigorous field analyses. The main advantage of this method is that effects of various perturbing objects (dielectrics, shields, etc.) can be calculated independently, regardless of the model of the unperturbed system. Equivalent circuit parameters are obtained for helices with several different forms of perturbing boundaries, including wedge-shaped dielectric rods, conducting boundaries, longitudinally conducting wires and fins, and combinations of these. The method of analysis is versatile so that the dispersion relation for any one particular form of the helix may be calculated from known characteristics of another using only three sets of universal curves.
71 citations
71 citations
TL;DR: The linearized hydrodynamic equations of motion for a thin, flat, superfluid helium film are derived in some detail from standard two-fluid hydrodynamics.
Abstract: The linearized hydrodynamic equations of motion for a thin, flat, superfluid helium film are derived in some detail from standard two-fluid hydrodynamics. Interactions of the film with both the He vapor and the substrate which are in contract with it are included and discussed in detail. Boundary conditions for both the film-substrate and film-gas interfaces are derived. It is indicated how one may construct the equations of motion for the entire coupled system (gas-film-substrate). The equations are actually constructed and solved for the case when a certain parameter is small, which includes all the third-sound experiments on unsaturated films. A dispersion equation is found which is exact in the limit of vanishing frequency, and which is eminently suited to describe both the velocity and the attenuation of third sound in the regime of unsaturated films. No hydrodynamic instability is found. Results for the attenuation are shown to be in good agreement with preliminary experiments on unsaturated He films.
67 citations
TL;DR: In this paper, a review of recent applications of kaon-nucleon forward dispersion relations, superconvergence relations, finite energy sum rules, derivative sum rules and the Adler-Weisberger sum rule are reviewed.
Abstract: Recent applications of kaon-nucleon forward dispersion relations, superconvergence relations, finite energy sum rules, derivative sum rules, and the Adler-Weisberger sum rule are reviewed. These dispersion relations and sum rules have been used for the determination of the KNA and KN coupling constants, the phases of the kaon-nucleon forward scattering amplitudes, and the Regge pole parameters, and have allowed tests of the PCAC hypothesis for strangeness-changing currents. They also provide important constraints which help to resolve ambiguities in the phenomenological analysis of the scattering data. A critical comparison of various methods which have been proposed is given, the theoretical predictions are compared with experiment when possible, and our present knowledge of the kaon-nucleon interaction parameters is summarized. Some new results are presented.
55 citations
TL;DR: In this article, the magnon dispersion relation for MnF2 at 4·2 °K has been measured by means of the triple-axis neutron scattering technique along the symmetry lines in the (010) plane of the Brillouin zone.
Abstract: The magnon dispersion relation for MnF2 at 4·2 °K has been measured by means of the triple-axis neutron scattering technique along the symmetry lines in the (010) plane of the Brillouin zone. Using an exact dipole model, the three nearest-neighbour exchange constants were found to be J1 = 0·028 ± 0·001 mev, J2 = -0·152 ± 0·001 mev and J3 = -0·004 ± 0·001 mev. The second moment was also calculated with this model. The density of magnon states was evaluated by applying a six-parameter simulation of the dispersion surface. The critical points in the density of states agree well with those obtained by optical double-magnon experiments, whereas the detailed shape of the density of states differs significantly, indicating that the effect of magnon-magnon interactions rather than that of distant-neighbour exchange is of primary importance in the optical measurements.
55 citations
TL;DR: Using inelastic scattering of slow neutrons, the frequency-wavevector dispersion relations for the lattice vibrations in the face-centered cubic alloys Ni3Fe, Ni0.5Fe 0.7, and Cu3Zn have been derived as discussed by the authors.
Abstract: Using inelastic scattering of slow neutrons, the frequency-wavevector dispersion relations for the lattice vibrations in the face-centered cubic alloys Ni3Fe, Ni0.5Fe0.5, Ni0.3Fe0.7, and Cu3Zn have...
TL;DR: In this paper, a systematic study of the multipole amplitudes for electro-and photoproduction of pions in the low energy region is presented, based on the integral equations following from fixedt dispersion relations and the Watson theorem.
Abstract: With this paper we start a systematic study of the multipole amplitudes for electro- and photoproduction of pions in the low energy region. It is based on the integral equations following from fixedt dispersion relations and the Watson theorem. We start with a discussion of general mathematical problems one encounters when solving the singular integral equations. Especially the non-uniqueness of their solutions poses difficult problems which cannot be solved within the framework of the dispersion theory. As boundary conditions “from outside” we use at threshold the predictions of the static theory. But thereby only the magnetic dipole excitation of the first isobar is determined. For the electric quadrupole amplitude one needs additional conditions.
TL;DR: In this article, the dispersion relation of electrothermal waves in a seeded, partially ionized gas is derived using a linear theory, and two modes appear, one is always damped, while the other is unstable in certain plasma situations.
Abstract: Using a linear theory the dispersion relation of electrothermal waves in a seeded, partially ionized gas is derived. Two modes appear, one of which is always damped, while the other is unstable in certain plasma situations. This is the ionization instability and the growth rate has been calculated as a function of the steady state electron temperature, the angle between the steady state current density and the wave vector, the Hall parameter, and the instability wavelength.
TL;DR: In this paper, the initial value problem for a semi-infinite Vlasov plasma, with no applied fields, is given, and terms corresponding to surface plasma waves, for which the dispersion relation is given.
Abstract: The solution of the initial value problem for a semi‐infinite Vlasov plasma, with no applied fields, is given. In the long‐wavelength limit, in addition to the usual plasma waves, terms corresponding to surface plasma waves, for which the dispersion relation is given, are found.
TL;DR: In this paper, the dispersion relation for low-frequency, collisional, electrostatic waves in a uniformly rotating plasma cylinder is obtained in terms of several positive-definite bilinear forms whose magnitude may be easily estimated.
Abstract: The dispersion relation for low‐frequency, collisional, electrostatic waves in a uniformly rotating plasma cylinder is obtained in terms of several positive‐definite bilinear forms whose magnitude may easily be estimated. The effects of ion transverse collisional viscosity, electron parallel resistivity, ion parallel motion, and an equilibrium radial electric field are included in the theory. The close correspondence between the present dispersion relation and the dispersion relation for localized, slab‐model modes justifies the use of the latter in the interpretation of Q‐machine experiments. Another result is that ion collisional viscosity stabilizes the density‐gradient driven drift wave if the axial wavelength λ‖ satisfies λ‖ < 2πσr0 (M/me)1/4, (σ ∼ 0.7; r0 is the density gradient scale length; M, me are the ion and electron masses, respectively). Overstable waves, which are driven by the centrifugal force and which resemble flutes with a finite parallel wavelength, can exist if λ‖ is sufficiently long.
Journal Article•
TL;DR: In this article, the frequency-wave-vector dispersion relation for the normal modes of vibration of terbium at room temperature has been measured by means of slow-neutron inelastic scattering techniques.
Abstract: The frequency-wave-vector dispersion relation for the normal modes of vibration of terbium at room temperature has been measured by means of slow-neutron inelastic scattering techniques. The triple-axis spectrometer at the Oak Ridge high flux isotope reactor was used, mostly in the constant-$Q$ mode of operation. Phonon frequencies for wave vectors along the principal symmetry directions have been determined and, in addition, measurements of phonon frequencies along the boundaries of the Brillouin zone and along a more general direction are reported. The data have been fitted with a Born-von K\'arm\'an force model which includes interactions out to the eighth nearest neighbor. The interactions have been assumed to be general (tensor) out to the fourth neighbor and axially symmetric beyond. The model has been used to calculate a frequency distribution function $g(\ensuremath{
u})$ and related quantities such as the lattice specific heat and Debye temperature.
TL;DR: In this article, the dispersion of ion-acoustic waves in quiescent rare-gas discharge plasmas has been investigated experimentally and theoretically and the experimental results show that two separate propagating phenomena appear.
Abstract: The dispersion of ion‐acoustic waves in quiescent rare‐gas discharge plasmas has been investigated experimentally and theoretically. Experimentally, various grid systems were used to generate the waves which were studied using a time‐of‐flight technique. The experimental results show that two separate propagating phenomena appear. The slower propagating disturbance is the ion‐acoustic wave, obeying the theoretically predicted dispersion behavior. The faster propagating disturbance, though superficially resembling a wave, is composed of bursts of ions produced by the driving potentials placed on the grids and would appear to be related to the “free streaming” term found by Landau. Previous theoretical models of ion‐wave propagation have untilized either purely initial‐value or steady‐state, boundary‐value calculations. A model is presented which more nearly simulates the experimental time‐of‐flight studies of finite packets of ion waves generated by finite sine‐wave bursts.
TL;DR: In this paper, the propagation of microwave magnetoelastic waves in a ferromagnet subjected to pulsed magnetic fields is investigated using a coupledmode approach, and it is found that plane spin waves propagate in magnetic field transients with negligible reflections, constant momentum and wavenumber, but variable frequency and power flow.
Abstract: The propagation of microwave magnetoelastic waves in a ferromagnet subjected to pulsed magnetic fields is investigated. In the first part of the theoretical analysis, which is restricted to spatially uniform bias fields, the interaction between the magnetic and elastic systems is neglected. Using a coupled‐mode approach, it is found that plane spin waves propagate in magnetic field transients with negligible reflections, constant momentum and wavenumber, but variable frequency and power flow. These results are further elucidated by the study of a simple step transient case. In the presence of magnetoelastic interaction, the theory indicates that besides changes in frequency and in power flow, the field gradient causes group velocity modulation and changes in the time duration of wave packets. In addition there is an exchange of momentum between the different branches of the dispersion relation; this exchange is calculated in terms of critical field gradients, The analysis reveals that negligible coupling ...
TL;DR: In this article, the dispersion relations, transition temperatures and dynamical structure factors for inelastic neutron scattering by spin waves are derived for antiferromagnetscal with the corundum structure.
TL;DR: In this article, a general dispersion relation governing the four-mode coupling of electrostatic waves is obtained in terms of linear susceptibilities of the plasma, which is applied to the analysis of the parametric excitation of ion-acoustic and Langmuir waves.
Abstract: Parametric effects of an alternating electric field on an inhomogeneous plasma in a constant magnetic field are studied by taking into account of density gradients. A general dispersion relation governing the four-mode coupling of electrostatic waves is obtained in terms of linear susceptibilities of the plasma. The dispersion relation is applied to the analysis of the parametric excitation of ion-acoustic and Langmuir waves. It is shown that the parametric coupling via density gradient may have important effects in the experimental condition of Stern and Tzoar. It is also shown that if the pumping frequency is about twice the Langmuir (or upper hybrid) frequency, the Langmuir (or upper hybrid) mode can be excited by the inhomogeneity of the plasma. The threshold intensity is sufficiently low to be attainable by microwave irradiations.
TL;DR: In this article, the frequencies of the normal modes of vibration of niobium at 296 °K have been measured by inelastic neutron scattering techniques, for several hundred phonons with wave vectors at general positions in the [11, macron0] reciprocal lattice plane.
Abstract: Measurements of the frequencies of the normal modes of vibration of niobium at 296 °K have been made by inelastic neutron scattering techniques. Results are presented for several hundred phonons with wave vectors at general positions in the [11, macron0] reciprocal lattice plane. The phonon dispersion relations in symmetry directions agree well with the previous work of Nakagawa and Woods. The measured frequencies cannot be fitted well by tensor force-constant models even when the range of the forces extends to tenth-nearest neighbours, but the critical points in the phonon density of states derived from the eighth-neighbour model agree with those observed in superconducting tunnelling experiments, and the calculated Debye temperature also agrees quite well with measured values.
TL;DR: In this article, the theory of two-stream plasma instability arising in the equatorial electrojet is extended to the nonlinear domain by means of a nonlinear treatment of the ion kinetic equation.
Abstract: The theory of the two-stream plasma instability arising in the equatorial electrojet is extended to the nonlinear domain by means of a nonlinear treatment of the ion kinetic equation. The solution for the ion distribution function is expressed in terms of a ‘perturbed orbit function,’ which is the solution for an average of the ion motion through the turbulent field of the plasma. The inclusion of the effects of turbulence on the ion orbit is found to introduce a damping term into the dispersion relation, which causes the growth rates of the linearly unstable waves to decrease to zero as the turbulence grows. The stabilization time needed for the electric field spectrum to achieve its asymptotic value is estimated. For an electrojet velocity of 500 m/sec it is found that the stabilization time is approximately 0.5 second and the energy density in macroscopic waves reaches 3 × 10−12 erg/cm³. Finally the asymptotic electric field spectrum resulting in the electrojet is estimated, assuming all modes grow in amplitude according to their linear growth rates for a time equal to the stabilization time.
TL;DR: In this paper, the crystal dynamics of the low temperature semiconducting allotrope of tin, α-Sn, have been studied at 90°K by means of thermal neutron inelastic scattering.
TL;DR: Guiding center Vlasov equation derived dielectric tensor of collisionless plasma, obtaining dispersion relation of Alfven waves in warm plasma as discussed by the authors, and obtained dispersion relations of the Alfven wave in collisionless plasmas.
Abstract: Guiding center Vlasov equation derived dielectric tensor of collisionless plasma, obtaining dispersion relation of Alfven waves in warm plasma
TL;DR: In this paper, the effect of amplitude dispersion on the propagation of small but finite amplitude plane whistlers in a cold plasma imbedded in a uniform magnetic field is studied.
Abstract: The propagation of small but finite amplitude plane “whistlers” in a cold plasma imbedded in a uniform magnetic field is studied. The usual frequency dispersion relation of linear theory is extended to include the effect of amplitude dispersion. The present analysis is based on a perturbation procedure in which the frequency, wavenumber, and amplitude relation is represented by a power series in the energy density or the square of the amplitude of the wave, i.e., ω = ω0(k) + ω2(k) a2 + ω4(k) a4 + …. It is found that the effect of amplitude dispersion is to cause the “whistlers” to undergo nonlinear instability if the wave vector k is not parallel to the direction of the undisturbed magnetic field. For plane whistlers which propagate along the mean magnetic field lines it is noted that the linear solution is also an exact solution of the two component cold plasma equations.
TL;DR: In this paper, the authors measured the refractive index of single-crystal CuCl at room temperature in the wavelength range 0.42 −1.2 μm using a V-block refractometer.
Abstract: The refractive index of single-crystal CuCl at room temperature was measured in the wavelength range 0.42–1.2 μm using a V-block refractometer. The range of wavelengths was extended to 22 μm by measuring the wavelength dependence of interference fringes in thin polished plates. A dispersion equation was fitted to the data over a limited wavelength range.
TL;DR: In this paper, partial wave N D equations for elastic n-d scattering are solved for the S = 1 2, 3 2 channels and three-particle contributions to unitarity are approximately incorporated by using final state interactions between pairs in threeparticle intermediate states.
TL;DR: In this article, the ππ scattering length and low-energy phase shifts are tabulated corresponding to various assumptions on the mass and width of the sigma meson using forward and first derivative dispersion relations.
CERN1
TL;DR: In this paper, the real part of the elastic amplitude for forward pion-deuteron scattering was calculated from the Galuber multiple scattering model and the results of the two approaches were critically compared in the light of present experiments.