Effective Phase Velocity Research Articles

Multiple scattering of elastic waves by cylinders of arbitrary cross section. II. Pair-correlated cylinders

Multiple scattering of elastic waves by randomly distributed cylinders of arbitrary cross section has been considered. Because the pair-correlation function, as well as the quasicrystalline approximation, has been incorporated in the presented formalism, the effective phase velocity, as well as the coherent attenuation in dense systems, has been investigated. A more efficient scattering formalism (SF) has been employed rather than the exciting field formalism (EF) used earlier by the authors. Closed form expressions for the phase velocity and the attenuation are given in the Rayleigh limit, and numerical results are presented for a wide range of frequencies and concentrations.

The "Phase Velocity" of Nonlinear Plasma Waves in the Laser Beat-Wave Accelerator

A calculational scheme for beat-wave accelerators is introduced that includes all orders in velocity and in plasma density, and additionally accounts for the influence of plasma nonlinearities on the wave's phase velocity. The main assumption is that the laser frequencies are very large compared to the plasma frequency - under which it is possible to sum up all orders of forward Raman scattering. It is found that the nonlinear plasma wave does not have simply a single phase velocity, but that the beat-wave which drives it is usefully described by a non-local ''effective phase velocity'' function. A time-space domain approach is followed. (LEW)

Rotational ground motion and seismic codes

The primary purpose of this paper is to discuss the separation of travelling wave effects from the mass center to resistance center eccentricity effects, and to propose means by which the torsional spectrum (or a torsional seismic factor) could be incorporated in the seismic provisions of the National Building Code of Canada. The paper begins the treatment of the subject matter by presenting a detailed review of previous work on the effects of torsional ground motion, emphasizing the methods which have been proposed to develop torsional response spectra. The travelling wave assumption is critically reviewed and the effective phase velocities applicable for design purposes are discussed. This is followed by a simple analysis showing how the torsional spectra can be derived directly from the corresponding translational response spectra. Formulae separating the torsional input effects from the accidental eccentricity effects are presented and discussed. Finally, it is shown how the torsional spectrum can be incorporated within the framework of the response spectrum procedure of the 1985 edition of the National Building Code of Canada. Key words: seismic, earthquake, structure, dynamic, rotation, code, torsion, foundation, eccentricity, response spectrum, acceleration, velocity, design.

Characteristic time constants and velocities of mid‐latitude Pi 2's

This study presents measurements of group delays, rise times, fall times, frequencies, and effective phase velocities of mid‐latitude (39°–55° geomagnetic latitude) Pi 2's recorded by the Air Force Geophysics Laboratory array of flux gate magnetometers. Measured group delays over the array are sometimes less than 5–10 s, indicating that in some instances Pi 2's can be used to give excellent timing of the onset of substorm expansive phases. Rise and fall times for the envelopes of Pi 2 oscillations are typically 60–100 s, bringing into doubt resonance theories for these types of waves. Most phase velocities indicate westward propagation, particularly near the center of the substorm current wedge, although there is some indication of eastward velocities far to the east of the center. We argue that these observations indicate that the magnetic fields associated with mid‐latitude Pi 2's are due to transient changes in the field‐aligned currents feeding the auroral electrojets at the beginning of the expansive phase of the substorm.

Dispersion and Field Analysis of a Microstrip Meander-Line Slow-Wave Structure

A structure which is important as an example of a spatially periodic medium for microwave propagation is analyzed theoretically, with rigorous consideration of its partial dielectric composition, symmetry properties; and field configuration relating to its use for electron-wave interaction in a crossed-field amplifier (CFA). The analysis is carried out in a quasi-TEM approximation, leading to determination of a complex potential function within the unit cell and the associated normal-mode parameters: effective dielectric constant, phase velocity, and characteristic impedance, as functions of phase per cell and mode symmetry. With imposition of meander-line boundary conditions, solutions of the characteristic equation for the dispersion law of the structure are computed, including the influence of the inhomogeneous dielectric-vacuum construction of microstrip. Agreement with the observed phase and stopband features of a representative structure is very good. Power distribution and group velocity are calculated, and an interaction impedance, representing the coupling between the RF field and an electron beam for estimation of CFA performance is also calculated. The method lends itself to detailed computations, including the effects of structural features of practical slow-wave circuits.

Radio-Frequency Size Effect in Potassium: Relation to Cyclotron Resonance, Helicon Waves, and Sound Waves

Studies are reported of the transmission of 1- to 100-MHz rf energy through a thin potassium slab when a magnetic field is applied either perpendicular or nearly parallel to the surface of the slab. In the perpendicular-field geometry for fields below the helicon Doppler-shifted cyclotron resonance edge, the phase of the transmitted signal increases linearly with applied field as predicted by Gantmakher and Kaner. Near zero applied field, the signal shows the increase in amplitude and extra $\frac{1}{2}\ensuremath{\pi}$ phase shift predicted by Baraff. When the field is nearly parallel to the slab surface, an attenuation of the transmitted signal is observed at the value of field where the effective phase velocity of the rf current distribution matches the phase velocity of an acoustic wave.

Model studies on the effect of a sloping interface on Rayleigh waves

Seismic models were studied to determine the effect of a sloping interface on the propagation of Rayleigh waves. The two-dimensional model, 1/16 inch thick, consisted of a plexiglass surface layer and a panelyte half-space. The surface layer ranged from ¼ to ¾ inch in width with a dip of approximately 2½°. When the variation in layer thickness is linear and gradual, a region of sloping interface (or a wedge-shaped structure sufficiently remote from its vertex) may be represented to a good approximation by an infinite number of stepped flat layers. The phase velocity of Rayleigh waves determined from a pair of adjacent stations in the region of sloping interface is an ‘effective phase velocity.’ As the distance between the stations approaches zero, the effective phase velocity approaches a limiting value defined as local phase velocity/which is independent of the direction of wave propagation. Outside the region of sloping interface and away from the points of discontinuous slope change, the Rayleigh wave velocities are those appropriate for the flat layer thicknesses; they seem to be unaffected by the nearby sloping interface. As an example, the phase velocities of Rayleigh waves for a generalized crust-mantle structure with a sloping interface are given.

Plasma oscillations (I)

This article is the first part of a review of the theory of wave phenomena in plasmas. The basic kinetic theory is developed taking into account coulomb collisions. From this magnetohydrodynamic equations are derived. It is demonstrated that it is legitimate to deal with a closed subset of these equations either in the limit of collision-dominated phenomena, or in the limit where the effective phase velocities of the phenomena of interest are much greater than thermal speeds. In case of collision-dominated plasmas the theory of transport coefficients is discussed.These equations are then applied to an extensive treatment of small amplitude wave phenomena in plasmas. A discussion of the dissipative effects on hydromagnetic waves is given. Hydromagnetic waves are also considered from the Chew, Goldberger and Low theory. Longitudinal and transverse oscillations in current-carrying plasmas are also discussed.Oscillations of a cylindrical plasma are considered and the phenomenon of ion cyclotron resonance is discussed. The possibility of radiation by plasma oscillations by a uniform sphere is exhibited. Some general results on the stability of longitudinal electron oscillations in non-uniform plasmas are given.A brief treatment of large amplitude electron oscillations is given and the breaking of these oscillations as a dissipative mechanism for the organized plasma motion is discussed.Part II of this paper, to appear in a future issue of this journal, will be devoted to the discussion of plasma oscillations directly from the kinetic theory.