Regions Of Negative Group Velocity Research Articles

Kinetic theory of instability in the interaction of an electron beam and plasma with an arbitrary anisotropic electron velocity distribution function

Based on the kinetic approach, this work investigates the stability of the system consisting of a fast electron beam and a dense plasma at an arbitrary (anisotropic) electron velocity distribution function. It is shown that during the interaction of a fast electron beam with a cold plasma, both the conditions for losing stability and the growth rate of disturbances do not depend on the form of the electron distribution function (EDF) of a plasma and are determined only by the ratio of the electron beam energy to the mean energy in a plasma. With an increase in the mean electron energy in the plasma, it becomes necessary to take into account the following energy moments of the EDF. It was found that the plasma anisotropy has a significant effect on both the stability loss conditions and the growth rate. The physical reason for this effect is the shift in the plasma frequency due to the Doppler effect caused by the plasma anisotropy in the coordinate system moving along with the beam. Other findings include a region of anomalous dispersion of the electron beam–plasma system and regions of negative group velocity of perturbations in such system. Physical interpretations are proposed for all the observed effects.

Nonlinear control of high-frequency phonons in spider silk.

Spider dragline silk possesses superior mechanical properties compared with synthetic polymers with similar chemical structure due to its hierarchical structure comprised of partially crystalline oriented nanofibrils. To date, silk's dynamic mechanical properties have been largely unexplored. Here we report an indirect hypersonic phononic bandgap and an anomalous dispersion of the acoustic-like branch from inelastic (Brillouin) light scattering experiments under varying applied elastic strains. We show the mechanical nonlinearity of the silk structure generates a unique region of negative group velocity, that together with the global (mechanical) anisotropy provides novel symmetry conditions for gap formation. The phononic bandgap and dispersion show strong nonlinear strain-dependent behaviour. Exploiting material nonlinearity along with tailored structural anisotropy could be a new design paradigm to access new types of dynamic behaviour.

Subbands of plasmon and vortex excitations spectra in a fluxon lattice of a layered superconductor

The oscillation modes of fluxon lattice in a layered superconductor under applied parallel constant magnetic field are examined within a model of stacked Josephson junctions. To find an analytical solution, we use a simple model assuming that ϕ n, n +1 ∝ x within period of the vortex lattice along the a-direction in the ab-plane. For a particular case, the dispersion law for the vortex and plasma elementary oscillations, Ω k, is obtained analytically. The result for the spectrum corresponds to three branches of Ω k (1,2,3) having regions of negative group velocity and are separated by gaps.

High-frequency scattering from a spherical shell: Thickness quasiresonance

Theoretical calculations have shown that the high-frequency scattering from a thin spherical shell is dominated by a single peak that occurs near the opening of the first symmetric Lamb wave. This peak is associated with a region of strong negative group velocity surrounding the opening of the first symmetric Lamb wave. Experimental verification of the existence of the thickness quasiresonance on a 2% stainless steel shell is given. In addition an analysis of the thickness quasiresonance in the complex-ka plane is presented for shells of different material parameters. It is shown that the thickness quasiresonance bifurcates as a function of Poisson’s ratio in such a manner that the region of negative group velocity remains close to the opening of the first symmetric Lamb wave. [Work supported by ONR.]

Scattering from a thin spherical shell: Higher-order Lamb waves

The acoustic scattering from thin spherical shells is marked by the existence of the thickness quasiresonance in the high-frequency regime. This quasiresonance is due to the existence of a region of negative group velocity surrounding the first symmetric Lamb wave. This article presents results on the existence of higher-order quasiresonancelike phenomena, and it considers the effects of Poisson’s ratio on the quasiresonance. Pole trajectories in the complex ka plane are exhibited for the first dozen modes on a spherical shell. This analysis reveals the existence of regions of negative group velocity surrounding higher-order Lamb waves. A time domain representation of the contributions of higher-order Lamb waves to the scattered field is presented. This analysis reveals the early time arrival nature of the thickness quasiresonance as reconstructed from the poles in the complex ka plane.

The acoustic scattering by a submerged, spherical shell. II: The high-frequency region and the thickness quasiresonance

This article presents a fundamentally oriented analysis of the complex-ka plane pole structure of the S matrix for spherical shells in the thickness range 0.02a⩽h⩽0.10a (a is the outer radius of the sphere) for the high-frequency region (100<ka<1000); the Poisson’s ratio for these shells is fixed at σ=0.34 (aluminum). Surprisingly, this analysis reveals that the most dominant feature in the backscattered form function of a thin spherical shell is a single prominent high-frequency peak. The underlying modal structure and accompanying regions of negative group velocity are related to this feature, which is interpreted as a thickness “quasiresonance.” In particular, the significance of stationary values of the group velocity to the relative amplitude of modal excitation is emphasized.

Acoustic scattering by a submerged spherical shell: Thickness resonances revisited

In previous meetings [J. Acoust. Soc. Am. Suppl. 1 85, S95 (1989); 86, S4 (1989)], a fundamentally oriented analysis of the acoustic scattering from a spherical shell in the high‐frequency region 0 < ka < 1000, based upon the analytic properties of the S matrix in the complex ka plane was presented. This analysis revealed the existence of an anomalously large thickness shear resonance as the single most dominant feature in the scattering from a thin spherical shell. This thickness resonance is associated with a region of negative group velocity near threshold for the plate‐wave analog of the first symmetric Lamb wave on a thin spherical shell. In this presentation, results for higher‐order modes and the effects of varying the material parameters of the shell on the thickness quasiresonance are presented. Results for a second thickness shear resonance associated with the opening of the fourth symmetric Lamb wave are also presented.

The acoustic scattering by a submerged, elastic spherical shell: The transition from thin to thick shells

A fundamentally oriented analysis of the pole structure of the acoustic scattering matrix in the low‐ to high‐frequency region (0⩽ka⩽1000) as a function of mode number, density, and sound speed for several shell thicknesses has been previously presented [J. Acoust. Soc. Am. Suppl. 1 83, S94 (1988); Suppl. 1 84, S185 (1988); Suppl. 1 85, S95 (1989)]. The three most interesting results of this analysis were: (1) Due to fluid loading, the vacuum antisymmetric Lamb mode a0 and the rigid Franz modes “switch tails” to produce a subsonic a0_ mode that resembles the vacuum antisymmetric Lamb mode at low ka and an a0+ mode that resembles a0 at high ka; (2) the mid‐frequency enhancement of a thin shell is associated with this bifurcation of the antisymmetric Lamb wave [J. Acoust. Soc. Am. 85, 114–124 (1989)]; and (3) the existence of strong thickness resonances associated with the existence of regions of negative group velocity for the third antisymmetric Lamb wave on a thin spherical shell. In this presentation, t...

Dielectric Measurements in Plasma at very High Frequencies (150–200 Mc/s.)

ABSTRACTInvestigations of the variation with frequency of permittivity and conductivity of ionized air and ionized argon in the VHF range are described. Impedance offered to a slab line by the plasma column (of the weakly ionized gas in the form of a plasma slab) is determined from VSWR measurements. The variation of phase constant β, phase velocity νp and group velocity νg with angular frequency ω of propagating wave are deduced. In the case of ionized air, observations are made in the anomalous region of collision frequency ν = ω and regions of negative group velocity are shown.

Propagation of transient leaking modes in a stratified elastic waveguide

By using a technique first applied to seismological problems by Haskell, it is a simple matter to obtain the secular function for any given elastic waveguide, when the waveguide is composed of homogeneous layers with plane parallel boundaries. Roots of the secular function are usually exhibited as dispersion curves. In this paper the independent variable is dimensionless wave number, K, and the dependent variable is dimensionless frequency, F. A plot of complex F versus K yields the diagnostic (F, K) diagram—a dispersion curve. The procedure employed is to expand the secular function about K = 0 and then to trace the behavior of each root, F(K), for increasing values of K. In each of the specific problems treated the initial position of each root, F(0), admits of a simple physical description. For example, in a simple continental waveguide (solid layer/solid half‐space), there are three sets of roots: the Lamb roots, consisting of and modes; the shear ‘Organ pipe’ roots; and the compressional ‘organ pipe’ roots. There is an infinite number of the two kinds of organ pipe roots. The low‐frequency PL wave arises from one of the roots, and the normal shear modes arise from transitions of all three kinds of roots. In a simple oceanic waveguide (fluid layer/solid half‐space) the shear organ pipe roots are absent. The low‐frequency PL wave again arises from one of the roots, and the normal modes arise from transitions of the Lamb roots and the compressional organ pipe roots. In a simple acoustic waveguide (fluid layer/fluid half‐space) only the compressional organ pipe roots are present, and the normal modes arise from transitions of these roots. The PL wave is absent. Its disappearance is clearly traced as the half‐space of the oceanic waveguide approaches a Poisson ratio of 0.5.The treatment of waveguides composed of more than one layer offers only the additional difficulty of finding the initial positions of the organ pipe roots. When these positions have been found, the analysis proceeds in a manner similar to that for simple waveguides. The initial positions of the organ pipe roots are complex, a situation that may be interpreted physically as radiation into the half‐space of the waveguide. It is the presence of such radiation that leads one to speak of leaking modes. The roots also have complex initial positions, if the half‐space is soft enough. In addition to being complex, the dispersion curves for the leaking modes sometimes have regions of negative group velocity. If one equates group velocity to velocity of energy transport along the waveguide, then one must conclude that there is an inward energy flux when the group velocity is negative. But when the group velocity is demonstrably not the velocity of energy transport, a simple physical picture of negative group velocity is sometimes unavailable. Plots of group velocity versus F show a banded structure in some cases but are generally quite complex. The situation can be clarified somewhat by rejecting those modes with weak excitation functions, large decay parameters, or both. Still, the (F, K) diagram is clearer. Now that seismic array processing procedures are being developed, one hopes that experimental (F, K) diagrams will become a standard tool in seismic analysis, leading to a clearer picture of seismic dispersion and propagation characteristics.