Analytical Expression For Dispersion Relation Research Articles

Unstable mode of ion-acoustic waves with two temperature q-nonextensive distributed electrons

The linear characteristics of the unstable mode of ion-acoustic waves are examined in an electrostatic electron-ion plasma composed of streaming hot electrons, non-streaming cold electrons and dynamical positive ions. The plasma under consideration is modeled by using a non-gyrotropic nonextensive q-distribution function in which the free energy source for wave excitation is provided by the relative directed motion of streaming hot electrons with respect to the other plasma species. In the frame work of kinetic model, a linearized set of Vlasov–Poisson’s equations are solved to obtain the analytical expressions for dispersion relation and Landau damping rate. The threshold condition for the unstable ion-acoustic wave is derived to assess the stability of the wave in the presence of nonextensive effects. Growth in the wave spectrum and nontrivial effects of q-nonextensive parameter on the ion-acoustic waves can be of interest for the readers in the regions of Saturns’s magnetosphere.

Tunable transverse-electric surface plasmon polariton waves in a parallel-plate graphene-based waveguide

In this study, a three-layered system consisting of a Kerr-type nonlinear medium confined between two semi-infinite linear media is considered. The nonlinear medium is a parallel-plate graphene waveguide with a thickness of d. Analytical expressions for dispersion relation and the field profiles in terms of Jacobi elliptic functions are performed and solved numerically. Plasmonic properties such as the effective mode index (), localization length () are studied. It is found that and of the system can be tuned by chemical potential of graphene, arising from its tunable optical conductivity. Localization of transverse electric (TE) surface waves increases with increasing the medium nonlinearity, providing deep-subwavelength confinement. Moreover, increasing d from 1 to 130 nm enhances the mode confinement. We also apply our scheme to a bilayer graphene (BLG) waveguide, allowing for predicting the existence of TE modes. Our results show that the TE modes in BLG are more pronounced than those in single-layer graphene. Therefore, the BLG structure is found to be promising in the fabrication of optical devices with TE plasmons.

Thermo-viscous damping of acoustic waves in narrow channels: A comparison of effects in air and water.

Recent work in the acoustic metamaterial literature has focused on the design of metasurfaces that are capable of absorbing sound almost perfectly in narrow frequency ranges by coupling resonant effects to visco-thermal damping within their microstructure. Understanding acoustic attenuation mechanisms in narrow, viscous-fluid-filled channels is of fundamental importance in such applications. Motivated by recent work on acoustic propagation in narrow, air-filled channels, a theoretical framework is presented that demonstrates the controlling mechanisms of acoustic propagation in arbitrary Newtonian fluids, focusing on attenuation in air and water. For rigid-walled channels, whose widths are on the order of Stokes's boundary layer thickness, attenuation in air at 10 kHz can be over 200 dB m-1; in water it is less than 37 dB m-1. However, in water, fluid-structure-interaction effects can increase attenuation dramatically to over 77 dB m-1 for a steel-walled channel, with a reduction in phase-speed approaching 70%. For rigid-walled channels, approximate analytical expressions for dispersion relations are presented that are in close agreement with exact solutions over a broad range of frequencies, revealing explicitly the relationship between complex phase-speed, frequency and channel width.

The effects of exchange–correlation on high-frequency electrostatic surface wave in magnetized quantum plasma through a porous medium

In this paper the propagation of an electrostatic surface wave at the interface between a vacuum and quantum plasma through a Brinkman porous medium is studied by considering exchange–correlation effects. A general analytical expression for dispersion relation is derived using the linearized quantum hydrodynamic model in conjunction with Poisson’s equation in the presence of a static and constant magnetic field. The growth and instability rates of electrostatic surface waves are obtained and separated. Numerical values are used to summarize and analyze the normalized dispersion relations for overcritical dense plasma condition in different cases. The results show that the behavior of surface plasmon waves can be significantly modified by the exchange–correlation effects which have different influences on the system stability. It is shown that the exchange–correlation effects caused the frequency of such waves to down-shift. It is found that the down-shift of the real part of frequency Re(Ω) by the exchange–correlation effect may increase by either increasing the plasmonic coupling H or increasing the porosity effects. In addition, it is shown that by increasing the magnetic field strength the group velocity is increased. Although the instability of the surface wave is decreased by increasing the plasmonic coupling H, it is increased by increasing the porosity effects (ν). The obtained results can help us in the physical understanding of the surface magnetized quantum wave on a semi-bounded quantum plasma through a porous media.

Two-dimensional modeling and analysis of a nanometer transistor as a THz emitter

In this paper, we report on the influences of quantum effects, electron exchange-correlation, Fermi velocity, gate to channel distance and viscosity on the plasma frequency and instability of the plasma waves in a nanometer transistor. By extending the analysis to two-dimensional case, allowing oblique wave propagation, including viscosity and departing from gradual channel approximation, we obtain a general analytical expression for dispersion relation, plasma frequency, and “increment.” We found that, while the plasma frequency decreases with the electron exchange-correlation effect, it increases with quantum effects and Fermi velocity. It is shown that the spectrums of plasma waves are discrete both in longitudinal and lateral (transverse) direction. We also express the total radiated power in terms of transistor parameters especially the lateral dimension. Viscosity which is inherently presented in the structure and cannot be neglected, dramatically decrease the emitted power and set a lower limit on the length of transistor. We show that a nanometer transistor with a long width (a long lateral dimension) has advantages for the realization of practical terahertz emitters.

High-Frequency Waves in a Random Distribution of Metallic Nanoparticles in an External Magnetic Field

Abstract Propagation of magnetoplasma waves at an angle to a static magnetic field is studied for a random distribution of spherical metallic nanoparticles. A general analytical expression for dispersion relation of the system is derived and useful expressions are obtained in the limiting cases. It is found that the interaction between longitudinal and transverse modes leads to coupled modes in the vicinity of the frequency f + ξ ω p , $\sqrt {f\, + \,\xi } {\omega _p},$ where ξ is the ratio of the volume occupied by all the nanoparticles to the entire volume, ω p the plasma frequency of electrons inside a nanoparticle, and f a geometrical factor of order unity (1/3 for spherical nanoparticles).

Electrostatic surface waves on a magnetized quantum plasma half-space

A theory of electrostatic surface waves on a quantum plasma half-space is developed with the inclusion of external magnetic field effects for the geometry in which the magnetic field is parallel to the surface and the direction of propagation is perpendicular to the magnetic field. A general analytical expression for dispersion relation of surface waves is obtained by solving Poisson and quantum magnetohydrodynamic equations with appropriate quantum boundary conditions.

Subwavelength localization and toroidal dipole moment of spoof surface plasmon polaritons

We experimentally and theoretically demonstrate subwavelength scale localization of spoof surface plasmon polaritons at a point defect in a two-dimensional groove metal array. An analytical expression for dispersion relation of spoof surface plasmon polaritons substantiates the existence of a band gap where a defect mode can be introduced. A waveguide coupling method allows us to excite localized spoof surface plasmon polariton modes and measure their resonance frequencies. Numerical calculations confirm that localized modes can have a very small modal volume and a high $Q$ factor both of which are essential in enhancing light-matter interactions. Interestingly, we find that the localized spoof surface plasmon polariton has a significant toroidal dipole moment, which is responsible for the high $Q$ factor, as well as an electric quadrupole moment. In addition, the dispersion properties of spoof surface plasmon polaritons are analyzed using a modal expansion method and numerical calculations.

Electrohydrodynamic Rayleigh - Taylor Instability in a Poorly Conducting Fluid Layer Bounded Above by a Nanostructured Porous Layer

Electrohydrodynamic Rayleigh - Talyor instability (ERTI) at the interface region between a thin poorly conducting incompressible viscous fluid saturated nanostructured porous layer and a poorly conducting fluid layer in the presence of a non-uniform electric field is investigated using linear stability analysis. A simple theory based on electrohydrodynamic approximations and Saffman slip condition is proposed. An analytical expression for dispersion relation is derived in the form of n = nb - Ilva, where n is the growth rate and Ilva is the effect of compression. It is shown that the porous lining and transverse electric field control the growth rate of ERTI depending on whether the applied electric field is opposing or aligning the direction of gravity. In particular, we found that n tends to zero for equipartition of energy (i. e., Weber number We = 1). © 2009 Begell House, Inc.

Multiple-scales analysis of plasma response to intense laser field and plasma excitation

A method of multiple scales is used to analyze a nonequilibrium distribution of the electron plasma in an intense laser field. A dielectric response function, which is nonlinear for the laser field, with wave vectors at arbitrary angles to the laser field is presented by using an appropriate small fluctuation of slowly varying quantities to linearize the kinetic equation of plasma. The numerical results for dielectric properties of plasma in various directions are displayed. The plasma instability in high electric field reported by Morawetz and Jauho [Phys. Rev. E 50, 474 (1994)] does not exist under any intensity laser fields. The most excited wave modes are damped even though the imaginary part of the dielectric function becomes negative in certain conditions. For the limit of the parameter k${\ensuremath{\lambda}}_{\mathrm{D}}$\ensuremath{\ll}1, a corrected analytical expression of dispersion relation is obtained. This modification of the excited wave dispersion relation results in a great change of the stimulated Raman scattering instability, particularly for the large-angle sideward Raman instability. The screening properties of plasma under the intense laser field and the dependence of wave mode excitation on plasma parameters and angles of the wave vector from the laser field are also discussed.

Analytical phonon dispersion relations for diamond-like structures

The phonon dispersion relations of diamond-like crystal structures are studied by using a Born-von Karman model with interatomic interactions up to and including second neighbours. Analytical expressions for dispersion relations in the principal symmetry directions are derived. The force constants of grey tin are determined by an optimization procedure using the dispersion data in the [00k], [kk0] and [kkk] directions. The dispersion curves calculated with a two-neighbour six-parameter Born-von Karman model give a reasonable fit to the dispersion data in the principal symmetry directions.

On the Analytical FMR Theory in the Normal Configuration

AbstractThe analytical expressions for dispersion relations, cross‐over effect conditions, effective penetration depth, surface impedance, and inflection linewidth for FMR in bulk metals in normal configuration are derived including electrical conductivity and the Landau‐Lifshits damping parameter (for the case of zero surface pinning). The possibility of excitation of Larmor and anti‐Larmor Kittel and surface modes in materials with negative surface anisotropy is investigated.

Excitation of electromagnetic waves in a relativistic backward wave oscillator with end reflectors

An investigation of the boundary effects on the operation of a relativistic backward wave oscillator (BWO) is presented. Analytical expressions for dispersion relation, global instability, and start oscillation current are obtained for the case of weak ripple of the slow wave structure. Numerical results show a periodic behavior of the start oscillation current with the length of the device. Results are also obtained depicting the variation of the start current with reflection coefficient and beam energy. A comparison of the results is made with those of earlier work [Phys. Fluids B 4, 2293 (1992)].