Dielectric Characteristics for Radio Frequency Waves in a Laboratory Dipole Plasma

Transverse and parallel dielectric permittivity elements have been derived for radio frequency waves in a laboratory dipole magnetic field plasma. Vlasov equation is resolved for both the trapped and untrapped particles as a boundary value problem to define their separate contributions to the dielectric tensor components. To estimate the wave power absorbed in the plasma volume the perturbed electric field and current density components are decomposed in a Fourier series over the poloidal angle. In this case, the dielectric characteristics can be analyzed independently of the solution of the Maxwell's equations. As usual, imaginary part of the parallel permittivity elements is necessary to estimate the electron Landau damping of radio frequency waves, whereas imaginary part of the transverse permittivity elements is important to estimate the wave dissipation by the cyclotron resonances. Computations of the imaginary part of the parallel permittivity elements are carried out in a wide range of the wave frequencies. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Electrohydrodynamic wave-packet collapse and soliton instability for dielectric fluids in (2 + 1)-dimensions

A weakly nonlinear theory of wave propagation in two superposed dielectric fluids in the presence of a horizontal electric field is investigated using the multiple scales method in (2 + 1)-dimensions. The equation governing the evolution of the amplitude of the progressive waves is obtained in the form of a two-dimensional nonlinear Schrödinger equation. We convert this equation for the evolution of wave packets in (2 + 1)-dimensions, using the function transformation method, into an exponentional and a Sinh-Gordon equation, and obtain classes of soliton solutions for both the elliptic and hyperbolic cases. The phenomenon of nonlinear focusing or collapse is also studied. We show that the collapse is direction-dependent, and is more pronounced at critical wavenumbers, and dielectric constant ratio as well as the density ratio. The applied electric field was found to enhance the collapsing for critical values of these parameters. The modulational instability for the corresponding one-dimensional nonlinear Schrödinger equation is discussed for both the travelling and standing waves cases. It is shown, for travelling waves, that the governing evolution equation admits solitary wave solutions with variable wave amplitude and speed. For the standing wave, it is found that the evolution equation for the temporal and spatial modulation of the amplitude and phase of wave propagation can be used to show that the monochromatic waves are stable, and to determine the amplitude dependence of the cutoff frequencies.Received: 23 November 2003, Published online: 15 March 2004PACS: 47.20.-k Hydrodynamic stability - 52.35.Sb Solitons; BGK modes - 42.65.Jx Beam trapping, self-focusing and defocusing; self-phase modulation - 47.65. + a Magnetohydrodynamics and electrohydrodynamicsM.F. El-Sayed: Permanent address: Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt     

Surface waves in a crystal with switching Kerr nonlinearity

In this paper, we explore transverse electric surface waves propagating along the crystal with jump change of Kerr nonlinearity in dependence on field amplitude. The dielectric permittivity in the proposed model of nonlinearity is characterized by abruptly changing unperturbed dielectric constant and Kerr nonlinearity coefficient from one value to another when field amplitude exceeds the threshold value of the switching field. This allows to find exact solutions of model equations in different cases of nonlinearity signs, and to obtain the dependence of wave characteristics, including total power flux, on effective refractive index in explicit form. Such solutions describe two new types of nonlinear surface waves with specific structure depending on electric field amplitude. We derive the conditions of surface domain formation. It is found that the largest percentage of radiation is concentrated within the domain.     

Nonlinear dynamics of the interface between fluids at the suppression of Kelvin–Helmholtz instability by a tangential electric field

The nonlinear dynamics of the interface between ideal dielectric fluids in the presence of tangential discontinuity of the velocity at the interface and the stabilizing action of the horizontal electric field is examined. It is shown that the regime of motion of the interface where liquids move along the field lines occurs in the state of neutral equilibrium where electrostatic forces suppress Kelvin–Helmholtz instability. The equations of motion of the interface describing this regime can be reduced to an arbitrary number of ordinary differential equations describing the propagation and interaction of structurally stable solitary waves, viz. rational solitons. It is shown that weakly interacting solitary waves recover their shape and velocity after collision, whereas strongly interacting solitary waves can form a wave packet (breather).     

On the stability of capillary waves on the surface of a space-charged dielectric liquid jet moving in a material medium

We have derived and analyzed the dispersion equation for capillary waves with an arbitrary symmetry (with arbitrary azimuthal numbers) on the surface of a space-charged cylindrical jet of an ideal incompressible dielectric liquid moving relative to an ideal incompressible dielectric medium. It has been proved that the existence of a tangential jump of the velocity field on the jet surface leads to a periodic Kelvin–Helmholtz- type instability at the interface between the media and plays a destabilizing role. The wavenumber ranges of unstable waves and the instability increments depend on the squared velocity of the relative motion and increase with the velocity. With increasing volume charge density, the critical value of the velocity for the emergence of instability decreases. The reduction of the permittivity of the liquid in the jet or an increase in the permittivity of the medium narrows the regions of instability and leads to an increase in the increments. The wavenumber of the most unstable wave increases in accordance with a power law upon an increase in the volume charge density and velocity of the jet. The variations in the permittivities of the jet and the medium produce opposite effects on the wavenumber of the most unstable wave.     

Gap solitons in metamaterials

Electromagnetic localization and the existence of gap solitons in nonlinear metamaterials, which exhibit a stop band in their linear spectral response, is theoretically investigated. For a self-focusing Kerr nonlinearity, the equation for the electric field envelope with carrier frequency in the stop band—where the magnetic permeability µ(?) is positive and the dielectric permittivity ε(?) is negative—is described by a nonlinear Klein-Gordon equation with a dispersive nonlinear term. A family of standing and moving localized waves for both electric and magnetic fields is found, and the role played by the nonlinear dispersive term on solitary wave stability is discussed.     

Wideband modulation instability at combination frequencies in wave beams

We study theoretically wideband modulation instability at combination frequencies in media having cubic nonlinearity of self-focusing type along with the higher-order defocusing nonlinearity. It is assumed that in a medium with a purely cubic nonlinearity, the medium dispersion does not permit modulation instability. In this case, a collapse of the wave field exists if the beam power is higher than the critical power of self-focusing. The higher-order nonlinearity limits the field at the nonlinear focus, and the instability at combination frequencies becomes possible. It turns out that the field at the nonlinear focus increases with increasing excess of the beam power over the critical power of self-focusing. The obtained values of the nonlinear dielectric permittivity are used for determination of the growth rates of instability at combination frequencies. These growth rates ensure an increase in the combination fields from noise levels up to values comparable with the field of the high-power beam. Such an increase takes place if the beam power is severalfold higher than the critical one. The developed theory can be used for explanation of spectrum superbroadening during self-focusing of sufficiently short laser pulses and high-harmonic generation. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 50, No. 6, pp. 522–532, June 2007.     

Stability of magnetopause boundary and generation of long period geomagnetic pulsations

The effect of irrotational electric field and tensorial plasma conductivity on the growth rate of Kelvin-Helmholtz instability has been investigated. It is shown that the presence of irrotational electric field alters the growth rate. The dependence of Pedersen conductivity on the growth rate has been shown. The Kelvin-Helmholtz perturbations generate a surface wave in the frozen-in plasma. The propagation of these waves gives rise to polarization of the transverse hydromagnetic pulsations. It is shown that the modified K-H spectrum would result in a corresponding change in polarization features of the hydromagnetic pulsations.     

Electromagnetic Time Reversal Algorithms and Source Localization in Lossy Dielectric Media

The problem of reconstructing the spatial support of an extended radiating electric current source density in a lossy dielectric medium from transient boundary measurements of the electric fields is studied. A time reversal algorithm is proposed to localize a source density from loss-less wave-field measurements. Further, in order to recover source densities in a lossy medium, we first build attenuation operators thereby relating loss-less waves with lossy ones. Then based on asymptotic expansions of attenuation operators with respect to attenuation parameter, we propose two time reversal strategies for localization. The losses in electromagnetic wave propagation are incorporated using the Debye's complex permittivity, which is well-adopted for low frequencies (radio and microwave) associated with polarization in dielectrics.     

Zero permittivity band characteristics in one-dimensional plasma dielectric photonic crystal

We consider the oblique propagation of electromagnetic waves in one-dimensional plasma dielectric photonic crystals, the superlattice structure consisting of alternating plasma and dielectric materials using transfer matrix method. Our results show that photonic band gaps for all polarizations can be obtained in one-dimensional plasma dielectric photonic crystals. These structures can exhibit a new type of band or gap, for the incidence angles other than normal incidence, near frequencies where the electric permittivity of the plasma layer changes sign. This new band or gap arises, from the dispersive properties of the plasma layer, only for TM polarized waves and its width increases with the increasing angle of incidence. This differential behaviour under polarization can be utilized in the design of an efficient polarization splitter. The band characteristic is affected by the plasma width, the plasma density, dielectric width, the dielectric constant of the dielectric medium and angle of incidence.     

Kinetic study of instability growth rate in a helicon plasma discharge source

In this work, a kinetic model is developed to study the effects of the radio frequency antenna wavenumber, helicon plasma electron density, as well as their drift velocity and temperature on the instability increment rate of the helicon wave in both longitudinal and transverse directions. The ion acoustic (IA) wave frequencies and wavenumbers of the helicon waves are obtained when the maximum wave energy is deposited on the plasma ions. Moreover, it is shown that, at the IA wavenumber and frequencies, while the longitudinal instability increment rates for both the helicon and IA waves are ignorable, the transverse instability increment rate for both the helicon and IA wave increases. Besides, the longitudinal instability increment rate for the helicon or IA wave has non‐zero resonant frequencies. On the other hand, the transverse instability increment rate of helicon or IA wave can be neglected. Furthermore, it is observed that, while both the imaginary part of longitudinal permittivity and longitudinal instability increment rate are not influenced by the electron temperature, their transverse component increases linearly with the electron temperature. In addition, the imaginary part of transverse permittivity increases almost linearly with the drift velocity of the plasma electrons.     

Optical hollow-core waves in nonlinear Epsilon-Near-Zero metamaterials

We investigate non-diffracting hollow-core nonlinear optical waves propagating in a layered nanoscaled metal-dielectric structure characterized by a very small average linear dielectric permittivity (Nonlinear Epsilon-Near-Zero metamaterial). We analytically show that hollow-core waves have a power flow exactly vanishing at a central region and exhibiting a sharp sloped profile at the edges of the regions surrounding the core. Physically, the absence of power flow at the core region is due to the vanishing of the transverse component of the electric displacement field, a condition that can be satisfied by the full compensation between the nonlinear and linear dielectric contributions.     

Interaction of strongly nonlinear waves on the free surface of a dielectric liquid in a horizontal electric field

The nonlinear dynamics of the free surface of an ideal dielectric liquid with a large relative permittivity in a strong horizontal electric field has been considered. It has been demonstrated that the interaction between oppositely propagating solitary waves in arbitrary geometry is elastic: they conserve their energy and momentum. The interaction between waves has been numerically simulated with the use of conformal variables. It has been shown that the interaction deforms the waves; this effect is weak for waves with a relatively small amplitude: deformation for oppositely propagating waves with the identical shape is determined by the fourth power of their amplitude. At multiple collisions of strongly nonlinear waves, a tendency to the formation of singularities, i.e., points with a high energy density of the field, is observed.     

Surface electromagnetic waves in thin-layer biaxial structure in a magnetic field

The conditions for the existence of surface electromagnetic waves at the planar interface between a homogeneous medium (vacuum) and a thin-layer periodic structure consisting of alternating semiconductor and dielectric layers in an external magnetic field have been investigated. This structure represents an optically biaxial crystal with the effective permittivity tensor components dependent both on the geometric parameters of the structure and on the physical characteristics (magnetic field strength, frequency, and thicknesses of the layers). It has been shown that the propagation of surface electromagnetic waves localized near the interface can occur in the thin-layer biaxial structure within specific ranges of frequencies and external magnetic field strengths.     

柱面非线性麦克斯韦方程组的行波解

柱面电磁波在各种非均匀非线性介质中的传播问题具有非常重要的研究价值.对描述该问题的柱面非线性麦克斯韦方程组进行精确求解,则是最近几年新兴的研究热点.但由于非线性偏微分方程组的极端复杂性,针对任意初边值条件的精确求解在客观上具有极高的难度,已有工作仅解决了柱面电磁波在指数非线性因子的非色散介质中的传播情况.因此,针对更为确定的物理场景,寻求能够精确描述其中更为广泛的物理性质的解,是一种更为有效的处理方法.本文讨论了具有任意非线性因子与幂律非均匀因子的非色散介质中柱面麦克斯韦方程组的行波精确解,理论分析表明这种情况下柱面电磁波的电场分量E已不存在通常形如E=g(r-kt)的平面行波解;继而通过适当的变量替换与求解相应的非线性常微分方程,给出电场分量E=g(lnr-kt)形式的广义行波解,并以例子展示所得到的解中蕴含的类似于自陡效应的物理现象.     

Electromagnetic waves in dielectrics with memory

We analyse electromagnetic wave propagation in a dielectric with memory of the Maxwell-Hopkinson type. We show that the components of the electric and magnetic fields satisfy two different scalar wave equations and we first look for their harmonic plane wave solutions. Then we prove that dielectrics with memory can also support approximate Courant-Hilbert waves. We discuss the equations to be solved to get all the components of the electromagnetic field from a scalar solution from each wave equation and TE, TM harmonic plane waves are explicitly given.     

Influence of bottom topography on the propagation of linear shallow water waves: an exact approach based on the invariant imbedding method

The wave equation for linear shallow water waves propagating over a varying bottom topography has the same form as that for p-polarized electromagnetic waves in inhomogeneous dielectric media. The role played by the dielectric permittivity in the case of electromagnetic waves is played by the inverse water depth. We apply the invariant imbedding theory of wave propagation, which has been developed mainly to study the electromagnetic wave propagation, to linear shallow water waves in the special case where the depth depends on only one coordinate. By comparing the numerical result obtained using our method, when the depth profile is linear, with an exact analytical formula, we demonstrate that our method is numerically reliable. The invariant imbedding method can be used in studying the influence of complicated bottom topography on the propagation of shallow water waves, in a numerically exact manner. We illustrate this by considering the case where a periodic modulation is added to a linear depth profile. Bragg scattering due to the periodic component competes with the tsunami effect due to the linear depth variation. This competition is seen to generate interesting physical effects. We also consider a ridge-type bottom topography and examine the resonant transmission phenomenon associated with the Fabry–Perot effect.     

Influence of bottom topography on the propagation of linear shallow water waves: an exact approach based on the invariant imbedding method

The wave equation for linear shallow water waves propagating over a varying bottom topography has the same form as that for p-polarized electromagnetic waves in inhomogeneous dielectric media. The role played by the dielectric permittivity in the case of electromagnetic waves is played by the inverse water depth. We apply the invariant imbedding theory of wave propagation, which has been developed mainly to study the electromagnetic wave propagation, to linear shallow water waves in the special case where the depth depends on only one coordinate. By comparing the numerical result obtained using our method, when the depth profile is linear, with an exact analytical formula, we demonstrate that our method is numerically reliable. The invariant imbedding method can be used in studying the influence of complicated bottom topography on the propagation of shallow water waves, in a numerically exact manner. We illustrate this by considering the case where a periodic modulation is added to a linear depth profile. Bragg scattering due to the periodic component competes with the tsunami effect due to the linear depth variation. This competition is seen to generate interesting physical effects. We also consider a ridge-type bottom topography and examine the resonant transmission phenomenon associated with the Fabry-Perot effect.     

Effective optical response of silicon to sunlight in the finite-difference time-domain method

The frequency dependent dielectric permittivity of dispersive materials is commonly modeled as a rational polynomial based on multiple Debye, Drude, or Lorentz terms in the finite-difference time-domain (FDTD) method. We identify a simple effective model in which dielectric polarization depends both on the electric field and its first time derivative. This enables nearly exact FDTD simulation of light propagation and absorption in silicon in the spectral range of 300-1000 nm. Numerical precision of our model is demonstrated for Mie scattering from a silicon sphere and solar absorption in a silicon nanowire photonic crystal.     

General solution of a system of equations for acoustic wave propagation in a partially ionized gas in an external electric field

In this paper a system of equations describing the propagation of acoustic waves in multicomponent partially ionized plasma in an external electric field is solved generally, when these waves are generated by an external neutral sound wave in plasma. The equations are solved by means of Laplace transformation. It has been found that a sound wave generates a group of waves with different frequencies and wave vectors. For the sake of comparison, the solution without an external field and the linear solution in the form of waves having the same frequencies as the frequency of the excitation wave are given.