Dispersion Relation For Electromagnetic Waves Research Articles

Influence of electron temperature anisotropy on wave mode propagation and power deposition characteristics in helicon plasma

As the core issue in helicon discharge, the physical mechanism behind the high ionization rate phenomenon is still not fully understood. Based on the warm plasma dielectric tensor model which contains both the particle drift velocity and temperature anisotropy effect, by employing the general dispersion relation of electromagnetic waves propagating in magnetized and uniform plasma with typical helicon discharge parameter conditions, wave mode propagation characteristic and collisional, cyclotron and Landua damping induced wave power deposition properties of azimuthally symmetric mode are theoretically investigated. Systematic analysis shows the following findings. 1) Under typical helicon plasma parameter conditions, i.e. wave frequency <i>ω</i>/(2π)=13.56 MHz, ion temperature is one tenth of the electron temperature, and for a given magnetic field <i>B</i><sub>0</sub> (or wave frequency <i>ω</i>), there exists a critical wave frequency <i>ω</i><sub>cr</sub> (or magnetic field <i>B</i><sub>0,cr</sub>), above which (or below <i>B</i><sub>0,cr</sub>) the damping of the <i>n = </i>1, 2, 3 cyclotron harmonics begins to increase sharply. 2) For the electron temperature isotropic case, the attenuation constants of different harmonics start to increase significantly and monotonically at different thresholds of magnetic field, while the phase constant abruptly increases monotonically from the beginning of the parameter interval. On the other hand, for the electron temperature anisotropic case, both the phase constant and attenuation constant have peaking phenomenon, i.e. the attenuation constant begins to increase sharply at a certain value of <i>B</i><sub>0</sub> and meanwhile the phase constant presents a maximum value near the same value of magnetic field, thus the phase constant starts to keep constant at a certain value of <i>B</i><sub><i>0</i></sub> and meanwhile the attenuation constant has a maximum value near this same value of magnetic field. 3) For the wave power deposition properties, under electron temperature anisotropy conditions, power deposition due to collisional damping of Trivelpiece-Gould (TG) wave plays a dominant role in a low field (<i>B</i><sub>0 </sub>= 48 Gs) (1 Gs = 10<sup>–4</sup> T); by considering the electron finite Larmor radius (FLR) effect, the power deposition of TG wave presents a maximum value at a certain point of parallel electron temperature<i> T</i><sub>e,</sub><sub>//</sub>; with the decrease of <i>T</i><sub>e,⊥</sub>/<i>T</i><sub>e,</sub><sub>//</sub>, the maximum value of power deposition increases gradually. All these findings are very important in further revealing the physical mechanism behind the high ionization rate in helicon plasma.

Elliptical and circular annular solid electron beam for excitation of hybrid modes in the plasma combined circular and elliptical waveguides

For two new configurations presented and by considering annular solid electron beam with background plasma the growth rates of the hybrid modes and the dispersion relation of electromagnetic waves propagating are studied. The interaction of elliptical and circular annular solid electron beams with plasma is investigated that it occurs microwave radiation generation dependent of configuration dimensions. The structures are including metallic elliptical(circular) waveguide with elliptical(circular) dielectric cladding and a core having a circular(elliptical) dielectric rod in center that it is surround by circular(elliptical)annular plasma and a circular(elliptical)annular relativistic electron beam is injected in to plasma. The electromagnetic fields components in each of regions in the considered configurations are calculated. By applying the boundary conditions dispersion relation and operating frequency are obtained. Furthermore for another case that it is applied an infinite magnetic field to considered structures,the problem is investigated. Numerical computations are made and results are graphically presented.

Parametric analysis of mode coupling and liner energy deposition properties of helicon and Trivelpiece-Gould waves in helicon plasma

Based on the finite temperature plasma dielectric tensor model which contains the particle thermal effect, by numerically solving the eigenmode dispersion relation of electromagnetic waves propagating in radially uniform and magnetized warm plasma column which is surrounded by conducting boundary, the mode coupling characteristic and liner damping mechanism induced wave power deposition properties of helicon and Trivelpiece-Gould (TG) waves are parametrically analyzed. The detailed investigations show as follows. Under typical helicon plasma parameter conditions, i.e. wave frequency <i>ω</i>/(2π) = 13.56 MHz, ion temperature is much smaller than electron temperature, for the helicon wave, there exist a cut-off magnetic field <i>B</i><sub>0,H,cutoff</sub> and a cut-off plasma density <i>n</i><sub>0,H,cutoff</sub>, for which under the conditions of <i>B</i><sub>0</sub> > <i>B</i><sub>0,H,cutoff</sub> or <i>n</i><sub>0</sub> < <i>n</i><sub>0,H,cutoff</sub>, the helicon wave becomes an evanescent wave. When the magnetic field intensity changes from 48.4 to 484 G, i.e., <i>ω</i>/<i>ω</i><sub>ce</sub> ranges from 0.01 to 0.1, for the power deposition intensity, Landau damping of TG wave dominates for the <i>m</i> = 0 mode, meanwhile, for the <i>m</i> = 1 mode, which wave, i.e. helicon wave or TG wave, plays a major role in power deposition mainly depends on the magnitude of the magnetic field. On the other hand, for a given magnetic field <i>B</i><sub>0</sub> = 100 G, when <i>ω</i><sub>pe</sub>/<i>ω</i><sub>ce</sub> changes from 3 to 100, for both the <i>m</i> = 0 mode and the <i>m</i> = 1 mode, the power deposition induced by Landau damping of TG wave plays a major role, further, one may notice that the power deposition of TG wave decreases while the power deposition of the helicon wave increases as plasma density increases. Finally, for both the <i>m</i> = 0 mode and the <i>m</i> = 1 mode, the power deposition due to the Landau damping plays a dominant role. All these conclusions provide us with some useful clues to better understanding the high ionization mechanism of helicon wave discharges.

Negative refractive index in cubic noncentrosymmetric superconductors

We study the negative refractive index in cubic noncentrosymmetric superconductors. We consider the Maxwell equations under the Meissner effect, and magnetoelectric effect arising due to broken inversion symmetry. We derive dispersion relations of electromagnetic waves, and show that the refractive index becomes negative at frequencies just below the Higgs gap. We find that the chiral mechanism of the negative refractive index, which is usually discussed in chiral materials with negative permittivity can be applied to superconductors with positive permittivity by replacing the plasma gap with the Higgs gap. Estimation from the experimental values of the penetration depth of LiPt$_3$B indicates that the negative refractive index may appear in UV regions. LiPt$_3$B may exhibit the negative refractive index at wavelengths shorter than any other material observed so far.

A new route to negative refractive index from topological metals

We theoretically discuss the possibility of realizing the negative refractive index in Weyl/Dirac semimetals. We consider the Maxwell equations with the plasma gap and the chiral magnetic effect. We study the dispersion relations of electromagnetic waves, and show that the refractive index becomes negative at frequencies (just) below the plasma frequency. We find that axial anomaly, or more specifically, negative magnetoresistance (electric current parallel to magnetic fields) opens a new route to realize the negative refractive index. Reflection and transmission coefficients are computed in a slab of Weyl/Dirac semimetals.

Non-minimal Einstein–Maxwell theory: the Fresnel equation and the Petrov classification of a trace-free susceptibility tensor

We construct a classification of dispersion relations for electromagnetic waves non-minimally coupled to space-time curvature, based on analysis of the susceptibility tensor which appears in the non-minimal Einstein–Maxwell theory. We classify solutions to the Fresnel equation for the model with a trace-free non-minimal susceptibility tensor according to the Petrov scheme. For all Petrov types we discuss specific features of the dispersion relations, and plot the corresponding wave surfaces.

Mesoporous anodic aluminum oxide photonic crystalline films and its applications

We have calculated the optical characteristics of mesoporous photonic crystalline film of aluminum oxide. We obtained the dispersion relation for electromagnetic waves in the film, calculated an effective refractive index of photonic crystal, worked out group velocities and effective masses of photons and polaritons in mesoporous medium. The results of theoretical analysis are in the good agreement with the measured reflection spectrum. It is shown that the mesoporous photonic crystalline films are good as the radiation amplifiers and highly efficient selective mirrors and filters.

Electromagnetic instability in plasmas heated by a laser field.

Electromagnetic instability is investigated in homogeneous plasmas heated by a laser wave in the range α=v_{0}^{2}/v_{t}^{2}≤2, where v_{0} is the electron quiver velocity and v_{t} is the thermal velocity. The anisotropic electron distribution function that drives unstable quasistatic electromagnetic modes is calculated numerically with the Vlasov-Landau equation in the high ion charge number approximation. A dispersion relation of electromagnetic waves which accounts for further nonlinear terms on v_{0}^{2} from previous results is derived. In typical simulation with ion charge number Z=13, a temperature T=5keV, a density n=9.8×10^{20}cm^{-3}, and a laser wavelength λ_{laser}=1.06μm, growth rates larger than 10^{12}s^{-1} in the quasicollisionless wave-number range were found for α≥1. In the same physical conditions and in the mildly collisional range a growth rate about 10^{11}s^{-1} was also obtained. The extent of the growth wave-number region increases significantly with increasing α.

Polariton excitation rates from time dependent dielectrics

We apply time dependent perturbation theory to a general class of problems involving time dependent dielectric media in cases where dissipation cannot be ignored. The theory is used to derive polariton excitation rates in three illustrative cases, including that of a travelling Gaussian perturbation to the susceptibility of an otherwise infinite homogeneous dielectric. We find that the excitation rate is increased when the wave-vector and frequency of each polariton in the pair is close to satisfying either the dispersion relation for electromagnetic waves, or is close to a material resonance. We thus predict that the time dependence of a medium can excite a pair of polaritons, only one of which may appear as a propagating electromagnetic wave.

Mesoporous Photonic-Crystal Films for Amplification and Filtering of Electromagnetic Radiation

We consider optical properties of mesoporous aluminum-oxide-based photonic crystal films, derive the dispersion relation for electromagnetic waves, obtain the effective refractive index of the photonic crystal, and determine group velocities and effective masses of photons and polaritons in the mesoporous media. We compare the reflection spectra calculated with the experimental results. We discuss the potential for using mesoporous photonic-crystal films as amplifiers of electromagnetic radiation, high-efficiency selective mirrors, and optical filters.

Excitation of THz hybrid modes in an elliptical dielectric rod waveguide with a cold collisionless unmagnetized plasma column by an annular electron beam

The dispersion relation of electromagnetic waves propagating in an elliptical plasma waveguide with a cold collisionless unmagnetized plasma column and a dielectric rod is studied analytically. The frequency spectrum of the hybrid waves and the growth rate for excitation of the waves by a thin annular relativistic elliptical electron beam (TAREEB) is obtained. The effects of relative permittivity constant of dielectric rod, geometrical dimensions, plasma frequency, accelerating voltage, and current density of TAREEB on the growth rate and frequency spectra of the waveguide will be investigated.

Optical properties of one-dimensional photonic crystals based on porous films of anodic aluminum oxide

The optical properties of one-dimensional photonic crystals based on porous anodic aluminum oxide films have been studied by measuring transmittance and specular reflectance spectra in the visible and UV spectral regions. Angular dependences of the spectral positions of optical stop bands are obtained. It is shown that the reflectance within the first stop band varies from point to point on the sample surface, reaching a level of 98–99% at some points. The dispersion relation for electromagnetic waves in the model of infinite periodic structure is calculated for the samples under study. The possibility of using models with an infinite or finite number of layers to calculate reflectance spectra near the first optical stop band is discussed.

Map of low‐frequency electromagnetic noise in the sky

AbstractThe Earth's natural electromagnetic environment is disturbed by anthropogenic electromagnetic noise. Here we report the first results from an electromagnetic noise survey of the sky. The locations of electromagnetic noise sources are mapped on the hemisphere above a distributed array of wideband receivers that operate in a small aperture configuration. It is found that the noise sources can be localized at elevation angles up to ∼60° in the sky, well above the horizon. The sky also exhibits zones with little or no noise that are found toward the local zenith and the southwest of the array. These results are obtained by a rigorous analysis of the residuals from the classic dispersion relation for electromagnetic waves using an array analysis of electric field measurements in the frequency range from ∼20 to 250 kHz. The observed locations of the noise sources enable detailed observations of ionospheric modification, for example, caused by particle precipitation and lightning discharges, while the observed exclusion zones enable the detection of weak natural electromagnetic emissions, for example, from streamers in transient luminous events above thunderclouds.

Electromagnetic plasma waves in the nonextensive statistics

This paper presents theoretical findings of new electromagnetic plasma waves in nonextensive and Maxwellian plasma below and above plasma frequency. The new waves are observed among the solutions of general and exact nonextensive dispersion relations for electromagnetic waves in unmagnetized collisionless plasma. The solutions for all values of nonextensive q parameter are also containing a light mode. The exact dispersion relations are obtained via calculation of kinetic dispersion integral using nonextensive distributions and hypergeometric function properties. Finally the effects of q parameter on the oscillation modes and damps are discussed.

Plasma Waves Dispersion Relation at Near of the Cosmological Black Holes in an Expanding Universe Dominated by Dark Energy

Propagation of waves in the relativistic plasma at near of the horizon of black holes embedded in Friedman-Robertson-Walker cosmologies is investigated. The metric of the class of black holes, cosmological black holes, is obtained by performing conformal transformation on isotropic black hole space-time. Here we use the Maxwell’s equations and relativistic two-fluid plasma in 3 + 1 formulation in Rindler coordinates system. By calculation of the time evolution of scale factor, the dispersion relation of electromagnetic waves near of the cosmological black holes horizon is obtained.

Kinetic transverse dispersion relation for relativistic magnetized electron-positron plasmas with Maxwell-Jüttner velocity distribution functions

We use a kinetic treatment to study the linear transverse dispersion relation for a magnetized isotropic relativistic electron-positron plasma with finite relativistic temperature. The explicit linear dispersion relation for electromagnetic waves propagating along a constant background magnetic field is presented, including an analytical continuation to the whole complex frequency plane for the case of Maxwell-Jüttner velocity distribution functions. This dispersion relation is studied numerically for various temperatures. For left-handed solutions, the system presents two branches, the electromagnetic ordinary mode and the Alfvén mode. In the low frequency regime, the Alfvén branch has two dispersive zones, the normal zone (where ∂ω/∂k > 0) and an anomalous zone (where ∂ω/∂k < 0). We find that in the anomalous zone of the Alfvén branch, the electromagnetic waves are damped, and there is a maximum wave number for which the Alfvén branch is suppressed. We also study the dependence of the Alfvén velocity and effective plasma frequency with the temperature. We complemented the analytical and numerical approaches with relativistic full particle simulations, which consistently agree with the analytical results.

Realization of one-way electromagnetic modes at the interface between two dissimilar metals

We calculate the dispersion relations for electromagnetic waves propagating at the interface between two dissimilar Drude metals in an external magnetic field B parallel to the interface. The propagating modes are bound to the inteface and travel perpendicular to B. In certain frequency ranges, the waves can propagate in one direction only. The frequency range for these one-way modes increases with increasing B. One group of modes occurs at moderate frequencies, between the lower and upper plasma frequencies of the two metals. The other occurs at much lower frequencies, between their lower and upper cyclotron frequencies. We discuss possible ways to realize such modes in real materials, including dissimilar superconductors.

Dispersion Relation of TM Mode Electromagnetic Waves in the Rippled-Wall Elliptical Plasma and Dielectric Waveguide in Presence of Elliptical Annular Electron Beam

The dispersion relation of electromagnetic waves in a rippled-wall elliptical waveguide with a degenerate plasma column protected by an elliptical annular dielectric layer is theoretically investigated. Using the linear field theory, the dispersion relation of electromagnetic waves in a rippled-wall elliptical waveguide with a plasma rod and an elliptical annular dielectric is obtained. In addition, by injecting a finite thick annular intense relativistic electron beam in this waveguide, the dispersion relation of these waves is investigated. In addition, a cold and uniform plasma-filled traveling wave tube with sinusoidally corrugated slow-wave structure is driven by a finite thick elliptical annular intense relativistic electron beam with the entire system immersed in a strong longitudinal magnetic field. Using the linear field theory, the dispersion relation for the elliptical relativistic traveling wave tube is derived.

The Rod Degenerate Plasma-Rippled-Wall Waveguide and Its Excitation by Relativistic Electron Beam Injection

The dispersion relation of electromagnetic waves in a rippled-wall waveguide with a degenerate plasma column protected by an annular dielectric layer is theoretically investigated. By injecting a thin annular relativistic electron beam (TAREB) in the region between dielectric and metallic cylinders in the aforementioned configuration as an energy source, the excitation of terahertz (THz) electromagnetic waves is investigated. Also, the dependence of dispersion relation and time growth rate on the radius of the dielectric, the corrugation amplitude, and period is studied. Furthermore, it is found that the presence of the degenerate plasma rod in the rippled-wall waveguide leads to obtain high-frequency modes in the THz frequency region. Finally, the electric-field profiles in this waveguide are plotted.

The dispersion relation and excitation of transverse magnetic mode electromagnetic waves in rippled-wall waveguide with a plasma rod and an annular dielectric

By using the linear field theory, the dispersion relation of electromagnetic waves in a rippled-wall waveguide with a plasma rod and an annular dielectric is obtained. In addition, by injecting a finite thick annular intense relativistic electron beam in this waveguide, the excitation of these waves is investigated. Furthermore, the effects of the radius of the plasma rod, the radius of the dielectric, the corrugation amplitude, and period on the frequency spectrum are investigated. Besides, the time growth rate of excitation of these waves by an annular relativistic electron beam is studied. Finally, to demonstrate the advantages of this rippled-wall waveguide, the dispersion relation and the growth rate of three simplified cases are investigated.