Extraordinary Electromagnetic Wave Research Articles

Effect of the magnetic field on coexisting stimulated Raman and Brillouin backscattering of an extraordinary mode

This paper presents a model to study the interplay between the stimulated Raman scattering (SRS) and stimulated Brillouin scattering (SBS) in the presence of background magnetic field. This formalism is applicable to laser produced plasma as well as to heating mechanism in toroidal system by an extraordinary electromagnetic wave. In the former case, the magnetic field is self-generated, while in the latter case (toroidal plasmas) magnetic field is applied externally. The behavior of one scattering process is explicitly dependent on the coexisting scattering process as well as on the magnetic field. Explicit expressions for the back-reflectivity of scattered beams (SRS and SBS) are presented. It has been demonstrated that due to the magnetic field and coexistence of the scattering processes (SRS and SBS) the back-reflectivity gets modified significantly. Results are also compared with the three wave interaction case (isolated SRS or SBS case).

Parametric decay of an extraordinary electromagnetic wave in relativistic plasma

Parametric instability of an extraordinary electromagnetic wave in plasma preheated to a relativistic temperature is considered. A set of self-similar nonlinear differential equations taking into account the electron “thermal” mass is derived and investigated. Small perturbations of the parameters of the heated plasma are analyzed in the linear approximation by using the dispersion relation determining the phase velocities of the fast and slow extraordinary waves. In contrast to cold plasma, the evanescence zone in the frequency range above the electron upper hybrid frequency vanishes and the asymptotes of both branches converge. Theoretical analysis of the set of nonlinear equations shows that the growth rate of decay instability increases with increasing initial temperature of plasma electrons. This result is qualitatively confirmed by numerical simulations of plasma heating by a laser pulse injected from vacuum.

Extraordinary electromagnetic localized structures in plasmas: Modulational instability, envelope solitons, and rogue waves

Abstract We have considered the nonlinear propagation of an extraordinary electromagnetic wave in a transversely magnetized plasma. It is found that, in a weakly relativistic regime, evolution of the amplitude of an extraordinary wave packet is governed by a nonlinear Schrodinger (NLS) equation. The modulational instability of an extraordinary plane wave is investigated. The analytical solutions of the NLS equation in the forms of envelope solitons and rogue waves are reviewed and dependence of their structural properties on relevant parameters of the system is addressed.

Additional electromagnetic waves in a uniaxial crystal with anisotropy fluctuations

It has been shown that the inclusion of orientational fluctuations of the axes of nonpolar axially symmetric molecules leads to a spatial dispersion of the permittivity of a uniaxial crystal. Expressions for the local field, polarization, and principal values of the permittivity tensor of the crystal have been derived. An estimate has been made of the wavelength above which the contribution to the spatial dispersion of orientational fluctuations of the molecular axes dominates. The phase velocities of the ordinary and extraordinary electromagnetic waves in a uniaxial crystal have been determined. It has been demonstrated that additional slow extraordinary electromagnetic waves can exist near the zeros of the principal values of the permittivity tensor of the crystal in particular ranges of angles between the wave vector and the optic axis of the crystal.

Controllable synthesis of porous Fe3O4@ZnO sphere decorated graphene for extraordinary electromagnetic wave absorption.

For the first time, mesoporous Fe3O4@ZnO sphere decorated graphene (GN-pFe3O4@ZnO) composites with uniform size, considerable porosity, high magnetization and extraordinary electromagnetic (EM) wave absorption properties were synthesized by a simple and efficient three-step method. Structure and morphology details were characterized by X-ray diffraction, transmission electron microscopy, high-resolution electron microscopy and field-emission scanning electron microscopy. Electron microscopy images reveal that pFe3O4@ZnO spheres with obvious porous and core-shell structures are uniformly coated on both sides of the GN sheets without significant numbers of vacancies or apparent aggregation. EM wave absorption properties of epoxy containing 30 wt% GN-pFe3O4@ZnO were investigated at room temperature in the frequency region of 0.2-18 GHz. The absorption bandwidth with reflection loss (RL) values less than -10 dB is up to 11.4 GHz, and the minimal RL is almost -40 dB. The intrinsic physical and chemical properties of the materials, the synergy of Fe3O4 and ZnO, and particularly the unique multi-interfaces are fundamental to the enhancement of EM absorption properties. The as-prepared GN-pFe3O4@ZnO composites are shown to be lightweight, have strong absorption, and broad frequency bandwidth EM absorbers.

Z‐mode maser instability

Although the cyclotron maser instability customarily involves the extraordinary (X) and ordinary (O) fast transverse electromagnetic wave modes, which directly escape and propagate long distances from the source region, the instability also excites the Z mode for a wide range of parameters. Even though Z mode is a nonescaping mode, it may convert to O mode in an inhomogeneous medium and be detected by remote means. This process is believed to explain radio emissions near cyclotron harmonics emitted both upward and downward from Earth's auroral ionosphere, as well as analogous emissions detected near Saturn. A more general analysis of the electron loss cone driven Z‐mode maser instability than previously reported reveals that for certain plasma‐to‐cyclotron‐frequency ratios, the unstable waves split into broadband and narrowband ranges of unstable modes and that these two bands are characterized by distinct polarizations. In previous studies of the Z‐mode maser, the maximum growth rate was considered without distinguishing the two bands. Although the maximum temporal growth rate sometimes corresponds to the narrowband feature, the broadband feature with a significant O‐mode‐like polarization may be of importance, since it can more easily convert to an escaping radiation. This paper presents analysis of maximum growth rates, wave propagation angles, and wave frequencies for the two band features of the loss cone driven Z‐mode maser instability as a function of the ratio of plasma‐to‐electron cyclotron frequency. The results are relevant to auroral radio emission phenomena, especially those observed near cyclotron harmonics at both Earth and Saturn.

Kinetic simulation of the O-X conversion process in dense magnetized plasmas

One scheme for heating a dense magnetized plasma core, such as in a tokamak, involves launching an ordinary (O) electromagnetic wave at the low density edge. It is converted to a reflected extraordinary (X) electromagnetic wave under certain conditions, and then transformed into an electron Bernstein wave able to reach high density regions inaccessible to most other waves. The O-X mode conversion is important in heating and diagnostic processes in different devices such as tokamaks, stellarators, and some types of pinches. The goal of this study has been to demonstrate that the kinetic particle-in-cell (PIC) scheme is suitable for modeling the O-X conversion process as the first step toward a more complete simulation of O-X-B heating. The O-X process is considered and simulated with a kinetic particle model for parameters of the TJ-II stellarator using the PIC code, XOOPIC. This code is able to model the non-monotonic density and the magnetic profile of the TJ-II stellarator. It can also statistically represent the self-consistent distribution function of the plasma, which has not been possible in previous fluid models. By considering the electric and magnetic components of launched and reflected waves, the O-mode and X-mode waves can be detected, and the O-X conversion can be demonstrated. In this work, the optimum angle for conversion efficiency, as predicted by the previous theory and experimentally confirmed, is used. Via considering the power of the launched O-mode wave and the converted X-mode wave, the efficiency of 63% for O-X conversion for the optimum theoretical launch angle of 47∘ is obtained, which is in good agreement with efficiencies computed via full-wave simulations.

Controlled synthesis of porous Fe3O4-decorated graphene with extraordinary electromagnetic wave absorption properties

Porous Fe3O4-decorated graphene (GN–Fe3O4) composites with different microstructures were successfully synthesized by a modified two-step method. The microstructure and morphology were confirmed by X-ray diffraction (XRD), transmission electron microscopy and scanning electron microscopy. XRD studies show that the products consist of highly crystallized Fe3O4 but disorderedly stacked GN sheets. Electron microscopy images reveal that Fe3O4 nanoparticles with different sizes and microstructures are uniformly coated on both sides of GN sheets, without large vacancies or apparent aggregation. Electromagnetic wave absorption properties of epoxy containing 30 wt.% GN–Fe3O4 composites were investigated at room temperature in the frequency range of 0.5–18GHz. In particular, the porous, flower-like Fe3O4-decorated GN sample exhibits an enhanced dielectric loss due to the porous microstructure of Fe3O4. The multiple absorbing mechanisms attribute to the improved impedance matching which indicates the as-prepared porous GN–Fe3O4 composites could be a potential candidate for lightweight electromagnetic wave absorption materials.

Stimulated Raman back scattering of extraordinary electromagnetic waves from periodically magnetized nanoparticle lattice

Stimulated Raman back scattering of extraordinary electromagnetic waves from the nanoparticle lattice is investigated in the presence of the static magnetic field. In the context of macroscopic theory, dispersion relation and growth rate of extraordinary mode for different values of static magnetic field and lattice parameters are derived and analyzed. It is found that when the static magnetic field is off, dispersion relation has two branches. These branches are related to the plasmonic and body wave branches of the plane polarized wave. Low frequency branch of the pump wave is not involved in the instability while the other branch is not stable, and the growth rate of Raman back scattered wave has one peak. If the electrons have cyclotron frequency by static magnetic field, dispersion has three branches. These branches are related to the plasmonic and body wave branches of left and right hand circularly polarized waves. In this situation, it is found that low frequency lower branch of the pump wave is stable while other branches are not stable, and the growth rate of Raman back scattered wave has three peaks. Numerical study of growth rate in various cyclotron frequencies shows that the growth rate increases and the instability band width decreases with increasing static magnetic field.

Electron Cyclotron Resonance Near the Axis of a Mirror Trap

Propagation of an extraordinary electromagnetic wave in the vicinity of electron cyclotron resonance surface in an open linear trap is studied analytically, taking into account inhomogeneity of the magnetic field in paraxial approximation. Ray trajectories are derived from a reduced dispersion equation that makes it possible to avoid the difficulty associated with a transition from large propagation angles to the case of strictly longitudinal propagation. As an example, results of general theory are applied to the electron cyclotron resonance heating experiment which is under preparation on the Gas Dynamic Trap in the Budker Institute of Nuclear Physics.

OBLIQUE SURFACE JOSEPHSON PLASMA WAVES IN LAYERED SUPERCONDUCTORS

In this paper the theoretical analysis of the oblique surface Josephson plasma waves propagating along a dielectric‐layered superconductor interface is first represented. The case when the superconductor layers are perpendicular to the interface is considered. The oblique surface Josephson plasma waves are the surface electromagnetic waves propagating in the interface plane at an arbitrary angle to the superconductor layers. The electromagnetic field of the waves is the superposition of ordinary and extraordinary surface electromagnetic waves. The dispersion equation of the oblique surface Josephson plasma waves has been derived. This equation is the most general dispersion equation of the surface Josephson plasma waves in the case under study. The problem on the excitation of oblique surface Josephson plasma waves by means of the attenuated total reflection method is solved. It has been established that the process of the excitation of oblique surface Josephson plasma waves is accompanied by the onset of an additional reflected wave in the prism with the polarization, being orthogonal to the polarization of the incident wave. It has been found that the reflection coefficient of the exciting wave in the prism can vanish for some optimal parameters of the structure.

Group velocity of extraordinary waves in superdense magnetized quantum plasma with spin-1/2 effects

Based on the one component plasma model, a new dispersion relation and group velocity of elliptically polarized extraordinary electromagnetic waves in a superdense quantum magnetoplasma are derived. The group velocity of the extraordinary wave is modified due to the quantum forces and magnetization effects within a certain range of wave numbers. It means that the quantum spin-1/2 effects can reduce the transport of energy in such quantum plasma systems. Our work should be of relevance for the dense astrophysical environments and the condensed matter physics.

Electron cyclotron resonance near the axis of a quadrupole linear trap

The quasi-longitudinal propagation of an extraordinary electromagnetic wave in the vicinity of the electron cyclotron resonance layer in an open linear trap with a quadrupole magnetic field is studied analytically, taking into account the inhomogeneity of the magnetic field in a paraxial approximation. The ray trajectories are derived from a simplified dispersion equation, that is, nonetheless able to accurately describe the transition from finite to zero perpendicular refractive index. A criterion for an on-axis resonance point to be an attractor for the ray trajectories is formulated, which generalizes a similar criterion for axisymmetric linear traps derived in a recent paper [D. S. Bagulov and I. A. Kotelnikov, Phys. Plasmas 19, 082502 (2012)].

Electron cyclotron resonance near the axis of the gas-dynamic trap

Propagation of an extraordinary electromagnetic wave in the vicinity of electron cyclotron resonance surface in an open linear trap is studied analytically, taking into account inhomogeneity of the magnetic field in paraxial approximation. Ray trajectories are derived from a reduced dispersion equation that makes it possible to avoid the difficulty associated with a transition from large propagation angles to the case of strictly longitudinal propagation. Our approach is based on the theory, originally developed by Zvonkov and Timofeev [Sov. J. Plasma Phys. 14, 743 (1988)], who used the paraxial approximation for the magnetic field strength, but did not consider the slope of the magnetic field lines, which led to considerable error, as has been recently noted by Gospodchikov and Smolyakova [Plasma Phys. Rep. 37, 768–774 (2011)]. We have found ray trajectories in analytic form and demonstrated that the inhomogeneity of both the magnetic field strength and the field direction can qualitatively change the picture of wave propagation and significantly affect the efficiency of electron cyclotron heating of a plasma in a linear magnetic trap. Analysis of the ray trajectories has revealed a criterion for the resonance point on the axis of the trap to be an attractor for the ray trajectories. It is also shown that a family of ray trajectories can still reach the resonance point on the axis if the latter generally repels the ray trajectories. As an example, results of general theory are applied to the electron cyclotron resonance heating experiment which is under preparation on the gas dynamic trap in the Budker Institute of Nuclear Physics [Shalashov et al., Phys. Plasmas 19, 052503 (2012)].

Effects of modification of the polar ionosphere with high-power short-wave extraordinary-mode HF waves produced by the spear heating facility

We present the results of modifying the F2 layer of the polar ionosphere experimentally with highpower HF extraordinary-mode waves. The experiments were performed in October 2010 using the short-wave SPEAR heating facility (Longyearbyen, Spitsbergen). To diagnose the effects of high-power HF waves by the aspect-scattering method in a network of diagnostic paths, we used the short-wave Doppler radar CUTLASS (Hankasalmi, Finland) and the incoherent scatter radar ESR (Longyearbyen, Spitsbergen). Excitation of small-scale artificial ionospheric irregularities was revealed, which were responsible for the aspect and backward scattering of the diagnostic signals. The measurements performed by the ESR incoherent scatter radar simultaneously with the heating demonstrated changes in the parameters of the ionospheric plasma, specifically, an increase in the electron density by 10–25 % and an increase in the electron temperature by 10–30 % at the altitudes of the F2 layer, as well as formation of sporadic ionization at altitudes of 140–180 km (below the F2 layer maximum). To explain the effects of ionosphere heating with HF extraordinary-mode waves, we propose a hypothesis of transformation of extraordinary electromagnetic waves to ordinary in the anisotropic, smoothly nonuniform ionosphere.

Effect of flux surface curvature on the linear coupling of electron cyclotron waves in tokamak plasmas

Specific features of the linear interaction of ordinary and extraordinary electromagnetic waves in the electron cyclotron frequency range in a nonuniform plasma confined in a toroidal magnetic trap are considered. Reduced wave equations taking into account the curvature of the cut-off surfaces in toroidal geometry are formulated. Using these equations, the distributions of the wave fields in the coupling region are analyzed. A method for calculating quasi-optical beams passed through the region of linear wave interaction is proposed.

The Frequency shift of an extraordinary (X) wave propagating through plasma

AbstractThe frequency shift is obtained for an extraordinary electromagnetic wave propagating through plasma as function of an external magnetic field. A linear theory is used here to calculate the frequency shift, and the numerical results are given for typical laboratory fusion plasma. A limit case where the wave is propagating through rarefied plasma in the presence of some weak magnetic field is also studied. Estimation is given on the basis of some simplifying approximation for the frequency upshift of a type III radio bursts interacting with the Earth's magnetosphere.

Derivation of the paraxial equation for extraordinary waves in uniaxial media

A relatively simple derivation of the paraxial equation for extraordinary electromagnetic waves in uniaxial media is presented. The propagation of the waves is described with both Abraham's and Minskowski's definitions of the electromagnetic momentum. A Gaussian beam is worked out to illustrate the sidewalk effect of extraordinary rays.

Extraordinary transmission in planar waveguide loaded with anisotropic metamaterials

Ordinary planar waveguide cannot support electromagnetic (EM) wave propagating at frequency below the cut-off frequency of the waveguide, due to the evanescent wave nature of the EM wave in such waveguide. We have found by theoretical analysis that extraordinary EM wave transmission could occur for transverse-electric modes at frequency below the cut-off frequency of the hollow waveguide by inserting different kinds of anisotropic metamaterials (AMMs) in the hollow waveguide. Such transmission of EM energy has no lower cut-off frequency and is due to the conversion of the evanescent wave into propagating mode inside the AMMs, which is quite different from that in the case of waveguide loaded with an isotropic left-handed material slab. We have verified the extraordinary phenomenon by performing circuit analog of the planar waveguide loaded with different kinds of AMMs through realization with transmission line metamaterials.

WIENER-HOPF ANALYSIS OF PLANAR CANONICAL STRUCTURES LOADED WITH LONGITUDINALLY MAGNETIZED PLASMA BIASED NORMALLY TO THE EXTRA-ORDINARY WAVE PROPAGATION

The canonical problem of an extra-ordinary Transverse Electromagnetic wave propagating in a parallel plane waveguide with a semi-infinite upper conductor and loaded with magnetized plasma is considered. The homogeneous biasing constant magnetic field is assumed parallel to the substrate and normal to the wave propagation,which incidents normally on the truncated edge. The Wiener-Hopf technique is employed and the corresponding equations are formulated for the open-radiating structure as well as for a closed one resulting from the placement of a metallic shield parallel to the waveguide planes. Closed form field expressions are obtained for the shielded geometry,while the open geometry Kernel factorization is left for future extensions. Important non-reciprocal wave propagation phenomena are involved,which lend non-even function properties to the involved Kernels. Hence,their factorization becomes non-trivial requiring new mathematical approaches. Finally,a review of the involved non-reciprocal and/or unidirectional surface waves is given, which is related to the involved mathematical complexities.