Theory of slow waves in transversely nonuniform plasma waveguides

A general method is developed for a numerical analysis of the frequency spectra of internal, internal-surface, and surface slow waves in a waveguide with transverse plasma density variations. For waveguides with a piecewise constant plasma filling, the spectra of slow waves are thoroughly examined in the limits of an infinitely weak and an infinitely strong external magnetic field. For a smooth plasma density profile, the frequency spectrum of long-wavelength surface waves remains unchanged, but a slow damping rate appears that is caused by the conversion of the surface waves into internal plasma waves at the plasma resonance point. As for short-wavelength internal waves, they are strongly damped by this effect. It is pointed out that, for annular plasma geometry, which is of interest from the experimental point of view, the spectrum of the surface waves depends weakly on the magnetic field strength in the waveguide.     

Boundary conditions for the electromagnetic field in a waveguide with a thin-walled annular plasma in the context of application to plasma microwave electronics

Effective boundary conditions for the electromagnetic field of the slow surface waves of a thinwalled annular plasma in a metal waveguide are derived and justified. With the boundary conditions obtained, there is no need to solve field equations in the plasma region of the waveguide, so that the dispersion properties of plasma waveguides can be investigated analytically for an arbitrary strength of the external magnetic field. Examples are given that show how to use the effective boundary conditions in order to describe surface waves with a normal and an anomalous dispersion. The boundary conditions are then employed to construct a theory of the radiative Cherenkov instabilities of a thin-walled annular electron beam in a waveguide with a thinwalled annular plasma. The single-particle and collective Cherenkov effects associated with low-and high-frequency surface waves in an arbitrary external magnetic field are studied analytically. The method of the effective boundary conditions is justified in the context of application to the problems of plasma relativistic microwave electronics.     

Emission of alfvén waves from a nonuniform MHD waveguide

The efficiency of the wave energy loss from a nonuniform MHD waveguide due to the conversion of the trapped magnetosonic waveguide modes into runaway Alfvén waves is estimated theoretically. It is shown that, if the waveguide parameters experience a jumplike change along the waveguide axis, the interaction between the waveguide modes and Alfvén waves occurs precisely at this “jump.” This effect is incorporated into the boundary conditions. A set of coupled integral equations with a singular kernel is derived in order to determine the transmission and reflection coefficients for the waveguide modes. The poles in the kernels of the integral operators correspond to the surface waves. When the jump in the waveguide parameters is small, analytic expressions for the frequency dependence of the transformation coefficients are obtained by using a model profile of the Alfvén velocity along the magnetic field. For the jump characterized by the small parameter value ε=0.3, the wave-amplitude transformation coefficient can amount to 5–10%. Under the phase synchronization condition (when the phase velocities of the waveguide modes on both sides of the jump are the same), the wave-energy transformation coefficient is much higher: it increases from a fraction of one percent to tens of percent. The transformation of fast magnetosonic waves into Alfvén waves is resonant in character, which ensures the frequency and wavelength filteringof the emitted Alfvén perturbations.     

Nonlinear ineraction of an annular electron beam with azimuthal surface waves

A nonlinear theory is developed that describes the interaction between an annular electron beam and an electromagnetic surface wave propagating strictly transverse to a constant external axial magnetic field in a cylindrical metal waveguide partially filled with a cold plasma. It is shown theoretically that surface waves with positive azimuthal mode numbers can be efficiently excited by an electron beam moving in the gap between the plasma column and the metal waveguide wall. Numerical simulations prove that, by applying a constant external electric field oriented along the waveguide radius, it is possible to increase the amplitude at which the surface waves saturate during the beam instability. The full set of equations consisting of the waveenvelope equation, the equation for the wave phase, and the equations of motion for the beam electrons is solved numerically in order to construct the phase diagrams of the beam electrons in momentum space and to determine their positions in coordinate space (in the radial variable-azimuthal angle plane).     

Diagnostics of plasma oscillations by the field of surface waves guided by a dielectric waveguide

The potentialities of the diagnostic method for determining the plasma parameters by recording the surface waves guided by a dielectric waveguide and scattered by plasma oscillations are discussed. The use of surface (slowed) waves makes it possible to improve both the sensitivity and spatial resolution of measurements. The scattering is the most intense near the waveguide cutoff, at which the dependence of the wave propagation constant on the plasma density is the steepest. It is shown experimentally that the method proposed makes it possible to determine the discharge plasma density and electron energy and to estimate the amplitude of the RF field of the plasma waves forming the discharge and the amplitude of plasma density oscillations in these waves. The data obtained from the measurements of the amplitudes of both high-and low-frequency plasma density oscillations by the proposed method agree satisfactorily with theoretical predictions. The experimental data on the plasma density are confirmed by other diagnostic measurements. The ways of reducing measurement errors are proposed.     

Surface waves in plasma waveguides with a smooth transverse inhomogeneity

A theory of cylindrical surface waves in a circular waveguide filled with a smoothly inhomogeneous plasma is presented. For a special radial profile of the plasma density, dispersion relations for the complex frequencies of surface waves are derived analytically. The dispersion relations are solved numerically (in the long-wavelength limit) and numerically. It is shown that there are two types of surface waves. When passing to the case of a sharply bounded plasma, one of the waves becomes an ordinary surface wave, while the other becomes strongly damped.     

Theory of transverse surface electromagnetic waves propagating along a plasma-metal boundary with a finite radius of curvature in a magnetic field

The spectra of electromagnetic waves propagating perpendicular to the axis of a plasma-filled metal waveguide in a magnetic field are studied with allowance for the effects exerted upon the wave frequency by the radial plasma density variation and by the emission of waves through a narrow axial slit in a waveguide wall. The case of wave propagation along the boundary between a plasma and a cylindrical metal waveguide wall with a periodically varying radius of curvature is also considered. The electromagnetic properties of the plasma are described by a dielectric tensor in the hydrodynamic approximation. The spatial distribution of the wave field is determined by the method of successive approximations. Results are presented from both analytical and numerical investigations. Analytical expressions for the corrections to the wave frequency due to the emission of the wave energy from the waveguide and due to the slight corrugation of the waveguide wall are obtained. The rates of wave damping due to the emission of the wave energy through a narrow axial slit and due to collisions between the plasma particles are found. The correction to the frequency that comes from the periodic variation of the radius of curvature of the plasma surface is calculated to within terms proportional to the square of the small parameter describing the azimuthal corrugation of the waveguide wall. The effect of the radial plasma density variation on the dispersion of the surface modes is examined both analytically and numerically.     

Influence of the shape of the cross section of a plasma-dielectric interface on the dispersion properties of high-frequency azimuthal surface modes

Theoretical study of the propagation of a packet of surface electromagnetic surface waves with a zero axial wavenumber in a circular-cross-section cylindrical metal waveguide within the frequency range that is higher than upper hybrid resonance is carried out. The waveguide is partially filled by plasma and immersed into axial magnetic field. The cross section of the plasma column is assumed to differ from circular shape. The effect of this shape on the dispersion properties of azimuthal surface modes is investigated by the method of successive approximations. The fields of the waves and their eigenfrequencies are determined up to terms of the second order in the deviation of the plasma cross section shape from the ring one. The correction to the eigenfrequency of azimuthal surface modes caused by this feature of the plasma column section is proved to increase with decreasing the external magnetic field and increasing the value of the dielectric constant of the dielectric, that separates the plasma from the metal wall of the waveguide. The spectral composition of the wave packet, in the form of which these modes propagate, is studied. The amplitudes of the satellite harmonics of these modes are found to increase with increasing the plasma density and decreasing the external magnetic field.     

Theory of propagation of ordinary surface cyclotron waves

The dispersion properties of ordinary surface cyclotron waves in a semiinfinite nonuniform plasma are investigated. The waves propagate across the external magnetic field directed along the plasma surface in a metal waveguide the internal surface of which is covered with a dielectric. The problem is solved analytically in the framework of a kinetic model for plasma particles under the assumption of weak spatial dispersion. The influence of the parameters of the dielectric layer separating the plasma from the metal wall, the shape of the plasma density profile, and the value of the external magnetic field on the dispersion properties of surface cyclotron waves is studied both numerically and analytically.     

Effect of the shape of the cross section of a plasma-dielectric interface on the dispersion properties of azimuthal surface modes

A theoretical study is made of the propagation of a packet of surface electromagnetic waves with a zero axial wavenumber in a circular-cross-section cylindrical metal waveguide partially filled with plasma in an axial magnetic field. The cross section of the plasma column is assumed to be noncircular. The effect of the noncircular shape of the plasma cross section on the dispersion properties of azimuthal surface modes is investigated by the method of successive approximations. The fields of the waves and their eigenfrequencies are determined to second order in a small parameter.     

Asymmetric long-wavelength surface waves in magnetized plasma waveguides entirely filled with plasma

A theoretical study is made of the dispersion properties of electromagnetic surface waves with arbitrary azimuthal mode numbers and with a small axial wavenumber in cylindrical metal waveguides entirely filled with a radially inhomogeneous, cold, magnetized plasma. The frequency ranges in which the extraordinary polarized waves under analysis can exist are found, and the conditions for their resonant interaction with an ordinary bulk wave are determined. The eigenfrequency of these surface waves is investigated as a function of the plasma parameters, the axial wavenumber, and the azimuthal mode number. Simple analytic expressions are derived for the eigenfrequencies of the surface waves under study propagating in a homogeneous plasma waveguide.     

Guiding Terahertz Waves by a Single Row of Periodic Holes on a Planar Metal Surface

In this paper, we show that surface plasmon polaritons (SPPs) can be sustained by a single row of holes periodically drilled on a perfect electric conductor surface. These SPPs can be strongly confined in the transverse plane and they possess an excellent modal shape. In the terahertz regime, large propagation length is available for highly confined SPPs on a real-metal surface waveguide. As the dispersion characteristics of such SPPs can be controlled by the surface geometry, unusual total reflection phenomenon occurs when waves travel along a nonuniform surface waveguide with gradually increasing hole depths.     

Spectral Properties of Plasma Waves in Periodic Plasma-Filled Structures

The dispersion properties and field distribution of plasma waves in a periodic plasma-filled waveguide are correctly analyzed for the first time with allowance for all spatial harmonics. It is shown that the plasma wave spectrum has a zonal structure and a lower cutoff frequency. The widths of the forbidden bands and the lower cutoff frequency are determined by the waveguide corrugation depth. For a planar periodic plasma-filled waveguide, the allowed and forbidden frequency bands are evaluated analytically. The waveguide periodicity substantially influences the field of the plasma waves at frequencies close to the forbidden bands. This leads to the formation of regions in which the energy density of plasma waves exceeds the average level by more than one order of magnitude. This effect is related to the contribution from the higher spatial harmonics.     

Effect of the radial plasma profile on the surface wave structure in a plasma waveguide

A study is made of the effect of the radial plasma profile on the spectra and fields of the surface waves in a plasma waveguide. It is shown that the surface wave is localized in the region where the plasma permittivity vanishes. In waveguides with smoother radial plasma profiles, the region where the surface wave can exist is narrower and may even disappear.     

Design of a Slit-Groove Coupler for Unidirectional Excitation of the Guided Surface Plasmon Polaritons Through a Plasmonic Slot Waveguide

In this paper, a plasmonic-photonic nanostructure has been introduced for efficient unidirectional coupling of free-space radiation to surface plasmon polariton (SPP) waves under normal illumination on a subwavelength slit. The structure consists of a conventional metallic slit-groove nanostructure integrated with a plasmonic waveguide to support SPP waves along the desired direction with a remarkable lateral confinement. The unidirectional coupling is achieved by using an integrated plasmonic distributed reflector designed under Bragg condition. This reflector basically distributes part of the light coupled through the slit into the SPP modes of the waveguide. Numerical simulations show that up to 26 % of the normally incident light couples to the transversely localized field of the surface plasmon. In addition, the ratio of mode current density of the surface plasmon, launched in the desired direction, to that in the opposite direction can reach about 23 times. This structure shows a 2.5-fold improvement in coupling efficiency relative to a standard slit-groove structure. Also, the transmission distance for the new nanostructure is shown to be more than 8 times greater than that of the standard nanostructure.     

Azimuthally asymmetric eigenmodes of a magnetized plasma cylinder around a dielectric rod in a circular waveguide

The electrodynamics of a circular waveguide with a dielectric rod surrounded by a magnetized plasma layer is considered. A general dispersion relation for azimuthally asymmetric perturbations is derived, and its solutions describing slow waves—specifically, electromagnetic and plasma modes, as well as (and primarily) hybrid waves that combine the properties of both mode types—are investigated numerically. For the fundamental waveguide mode of the system—the HE₁₁ mode—the parameters of the plasma layer are determined at which the mode cannot be subject to Cherenkov interaction with a relativistic electron beam at a given frequency. For both waveguide and plasma modes, the radial profiles of the longitudinal components of the electric field and Poynting vector, the fractions of RF power carried within the dielectric and plasma regions and vacuum gap, and the coupling impedance are calculated as functions of the parameters of the plasma layer. The evolution of the field structure during the formation of asymmetric hybrid waves is traced. The results of calculating the dispersion and coupling impedance are analyzed as applied to an antenna-amplifier—a relativistic traveling-wave tube operating on the HE₁₁ mode of the dielectric rod: specifically, the implementability of the concept in the presence of a plasma at the rod surface is estimated, and the possible role of azimuthally asymmetric and symmetric plasma modes is examined.     

Excitation of azimuthal surface modes by relativistic flows of electrons in the high-frequency range

Excitation of extraordinarily polarized azimuthal surface eigenwaves is shown to be possible in the frequency range above the upper hybrid resonance in waveguides with metal walls which are partially filled by cold magnetoactive plasma. Interaction of these waves with flows of electrons which rotate around the plasma column in the narrow gap separating the plasma from the wall of the waveguide is studied. Conditions of resonant interaction of the beam with the mentioned high-frequency azimuthal surface waves are shown by numerical methods to be reachable ones in the case of enough strong external magnetic fields without passing to the field of ultra-relativistic velocities of the beam.     

Excitation of high-frequency azimuthal surface waves by an annular electron beam in a waveguide with a noncircular interface of the plasma column

An initial stage of the interaction of an electron beam ring rotating along Larmor orbits in a gap between the plasma column and a circular metal chamber of a cylindrical waveguide with extraordinarily polarized electromagnetic waves of the surface type is studied. These waves propagate along the azimuthal angle across an axial magnetic field in the range above the upper hybrid frequency. Using numerical analysis of the dispersion relation, it is shown that by the aid of an appropriate choice of the shape of the plasmavacuum interface one can achieve a significant increasing of growth rates of the resonant beam instability of these waves.     

Robust and Tunable One-Way Magnetic Surface Plasmon Waveguide: An Experimental Demonstration

We have demonstrated experimentally a one-way magnetic surface plasmon (MSP) electromagnetic (EM) waveguide in the microwave range based on the magnetic photonic crystals (MPCs). The waveguide exhibits asymmetric transmission of EM waves in the frequency range near the MSP resonance for an MPC, such that a significant one-way propagation can be observed in the channel between the two MPC slabs, each in an external static magnetic field (ESMF) of opposite directions. The one-way waveguide is not only immune to interstitial metal defects but also robust against the disorder of rod position. Furthermore, its working frequency can be flexibly tuned by an ESMF, which makes it more favorable for the design of EM devices. The physics is related to the broken time-reversal symmetry of the MSP band states and the excitation of a giant circulation of the energy flow, similar to the case in the quantized Hall effect.     

Parametric excitation of surface waves at the boundary between a magnetized plasma and a metal

A study is made of the parametric excitation of potential surface waves propagating in a planar plasma-metal waveguide structure in a magnetic field perpendicular to the plasma-metal boundary. An external, spatially uniform, alternating electric field at the second harmonic of the excited wave is used as the source of parametric excitation. A set of equations is derived that describes the excitation of surface waves due to the onset of decay instability. Expressions for the growth rates in the linear stage of instability are obtained, and the threshold amplitudes of the external electric field above which the parametric instability can occur are found. Analytic expressions for the saturation amplitudes are derived with allowance for the self-interaction of each of the excited waves and the interaction between them. The effect of the plasma parameters and the strength of the external magnetic field on the saturation amplitude, growth rates, and the threshold amplitudes of the pump electric field are analyzed.