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.     

Splitting of the modes of a low-frequency magnetosonic wave in a polydisperse dusty plasma

The properties of magnetosonic waves that propagate perpendicularly to the external magnetic field in a polydisperse dusty plasma and the frequencies of which are about the dust cyclotron frequency are analyzed. A dispersion relation containing integrals of functions of the dust grain radius is derived and investigated as a function of the parameters characterizing the polydisperse properties of dust. It is found that, in a polydisperse dusty plasma, the low-frequency magnetosonic mode splits into two branches. The first, lower frequency branch has a cutoff, while the higher frequency branch has a resonance. Between the two branches, there is a forbidden frequency range within which electromagnetic waves cannot propagate perpendicular to the magnetic field. The width of the forbidden frequency range is determined as a function of the slope of the distribution function of dust grains over radii and the interval within which the dust grain radii lie.     

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.     

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 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.     

Investigation of low-frequency waves in plasma-filled microwave oscillators

The excitation of microwave oscillations by an electron beam in a hybrid plasma waveguide—a slow-wave structure (a sequence of inductively coupled resonators) with a plasma-filled transport channel—is studied both experimentally and theoretically. It is shown that the governing role in the generation of microwaves and their transmission to a feeder line is played by the spatial and temporal plasma-density variations associated with low-frequency ion plasma oscillations. The microwave pressure gives rise to low-frequency plasma oscillations with a rise time shorter than their period. This nonlinear mechanism for the excitation of low-frequency oscillations has a threshold in terms of the microwave power. The unsteady character of the spatial distribution of the plasma density results in intermittent microwave generation and shortens the duration of microwave pulses.     

Generation of auroral kilometric radiation by a finite-size source in a dipole magnetic field

Generation, amplification, and propagation of auroral kilometric radiation in a narrow three-dimensional plasma cavity in which a weakly relativistic electron beam propagates is studied in the geometrical optics approximation. It is shown that the waves that start with a group velocity directed earthward and have optimal relation between the wave vector components determining the linear growth rate and the wave residence time inside the amplification region undergo the largest amplification. Taking into account the longitudinal velocity of fast electrons results in the shift of the instability domain toward wave vectors directed to the Earth and leads to a change in the dispersion relation, due to which favorable conditions are created for the generation of waves with frequencies above the cutoff frequency for the cold background plasma at the wave generation altitude. The amplification factor for these waves is lower than for waves that have the same wave vectors but are excited by the electron beams with lower velocities along the magnetic field. For waves excited at frequencies below the cutoff frequency of the background plasma at the generation altitude, the amplification factor increases with increasing longitudinal electron velocity, because these waves reside for a longer time in the amplification region.     

Dispersion properties of a magnetoactive plasma-filled waveguide in the vicinity of the upper hybrid frequency. Part II

The dispersion properties of a magnetoactive plasma-filled waveguide in the vicinity of the upper hybrid frequency ω₁ = (ω _p ² + ω _B ² )^1/2 (ω₁ ? δ < ω < ω₁) are studied. It is shown that, in this frequency range, the eigenmodes of the plasma-filled waveguide are represented by the families of EH and cyclotron HE modes, the interaction between which is weak everywhere except for the vicinities of certain points in the (ω, k _z ) plane. The equations describing the behavior of the dispersion curves in these vicinities are derived. It is shown that, as a result of the interaction, the high-frequency branches of EH modes acquire the cutoff frequencies corresponding to the high-order propagating HE modes. It is established that the anisotropic HE_+l mode can also interact with cyclotron HE modes. In this case, its dispersion curve enters the lower half-vicinity of the upper hybrid frequency, where it is modified due to the interaction, and then leaves it.     

On the theory of a Cherenkov relativistic plasma emitter with a coaxial electrodynamic system

A plasma microwave amplifier based on a relativistic electron beam in an electrodynamic system in the form of a coaxial waveguide with a thin tubular plasma in a strong external magnetic field has been considered. Dispersion relations for determining the spectra of plasma and beam waves in the coaxial waveguide, as well as the general dispersion relation describing beam-plasma interaction, have been obtained in the linear approximation. The frequency dependences of the spatial growth rates for different plasma radii and different plasma frequencies, as well as the characteristic frequencies of the plasma amplifier, have been obtained by numerically and analytically solving the dispersion relations. The parameters of the plasma amplifier and generator with the coaxial electrodynamic system have been estimated for their experimental implementation.     

ECE measurements via B-X-O mode conversion: A proposal to diagnose the q profile in spherical tokamaks

Generation of electron Bernstein waves by the ordinary-extraordinary-Bernstein (O-X-B) mode conversion process has been successfully demonstrated on W7-AS. According to Kirchoff’s law, the inverse process of plasma EC emission by B-X-O mode conversion at particular angles must take place in tokamak plasmas. The optical depth at electron cyclotron harmonics is generally very high for electron Bernstein waves in tokamak plasmas. Consequently the O-mode ECE spectrum measured below the plasma frequency will show steps in the emitted power when each EC harmonic coincides with the upper hybrid resonance zone, where the mode conversion occurs, giving a local measurement of the relationship between the total magnetic field and plasma density. In a spherical tokamak, there are several EC harmonics below the plasma frequency, so several such steps can be observed via the B-X-O mode conversion mechanism. This is a very promising way to get information about the q profile in ST plasmas.     

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.     

On the minimal set of plasma parameters to determine the dispersion law of electron whistler waves

The minimal sufficient set of plasma parameters is presented to describe the dispersion properties of electron whistler waves (helicons) in a wide frequency range above the ion cutoff frequency, provided that the wave frequency is significantly lower than the electron plasma frequency. When the gyrofrequency of the lightest ions is much higher than those of heavier ions, it is sufficient to know the relative content of the lightest ions, the highest ion cutoff frequency, the lower hybrid resonance frequency, and the electron gyro- and plasma frequencies. In this case, the frequency of electron whistler waves is determined by the upper root of the biquadratic equation derived, whereas the lower root corresponds to a resonant mode with its refractive index increasing when the frequency tends toward the highest ion gyrofrequency from below. The developed approach is also efficient in plasmas containing a substantial amount of negative ions and/or heavy dust particulates. The accuracy of the approximate solution of the total cold plasma dispersion relation is illustrated graphically.     

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.     

Dynamics of beam instability in a finite plasma volume: Numerical experiment

Results are presented from numerical simulations of the dynamics of beam instability in a finite plasma volume (plasma-filled cavity) in a weak magnetic field. It is shown that, in such a system, the low group velocity of the plasma waves excited by an electron beam can result in the generation and amplification of an electric field; strong electron heating in the axial region; and, as a consequence, the generation of a high potential at the axis. The quasistatic radial electric field so produced accelerates ions toward the periphery of the plasma column, forming a directed ion beam with an energy much higher than the thermal energy of the bulk plasma electrons.     

Nonlinear Nanowire Close to a Truncated Metallic Film: a Step Toward Nanosized Light Sources

A controllable nanosized light source based on nonlinear interaction of light and a semiconductor nanowire is proposed. Surface plasmon polariton (SPP) waves with different frequencies propagate along the upper and lower surfaces of a truncated metallic film and are scattered at its end face. A nanowire, in that vicinity, is pumped by the scattered light, and new harmonics are generated via second-order nonlinear optical effects. Green's function surface integral equation method is exploited to numerically calculate the electric field, the magnetic field, and the power of the generated frequency components. Results show that the power of the generated harmonics depends on the position and radius of the nanowire, thickness of the metallic film, as well as the wavelength of the incident SPP waves. On the other hand, by controlling the phase difference between incident SPP waves having the same frequencies, it is possible to manipulate the electric field pattern and also to change the power of the generated harmonics.     

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.     

Theory of longitudinal plasma waves with allowance for ion motion

A study is made of the propagation of steady-state large-amplitude longitudinal plasma waves in a cold collisionless plasma with allowance for both electron and ion motion. Conditions for the existence of periodic potential waves are determined. The electric field, potential, frequency, and wavelength are obtained as functions of the wave phase velocity and ion-to-electron mass ratio. Taking into account the ion motion results in the nonmonotonic dependence of the frequency of the waves with the maximum possible amplitudes on the wave phase velocity. Specifically, at low phase velocities, the frequency is equal to the electron plasma frequency for linear waves. As the phase velocity increases, the frequency first decreases insignificantly, reaches its minimum value, and then increases. As the phase velocity increases further, the frequency continues to increase and, at relativistic phase velocities, again becomes equal to the plasma frequency. Finally, as the phase velocity approaches the speed of light, the frequency increases without bound.     

Dispersion properties of a magnetoactive plasma-filled waveguide in the vicinity of the upper hybrid frequency. Part I

The dispersion properties of a magnetoactive plasma-filled waveguide in the vicinity of the upper hybrid frequency ω₁ = (ω _p ² + ω _B ² )^1/2 (ω₁ ≤ ω < ω₁ + δ) are studied. In this frequency range, the eigenfrequency spectrum and the structure of the waveguide eigenfields are difficult to analyze, because one of the transverse wavenumbers tends to infinity as the upper hybrid frequency is approached. It is shown that this problem can be solved by transforming the dispersion relation into a form independent of this transverse wavenumber. It is also found that the upper hybrid frequency itself can also be a solution to the dispersion relation. The influence of the properties of the magnetoactive plasma-filled waveguide on such solutions is studied. The structure of the fields for modes with frequencies equal to the upper hybrid frequency and an infinitely large absolute value of one of the transverse wavenumbers is analyzed.     

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.     

Effect of the microwave ponderomotive force on the development of the beam instability at different plasma and beam parameters

A study is made of the effect of the parameters of a beam and a plasma-filled waveguide in a traveling-wave tube amplifier on the stability of the amplification regime against the excitation of ion acoustic waves by the microwave ponderomotive force. It is shown that, in such an amplifier, the stability of the amplification of a microwave can be achieved by simultaneously increasing the density and energy of the electron beam.