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.     

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.     

Ray trajectories near the electron cyclotron resonance surface in an axisymmetric magnetic trap

Characteristic features of the propagation of electromagnetic electron cyclotron waves in the vicinity of the electron cyclotron resonance surface are investigated both analytically and numerically with allowance for variation in the magnetic field strength and a corresponding variation in the magnetic field direction. It is demonstrated that variation in the magnetic field direction can qualitatively change the wave propagation pattern and can markedly affect the efficiency of electron cyclotron resonance plasma heating in an axisymmetric magnetic trap.     

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.     

Resonant effect of the noncircular shape of the plasma surface on the dispersion properties of extraordinary azimuthal surface modes in magnetoactive waveguides

A theoretical study is made of the resonant effect of the shape of the cross section of the plasma column on the propagation of a packet of extraordinary electromagnetic waves with a zero axial wavenumber in a circular-cross-section cylindrical metal waveguide in an axial magnetic field. The waveguide is assumed to be partially filled with a plasma. The effect of the noncircular shape of the plasma cross section on the dispersion properties of surface eigenmodes propagating strictly transverse to the external magnetic field is investigated by the method of successive approximations for the case in which the angular period of the wave perturbations is twice the ripple period of the interface between the plasma and the dielectric. In this resonant case, the fields and eigenfrequencies of the eigenmodes are determined to second order in the small parameter describing the rippling of the plasma-dielectric interface.     

Excitation of waves in an inhomogeneous plasma

The evolution of initial perturbations in a spatially inhomogeneous cold electron plasma in the absence of an external magnetic field is considered. The excitation of both continuous-spectrum bulk plasma waves and surface plasma waves with a discrete frequency spectrum is investigated. Analytic solutions are obtained in the long-wavelength limit, and the excitation of waves of arbitrary length is analyzed numerically. The local, integral, and spatial spectra are calculated, as well as the field structures and dispersion properties of waves in waveguides filled nonuniformly with a plasma. It is shown that, in a plasma with a smooth boundary, there also exist surface waves with a discrete spectrum (although with somewhat different properties as compared to those in a plasma with a sharp boundary), which are excited together with continuous-spectrum bulk waves during the evolution of the initial perturbation.     

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.     

Coupled transverse modes of coaxial metal waveguides completely filled with magnetoactive current-carrying plasma

The propagation of ordinary bulk modes coupled with extraordinary surface modes in coaxial metal waveguides completely filled with cold magnetoactive plasma is investigated theoretically. The interaction between modes propagating across the waveguide axis in the presence of the axial and azimuthal components of the external magnetic field is examined. The effect of the azimuthal magnetic field on the dispersion properties of these modes is thoroughly studied for the case of a uniform plasma.     

On the Spectra of Natural Waves in a Plasma Waveguide in the Presence of Collisions

Plasma Physics Reports - The dispersion characteristics of surface and evanescent waves in ф metal–dielectric–plasma–dielectric–metal structure in the presence of...     

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.     

Diagnostics of a magnetized plasma by the field of surface waves guided by a discharge channel

A diagnostic method for determining plasma density from the dispersion of surface waves guided by a discharge channel in an axial magnetic field is discussed. The diagnostic characteristics that are the easiest to record experimentally are determined by analyzing the theoretical dispersion curves, and the ways of exploiting these characteristics for plasma diagnostics are suggested. To determine the slowing-down factor of a probing wave in a plasma channel, it is proposed to use diagnostic-signal resonances that occur when the wavelength of the slowed wave becomes equal to the length of the emitting or receiving antenna. The dependence of the plasma density averaged over the cross section of the plasma column on the strength of the external magnetic field is determined for a discharge channel formed as a result of the ionization self-channeling of plasma (lower hybrid) waves and whistlers.     

Asymmetric long-wavelength surface modes of isotropic plasma waveguides

A theoretical study is made of the dispersion properties of electromagnetic surface waves with arbitrary azimuthal mode numbers and a small axial wavenumber in cylindrical isotropic waveguides partially filled with plasma. The plasma is assumed to be cold and radially inhomogeneous, and the problem is solved in the hydrodynamic approximation. The eigenfrequency of the waves is investigated as a function of the plasma parameters, the width and the permittivity of the dielectric gap between the metal waveguide wall and the plasma column, the axial wavenumber, and the azimuthal mode number. It is shown that the axial phase velocities of asymmetric surface modes are higher than the speed of light in a dielectric and that the surface modes do not propagate in a waveguide with a vanishingly small width of the dielectric gap. The theory developed is employed in practice in the calculation of the electrodynamic model of a gas discharges maintained by asymmetric long-wavelength surface modes. The power absorbed by the gas-discharge plasma in the regimes of Ohmic damping and resonant damping is calculated, and the plasma produced during the discharge is shown to be azimuthally homogeneous.     

Electromagnetic wave in a relativistic magnetized plasma

Results are presented from a theoretical investigation of the dispersion properties of a relativistic plasma in which an electromagnetic wave propagates along an external magnetic field. The dielectric tensor in integral form is simplified by separating its imaginary and real parts. A dispersion relation for an electromagnetic wave is obtained that makes it possible to analyze the dispersion and collisionless damping of electromagnetic perturbations over a broad parameter range for both nonrelativistic and ultrarelativistic plasmas.     

Nonlinear Right-Hand Polarized Wave in Plasma in the Electron Cyclotron Resonance Region

The propagation of a nonlinear right-hand polarized wave along an external magnetic field in subcritical plasma in the electron cyclotron resonance region is studied using numerical simulations. It is shown that a small-amplitude plasma wave excited in low-density plasma is unstable against modulation instability with a modulation period equal to the wavelength of the excited wave. The modulation amplitude in this case increases with decreasing detuning from the resonance frequency. The simulations have shown that, for large-amplitude waves of the laser frequency range propagating in plasma in a superstrong magnetic field, the maximum amplitude of the excited longitudinal electric field increases with the increasing external magnetic field and can reach 30% of the initial amplitude of the electric field in the laser wave. In this case, the energy of plasma electrons begins to substantially increase already at magnetic fields significantly lower than the resonance value. The laser energy transferred to plasma electrons in a strong external magnetic field is found to increase severalfold compared to that in isotropic plasma. It is shown that this mechanism of laser radiation absorption depends only slightly on the electron temperature.     

Magnetosonic oscillations of thin plasma columns

Oscillations of a plasma column in a longitudinal magnetic field are considered. It is found that eigenmodes with frequencies close to the ion cyclotron frequency can be excited in columns the radii of which are smaller than the characteristic wavelength of magnetosonic oscillations predicted by the theory of homogeneous plasma. The eigenmodes have the form of waves running around the column axis in the direction of electron gyration in the magnetic field. Magnetosonic oscillations can be excited as a side effect when using helical antennas for ion cyclotron resonance heating of plasma. These oscillations should enhance electron heating in the plasma core, as well as both electron and ion heating at the periphery of the plasma column. The spectrum of eigenmodes of inhomogeneous plasma columns includes oscillations of different nature. Comparative analysis of their properties performed in the present paper is useful for understanding the full picture of the physical processes occurring during ion cyclotron resonance heating and clarifying the characteristic features of the magnetosonic oscillations under study.     

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).     

Multimode parametric instability during electron cyclotron heating

A study is made of the generation of electron Bernstein waves in the interaction of a microwave field with a magnetized plasma during electron cyclotron heating. Parametric resonance accompanied by simultaneous conversion of microwave-field energy into the energy of numerous waves is analyzed. The relevant dispersion relation is investigated using the Hill method, which has recently been applied for the first time to examine the parametric interaction between high-power microwave radiation and plasmas. It is shown that the dispersion relation can be used to describe the onset of modulational instability at multimode parametric resonance. The growth rate of the modulational instability is obtained. Efficient energy transfer from the microwave field into Bernstein modes and, accordingly, into plasma electrons may be one of the main mechanisms for electron cyclotron resonance plasma heating.     

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.     

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.