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.     

Theory of Electromagnetic Surface Waves in Plasma with Smooth Boundaries

A theory of nonpotential surface waves in plasma with smooth boundaries is developed. The complex frequencies of surface waves for plasma systems of different geometries and different profiles of the plasma density are calculated. Expressions for the rates of collisionless damping of surface waves due to their resonance interaction with local plasma waves of continuous spectrum are obtained. The influence of collisions in plasma is also considered.     

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.     

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.     

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.     

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.     

High-frequency surface waves at a plasma-metal interface: I. Linear model

A study is made of the dispersion properties of surface waves at a plasma-metal interface under thermodynamically nonequilibrium conditions such that a space charge sheath forms at the plasma boundary. In the simplest model, the sheath is described as a dielectric with a given permittivity. The wave parameters in a highly collisional plasma are discussed. The effect of interaction between waves propagating near the opposite plasma boundaries is considered, in particular, for space charge sheaths of different thicknesses. Conditions are determined under which the parameters of surface waves are substantially altered by the plasma-sheath geometric resonance.     

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.     

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.     

Dissipative surface waves in plasma

Debatable aspects of the theory of nonpotential surface waves propagating along the boundary of a dissipative medium with frequency dispersion are discussed. On the basis of the known theoretical results and theoretical analysis carried out in this work, a theory of surface waves that is valid for any dissipation of the perturbation energy in the medium is developed. It is shown that, if dissipation is sufficiently strong, there can be surface waves the physical nature and dispersion law of which differ radically from those of ordinary surface waves. The damping rate of such waves is low even at large dissipation in the medium, and their group and phase velocities exceed the speed of light. In particular, surface waves on the interface between vacuum and cold collisional electron plasma are considered. The existence of such surface waves for different media of laboratory and natural origin is discussed.     

Surface waves on the boundary of a conducting medium and their excitation by a relativistic electron beam

Excitation of surface waves by a relativistic electron beam propagating over a conducting cylindrical medium (metal or highly ionized plasma) is investigated theoretically. Dispersion relations describing the linear interaction of surface electromagnetic waves with a monoenergetic electron beam are derived, and the growth rates and spatial amplification factors of excited waves are determined. Condition for the nonlinear trapping of the beam electrons by a surface wave is used to determine the maximum amplitude of the excited wave and the optimal radiator length. The electric field of a surface wave excited by an electron beam is estimated for a particular case.     

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.     

Escape of electron Langmuir waves from a magnetized plasma

A study is made of electromagnetic oscillations of a plasma in open field line geometry (open magnetic devices). The oscillations that propagate from the critical surface and are originally of the nature of the electron Langmuir waves are shown to continuously change their nature and to escape from the plasma into vacuum in the form of electromagnetic waves. This phenomenon may give rise to wave energy losses from a thermodynamically nonequilibrium (unstable) plasma, e.g., a plasma penetrated by charged particle beams.     

Excitation of surface waves at a plasma boundary by a short laser pulse

The excitation of surface waves by a laser pulse as it crosses a vacuum-plasma interface is considered. Surface waves are excited by a vortex electric current that is generated at the plasma boundary by the ponderomotive force of the pulse. The question is considered of how the duration and transverse dimensions of the pulse affect the spatiotemporal distribution and the spectral and energy parameters of the excited surface waves.     

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.     

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.     

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.     

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.     

Effect of toroidal magnetic field variations on the spectra of azimuthal surface waves in metal waveguides entirely filled with plasma

The propagation of surface waves transverse to the circular axis of a toroidal magnetized metal waveguide entirely filled with a plasma is studied using perturbation theory. The distribution of the fields of these waves in such a waveguide structure is investigated. It is shown that the toroidicity introduces a second-order correction to the eigenfrequency of the surface waves.     

High-frequency surface waves at a plasma-metal interface: II. Dispersion of a nonlinear wave

A study is made of the dispersion properties of nonlinear surface waves propagating along a plasma-metal interface under conditions corresponding to the formation of a space charge sheath that equalizes the electron and ion fluxes to the wall. Oscillations of the plasma boundary under the action of the surface wave field are taken into account. It is shown that these oscillations are the main nonlinear mechanism for generating wave field harmonics and are analogous to the nonlinearity in the current-voltage characteristic of the space charge sheath. The effect of the nonlinearity on the dispersion properties of surface waves due to the relationship between the sheath thickness and wave amplitude is calculated with allowance for harmonic generation. The energy transported by surface waves under conditions typical of RF and microwave discharges is calculated.