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.     

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.     

On reverberatory processes in homogeneous neuronal spaces

Reverberating neural activity is strictly defined and examined in continuous and discrete neuronal spaces with homogeneous structure. Reverberations start with a specific population of firing neurons called the initial excitation and spread out in waves of firing and refractory bands of neurons toward the periphery. The necessary and sufficient conditions for having reverberations are obtained for continuous space and discrete one-dimensional space. The excitation fronts of reverberating waves have stable shapes which depend only upon the structure of the neuronal space. The reverberatory processes in high-threshold discrete neuronal spaces show strongly nonlinear properties. Relation between reverberations and nervous functions is discussed.     

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.     

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.     

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.     

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.     

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.     

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.     

Self-consistent model of a pulsed air discharge excited by surface waves

A complete self-consistent electrodynamic model of a pulsed gas discharge excited by surface waves is developed. The model allows one to calculate both the initial phase of the discharge front propagation and the parameters of the produced plasma. The spatiotemporal evolution of the electromagnetic field and plasma parameters at the discharge front is investigated for the first time. It is shown that discharge propagation is mainly governed by a breakdown wave in an inhomogeneous electric field at the leading edge of the ionization front. It is found that the effect of the electric field enhancement in the plasma resonance region significantly affects the velocity of the breakdown wave. The results of calculations agree well with experimental data.     

Nonresonant excitation of surface waves by a normal electric field

A study is made of nonresonant parametric excitation of surface waves by a spatially uniform, time-dependent electric pump field directed perpendicular to a plane plasma-dielectric interface. A set of equations is derived that describes the dynamics of surface wave excitation. Expression for the growth rate in the linear stage of instability is obtained, and the threshold amplitude of the external electric field above which the parametric instability can occur is found. The spectrum of the excited waves is analyzed. Published in Russian in Fizika Plazmy, 2006, Vol. 32, No. 11, pp. 994–998. The article was translated by the author.     

Amplification of surface waves in a plasma waveguide by a straight relativistic electron beam in a finite magnetic field

The problem of the excitation of electron waves in a thin-walled annular cold plasma in a cylindrical waveguide by a straight relativistic electron beam in a finite magnetic field is considered. The dispersion properties of a waveguide system with parameters close to the experimental ones are investigated. It is shown that the growth rate of the excited high-frequency plasma wave is comparable to that of the low-frequency wave, which is weakly sensitive to the strength of the longitudinal magnetic field.     

Cherenkov Excitation of Spatial Waves by a Straight Nonrelativistic Electron Beam in a Plasma Waveguide

The problem of the excitation of plasma waves by a thin-walled annular electron beam in a waveguide filled entirely with a plasma is analyzed in the quasistatic approximation. The instability growth rates are derived and are studied as functions of the waveguide parameters. The evolution of different seed perturbations in the nonlinear stage of the instability is investigated.     

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.     

Polarization splitting of the Alfvén wave spectrum in a dipole magnetosphere with a rotating plasma

Alfvén waves in a dipole magnetosphere with a rotating plasma are studied theoretically. The plasma-motion-related properties of azimuthally small-scale standing Alfvén waves having nearly poloidal or nearly toroidal polarization are analyzed. Equations are obtained that describe the longitudinal (along the magnetic field) structure and spectra of the waves having such polarizations. The equations obtained are then solved both analytically (in the Wentzel-Kramers-Brillouin approximation) and numerically. Attention is focused on the polarization splitting of the spectrum—the difference between the eigenfrequencies of the toroidally and poloidally polarized Alfvén waves. The distribution of this difference in a direction across the magnetic shells is analyzed. It is shown that, unlike in the models in which the plasma is assumed to be at rest, taking into account rotation of the magnetosphere plasma results in an additional splitting of the spectrum of the poloidal Alfvén waves due to the difference in their azimuthal mode numbers.     

Effect of Long-Wavelength Magnetic Field Disturbances on the Generation of Auroral Kilometric Radiation

The effect of long-wavelength magnetic field disturbances typical of the Earth’s auroral region on the generation of auroral kilometric radiation in a narrow three-dimensional plasma cavity in which a weakly relativistic electron flow propagates against the background of cold low-density plasma is analyzed. The dynamics of the propagation and amplification of fluctuation waves with initial group velocities directed toward the higher magnetic field is considered in the geometrical optics approximation. Analysis of wave trajectories shows that the wave amplification coefficients depend on the magnetic field gradient in the reflection region. If the wave reflection point lies in the region where the gradient of the disturbed magnetic field is less than that of the undisturbed dipole field, then the wave amplification coefficients exceed those of waves propagating in the undisturbed field, and vice versa. Thus, the shape of the spectrum of generated waves changes in the presence of long-wavelength disturbances of the dipole magnetic field in such a way that segments with different curvatures can form in the spectrum.     

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.     

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 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.     

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.