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.     

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.     

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.     

Nonlinear theory of the excitation of azimuthal surface waves during dissipative instability

A theoretical study is made of the surface electromagnetic eigenmodes that are excited by an annular charged-particle beam due to dissipative instability and propagate across the external axial magnetic field in a cylindrical metal waveguide partially filled with plasma. A self-consistent set of differential equations for a cold low-density charged-particle beam moving above the plasma surface is constructed in the single-mode approximation and is solved numerically. It is shown that the larger the dissipation, the slower the instability growth rate and the larger the wave amplitude in the saturation stage of the instability. An increase in the transverse dimensions of a charged-particle beam results in a slower growth of the dissipative instability, in which case, however, the beam transfers a larger fraction of its kinetic energy to the wave.     

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.     

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.     

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.     

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.     

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.     

Waveguide regime of cyclotron maser instability in plasma regions of depressed density

The generation of auroral kilometric radiation from the Earth is studied in a waveguide model that describes the development of cyclotron maser instability in plasma regions of depressed density that have a finite length in one of the directions perpendicular to the magnetic field. A general dispersion relation for waves propagating in an arbitrary direction is derived. Numerical solutions to the dispersion relation show that the instability growth rate increases with wave vector component directed along a tangent to the source boundary in a plane perpendicular to the magnetic field. Waveguide eigenmodes are constructed, and it is shown that, in the general case, the electromagnetic field in the source has an asymmetric structure, the ratio of the electric field components in the source depends on the coordinates, and the electric field component transverse to the source boundary can substantially exceed the component parallel to the boundary. The results obtained are discussed from the standpoint of comparing them with satellite observational data.     

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).     

ECR heating of a dense plasma by helicon waves

Eigenmodes of an axisymmetric plasma column that is uniform along the magnetic field are investigated. It is shown that, as the plasma density increases, eigenmodes with frequencies close to the electron gyrofrequency tend to localize at the plasma periphery. This effect is likely to restrict the electron density at which the plasma can be heated by means of such modes. A theory is developed for the excitation of the eigenmodes of a plasma column in a weakly nonuniform magnetic field by an external antenna.     

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.     

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.     

Effect of the periodic ripple in an axial confining magnetic field on the Alfvén heating of a cylindrical plasma

In a uniform axial magnetic field, the structure of local Alfvén resonance and the resonant absorption of RF power are governed by collisions, finite ion Larmor radius effects, and electron inertia. It is shown that, in a cylindrical plasma in a constant, periodically rippled, axial magnetic field, the structure of Alfvén resonance and the absorption of RF power can strongly depend on the ripple amplitude. The conditions under which the effect in question is dominant are intrinsic, e.g., to the modular Wendelstein stellarators.     

Tearing instability in a tokamak with a noncircular cross section

Using a straight-column model to describe tokamak plasma with a noncircular cross section, it is shown how to (i) find the boundary of tearing instability from the condition of existence of a magnetohydrodynamic plasma equilibrium different from that of a straight cylinder by solving a two-dimensional linear boundary-value problem with a second-order equation with respect to the flux coordinate and (ii) find the spatial structure of the tearing mode and the corresponding effective Δ' when there is only one resonance magnetic surface in the plasma for a given axial wavenumber by solving some kind of a boundary-value problem for the perturbation. The proposed approach is illustrated by numerical calculations for the case of an elliptical cross section as an example.     

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.     

Structure of the controlled halo-current magnetic field in the T-10 tokamak

In the T-10 tokamak, the magnetic field spatially resonant with a helical MHD perturbation is generated using the controlled halo current supplied using a contact method in the scrape-off-layer plasma. This paper is concerned with studying the spatial structure of the halo current and its magnetic field. For this purpose, the magnetic field of the halo current was measured in one of the cross sections of the torus near the tokamak vacuum vessel wall. The spatial distribution of the magnetic field as a function of the halo current configuration was calculated in the cylindrical approximation. The terms proportional to the plasma pressure were disregarded. The configuration of the halo current and the spatial structure of its magnetic field were determined by comparing the calculated and experimental results.     

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.     

On the characteristic features of the magnetic field diffusion in an inhomogeneous plasma in the EMHD approximation

The magnetic field transport in a spatially inhomogeneous plasma is studied theoretically in the electron MHD approximation. A model problem with a given periodic plasma density profile is considered in plane geometry. In this case, the magnetic field is transported diffusively and the effective diffusion coefficient is determined by the geometric and time parameters of the perturbed density, as well as by the magnetization parameter. It is found that, under certain relationships between the parameters of the problem, there is a kind of resonant effect—a decrease in the plasma conductivity. The problem under consideration does not refer solely to plasma physics: the results obtained here can also be used to describe transport processes in other branches of physics.