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.     

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.     

Geometric properties of magnetic field lines on toroidal magnetic surfaces in the context of plasma equilibrium

An analysis of plasma equilibrium in a magnetic confinement system includes studies of how the shape of the magnetic surfaces is distorted with varying magnitude and profile of the plasma pressure. Such studies allow one, in particular, to determine the maximum β value consistent with equilibrium, β_eq, i.e., the maximum plasma pressure above which the equilibrium in a confinement system under analysis is impossible. Since the magnetic field lines form magnetic surfaces, their global relationship with equilibrium is obvious. Here, special attention is paid to a local relationship between equilibrium and geometric properties of the magnetic field lines.     

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.     

On the dispersion properties of waveguides filled with a magnetized plasma

A study is made of the dispersion properties of waveguides filled with a magnetized plasma. It is shown that the eigenmodes of the waveguides filled with a low-density magnetized plasma fall into two families, which are weakly coupled to one another at all frequencies, in particular, in the cyclotron resonance frequency range. These families differ in transverse wavenumbers and the modes in them have hybrid polarization. Attention is focused on the study of the modes that have predominantly TE polarization at frequencies close to the cutoff frequency. The dependence of the critical frequencies of the TE modes on the plasma frequency, as well as the influence of the plasma on the energy flux and energy density of these modes, is investigated. The effect of mode crowding (the existence of an arbitrarily large number of dispersion curves in a finite frequency range between the cyclotron frequency and the upper hybrid frequency) is examined in detail. The results obtained are used to analyze how the plasma affects the electromagnetic properties of the cavity of the 1-MW 140-GHz continuous-wave gyrotron developed at the Institute of Pulsed and Microwave Technology of the Research Center in Karlsruhe, Germany (Institut für Hochleistungsimpuls-und Mikrowellentechnik Forschungszentrum Karlsruhe) for plasma heating in the W7-X stellarator, which is being constructed in Greifswald, Germany.     

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).     

Choice of coordinates on a toroidal magnetic surface

Construction of global angular coordinates on an arbitrarily shaped toroidal surface is considered. It is shown that global orthogonal, isothermal, and semigeodesic geometric coordinates can always be introduced on a toroidal surface. Such coordinates can be rather efficient in solving problems of plasma equilibrium and stability in a magnetic field. At the same time, it is impossible to introduce global geodesic coordinates and coordinates based on curvature lines. It is proposed to use a magnetic analogy to search for transformations of global angular geometric coordinates that simplify the expression for the length element on an arbitrary toroidal surface. An algorithm for the computation of such coordinates is offered. With this approach, a “virtual” magnetic field such that its force lines, as well as the lines orthogonal to them, are closed is searched for on the toroidal surface. These lines comprise a geometric coordinate grid on an actual magnetic surface formed by the actual magnetic field.     

Propagation of MHD waves in a plasma in a sheared magnetic field with straight field lines

The propagation of MHD plasma waves in a sheared magnetic field is investigated. The problem is solved using a simplified model: a cold plasma is inhomogeneous in one direction, and the magnetic field lines are straight. The waves are assumed to travel in the plane perpendicular to the radial coordinate (i.e., the coordinate along which the plasma and magnetic field are inhomogeneous). It is shown that the character of the singularity at the resonance surface is the same as that in a homogeneous magnetic field. It is found that the shear gives rise to the transverse dispersion of Alfvén waves, i.e., the dependence of the radial component of the wave vector on the wave frequency. In the presence of shear, Alfvén waves are found to propagate across magnetic surfaces. In this case, the transparent region is bounded by two turning points, at one of which, the radial component of the wave vector approaches infinity and, at the other one, it vanishes. At the turning point for magnetosonic waves, the electric and magnetic fields are finite; however, the radial component of the wave vector approaches infinity, rather than vanishes as in the case with a homogeneous field.     

Effect of the external magnetic field on the MHD turbulence spectra

The turbulent properties of conducting fluids in an external constant magnetic field are known to change with increasing field strength. A study is made of the behavior of the second-order structural function of the velocity field in a homogeneous incompressible turbulent fluid in the presence of an external uniform magnetic field. It is shown that, depending on the magnetic field strength, there may be different governing parameters of the system in both the inertial and dissipative intervals of turbulence. This leads to new spectral scalings that are consistent with experimental ones.     

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.     

Monitoring of the plasma isotope composition by charge-exchange neutral fluxes in a rippled toroidal magnetic field

To determine the hydrogen isotope ratio in plasma from charge-exchange neutral fluxes, certain assumptions are traditionally adopted, the most restrictive of which concerns the form of the ion distribution function, which is usually assumed to be Maxwellian. For large tokamaks, however, additional analysis is required in order to determine the energy range in which distortions of the distribution function will not lead to errors in isotope ratio measurements. The possible influence of drift motion on the ion distribution function is considered. Experimental results obtained in the ASDEX-Upgrade tokamak are presented. The role this mechanism plays during the transition to the H-mode in the auxiliary heating regime is compared to that in the ohmic heating regime.     

Effect of viscosity on the plasma decay in a magnetic field

The effect of viscosity on the evolution of an axisymmetric plasma column in a longitudinal magnetic field is considered. It is found that, under the action of viscosity, the plasma density profile tends to become Gaussian.     

Relaxation of plasma rotation in toroidal magnetic confinement systems

A study is made of the relaxation of plasma rotation in nonaxisymmetric toroidal magnetic confinement systems, such as stellarators and rippled tokamaks. In this way, a solution to the drift kinetic equation is obtained that explicitly takes into account the time dependence of the distribution function, and expressions for the diffusive particle fluxes and longitudinal viscosity are derived that make it possible to write a closed set of equations describing the time evolution of the ambipolar electric field E and the longitudinal (with respect to the magnetic field) plasma velocity U₀. Solutions found to the set of evolutionary equations imply that the relaxation of these two parameters to their steady-state values occurs in the form of damped oscillations whose frequency is about 2v_T/R (where v_T is the ion thermal velocity and R is the major plasma radius) and whose damping rate depends on the ion-ion collision frequency and on the magnetic field parameters. In particular, it is shown that, for tokamaks with a slightly rippled longitudinal magnetic field, the frequency of oscillations in the range q>2 (where q is the safety factor) is, as a rule, much higher than the damping rate. For stellarators, this turns out to be true only of the central plasma region, where the helical ripple amplitude ? of the magnetic field is much smaller than the toroidal ripple amplitude δ=r/R.     

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.     

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.     

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.     

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.     

Formation of shock waves in a discharge plasma in the presence of a magnetic field

The effect of an external magnetic field on the dynamics of shock waves generated in an argon plasma due to both explosive processes on the cathode and expansion of the spark channel has been studied experimentally. It is shown that the expanding plasma of the cathode spot forms a shock wave and that the application of a longitudinal magnetic field decelerates the radial expansion of the cathode plasma. It is found that the intensities of some argon spectral lines increase in the presence of a magnetic field.     

Solitary fast magnetosonic waves propagating obliquely to the magnetic field in cold collisionless plasma

Solutions describing solitary fast magnetosonic (FMS) waves (FMS solitons) in cold magnetized plasma are obtained by numerically solving two-fluid hydrodynamic equations. The parameter domain within which steady-state solitary waves can propagate is determined. It is established that the Mach number for rarefaction FMS solitons is always less than unity. The restriction on the propagation velocity leads to the limitation on the amplitudes of the magnetic field components of rarefaction solitons. It is shown that, as the soliton propagates in plasma, the transverse component of its magnetic field rotates and makes a complete turn around the axis along which the soliton propagates.