Spatial distribution of the RF power absorbed in a helicon plasma source

The spatial distributions of the RF power absorbed by plasma electrons in an ion source operating in the helicon mode (ω _ci < ω < ω _ce < ω _pe ) are studied numerically by using a simplified model of an RF plasma source in an external uniform magnetic field. The parameters of the source used in numerical simulations are determined by the necessity of the simultaneous excitation of two types of waves, helicons and Trivelpiece-Gould modes, for which the corresponding transparency diagrams are used. The numerical simulations are carried out for two values of the working gas (helium) pressure and two values of the discharge chamber length under the assumption that symmetric modes are excited. The parameters of the source correspond to those of the injector of the nuclear scanning microprobe operating at the Institute of Applied Physics, National Academy of Sciences of Ukraine. It is assumed that the mechanism of RF power absorption is based on the acceleration of plasma electrons in the field of a Trivelpiece-Gould mode, which is interrupted by pair collisions of plasma electrons with neutral atoms and ions of the working gas. The simulation results show that the total absorbed RF power at a fixed plasma density depends in a resonant manner on the magnetic field. The resonance is found to become smoother with increasing working gas pressure. The distributions of the absorbed RF power in the discharge chamber are presented. The achievable density of the extracted current is estimated using the Bohm criterion.     

Current generation by helicons and lower hybrid waves in modern tokamaks and reactors ITER and DEMO. Scenarios, modeling and antennae

The innovative concept and 3D full-wave code modeling the off-axis current drive by radio-frequency (RF) waves in large-scale tokamaks, ITER and DEMO, for steady-state operation with high efficiency is proposed. The scheme uses the helicon radiation (fast magnetosonic waves at high (20–40) ion cyclotron frequency harmonics) at frequencies of 500–700 MHz propagating in the outer regions of the plasmas with a rotational transform. It is expected that the current generated by helicons, in conjunction with the bootstrap current, ensure the maintenance of a given value of the total current in the stability margin q(0) ≥ 2 and q(a) ≥ 4, and will help to have regimes with a negative magnetic shear and internal transport barrier to ensure stability at high normalized plasma pressure β _N > 3 (the so-called advanced scenarios) of interest for the commercial reactor. Modeling with full-wave three-dimensional codes PSTELION and STELEC showed flexible control of the current profile in the reactor plasmas of ITER and DEMO, using multiple frequencies, the positions of the antennae and toroidal wave slow down. Also presented are the results of simulations of current generation by helicons in the DIII-D, T-15MD, and JT-60AS tokamaks. Commercially available continuous-wave klystrons of the MW/tube range are promising for commercial stationary fusion reactors. The compact antennae of the waveguide type are proposed, and an example of a possible RF system for today’s tokamaks is given. The advantages of the scheme (partially tested at lower frequencies in tokamaks) are a significant decline in the role of parametric instabilities in the plasma periphery, the use of electrically strong resonator-waveguide type antennae, and substantially greater antenna-plasma coupling.     

Mechanism for ion acceleration along the normal to the axis of a beam-plasma discharge in a weak magnetic field

The mechanism responsible for the previously discovered phenomenon of acceleration of an ion flow along the normal to the axis of a beam-plasma discharge in a weak magnetic field is investigated. It is suggested that the ions are accelerated in the field of a helicon wave excited in the discharge plasma column. It is shown theoretically that, under actual experimental conditions, a helicon wave can be excited at the expense of the energy of an electron beam. The spectral parameters and spatial structure of the waves excited in a beam-plasma discharge in the frequency ranges of Langmuir and helicon waves are studied experimentally and are shown to be related to the parameters of the ion flow. Theoretical estimates are found to agree well with the experimental results.     

Effect of an External Magnetic Field on the Absorption Efficiency of the RF Power in a Spatially Bounded Inductive Plasma Source

The measured dependences of the equivalent plasma resistance on the external magnetic field (0–50 G) in a 46-cm-diameter RF inductive plasma source operating at frequencies of 2, 4, and 13.56 MHz and a power of 100–500 W are presented. The experiments were carried out in argon at pressures of 0.1–30 mTorr. The presence of the external magnetic field leads to the appearance of resonance domains of efficient RF power absorption corresponding to the conditions of resonance excitation of helicons coupled with Trivelpiece–Gould modes. It is shown that RF power absorption at frequencies of 2 MHz can be optimized by applying an external magnetic field corresponding to the domains of resonance absorption. The effect is enhanced with increasing operating frequency.     

Distinctive features of collisionless gradient drift instabilities in a high-β plasma in a highly nonuniform magnetic field

A set of Vlasov-Maxwell equations for collisionless electromagnetic drift instabilities of high-β plasma configurations with a nonuniform magnetic fields is solved. The effect of the transverse static magnetic field variation and magnetic field line curvature, as well as the plasma temperature and density gradients, is considered. It is shown that, in a nonuniform magnetic field, the behavior of the instabilities differs substantially from that in a uniform field. Electromagnetic modes propagating strictly transverse to the lines of the static magnetic field are analyzed in detail, and unstable solutions are obtained for both extraordinary and ordinary waves. Numerical results show that, in the latter case, instability occurs when the magnetic field decreases toward the periphery and the plasma temperature and density gradients are oppositely directed.     

Helicon plasma in a nonuniform magnetic field

The distributions of the electron density in a plasma produced by helicon waves and the correspond-ing wave amplitudes and phases are studied experimentally. The measurements were carried out in an argon plasma at a pressure of 3 mtorr and at an input RF power of up to 600 W. The magnetic field was caried in the range from 0 to 200 G. The efficiency of plasma production in both uniform and nonuniform fields is investigated. It is shown that, in a nonuniform magnetic field, the electron density can be substantially increased (up to 5×10¹² cm^?3) by placing an antenna in the region in which the magnetic field is weaker than in the main plasma.     

Near field of a loop antenna operating in plasma in the whistler frequency range

The structure of the RF magnetic field in the vicinity of a loop antenna operating in the whistler frequency range has been studied experimentally and theoretically. The experiments were performed over a wide frequency range at different values of the plasma density, electron temperature, and ambient magnetic field strength. It is shown that, when a loop antenna is smaller than the wavelength of a quasi-longitudinal whistler, the structure of the magnetic field of such an antenna is nearly the same as that of the field of a current-carrying loop in vacuum; otherwise, the RF field is localized near the antenna wire. The results of numerical calculations agree with the measured field distributions. The antenna field is calculated by expanding it in the eigenmodes of a magnetized plasma with allowance for not only propagating but also nonpropagating (exponentially decaying) waves, which make the main contribution to the near field. An analytic estimate of the depth to which the RF magnetic field of a loop antenna penetrates into the plasma is obtained.     

Modeling of the Excitation of Electron Bernstein Modes in Spherical Tokamaks

The possibility is studied of using electron cyclotron waves to heat plasmas and to drive currents in spherical tokamaks when the cutoff layer for the waves is located at the plasma edge. It is shown that, by optimizing the method for the excitation of electron cyclotron waves, it is possible to achieve conditions corresponding to the so-called “radio window” effect, i.e., conditions under which the efficient conversion of incident waves into Bernstein modes propagating toward the plasma center occurs already at the plasma edge. As an example, the parameters of multiwaveguide antennas capable of emitting directed penetrating radiation are calculated.     

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).     

Low-frequency electromagnetic instabilities caused by a rotating dust flow

Low-frequency electromagnetic waves propagating obliquely to an external magnetic field in a plasma with an anisotropic dust component are considered. The cold dust is assumed to have considerable longitudinal and transverse velocity components with respect to the magnetic field. A dispersion relation demonstrating that both fast and slow waves can be unstable is derived in the framework of kinetic theory. Mechanisms and consequences of these instabilities are discussed in the context of the problem of plasma transition into a turbulent state behind the shock front of a supernova.     

On the minimal set of plasma parameters to determine the dispersion law of electron whistler waves

The minimal sufficient set of plasma parameters is presented to describe the dispersion properties of electron whistler waves (helicons) in a wide frequency range above the ion cutoff frequency, provided that the wave frequency is significantly lower than the electron plasma frequency. When the gyrofrequency of the lightest ions is much higher than those of heavier ions, it is sufficient to know the relative content of the lightest ions, the highest ion cutoff frequency, the lower hybrid resonance frequency, and the electron gyro- and plasma frequencies. In this case, the frequency of electron whistler waves is determined by the upper root of the biquadratic equation derived, whereas the lower root corresponds to a resonant mode with its refractive index increasing when the frequency tends toward the highest ion gyrofrequency from below. The developed approach is also efficient in plasmas containing a substantial amount of negative ions and/or heavy dust particulates. The accuracy of the approximate solution of the total cold plasma dispersion relation is illustrated graphically.     

Nonlinear dynamics of Kelvin-Helmholtz instability in a finite-width plasma flow

The nonlinear stage of Kelvin-Helmholtz (KH) instability in a finite-width plane-parallel plasma flow is analyzed. The analysis is performed by means of two-dimensional numerical simulations with the use of ideal magnetohydrodynamic equations describing isothermal plasma flows propagating along the magnetic field. The influence of the magnetic field strength, the plasma temperature, and the ratio of the flow width to the width of the transition layer on the formation of vortex layers and large-scale flow perturbations is investigated. It is shown that, if the wavelength of periodic perturbations is shorter than the flow width, the symmetric and antisymmetric modes develop in a qualitatively similar manner. For waves with wavelengths longer than the flow width, the development of such modes is very different due to the mutual influence of the flow boundaries. Analysis of the development of instability at different values of the Alfvén Mach number M _A shows that long-lived vortices with a characteristic scale length on the order of the flow width appear in a weak magnetic field for both symmetric and antisymmetric modes; however, the vortex geometries for these modes are different. In a strong magnetic field, M _A ～ 5, the phase of vortex decay for both types of modes occurs faster than in a weak field; however, in the case of an antisymmetric mode, large-scale perturbations of the flow boundary are retained for a longer time. Analysis of the evolution of the initial disturbance produced by an ensemble of random small perturbations (noise) at different plasma temperatures shows that, for a flow width comparable with the width of the transition region, the development of KH instability is always antisymmetric in character and leads to well-developed large-scale perturbations of the flow as a whole. For a cold plasma with C _S < 0.5U (where C _S is the speed of sound and U is the flow velocity), in contrast to hot plasma with C _S > 0.5U, the development of KH instability leads to the growth of the antisymmetric mode even if the flow width is much larger than the width of the transition region.     

Formation and evolution of flapping and ballooning waves in magnetospheric plasma sheet

By adopting Lembége & Pellat’s 2D plasma-sheet model, we investigate the flankward flapping motion and Sunward ballooning propagation driven by an external source (e.g., magnetic reconnection) produced initially at the sheet center. Within the ideal MHD framework, we adopt the WKB approximation to obtain the Taylor–Goldstein equation of magnetic perturbations. Fourier spectral method and Runge–Kutta method are employed in numerical simulations, respectively, under the flapping and ballooning conditions. Studies expose that the magnetic shears in the sheet are responsible for the flapping waves, while the magnetic curvature and the plasma gradient are responsible for the ballooning waves. In addition, the flapping motion has three phases in its temporal development: fast damping phase, slow recovery phase, and quasi-stabilized phase; it is also characterized by two patterns in space: propagating wave pattern and standing wave pattern. Moreover, the ballooning modes are gradually damped toward the Earth, with a wavelength in a scale size of magnetic curvature or plasma inhomogeneity, only 1–7% of the flapping one; the envelops of the ballooning waves are similar to that of the observed bursty bulk flows moving toward the Earth.     

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.     

One-dimensional model of a helicon discharge

A simplified model describing the steady state of a helicon discharge in a low-pressure plasma is considered. The electron Langmuir frequency of the plasma produced by the discharge is shown to be much higher than the electron gyrofrequency. It is found that the gas medium is ionized and the electrons are heated primarily by the extraordinary mode. The calculated electron density depends nonmonotonically on the magnetic field, in agreement with the results of numerous experiments.     

Instability of a magnetic drift wave in the vicinity of the dust-ion hybrid resonance

Low-frequency electromagnetic waves propagating perpendicular to the gradients of the density and magnetic field in an inhomogeneous dusty plasma whose mass density is determined primarily by the dust component are analyzed. It is shown that, in analyzing the dispersion properties of inhomogeneous plasma, it is important to take into account the dynamic properties of ions in the vicinity of the dust-ion hybrid resonance. The conditions for the onset of instability of a magnetic drift wave are investigated for different relations between parameters of the inhomogeneity and the value of the Alfvén velocity. The differences from the previous results, as well as possible astrophysical applications, are discussed.     

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.     

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.     

Passage of electromagnetic waves through the critical surface

A study is made of the passage of electromagnetic waves through the critical surface at small angles between the plasma density gradient and the magnetic field. Expressions are derived for the transmission and reflection coefficients of electromagnetic oscillations that are periodic in the direction transverse to the density gradient. The penetration of wave beams is also analyzed. In the case of a wide beam, the incident and transmitted ray trajectories are shown to be mirror-image about the resonance surface. Behind the resonance surface, a narrow incident wave beam generates a beam propagating along the magnetic field.     

On the possibility of reflection of Alfvén waves in a curvilinear magnetic field

The propagation of Alfvén waves in a plasma immersed in a curvilinear magnetic field is investigated by using a 2D model. The waves are described by a 1D equation that formally coincides with the equation for the case of a quasi-uniform straight magnetic field with a modified Alfvén velocity that takes into account the longitudinal dependence of the Lame coefficients. It is shown that toroidal and poloidal Alfvén modes depend differently on the magnetic-field geometry. In the case of a 2D plane-parallel configuration of the magnetic field, poloidal modes are efficiently reflected from regions where the magnetic field lines sharply converge or diverge. This effect can result in the formation of open-field-line Alfvén quasi-resonators.