Nonlocal theory of the spectra of modified ion cyclotron oscillations in a charged plasma produced by gas ionization

The problem of the stability of a charged plasma cylinder in crossed longitudinal magnetic and radial electric fields is considered under the assumption that the plasma electrons are magnetized and distributed uniformly in space and that the plasma ions have a low density and move without collisions. By using the Vlasov and Poisson equations for the electric and magnetic fields of arbitrary strengths and by expanding the radial eigenfunctions in Bessel functions, a dispersion relation is obtained for the modified ion cyclotron frequencies. The dispersion relation obtained is solved for the case of hot plasma electrons. At low ion densities, the oscillation spectra are stable and are described by the families of dispersion curves lying closely around the harmonics of the modified cyclotron frequency (including the zeroth harmonic). At higher ion densities, the dispersion curves for the frequencies of the lowest radial oscillation modes in neighboring families can intersect, leading to instability. The maximum instability growth rate can be several tenths of the modified ion cyclotron frequency.     

Nonstationary kinetic theory of ion transport in plasma with small perturbations

A theory of charged particle transport for small potential perturbations in a fully ionized plasma is developed on the basis of solving a linearized kinetic equation with the Landau collision integral. This theory is free of any constraints on the characteristic time and spatial scales of perturbations. Ion fluxes appropriate for an arbitrary ion-ion collision frequency that can ensure nonlocal space-time transport in the plasma are calculated. The obtained ion transport coefficients are used to calculate the partial contribution of ions to the longitudinal permittivity of collisional plasma. The resulting expression for the plasma permittivity is applicable in the entire range of frequencies and wavenumbers.     

Peculiarities of collisionless drift instabilities in poloidal magnetic configurations

Results of the numerical analysis of collisionless drift instabilities as applied to magnetic configurations with a purely poloidal magnetic field are presented. Instabilities caused by the gradients of the ion and electron temperatures and plasma density are considered within a wide range of wavenumbers. An electromagnetic model taking into account the finite plasma pressure and magnetic field curvature is formulated for configurations with a nonuniform magnetic field.     

Oscillation spectrum of an electron gas with a small density fraction of ions

The problem is solved of the stability of a nonneutral plasma that completely fills a waveguide and consists of magnetized cold electrons and a small density fraction of ions produced by ionization of the atoms of the background gas. The ions are described by an anisotropic distribution function that takes into account the characteristic features of their production in crossed electric and magnetic fields. By solving a set of Vlasov-Poisson equations analytically, a dispersion equation is obtained that is valid over the entire range of allowable electric and magnetic field strengths. The solutions to the dispersion equation for the m = +1 main azimuthal mode are found numerically. The plasma oscillation spectrum consists of the families of Trivelpiece-Gould modes at frequencies equal to the frequencies of oblique Langmuir oscillations Doppler shifted by the electron rotation and also of the families of “modified” ion cyclotron (MIC) modes at frequencies close to the harmonics of the MIC frequency (the frequencies of radial ion oscillations in crossed fields). It is shown that, over a wide range of electric and magnetic field strengths, Trivelpiece-Gould modes have low frequencies and interact with MIC modes. Trivelpiece-Gould modes at frequencies close to the harmonics of the MIC frequency with nonnegative numbers are unstable. The lowest radial Trivelpiece-Gould mode at a frequency close to the zeroth harmonic of the MIC frequency has the fastest growth rate. MIC modes are unstable over a wide range of electric and magnetic field strengths and grow at far slower rates. For a low ion density, a simplified dispersion equation is derived perturbatively that accounts for the nonlocal ion contribution, but, at the same time, has the form of a local dispersion equation for a plasma with a transverse current and anisotropic ions. The solutions to the simplified dispersion equation are obtained analytically. The growth rates of the Trivelpiece-Gould modes and the behavior of the MIC modes agree with those obtained by numerical simulation.     

Effects of finite heat conductivity on instabilities in a rotating plasma

Analytical theory of magnetorotational and convective instabilities in a rotating cylindrical plasma with finite heat conductivity is developed and discussed. The heat conductivity is incorporated into the standardized equations of the regular magnetohydrodynamic approach to studying these instabilities. A case of high-β plasma (β is the ratio of plasma pressure to the magnetic field pressure) and the modes with parallel phase velocity much smaller than the sound velocity is particularly emphasized and considered in the quasi-incompressible approximation. It is shown that this approximation is more adequate than the Boussinesq approximation. Both these approximations lead to the same results for aperiodical instabilities of the axisymmetric modes which are hybrids of the magnetorotational and convective instabilities. On the other hand, the Boussinesq approximation overlooks the heat-conductivity-induced instabilities predicted by the quasi-incompressible approximation describing the dissipative excitation of the slow magnetoacoustic and Alfvén waves. Non-axisymmetric aperiodical instabilities are considered. It is shown that, for such modes, the role of convective instabilities is greater than for the magnetorotational instability.     

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.     

Low-frequency instabilities of collisionless plasma and the 16-moment approximation

Using the 16-moment equations that take into account heat fluxes in anisotropic collisionless plasma, the properties of magnetohydrodynamic (MHD) instabilities are investigated. For all instabilities occurring in the MHD approach (the normal incompressible firehose instability, the second compressible almost longitudinal firehose instability, and the almost transverse mirror instability of slow magnetosonic modes, as well as thermal instability caused by the heat flux directed along the magnetic field), their kinetic analogs are considered. The kinetic dispersion relation in the low-frequency range in the vicinity of the ion thermal velocity is analyzed. The flow of plasma ions along the magnetic field is taken into account. The thresholds and instability growth rates obtained in the MHD and kinetic approaches are found to be in good agreement. This indicates that the 16-moment MHD equations adequately describe the dynamics of collisionless plasma.     

Axisymmetric magnetorotational instability in ideal and viscous laboratory plasmas

The original analysis of the axisymmetric magnetorotational instability (MRI) by Velikhov (Sov. Phys. JETP 9, 995 (1959)) and Chandrasekhar (Proc. Nat. Acad. Sci. 46, 253 (1960)), applied to the ideally conducting magnetized medium in the laboratory conditions and restricted to the incompressible approximation, is extended by allowing for the compressibility. Thereby, two additional driving mechanisms of MRI are revealed in addition to the standard drive due to the negative medium rotation frequency gradient (the Velikhov effect). One is due to the squared medium pressure gradient and another is a combined effect of the pressure and density gradients. For laboratory applications, the expression for the MRI boundary with all the above driving mechanisms and the stabilizing magnetoacoustic effect is derived. The effects of parallel and perpendicular viscosities on the MRI in the laboratory plasma are investigated. It is shown that, for strong viscosity, there is a family of MRI driven for the same condition as the ideal one. It is also revealed that the presence of strong viscosity leads to additional family of instabilities called the viscosity-driven MRI. Then the parallel-viscositydriven MRI looks as an overstability (oscillatory instability) possessing both the growth rate and the real part of oscillation frequency, while the perpendicular-viscosity MRI is the aperiodical instability. Published in Russian in Fizika Plazmy, 2008, Vol. 34, No. 10, pp. 908–917. The text was submitted by the authors in English.     

Nonlocal transport in hot plasma. Part II

The second part of the review, the first part of which was published earlier in Plasma Phys. Rep. 39, 698 (2013), is presented. A wide range of electromagnetic phenomena in laser plasma under nonlocal transport conditions requiring kinetic consideration are described. Among them, there are nonlocal transport in magnetized plasma, absorption and penetration of laser radiation in dense plasma, nonlocal effects related to inverse-bremsstrahlung heating and ponderomotive interaction, plasma fluctuations caused by a speckled laser beam, propagation of laser radiation and parametric instabilities in low-density plasma, and ion-acoustic instability of the return current. Many results are applicable for arbitrary relations between the characteristic spatial and time scales of the plasma parameters, which substantially advances the concept of laser-plasma interaction in hot plasma as compared to the conventional theories of collisionless and strongly collisional plasmas.     

On the influence of Alfvén resonance on ion cyclotron resonance heating

Physical processes determining the excitation of RF electromagnetic fields in a plasma column in a magnetic field are analyzed. The Alfvén resonance plays an important role at frequencies close to the ion cyclotron frequency. It leads to the enhancement of the RF electric field and transformation of Alfvén oscillations with a predominantly transverse polarization of the electric field into lower hybrid ones, which have a significant longitudinal component of the electric field. Lower hybrid oscillations efficiently interact with electrons causing their heating. Difficulties in the implementation of ion cyclotron resonance heating by the magnetic beach method are outlined. The processes considered in this work can be important for the VASIMR plasma engine.     

Linear theory of electron cyclotron instability of electromagnetic waves in a magnetoactive plasma waveguide

The linear stage of electron cyclotron instability of quasi-TE modes in a waveguide filled with a magnetoactive plasma is studied using a kinetic approach. The dispersion relation of the instability is derived analytically. It is shown that the presence of the plasma can reduce both the linear instability growth rate and the instability region; in this case, the maximum of the growth rate is displaced toward lower frequencies. The results obtained are compared with the available experimental observations. They can be useful for optimizing the operating regimes of high-power continuous-wave gyrotrons.     

Stability of hybrid modes of a single-component electron plasma containing an admixture of background gas ions

The spectrum of eigenmodes of a waveguide completely filled with a cold electron plasma containing a small admixture of ions produced due to electron-impact ionization of background gas atoms is calculated numerically. The calculations were performed within the entire range of allowable values of the radial electric and longitudinal magnetic fields for both magnetized and unmagnetized ions by using the earlier derived nonlocal dispersion relation [Plasma Phys. Rep. 36, 563 (2010)]. The spectrum consists of three families of electron modes with frequencies equal to the Doppler-shifted upper and lower hybrid frequencies and modified ion cyclotron (MIC) modes. When the Doppler shift caused by electron rotation in the crossed electric and magnetic fields compensates for the hybrid frequency, the electron modes become low-frequency modes and interact with the ion modes. For m = 1, only the lower hybrid modes can be low-frequency ones, whereas at m ≥ 2, both lower and upper hybrid modes can be low-frequency ones. The spectrum of modes having the azimuthal number m = 2 is thoroughly analyzed. It is shown that, in this case, the lower hybrid modes behave similar to the m = 1 modes. The dispersion curves of the upper hybrid modes intersect with all harmonics of the MIC frequency (positive, negative, and zero) and are unstable in the vicinities of the intersections. The maximum value of the instability growth rate is several times higher than the ion plasma frequency. The MIC modes are unstable within a wide range of the field strengths, and their growth rates are two orders of magnitude slower. Instabilities are caused by the relative motion of electrons and ions (the transverse current) and the anisotropy of the ion distribution function.     

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.     

Particle diagnostics of ion cyclotron resonance plasma heating in the Globus-M tokamak

Basic experimental results on cyclotron heating of the ion plasma component in the Globus-M spherical tokamak obtained by means of the ACORD-12 charge-exchange ion analyzer are presented. A procedure for determining the maximum energy of fast ions confined in the plasma is described. The procedure was applied to estimate the limiting energy of hydrogen minority ions accelerated during ion cyclotron heating in the Globus-M tokamak. The experimental evaluation of the maximum hydrogen ion energy is confirmed by simulations of ion orbits. Recommendations for optimizing experiments on ion cyclotron heating in the Globus-M tokamak are formulated.     

Nonlineart theory of relativistic beam-plasma instabilities in the regime of the collective Cherenkov effect

A general mathematical model is proposed that is based on the Vlasov kinetic equation with a self-consistent field and describes the nonlinear dynamics of the electromagnetic instabilities of a relativistic electron beam in a spatially bounded plasma. Two limiting cases are analyzed, namely, high-frequency (HF) and low-frequency (LF) instabilities of a relativistic electron beam, of which the LF instability is a qualitatively new phenomenon in comparison with the known Cherenkov resonance effects. For instabilities in the regime of the collective Cherenkov effect, the equations containing cubic nonlinearities and describing the nonlinear saturation of the instabilities of a relativistic beam in a plasma are derived by using the methods of expansion in small perturbations of the trajectories and momenta of the beam electrons. Analytic expressions for the amplitudes of the interacting beam and plasma waves are obtained. The analytical results are shown to agree well with the exact solutions obtained numerically from the basic general mathematical model of the instabilities in question. The general mathematical model is also used to discuss the effects associated with variation in the constant component of the electron current in a beam-plasma system.     

Quasilinear modification of the spectra of cyclotron emission from a toroidal plasma near the ECRH frequency

A study is made of the modification of the spectra of electron cyclotron emission from an ECR heated plasma in a toroidal magnetic confinement system into which the heating radiation is launched from the low-field side. It is shown that, at frequencies close to the heating frequency, cyclotron emission can become more intense because of the deformation of the distribution function of the resonant electrons. This effect can be used to diagnose the slightly pronounced quasilinear perturbations of the electron distribution in the thermal energy range, which are typical of experiments on ECR plasma heating. Results of a qualitative analysis carried out for model electron distribution functions are presented, and examples of three-dimensional numerical simulations of a circular tokamak are described.     

Helicon plasma source in the ion-acoustic frequency range

A helicon plasma source operating in the ion cyclotron frequency range is studied theoretically. It is shown that, even with a purely inductive antenna exciting a helicon wave in a plasma at ion-acoustic frequencies, the effective resistance characterizing the absorption of high-frequency field energy is determined by the ion-acoustic field generated by the helicon wave. Calculations show that such a plasma source can operate very efficiently.     

Classification of the regimes of Cherenkov beam instabilities in plasma waveguides

The regimes of the instabilities of an annular relativistic electron beam in a waveguide with an annular plasma are systematically analyzed and classified. The growth rates of the instabilities are calculated different limiting cases, and the resonance conditions for the development of the instabilities are determined. The fastest growing instability of a high-current relativistic electron beam in a waveguide with a dense plasma is considered. The possible onset of a low-frequency instability of a beam in a waveguide with a low-density plasma is investigated. Typical examples of how the growth rates depend on the perturbation wavenumbers are presented for systems with parameters close to the experimental ones.     

On the nature of global plasma oscillations in a tokamak. Part II: Spatial structure and propagation of perturbations observed at the T-10 tokamak

Large-scale plasma oscillations (so-called MHD oscillations) observed at the T-10 tokamak are investigated. The central electron cyclotron heating was used to enhance oscillations at the m/n = 1/1 mode with the goal of determining the internal characteristics of the process. The spatially resolved electron cyclotron emission diagnostics allowed analyzing the propagation characteristics of plasma perturbations. The experiments have revealed that excitation of oscillations in a particular mode occur simultaneously in the entire area located within the corresponding rational magnetic surface. The propagation of plasma perturbations along the torus is found to be inhomogeneous. The electron cyclotron emission diagnostics allowed finding eigen (resonance) frequencies of plasma oscillations from the parameters of their inhomogeneous propagation in the plasma core and comparing them with spectra of oscillations of the magnetic field induced by the plasma current in the edge plasma, which were recorded by magnetic probes. It is established that the frequencies of eigenmodes are independent of the electron temperature, plasma density, and auxiliary heating power. Even spatial harmonics of the principal magnetic surface are observed under strong excitation of oscillations. The rational magnetic surfaces that determine oscillation harmonics retain their position during the entire steady-state phase of the total plasma current in spite of the strong sharpening of the temperature profile due to central heating.     

Theory of the ICR heating of a plasma column: Methodological note

A set of wave equations is derived that describes electromagnetic waves at frequencies on the order of the ion gyrofrequency in a plasma column with an arbitrary electron temperature. This set takes into account, in particular, the resonant interaction of electrons with waves in the transit-time magnetic pumping regime. The effect of the amplification of the electromagnetic fields of current-carrying antennas by the plasma is analyzed. The evolution of the fields with an increase of plasma density from a zero value (vacuum) is considered. The main parameters are determined for minority ion cyclotron resonance heating in the planned EPSILON system.