V.P. Lakhin

On the theory of Alfven vortices

The revision of the previous theory of shear Alfven vortices in a homogeneous plasma is given. In the previous papers the solutions were not matched adequately on the singular line of the vortex so that they do not satisfy the charge conservation law. The influence of the magnetic viscosity on the character of the admitted discontinuities in the shear Alfven vortices is studied. The nonlinear equations of the shear Alfven waves in the usual approximation of cold ions and also with allowance for the ion temperature are obtained. The solution, in the form of the dipole vortex with spatially decreasing amplitude, is found. The specific character of the solution obtained consists of a power decrease of the transverse potential on sufficiently far vortex periphery. It is shown that the integral characteristics of the vortices (energy, generalized enstrophy) are finite. The numerical analysis of the solution obtained is performed.

Continuum modes in rotating plasmas: General equations and continuous spectra for large aspect ratio tokamaks

A theory for localized low-frequency ideal magnetohydrodynamical (MHD) modes in axisymmetric toroidal systems is generalized to take into account both toroidal and poloidal equilibrium plasma flows. The general set of equations describing the coupling of shear Alfven and slow (sound) modes and defining the continuous spectrum of rotating plasmas in axisymmetric toroidal systems is derived. The equations are applied to study the continuous spectra in large aspect ratio tokamaks. The unstable continuous modes in the case of predominantly poloidal plasma rotation with the angular velocity exceeding the sound frequency are found. Their stabilization by the shear Alfven coupling effect is studied.

Fluid theory and simulations of instabilities, turbulent transport and coherent structures in partially-magnetized plasmas of discharges

Partially-magnetized plasmas with magnetized electrons and non-magnetized ions are common in Hall thrusters for electric propulsion and magnetron material processing devices. These plasmas are usually in strongly non-equilibrium state due to presence of crossed electric and magnetic fields, inhomogeneities of plasma density, temperature, magnetic field and beams of accelerated ions. Free energy from these sources make such plasmas prone to various instabilities resulting in turbulence, anomalous transport, and appearance of coherent structures as found in experiments. This paper provides an overview of instabilities that exist in such plasmas. A nonlinear fluid model has been developed for description of the Simon-Hoh, lower-hybrid and ion-sound instabilities. The model also incorporates electron gyroviscosity describing the effects of finite electron temperature. The nonlinear fluid model has been implemented in the BOUT++ framework. The results of nonlinear simulations are presented demonstrating turbulence, anomalous current and tendency toward the formation of coherent structures.

Revision of the theory of drift solitons

Abstract The theory of drift solitons is revised. It is concluded that drift solitons may exist in a plasma with a homogeneous temperature but there is a nonvanishing lower threshold in the amplitude.

Electron drift solitons in an inhomogeneous magnetized plasma

Abstract It is shown that electron drift solitons can exist in an inhomogeneous magnetized plasma. Two such types of solitons are discussed, one which is similar to the solitons described by the one-dimensional Korteweg-de Vries equation, and a second which is an analog of the two-dimensional Rossby solitons.

Global geodesic acoustic mode in a tokamak with positive magnetic shear and a monotonic temperature profile

The analytical solution for global geodesic acoustic modes (GGAMs) in a tokamak with a positive magnetic shear profile and a monotonic temperature profile is found in the framework of magnetohydrodynamic theory. The axisymmetric eigenvalue problem for perturbed pressure and electrostatic potential is formulated as a recurrent set of equations for poloidal Fourier harmonics. The integral condition for the existence of GGAMs is obtained. It is shown that the traditional paradigm of having a off-axis maximum of the local geodesic acoustic frequency is not necessary for the existence of GGAMs; a representative example is designed.

Geodesic acoustic modes and zonal flows in rotating large-aspect-ratio tokamak plasmas

The effect of equilibrium plasma rotation (toroidal and poloidal) on low-frequency, electrostatic modes—the geodesic acoustic modes (GAMs) and the zonal flows (ZFs)—in large aspect ratio tokamaks is studied within the framework of ideal MHD. It is shown that the plasma rotation results in a frequency up-shift of the ordinary GAM. The new branch of continuum modes induced by the poloidal rotation is found. This mode originates from the opposite sign Doppler shift of frequency due to poloidal rotation for m = ±1 poloidal side-band harmonics of the perturbed mass density, pressure and parallel velocity. In the case of slow poloidal rotation (ΩP cs/qR0) its frequency is close to the sound frequency cs/qR0 (ΩP is the poloidal angular velocity, cs is the speed of sound, q is the safety factor and R0 is the major radius of tokamak). The mode can be called the rotation-induced acoustic mode. This mode disappears in the case of purely toroidal plasma rotation. The frequency of the new mode in the case of relatively slow poloidal rotation (ΩP ≤ cs/qR0) is lower than the frequency of the ordinary GAM modified by plasma rotation. In the case of larger poloidal angular velocities ΩP (ΩP ≥ 2cs/qR0) the mode becomes unstable and is identified as the unstable ZF. With a further increase in the poloidal angular velocity at constant toroidal angular velocity the instability is suppressed, and the mode turns again into a marginally stable, oscillating mode.

Finite ion Larmour radius effects in the problem of zonal flow generation by kinetic drift-Alfvén turbulence

A theory of spontaneous generation of zonal flows by kinetic drift-Alfven turbulence in the finite-pressure plasma (β > m e /m i ) is generalized to include the ion diamagnetic effects and the finite ion Larmour radius effects. In the framework of the corresponding set of generalized two-fluid magnetohydrodynamic equations and on the assumption of a distinct time- and space-scale separation between the turbulent oscillations and the zonal flow, a set of coupled equations is derived to describe the interaction between the turbulence and the flow, consisting of the evolution equation for the spectral function of turbulence and the mean-field equations for zonal flow. The possibility of spontaneous zonal flow generation by the kinetic drift-Alfven turbulence is investigated in details in several cases. In the case of kinetic drift-Alfven turbulence with the space scale of the order of the ion Larmour radius or below, the instability caused by the resonant interaction of the wave packet with the slow modulations of zonal flow has been analysed, and the criterion for the onset of the zonal flow instability has been derived. In the case of short-wavelength turbulence, two regimes are considered. It is shown, that, when the frequency of short-wavelength oscillations is close to the electron-drift frequency and the zonal perturbation of plasma density can be described by the Boltzmann Law, the instability criterion is a generalization of the previously obtained result to the case of non-equal temperatures of the ions and electrons. The new regime is found, in which the zonal perturbation of plasma density is negligible. The condition for the onset of resonant instability is obtained.

One-fluid approach to the theory of viscous-resistive ballooning modes in a Tokamak. I. The averaged ballooning equations

The one-fluid approach to the theory of viscous-resistive ballooning modes in a Tokamak is developed. Qualitative ideas about essential viscous effects (inertia renormalization and viscous resistive effect) are given. A procedure for simplifying the MHD equations in a resistive layer, which takes into account viscosity and other typical effects, is described. The weakly ballooning approximation is used for averaging the ballooning equations. The equations obtained are a generalization of a number of different particular cases of ballooning equations obtained by previous authors.

Current-vortex filaments in magnetized plasmas

Current-vortex filament solutions to the two-fluid plasma equations that describe drift-Alfven waves are presented. Such filament systems are Hamiltonian. Integrable three and four filament systems are discussed in some detail. A wide variety of orbit topologies exists in the plasma case. Special attention is paid to collapses where all filaments contract to a single point. The differences and extensions with respect to point vortex solutions in two-dimensional (2D) incompressible Euler systems is pointed out.