Flute mode instability of rotating plasma

The influence of rotation on flute instability is studied in the frame of one-fluid magnetohydrodynamics. We consider the simplest model of gravitating cylindrical plasma in the straight nonuniform magnetic field to simulate plasma behavior in mirrors. Using linear stability analysis, we derive dispersion equation and integral expression for the increment of instability. In virtue of this expression, it is shown that rotation itself appears to be destabilizing factor due to centrifugal effect; we prove the corresponding theorem in general. Eigenmode structure and the dependence of the threshold on the frequency of rotation are calculated for linear radial profile of the angular velocity.В рамках одножидкостной магнитной гидродинамики исследуется влияние вращения на желобковую неустойчивость. Предполагается простейшая модель цилиндрической гравитирующей плазмы в прямом неоднородном магнитном поле для моделирования поведения плазмы в зеркальных ловушках. С помощью линейного анализа получено дисперсионное уравнение и интегральное выражение для инкремента неустойчивости. Показано, что в данной постановке задачи вращение из-за центробежного эффекта является сугубо дестабилизирующим фактором; в общем случае доказывается соответствующая теорема. Для линейного радиального профиля угловой скорости вращения рассчитана структура собственных мод и зависимость порога неустойивости от частоты вращения.В рамках однорідинної магнітної гідродинаміки досліджується вплив обертання на желобкову нестійкість. Припускається простіша модель циліндричної гравітуючої плазми в прямому неоднорідному магнітному полі для моделювання поведінки плазми в дзеркальних пастках. За допомогою лінійного аналізу отримано дисперсійне рівняння й інтегральний вираз для інкремента нестійкості. Показано, що в такій постановці задачі обертання завдяки центробіжного ефекту є сугубо дестабілізуючим фактором; в загальному випадку доводиться відповідна теорема. Для лінійного радіального профілю кутової швидкості обертання розраховано структуру власних мод та залежність порога нестійкості від частоти обертання

Geodesic acoustic eigenmode for tokamak equilibrium with maximum of local GAM frequency

The geodesic acoustic eigenmode for tokamak equilibrium with the maximum of local GAM frequency is found analytically in the frame of MHD model. The analysis is based on the asymptotic matching technique. © 2013 Elsevier B.V

Response to Comment on Continuum modes in rotating plasmas: General equations and continuous spectra for large aspect ratio tokamaks' [Phys. Plasmas 19, 064701 (2012)]

The equations for the continuous spectra derived in our paper [V. P. Lakhin and V. I. Ilgisonis, Phys. Plasmas 18, 092103 (2011)] can be reduced to the matrix form used by Goedbloed [Phys. Plasmas 11, 28 (2004)]. It is shown that the assumptions made in our paper provide the elliptic flow regime and guarantee the existence of plasma equilibrium with nested magnetic surfaces of circular cross-section. The new results on magnetohydrodynamic instabilities of such tokamak equilibria obtained in our paper but absent in the paper by Goedbloed are emphasized. © 2012 American Institute of Physics

Low-frequency magnetohydrodynamic spectra of plasmas with anisotropic pressure in axisymmetric toroidal systems

The low-frequency ideal magnetohydrodynamic (MHD) spectra of anisotropic pressure plasmas in axisymmetric toroidal systems are analyzed. In the framework of the Chew-Goldberger-Low model, the continuum spectrum equations for the coupled localized Alfvén and slow magnetosonic modes are derived. The equations are applied to study the continuous spectra for low-pressure plasmas in large aspect ratio tokamaks. It is shown that for some classes of plasma equilibria the pressure anisotropy results in instability of continuous modes. Such an instability is due to anisotropic plasma stratification over poloidal angle on the magnetic surfaces. It takes place for both the zonal flow modes with (m, n) = 0 and the general electromagnetic modes with (m, n) ≠ 0. The latter are unstable only if they are localized near the rational magnetic surface. A stabilization of this instability due to the Alfvén effect is shown for the modes localized away from the rational magnetic surface. © 2018 Author(s)

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 Alfvén 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 Alfvén coupling effect is studied. © 2011 American Institute of Physics

On the generation of mean fields by small-scale electron magnetohydrodynamics turbulence

The problem of the generation of mean magnetic fields by small-scale turbulence within the framework of electron magnetohydrodynamics (EMHD) is considered. Two EMHD models are investigated, a two and one-half dimensional (2½D) model in which the magnetic field has all three spatial components but, due to a strong external field, depends only on two coordinates, and a fully three-dimensional (3D) model with an imposed stationary and homogeneous magnetic field. It is shown that in the case of 2½D turbulence two possible mechanisms are responsible for the generation of mean magnetic fields. The first one is similar to the a-effect in the MHD dynamo problem and is due to a nonzero helicity of the turbulence. The second one is related to the anisotropy of the turbulence, which can give rise to negative dissipation (resistivity, viscosity) of the mean field. The influence of electron inertia on the above effects is analyzed. Inertia results in a qualitative modification of the helicity effects and may lead to a change in sign of the turbulent viscosity. The criteria for the generation of mean magnetic fields are obtained. In the case of the 3D model, the generation of large-scale helicons by the small-scale helicon turbulence is studied within the framework of the adiabatic approximation. A closed set of equations for the evolution of both the magnetic field of the large-scale helicon and of the generalized action of the small-scale turbulence is obtained. The criterion for the resonant instability of a large-scale helicon due to its interaction with small-scale helicon turbulence is obtained

Response to Comment on Continuum modes in rotating plasmas: General equations and continuous spectra for large aspect ratio tokamaks' [Phys. Plasmas 19, 064701 (2012)]

The equations for the continuous spectra derived in our paper [V. P. Lakhin and V. I. Ilgisonis, Phys. Plasmas 18, 092103 (2011)] can be reduced to the matrix form used by Goedbloed [Phys. Plasmas 11, 28 (2004)]. It is shown that the assumptions made in our paper provide the elliptic flow regime and guarantee the existence of plasma equilibrium with nested magnetic surfaces of circular cross-section. The new results on magnetohydrodynamic instabilities of such tokamak equilibria obtained in our paper but absent in the paper by Goedbloed are emphasized. © 2012 American Institute of Physics

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 Alfvén 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 Alfvén coupling effect is studied. © 2011 American Institute of Physics

Low-Frequency Continuous MHD Spectrum of Toroidally Rotating Tokamak Plasmas with Anisotropic Pressure

Abstract: Continuous-spectrum equations for low-frequency ideal magnetohydrodynamic perturbations in toroidally rotating plasmas with anisotropic pressure in axisymmetric tokamaks are derived in the framework of the Chew–Goldberger–Low model. In the rotating coordinate system, these equations describe the toroidal coupling of Alfvén and slow magnetosonic modes due to the curvature of magnetic field lines, the pressure anisotropy, and the centrifugal and Coriolis effects. The derived general equations are applied to study the spectra of both the zonal flows and the general electromagnetic modes in low-pressure large-aspect-ratio tokamaks. The condition for the instability of zonal flows due to plasma stratification over the poloidal angle on a magnetic surface is obtained. It is shown that a similar instability takes place for the general modes localized in the vicinities of rational magnetic surfaces. Stabilization of this instability by the Alfvén effect for the modes localized far from rational surfaces is shown. © 2019, Pleiades Publishing, Ltd