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Title: Contributions to the theory of magnetorotational instability and waves in a rotating plasma

Abstract

The one-fluid magnetohydrodynamic (MHD) theory of magnetorotational instability (MRI) in an ideal plasma is presented. The theory predicts the possibility of MRI for arbitrary {beta}, where {beta} is the ratio of the plasma pressure to the magnetic field pressure. The kinetic theory of MRI in a collisionless plasma is developed. It is demonstrated that as in the ideal MHD, MRI can occur in such a plasma for arbitrary {beta}. The mechanism of MRI is discussed; it is shown that the instability appears because of a perturbed parallel electric field. The electrodynamic description of MRI is formulated under the assumption that the dispersion relation is expressed in terms of the permittivity tensor; general properties of this tensor are analyzed. It is shown to be separated into the nonrotational and rotational parts. With this in mind, the first step for incorporation of MRI into the general theory of plasma instabilities is taken. The rotation effects on Alfven waves are considered.

Authors:
 [1];  [2];  [3];  [4];  [5];  [6];  [5];  [7];  [8];  [9];  [4]
  1. Russian Research Centre Kurchatov Institute, Institute of Nuclear Fusion (Russian Federation), E-mail: abmikh@list.ru
  2. Georgian National Astrophysical Observatory (Georgia), E-mail: j.lominadze@astro-ge.org
  3. Syzran Branch of Samara Technical University (Russian Federation)
  4. Brazilian Center for Physics Research (Brazil)
  5. Russian Research Centre Kurchatov Institute, Institute of Nuclear Fusion (Russian Federation)
  6. Russian Academy of Sciences, Space Research Institute (Russian Federation)
  7. National Academy of Sciences of Ukraine, Institute of Physics (Ukraine)
  8. Russian Academy of Sciences, Pulkovo Observatory (Russian Federation)
  9. University of Sydney, School of Physics (Australia)
Publication Date:
OSTI Identifier:
21075624
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Experimental and Theoretical Physics; Journal Volume: 106; Journal Issue: 1; Other Information: DOI: 10.1007/s11447-008-1013-4; Copyright (c) 2008 Pleiades Publishing, Ltd; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; ALFVEN WAVES; COLLISIONLESS PLASMA; DISPERSION RELATIONS; ELECTRIC FIELDS; MAGNETIC FIELDS; MAGNETOHYDRODYNAMICS; PERMITTIVITY; PLASMA INSTABILITY; PLASMA PRESSURE; ROTATING PLASMA; TENSORS

Citation Formats

Mikhailovskii, A. B., Lominadze, J. G., Churikov, A. P., Tsypin, V. S., Erokhin, N. N., Erokhin, N. S., Konovalov, S. V., Pashitskii, E. A., Stepanov, A. V., Vladimirov, S. V., and Galvao, R. M. O. Contributions to the theory of magnetorotational instability and waves in a rotating plasma. United States: N. p., 2008. Web. doi:10.1007/S11447-008-1013-4.
Mikhailovskii, A. B., Lominadze, J. G., Churikov, A. P., Tsypin, V. S., Erokhin, N. N., Erokhin, N. S., Konovalov, S. V., Pashitskii, E. A., Stepanov, A. V., Vladimirov, S. V., & Galvao, R. M. O. Contributions to the theory of magnetorotational instability and waves in a rotating plasma. United States. doi:10.1007/S11447-008-1013-4.
Mikhailovskii, A. B., Lominadze, J. G., Churikov, A. P., Tsypin, V. S., Erokhin, N. N., Erokhin, N. S., Konovalov, S. V., Pashitskii, E. A., Stepanov, A. V., Vladimirov, S. V., and Galvao, R. M. O. 2008. "Contributions to the theory of magnetorotational instability and waves in a rotating plasma". United States. doi:10.1007/S11447-008-1013-4.
@article{osti_21075624,
title = {Contributions to the theory of magnetorotational instability and waves in a rotating plasma},
author = {Mikhailovskii, A. B. and Lominadze, J. G. and Churikov, A. P. and Tsypin, V. S. and Erokhin, N. N. and Erokhin, N. S. and Konovalov, S. V. and Pashitskii, E. A. and Stepanov, A. V. and Vladimirov, S. V. and Galvao, R. M. O.},
abstractNote = {The one-fluid magnetohydrodynamic (MHD) theory of magnetorotational instability (MRI) in an ideal plasma is presented. The theory predicts the possibility of MRI for arbitrary {beta}, where {beta} is the ratio of the plasma pressure to the magnetic field pressure. The kinetic theory of MRI in a collisionless plasma is developed. It is demonstrated that as in the ideal MHD, MRI can occur in such a plasma for arbitrary {beta}. The mechanism of MRI is discussed; it is shown that the instability appears because of a perturbed parallel electric field. The electrodynamic description of MRI is formulated under the assumption that the dispersion relation is expressed in terms of the permittivity tensor; general properties of this tensor are analyzed. It is shown to be separated into the nonrotational and rotational parts. With this in mind, the first step for incorporation of MRI into the general theory of plasma instabilities is taken. The rotation effects on Alfven waves are considered.},
doi = {10.1007/S11447-008-1013-4},
journal = {Journal of Experimental and Theoretical Physics},
number = 1,
volume = 106,
place = {United States},
year = 2008,
month = 1
}
  • The one-fluid magnetohydrodynamic (MHD) theory of magnetorotational instability (MRI) in an ideal plasma is presented. The theory predicts the possibility of MRI for arbitrary {beta}, where {beta} is the ratio of the plasma pressure to the magnetic field pressure. The kinetic theory of MRI in a collisionless plasma is developed. It is demonstrated that as in the ideal MHD, MRI can occur in such a plasma for arbitrary {beta}. The mechanism of MRI is discussed; it is shown that the instability appears because of a perturbed parallel electric field. The electrodynamic description of MRI is formulated under the assumption thatmore » the dispersion relation is expressed in terms of the permittivity tensor; general properties of this tensor are analyzed. It is shown to be separated into the nonrotational and rotational parts. With this in mind, the first step for incorporation of MRI into the general theory of plasma instabilities is taken. The rotation effects on Alfven waves are considered.« less
  • The linear stability of a differential rotating magnetized plasma is analyzed in the collisionless approximation along with heat flux vector. The dispersion relation is derived and simplified cases are discussed with instability criteria presented. Anisotropic pressures are shown to not only alter the classical instability criterion but also induce new unstable regions. The shear rotating instability in a collisional magnetized plasma with a scalar kinetic pressure in the presence of self-gravitational effect is then considered. Three cases are discussed specifically according to the general dispersion relation. The effects of Jeans term and compressibility on the local shear instability induced bymore » differential rotation are examined and the analytic instability criteria are presented.« less
  • By using the two fluid and Maxwell equations, the properties of electromagnetic waves in a rotating positive-negative dusty magnetoplasmas are investigated. It is found that the cross-coupling between the equilibrium dust flows and the perturbed magnetic field produces a Lorentz force that separates positive and negative dust grains. A new dispersion relation is derived and analyzed numerically. The effects of the dust grain radius, the equilibrium streaming speed, Jeans frequency, and the rotational frequency on the behavior of the real and imaginary parts of the wave frequency are examined. It is found that for small dust grain radius, the growthmore » rate (the real frequency) increases (decreases) with the increase of the streaming dust speed and Jeans frequency. However, the dust rotational frequency does not have an important role in this case. For large dust grain radius, only the imaginary part of the wave frequency is presented. It is found that the rotational frequency (Jeans frequency and dust streaming speed) decreases (increase) the growth rate.« less
  • A theory of magnetorotational instability (MRI) allowing an equilibrium plasma pressure gradient and nonaxisymmetry of perturbations is developed. This approach reveals that in addition to the Velikhov effect driving the MRI due to negative rotation frequency profile, d{theta}{sup 2}/dr < 0, there is an opposite effect (the anti-Velikhov effect) weakening this driving (here, {theta} is the rotation frequency and r is the radial coordinate). It is shown that in addition to the Velikhov mechanism, two new mechanisms of MRI driving are possible, one of which is due to the pressure gradient squared and the other is due to the productmore » of the pressure and density gradients. The analysis includes both the one-fluid magnetohydrodynamic plasma model and the kinetics allowing collisionless effects. In addition to the pure plasma containing ions and electrons, the dusty plasma is considered. The charged dust effect on stability is analyzed using the approximation of immobile dust. In the presence of dust, a term with the electric field appears in the one-fluid equation of plasma motion. This electric field affects the equilibrium plasma rotation and also gives rise to a family of instabilities of the rotating plasma, called the dust-induced rotational instabilities.« less
  • The magnetorotational instability (MRI) in the Hall regime in a hot-electron plasma is analyzed. The dispersion relation is derived for a rotating plasma with both finite electron pressure and pressure anisotropy. It is pointed out that the former effect has to be taken into account in the Hall regime, for {beta} > or approx.l 1, where {beta} is the ratio of electron pressure to the magnetic field pressure. As a whole, the effects of order {beta} weaken or suppress the MRI. It is shown that in the presence of electron pressure anisotropy, a hybrid of MRI and anisotropic instability appears,more » and that anisotropy of type T{sub perpendicular}>T{sub parallel} is destabilizing, while T{sub parallel}>T{sub perpendicular} is stabilizing, where T{sub perpendicular} and T{sub parallel} are the perpendicular and parallel electron temperatures, respectively.« less