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Axisymmetric magnetorotational instability in ideal and viscous laboratory plasmas

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Abstract

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.

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Authors and Affiliations

  1. Institute of Nuclear Fusion, Russian Research Centre Kurchatov Institute, pl. Kurchatova 1, Moscow, 123182, Russia

    A. B. Mikhailovskii, N. N. Erokhin, V. D. Pustovitov & S. V. Konovalov

  2. Kharadze Abastumani National Astrophysical Observatory, Kazbegi Ave. 2a, Tbilisi, 0160, Georgia

    J. G. Lominadze

  3. Nodia Institute of Geophysics, Aleksidze Str. 1, Tbilisi, 0193, Georgia

    J. G. Lominadze

  4. Syzran Branch of Samara Technical University, Sovetskaya ul. 45, Syzran, Samara Region, 446001, Russia

    A. P. Churikov

Authors
  1. A. B. Mikhailovskii
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  2. J. G. Lominadze
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  3. A. P. Churikov
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  4. N. N. Erokhin
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  5. V. D. Pustovitov
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  6. S. V. Konovalov
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Additional information

Published in Russian in Fizika Plazmy, 2008, Vol. 34, No. 10, pp. 908–917.

The text was submitted by the authors in English.

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Mikhailovskii, A.B., Lominadze, J.G., Churikov, A.P. et al. Axisymmetric magnetorotational instability in ideal and viscous laboratory plasmas. Plasma Phys. Rep. 34, 837–846 (2008). https://doi.org/10.1134/S1063780X08100048

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  • DOI: https://doi.org/10.1134/S1063780X08100048

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