Abstract
This paper analyzes transversal small-scale perturbations in arbitrary three-dimensional (3D) spatially nonuniform space plasma systems with magnetic surfaces and deduces a system of equations for these perturbations. It shows that a dipole magnetic field can have perturbations of two different polarizations. Within dipole geometry, it derives equations for MHD-eigenmodes and investigates stability of the perturbations.
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References
B. B. Kadomtsev, “Hydromagnetic Stability of Plasma,” in Reviews of Plasma Physics, Ed. by M. A. Leontovich (Gosatomizdat, Moscow, 1963), No. 2, pp. 132–176 [in Russian].
B. B. Kadomtsev, Collective Phenomena in a Plasma (Nauka, Moscow, 1988) [in Russian].
I. A. Kremenetskii and O. K. Cheremnykh, Cosmic Weather: Mechanisms and Demonstrations (Naukova Dumka, Kiev, 2009) [in Russian].
A. B. Mikhailovskii, Theory of Plasma Instabilities (Atomizdat, Moscow, 1977; Consultants Bureau, New York, 1974).
O. P. Pogutse and E. I. Yurchenko, “Balloning Effects and Plasma Stability in Tokamak,” in Reviews of Plasma Physics, Ed. by B. B. Kadomtsev (Energoizdat, Moscow, 1987) [in Russian].
V. D. Pustovitov and V. D. Shafranov, “The Equilibrium and Stability of the Plasma in Stellarotors,” in Reviews of Plasma Physics, Ed. by B. B. Kadomtsev (Energoizdat, Moscow, 1987) [in Russian].
Yu. T. Tsap, Yu. G. Kopylova, and A. V. Stepanov, “Ballooning Instability and Oscillations of Coronal Loops,” Astron. Zh. 83, 1142–1152 (2006) [Astron. Rep. 50, 1026 (2006)].
O. K. Cheremnykh, “To the Question on Resonant MHD-Perturbations in Magnetospheric plasma,” Kosm. Nauka Tekhnol. 16, 57–63 (2010).
I. B. Bernstein, E. A. Frieman, M. D. Kruskal, and R. M. Kulsrud, “An Energy Principle for Hydromagnetic Stability Problems,” Proc. R. Soc. London A 244, 17–40 (1958).
C. Z. Cheng, T. C. Chang, C. A. Lin, and W. H. J. Tsai, “Magnetihydrodynamic Theory of Field Line Resonances in the Magnetosphere,” J. Geophys. Res. A 98, 11339–11347 (1993).
O. K. Cheremnykh, “Transversally Small-Scale Perturbations in Arbitrary Plasma Configurations with Magnetic Surfaces,” Plasma Phys. Control. Fusion 52 (2010).
O. K. Cheremnykh and A. S. Parnovkski, “Flute and Ballooning Modes in the Inner Magnetosphere of the Earth: Stability and Influence of the Ionospheric Conductivity,” in Space Science: New Research, Ed. by N. S. Maravell (Nova Sci., New York, 2006), pp. 71–108.
O. Cheremnykh, A. Pranowski, and O. Burdo, “Ballooning Modes in the Inner Magnetosphere of the Earth,” Planet. Space Sci. 55, 1217–1229 (2004).
R. L. Dewar and A. H. Glasser, “Ballooning Mode Spectrum in General Toroidal Systems,” Phys. Fluids 26, 3038–3052 (1983).
T. I. Gold, “Motions in the Magnetosphere of the Earth,” J. Geophys. Res. 64, 1219–1226 (1959).
P. Guthbert, J. L. V. Lewandowski, H. J. Gardner, et al., “Toroidally Localized and Nonlocalized Ballooning Instabilities in a Stellarator,” Phys. Plasma 5, 2921–2931 (1998).
R. D. Hazeltine and J. D. Meiss, “Shear-Alfven Dynamics of Toroidally Confined Plasmas,” Phys. Rep. 121, 1–167 (1985).
O. A. Hurricane, B. H. Fong, S. C. Cowley, et al., “Substorm Detonation,” J. Geophys. Res. A 104, 10221–10231 (1999).
N. Nakajima, “High-Mode-Number Ballooning Modes in a Heliotron/Torsatron System. II. Stability,” Phys. Plasma 3, 4556–4567 (1996).
G. P. Spies, “Magnetohydrodynamic Stability Theory with Closed Magnetic Field Lines,” Phys. Fluids 17, 400–407 (1974).
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Original Russian Text © O.K. Cheremnykh, V.V. Danilova, 2011, published in Kinematika i Fizika Nebesnykh Tel, 2011, Vol. 27, No. 2, pp. 63–78.
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Cheremnykh, O.K., Danilova, V.V. Transversal small-scale MHD perturbations in space plasma with magnetic surfaces. Kinemat. Phys. Celest. Bodies 27, 98–108 (2011). https://doi.org/10.3103/S0884591311020036
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DOI: https://doi.org/10.3103/S0884591311020036