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Dispersion equation for ballooning modes in two-component plasma

Published online by Cambridge University Press:  13 December 2013

D. A. Kozlov ,
N. G. Mazur ,
V. A. Pilipenko  and
E. N. Fedorov
D. A. Kozlov
Affiliation:
Institute of Solar-Terrestrial Physics, Irkutsk, Russia
N. G. Mazur
Affiliation:
Institute of Physics of the Earth, 123995 Moscow, Russia
V. A. Pilipenko*
Affiliation:
Space Research Institute, 117997 Moscow, Russia
E. N. Fedorov
Affiliation:
Institute of Physics of the Earth, 123995 Moscow, Russia
*
†Email address for correspondence: pilipenk@augsburg.edu
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Abstract

The ballooning magnetohydrodynamic (MHD) modes have been often suggested as a possible instability trigger of the substorm onset, and a mechanism of compressional waves in the outer magnetosphere and magnetotail. Commonly, these disturbances are characterized by the local dispersion equation that is widely applied for the description of ultra-low-frequency oscillatory disturbances and instabilities in the nightside magnetosphere. In realistic situations, especially in the inner magnetosphere, the magnetospheric plasma is composed of two components: background ‘cold’ plasma and ‘hot’ particles. The ballooning disturbances in a two-component plasma immersed into a curved magnetic field are described with the system of coupled equations for the Alfvén and slow magnetosonic (SMS) modes. We have reduced the basic system of MHD equations to the dispersion equation for the small-scale in transverse direction disturbances, and applied WKB approximation along a field line. As a result, we have derived a dispersion equation that can be used for geophysical applications. In particular, from this relationship the dispersion, instability threshold, and stop-bands of the Alfvén and SMS modes in two-component plasma have been examined.

Type
Papers
Information
Journal of Plasma Physics , Volume 80 , Issue 3 , June 2014 , pp. 379 - 393
Copyright
Copyright © Cambridge University Press 2013 

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References

REFERENCES

Agapitov, A. V., Cheremnykh, O. K. and Parnowski, A. S. 2007 Ballooning perturbations in the inner magnetosphere of the Earth: spectrum, stability and eigenmode analysis. Adv. Space Res. 41, 1682.Google Scholar
Cheng, C. Z. 2003 MHD field line resonances and global modes in three-dimensional magnetic fields. J. Geophys. Res. 108 (A1), 1002.Google Scholar
Cheng, C. Z. and Lin, C. S. 1987 Eigenmode analysis of compressional waves in the magnetosphere. Geophys. Res. Lett. 14, 884.Google Scholar
Cheng, C. Z. and Qian, Q. 1994 Theory of ballooning-mirror instabilities for anisotropic pressure plasmas in the magnetosphere. Geophys. Res. Lett. 99, 11193.CrossRefGoogle Scholar
Cheng, C. Z., Qian, Q., Takahashi, K. and Lui, A. T. Y. 1994 Ballooning-mirror instability and internally driven Pc 4-5 wave events. J. Geomagn. Geoelectr. 46, 997.Google Scholar
Cheremnykh, O. K. and Parnowski, A. S. 2004 The theory of ballooning perturbations in the inner magnetosphere of the Earth. Adv. Space Res. 33, 769–773.Google Scholar
Cheremnykh, O. K. and Parnowski, A. S. 2006 Influence of ionospheric conductivity on the ballooning modes in the inner magnetosphere of the Earth. Adv. Space Res. 37, 599–603.CrossRefGoogle Scholar
Du, J., Zhang, T. L., Nakamura, R., Wang, C., Baumjohann, W., Du, A. M., Volwerk, M., Glassmeier, K.-H. and McFadden, J. P. 2011 Mode conversion between Alfvén and slow waves observed in the magnetotail by THEMIS. Geophys. Res. Lett. 38, L07101.Google Scholar
Golovchanskaya, I. V. and Maltsev, Y. P. 2005 On the identification of plasma sheet flapping waves observed by Cluster. Geophys. Res. Lett. 32, L02102.Google Scholar
Golovchanskaya, I. V. and Mingalev, O. V. 2006 Propagation of the ballooning waves in the Earth's magnetotail. In: Proc. 29th Ann. Sem. on ‘Physics of Auroral Phenomena', Apatity, 27 February–3 March 2006. Apatity: Kola Science Centre RAS, pp. 126–132.Google Scholar
Hurricane, O. A., Fong, B. H., Cowley, S. C., Coroniti, F. V., Kennel, C. F. and Pellat, R. 1999 Substorm detonation. J. Geophys. Res. 104, 10221–10232.Google Scholar
Ivanov, V. N., Pokhotelov, O. A., Feygin, F. Z., Roux, A., Perrot, S. and Lekau, D. 1992 Balloon instability in the Earth's magnetosphere under non-constant pressure and finite β. Geomagn. Aeronomy 32, 68–74.Google Scholar
Keiling, A. 2009 Alfvén waves and their roles in the dynamics of the Earth's magnetotail: a review. Space Sci. Rev. 142, 73–156.CrossRefGoogle Scholar
Klimushkin, D. Yu. 1998 Theory of azimuthally small-scale hydromagnetic waves in the axisymmetric magnetosphere with finite plasma pressure. Ann. Geophys. 16, 303–321.CrossRefGoogle Scholar
Klimushkin, D. Yu. and Mager, P. N. 2008 On the spatial structure and dispersion of slow magnetosonic modes coupled with Alfvén modes in planetary magnetospheres due to field line curvature. Planet. Space Sci. 56, 1273.CrossRefGoogle Scholar
Klimushkin, D. Yu., Mager, P. N. and Pilipenko, V. A. 2012 On the ballooning instability of the coupled Alfvén and drift compressional modes. Earth Planets Space 64, 777–781.CrossRefGoogle Scholar
Liu, W. W. 1997 Physics of the explosive growth phase: ballooning instability revisited. J. Geophys. Res. 102, 4927–4931.CrossRefGoogle Scholar
Mager, P. N., Klimushkin, D. Yu., Pilipenko, V. A. and Schafer, S. 2009 Field-aligned structure of poloidal Alfvén waves in a finite pressure plasma. Ann. Geophys. 27, 3875–3882.Google Scholar
Mazur, N. G., Fedorov, E. N. and Pilipenko, V. A. 2012 Dispersion relation for ballooning modes and condition of their stability in near-Earth plasma. Geomagn. Aeronomy 52, 603–612.Google Scholar
Miura, A., Ohtani, S. and Tamao, T. 1989 Ballooning instability and structure of diamagnetic waves in a model magnetosphere. J. Geophys. Res. 94, 15231.Google Scholar
Nakamizo, A. and Iijima, T. 2003 A new perspective on magnetotail disturbances in terms of inherent diamagnetic processes. J. Geophys. Res. 108, 1286.Google Scholar
Ohtani, S. and Tamao, T. 1993 Does the ballooning instability trigger substorms in the near-Earth magnetotail? J. Geophys. Res. 98, 19369–19379.Google Scholar
Panov, E. V., Sergeev, V. A., Pritchett, P. L., Coroniti, F. V., Nakamura, R., Baumjohann, W., Angelopoulos, V., Auster, H. U. and McFadden, J. P. 2012 Observations of kinetic ballooning/interchange instability signatures in the magnetotail. Geophys. Res. Lett. 39, L08110.Google Scholar
Pokhotelov, O. A., Buloshnikov, A. M. and Pilipenko, V. A. 1980 Hydromagnetic instability of the outer border of the trapped radiation. Geomagn. Aeronomy 20, 419–424.Google Scholar
Pokhotelov, O. A., Pilipenko, V. A. and Amata, E. 1985 Drift-anisotropy instability of a finite-beta magnetospheric plasma. Planet. Space Sci. 33 (11), 1229–1241.Google Scholar
Pritchett, P. L. and Coroniti, F. V. 2010 A kinetic ballooning/interchange instability in the magnetotail. J. Geophys. Res. 115, A06301.Google Scholar
Pritchett, P. L. and Coroniti, F. V. 2011 Plasma sheet disruption by interchange-generated flow intrusions. Geophys. Res. Lett. 38, L10102.Google Scholar
Raeder, J., Zhu, P., Ge, Y. and Siscoe, G. 2010 Open Geospace General Circulation Model simulation of a substorm: axial tail instability and ballooning mode preceding substorm onset. J. Geophys. Res. 115, A00I16.Google Scholar
Roux, A., Perraut, S., Robert, P., Morane, A., Pedersen, A., Korth, A., Kremser, G., Aparicio, B., Rodgers, D. and Pellinen, R. 1991 Plasma sheet instability related to the westward travelling surge. J. Geophys. Res. 96, 17697–17714.CrossRefGoogle Scholar
Safargaleev, V. V. and Maltsev, Yu. P. 1986 Internal gravity waves in the plasmasheet. Geomagn. Aeronomy 26, 220–223.Google Scholar
Southwood, D. J. and Saunders, M. A. 1985 Curvature coupling of slow and Alfvén MHD waves in a magnetotail field configuration. Planet. Space Sci. 33, 127–134.Google Scholar
Tsap, Y. T., Kopylova, Y. G., Stepanov, A. V., Melnikov, V. F. and Shibasaki, K. 2008 Ballooning instability in coronal flare loops. Solar Phys. 253, 161–172.Google Scholar
Walker, A. D. M. 1987 Theory of magnetospheric standing hydromagnetic waves with large azimuthal wave number 1. Coupled Magnetosonic and Alfvén waves. J. Geophys. Res. 92, 10039–10045.Google Scholar
Zhu, P., Raeder, J., Germaschewski, K. and Hegna, C. C. 2009 Initiation of ballooning instability in the near-Earth plasma sheet prior to the 23 March 2007 THEMIS substorm expansion onset. Ann. Geophys. 27, 1129–1138.Google Scholar