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Gauge condition for studying intrinsic magnetospheres

Published online by Cambridge University Press:  22 December 2015

Miller Mendoza  and
John Morales
Miller Mendoza*
Affiliation:
Departamento de Física, Universidad Nacional de Colombia, Bogotá, D.C., Colombia Computational Physics for Engineering Materials, Institute for Building Materials, ETH Zürich, Schafmattstrasse 6, HIF, CH-8093 Zürich, Switzerland
John Morales
Affiliation:
Departamento de Física, Universidad Nacional de Colombia, Bogotá, D.C., Colombia Centro Internacional de Física, Santafé de Bogotá, Colombia
*
†Email address for correspondence: [email protected]
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Abstract

We propose an analytical model based on the solution of the magnetohydrodynamics (MHD) equations for studying intrinsic magnetospheres. For this purpose, we introduce a new gauge condition for the electromagnetic vector potential, which simplifies the solution of this complex system of nonlinear equations. Using this model, we analyse the deformation of the terrestrial magnetic field due to the presence of the solar wind. By comparing the results with experimental observations, we find that our model reproduces with good agreement the geometrical configuration of the magnetosphere, and that the solar wind should have a finite conductivity. This model could also be used to perform linear stability analysis of fluid and magnetic instabilities. Finally, our solution is not limited to magnetospheric configurations but also applies to a steady-state incompressible and irrotational flow with large plasma parameter and small velocity fluctuations.

JFM classification

Geophysical and Geological Flows: Geophysical and Geological Flows Mathematical Foundations: Mathematical Foundations MHD and Electrohydrodynamics: MHD and Electrohydrodynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 788 , 10 February 2016 , pp. 118 - 128
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Copyright
© 2016 Cambridge University Press 

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References

Alexeev, I. I. 1978 Regular magnetic field in the Earth’s magnetosphere. Geomagn. Aeron. 18 (4), 656–665.Google Scholar
Arfken, G. B. & Weber, H. J. 2005 Mathematical Methods for Physicists. Elsevier.Google Scholar
Cowling, T. G. 1976 Magnetohydrodynamics. Adam Hilger.Google Scholar
David, J. J. 1966 Electrodinámica clásica, 1st edn. Editorial Alhambra S.A.Google Scholar
Fisk, L. A. & Sari, J. W. 1973 Correlation length for interplanetary magnetic field fluctuations. J. Geophys. Res. 78 (28), 6729–6736.Google Scholar
Frey, H. U., Phan, T. D., Fuselier, S. A. & Mende, S. B. 2003 Continuous magnetic reconnection at Earth’s magnetopause. Nature 426 (6966), 533–537.Google Scholar
Grad, H. & Rubin, H. 1958 Hydromagnetic equilibria and force-free fields. J. Nucl. Energy 7 (3), 284–285.Google Scholar
Hilmer, R. V & Voigt, G.-H. 1995 A magnetospheric magnetic field model with flexible current systems driven by independent physical parameters. J. Geophys. Res. Space Phys. 100 (A4), 5613–5626.CrossRefGoogle Scholar
Jordan, C. E. 1994 Empirical models of the magnetospheric magnetic field. Rev. Geophys. 32 (2), 139–157.CrossRefGoogle Scholar
Lyon, J. G. 2000 The solar wind-magnetosphere-ionosphere system. Science 288 (5473), 1987–1991.Google Scholar
Mendoza, M. & Muñoz, J. D. 2008 Three-dimensional lattice Boltzmann model for magnetic reconnection. Phys. Rev. E 77, 026713.Google Scholar
Olson, P. & Amit, H. 2006 Changes in Earth’s dipole. Naturwissenschaften 93 (11), 519–542.Google Scholar
Priest, E. & Forbes, T. 2007 Magnetic Reconnection: MHD Theory and Applications. Cambridge University Press.Google Scholar
Ratcliffe, J. A. 1972 An Introduction to the Ionosphere and Magnetosphere. Cambridge University Press.Google Scholar
Romashchenko, Y. & Reshetnikov, P. 2000 Simple analytical model of the magnetosphere. Intl J. Geomagn. Aeron. 2, 105–108.Google Scholar
Russell, C. T. 2000 The solar wind interaction with the Earth’s magnetosphere: a tutorial. IEEE Trans. Plasma Sci. 28 (6), 1818–1830.Google Scholar
Sazhin, S. S. 1978 The conductivity of solar wind plasma. Sov. Astron. Lett. 4, 174–175.Google Scholar
Sergeev, V. A. & Tsyganenko, N. A. 1980 The Earth’s Magnetosphere. Izdatel’stvo Nauka.Google Scholar
Shafranov, V. D. 1966 Plasma equilibrium in a magnetic field. Rev. Plasma Phys. 2, 103.Google Scholar
Shi, Q. Q., Zong, Q.-G., Fu, S. Y., Dunlop, M. W., Pu, Z. Y., Parks, G. K., Wei, Y., Li, W. H., Zhang, H., Nowada, M. et al. 2013 Solar wind entry into the high-latitude terrestrial magnetosphere during geomagnetically quiet times. Nat. Commun. 4, 1466.CrossRefGoogle ScholarPubMed
Sibeck, D. G., Lopez, R. E. & Roelof, E. C. 1991 Solar wind control of the magnetopause shape, location, and motion. J. Geophys. Res. 96 (A4), 5489–5495.Google Scholar
Siscoe, G. L. 2001 70 years of magnetospheric modeling. Geophys. Monograph Ser. 125, 211–227.Google Scholar
Stadelmann, A., Vogt, J., Glassmeier, K.-H., Kallenrode, M.-B. & Voigt, G.-H. 2010 Cosmic ray and solar energetic particle flux in paleomagnetospheres. Earth Planet. Space 62 (3), 333–345.Google Scholar
Stern, D. P. 1985 Parabolic harmonics in magnetospheric modeling: the main dipole and the ring current. J. Geophys. Res. 90 (A11), 10851–10863.Google Scholar
Stern, D. P. 1994 The art of mapping the magnetosphere. J. Geophys. Res. Space Phys. 99 (A9), 17169–17198.Google Scholar
Tsyganenko, N. A. 1987 Global quantitative models of the geomagnetic field in the cislunar magnetosphere for different disturbance levels. Planet. Space Sci. 35 (11), 1347–1358.Google Scholar
Tsyganenko, N. A. 1989 A magnetospheric magnetic field model with a warped tail current sheet. Planet. Space Sci. 37 (1), 5–20.Google Scholar
Tsyganenko, N. A. 1990 Quantitative models of the magnetospheric magnetic field: methods and results. Space Sci. Rev. 54 (1–2), 75–186.CrossRefGoogle Scholar
Tsyganenko, N. A. 2002 A model of the near magnetosphere with a dawn-dusk asymmetry 1. Mathematical structure. J. Geophys. Res. 107 (A8), 1179.Google Scholar
Tsyganenko, N. A. & Usmanov, A. V. 1982 Determination of the magnetospheric current system parameters and development of experimental geomagnetic field models based on data from IMP and HEOS satellites. Planet. Space Sci. 30 (10), 985–998.CrossRefGoogle Scholar
Voigt, G.-H. 1981 A mathematical magnetospheric field model with independent physical parameters. Planet. Space Sci. 29 (1), 1–20.Google Scholar
Voigt, G.-H., Behannon, K. W. & Ness, N. F. 1987 Magnetic field and current structures in the magnetosphere of Uranus. J. Geophys. Res. Space Phys. 92 (A13), 15337–15346.CrossRefGoogle Scholar
Voigt, G.-H. & Ness, N. F. 1990 The magnetosphere of Neptune: its response to daily rotation. Geophys. Res. Lett. 17 (10), 1705–1708.Google Scholar
Willis, D. M., Holder, A. C. & Davis, C. J. 1999 Possible configurations of the magnetic field in the outer magnetosphere during geomagnetic polarity reversals. In Annales Geophysicae, vol. 18, pp. 11–27. Springer.Google Scholar