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Annales Geophysicae An interactive open-access journal of the European Geosciences Union
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Volume 34, issue 4
Ann. Geophys., 34, 473–484, 2016
https://doi.org/10.5194/angeo-34-473-2016
© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.
Ann. Geophys., 34, 473–484, 2016
https://doi.org/10.5194/angeo-34-473-2016
© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.

Regular paper 02 May 2016

Regular paper | 02 May 2016

Hydromagnetic waves in a compressed-dipole field via field-aligned Klein–Gordon equations

Jinlei Zheng1, Qiang Hu1,2, Gary M. Webb2, and James F. McKenzie2,3,† Jinlei Zheng et al.
  • 1Department of Space Science, University of Alabama, Huntsville, AL, USA
  • 2Center for Space Plasma and Aeronomic Research (CSPAR), University of Alabama, Huntsville, AL, USA
  • 3Department of Mathematics and Statistics, Durban University of Technology, Steve Biko Campus, Durban, South Africa
  • deceased

Abstract. Hydromagnetic waves, especially those of frequencies in the range of a few millihertz to a few hertz observed in the Earth's magnetosphere, are categorized as ultra low-frequency (ULF) waves or pulsations. They have been extensively studied due to their importance in the interaction with radiation belt particles and in probing the structures of the magnetosphere. We developed an approach to examining the toroidal standing Aflvén waves in a background magnetic field by recasting the wave equation into a Klein–Gordon (KG) form along individual field lines. The eigenvalue solutions to the system are characteristic of a propagation type when the corresponding eigenfrequency is greater than a critical frequency and a decaying type otherwise. We apply the approach to a compressed-dipole magnetic field model of the inner magnetosphere and obtain the spatial profiles of relevant parameters and the spatial wave forms of harmonic oscillations. We further extend the approach to poloidal-mode standing Alfvén waves along field lines. In particular, we present a quantitative comparison with a recent spacecraft observation of a poloidal standing Alfvén wave in the Earth's magnetosphere. Our analysis based on the KG equation yields consistent results which agree with the spacecraft measurements of the wave period and the amplitude ratio between the magnetic field and electric field perturbations.

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This work provides an alternative approach to examine one commonly occurring type of electromagnetic waves in Earth's inner magnetosphere. In certain wave modes, the waves propagate along individual field lines of Earth's magnetic field. Governed by the coupled system between the magnetic field and ionized gas of low temperature, the waves show certain characteristics similar to standing waves along an elastic string. We present solutions in agreement with spacecraft observations.
This work provides an alternative approach to examine one commonly occurring type of...
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