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Annales Geophysicae An interactive open-access journal of the European Geosciences Union
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Volume 28, issue 3
Ann. Geophys., 28, 737–742, 2010
https://doi.org/10.5194/angeo-28-737-2010
© Author(s) 2010. This work is distributed under
the Creative Commons Attribution 3.0 License.
Ann. Geophys., 28, 737–742, 2010
https://doi.org/10.5194/angeo-28-737-2010
© Author(s) 2010. This work is distributed under
the Creative Commons Attribution 3.0 License.

  11 Mar 2010

11 Mar 2010

Klein-Gordon equations for toroidal hydromagnetic waves in an axi-symmetric field

J. F. McKenzie1,2 and Q. Hu2 J. F. McKenzie and Q. Hu
  • 1Department of Mathematics and Statistics, Durban University of Technology, Steve Biko Campus, Durban, South Africa
  • 2CSPAR, University of Alabama, Huntsville, AL, USA

Abstract. In this paper we develop the hydromagnetic wave equations for toroidal Alfvén waves in a background axi-symmetric magnetic field. In the case where spatial variations are directed along the ambient magnetic field direction, the equations can be cast in a Klein-Gordon form in which the adiabatic-geometric amplitude factor of the perturbations varies as √ρL5sin5θ along a magnetic field line (where θ is colatitude and L the L-shell number) and the cut-off frequency, associated with the Klein-Gordon form, displays an astonishing variation with distance along a field line (see Eqs. 35 and 37 of the text), in the case of a dipole magnetic field. We compute the eigenvalues and eigenfunctions for the Earth's dipole field which are relevant to geomagnetic pulsations.

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