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Ann. Geophys., 22, 267-287, 2004
www.ann-geophys.net/22/267/2004/
© European Geosciences Union 2004
Toroidal and poloidal Alfvén waves with arbitrary azimuthal wavenumbers in a finite pressure plasma in the Earth's magnetosphere
D. Yu. Klimushkin1, P. N. Mager1, and K.-H. Glassmeier2
1Institute of Solar-Terrestrial Physics (ISTP), Russian Academy of Science, Siberian Branch, Irkutsk, P.O.Box 4026, 664033, Russia
2Institut für Geophysik und Meteorologie, Mendelssohnstr. 3, D-38106 Braunschweig, Germany
Abstract. In this paper, in terms of an axisymmetric model of the magnetosphere,
we formulate the criteria for which the Alfvén waves in the
magnetosphere can be toroidally and poloidally polarized (the
disturbed magnetic field vector oscillates azimuthally and radially,
respectively). The obvious condition of equality of the wave frequency
ω to the toroidal (poloidal) eigenfrequency ΩTN
(ΩPN) is a necessary and sufficient one for the toroidal
polarization of the mode and only a necessary one for the poloidal
mode. In the latter case we must also add to it a significantly
stronger condition ∣ΩTN–ΩPN∣/ΩTN ≫ m–1
where m is the azimuthal wave number, and N is the longitudinal
wave number. In cold plasma (the plasma to magnetic pressure ratio
β = 0) the left-hand side of this inequality is too small for the
routinely recorded (in the magnetosphere) second harmonic of radially
polarized waves, therefore these waves must have nonrealistically
large values of m. By studying several models of the magnetosphere
differing by the level of disturbance, we found that the left-hand
part of the poloidality criterion can be satisfied by taking into
account finite plasma pressure for the observed values of m ∼ 50 – 100
(and in some cases, for even smaller values of the azimuthal
wave numbers). When the poloidality condition is satisfied, the
existence of two types of radially polarized Alfvén waves is
possible. In magnetospheric regions, where the function ΩPN
is a monotonic one, the mode is poloidally polarized in a part of its
region of localization. It propagates slowly across magnetic shells
and changes its polarization from poloidal to toroidal. The other type
of radially polarized waves can exist in those regions where this
function reaches its extreme values (ring current, plasmapause). These
waves are standing waves across magnetic shells, having a poloidal
polarization throughout the region of its existence. Waves of this type
are likely to be exemplified by giant pulsations. If the
poloidality condition is not satisfied, then the mode is toroidally
polarized throughout the region of its existence. Furthermore, it has
a resonance peak near the magnetic shell, the toroidal eigenfrequency
of which equals the frequency of the wave.
Key words. Magnetospheric physics (plasmasphere; MHD
waves and instabilities) – Space plasma physics (kinetic and
MHD theory)
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