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Ann. Geophys., 25, 1391-1403, 2007
www.ann-geophys.net/25/1391/2007/
© European Geosciences Union 2007
Eigenmode analysis of ballooning perturbations in the inner magnetosphere of the Earth
A. S. Parnowski
Space Research Institute NASU-NSAU, Kyiv, Ukraine
Abstract. We analyze coupled Alfvén and slow magnetosonic eigenmodes in a dipole
geomagnetic field with different ionospheric conductivities in the framework
of ideal magnetic hydrodynamics (MHD) with finite pressure. We use numerical
and, if possible, analytical methods to describe eigenmode frequencies,
growth rates and eigenfunctions. The spectrum of Alfvén and slow
magnetosonic modes is discrete and equidistant. The frequencies of the first
Alfvén and slow magnetosonic eigenmodes are estimated as ~1 Hz and
~1 mHz, respectively. In the case of finite conductivity, periodic and
aperiodic modes are separated and their interaction analyzed. It was shown
that periodic and aperiodic perturbations can mutually transform into each
other. A new flute stability criterion is derived (α~4.25),
which is stricter than the Gold criterion (α=20/3). Here, as usual,
α=−L/p dp/dL. For flute perturbations, the
deviations of transversal displacement from a constant are calculated. An
approximation for longitudinal displacement is derived. We determined the
position of the main longitudinal peak, which can be responsible for
nonlinear structures observed by Freja. An influence of nonlinear terms in
pressure is estimated as well.
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