ULF-Waves on the Ground and in Space - Hydromagnetic Waves in the Magnetosphere and the Ionosphere - page 49

wavenumbers. Small-scale perturbations are reflected in the outer parts of the
magnetosphere and return to its boundary. Closer to the Earth, the FMS-wave
spectrum is depleted of small-scale perturbations. After the reflection point
the FMS-wave intensity exponentially decays at distance of the order of az-
imuthal scale. In the inner parts of the plasmasphere, the FMS-wave frequency
becomes comparable to the frequency of the standing Alfven oscillations and
its spatial scale become comparable to the length of the corresponding field-
line. A resonance surface emerges in this region of non-dissipative attenuation.

Cavity Resonance

Dungey predicted the emergence of global axially symmetric resonance oscilla-
tions on the FMS with discrete eigenfrequencies ([15], [17]). Cavity oscillations
appear between the reflection (turning) point and the magnetopause. Their
properties are identical with the axially symmetric oscillations of an acoustic
resonator.
For asymmetric perturbations, when FMS and Alfven modes couple, the
notions of cavity resonance oscillations remain correct on the whole. However,
additional energy losses appear because the wave energy is transferred from
a global large-scale FMS-mode to local small-scale Alfven oscillations. The
most effective transformation takes place in the vicinity of the field line where
the frequencies of its FLR and of the cavity mode harmonics coincide. Exper-
iments with laboratory plasma confirm that there is a significant attenuation
of cavity modes due to excited Alfven resonances. On large tokamaks notice-
able warm-up was observed during excitation and subsequent dissipation of
FMS-cavity modes ([62], [91]).
Unlike laboratory plasma in Tokamak-type systems, the magnetosphere is
an open system for FMS-waves, which results in radiation losses of cavity-
mode energy. And this peculiarity might seem the strongest argument against
the hypothesis of cavity resonances, especially for the low-frequency part of
the spectrum. Indeed, high-frequency waves with wavelength smaller than the
geocentric distance to the plasmapause can be captured in the plasmasphere.
A low-frequency wave must go to the tail of the magnetosphere and then leave
it. However, if such conditions emerge on the magnetopause, in the magne-
tosphere tail that velocity along the magnetopause will noticeably change on
smaller scales than the transverse dimensions of the magnetosphere, i.e. about
10

20R E , that region will effectively reflect FMS-waves. The magnetosphere
can then be likened to an open resonator.
Oscillations of such systems are known to be accompanied by the radia-
tion into free space. An essential peculiarity of open resonators is the large
difference in damping rates between the main (corresponding to small mode
numbers) and the higher modes. Among the resonance modes, a mode ap-
pears with a high Q -factor. As the transverse wavenumber rises, radiation
losses increase rapidly. The low Q -factor of the high frequency modes results
in effective rarefaction of the open resonator's spectrum. Additional selection,

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