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mode together with higher harmonic of the same field-line shell has been detected
by Singer et al. (
1979
), Baumjohann and Glassmeier (
1984
) and Engebretson et al.
(
1986
).
A detailed review of observations of the ULF pulsation is outside the scope of
this section, and the interested reader is referred to the excellent tutorial review by
Glassmeier (
1995
) for detail about the horizontal polarization, wave propagation
across the ambient magnetic field and other properties of the ULF fields.
Only a few observations may have interpreted as global poloidal eigenoscillations
that may be associated with the cavity mode (Higbie et al.
1982
;Kivelsonetal.
1984
). An observational hint toward the existence of cavity mode has been reported
by Crowley et al. (
1987
) on the basis of measurements of the ionospheric Pedersen
conductivity and damping rates of the ULF pulsations
The short-period pulsations such as Pi1, Pc1, Pc2 contain a wide variety of
shape compared to the long-period pulsations. To describe this diversity of the
short-period pulsations, we use the additional nomenclature including “pearl-type
micropulsations,” “interval of pulsations of diminishing periods” (IPDP), “hydro-
magnetic whistler,” “pulsation burst” (Guglielmi and Troitskaya
1973
), “continuous
emissions”, and so on. A typical amplitude of the short-period pulsations is smaller
than 1 nT, and these pulsations cover the frequency range from 0:025 to 5 Hz. It
is generally believed that the main excitation of the short-period pulsations is due
to kinetic plasma instabilities (Trakhtengerts and Rycroft
2008
) resulted in the
generation of MHD and ion-cyclotron waves in the frequency range of Pi1, Pc1,
and Pc2.
6.3.2
Kelvin-Helmholtz Instability at the Magnetopause
The most prominent mechanism for Pc5 pulsations is thought to be the Kelvin-
Helmholtz instability at the Earth's magnetopause (Dungey
1954
). This effect is
believed to be due to surface waves propagating at the flanks of the magnetopause.
The surface wave may be in turn excited due to the interaction between the solar
wind and the planetary magnetic field as illustrated in Fig.
6.4
(Atkinson and
Watanabe
1966
; Kivelson and Southwood
1985
). This kind of instability may arise
in a fluid flow at the boundary between two regions which are separated by a
tangential discontinuity of the fluid velocity. This means that the fluid flow velocities
are both parallel to the boundary and have a jump across the boundary whereas
the fluid pressure is kept continuous. Consider a small random variation of the
equilibrium position of the boundary. This variation, shown in Fig.
6.10
with a bulge
of the boundary surface, results in restriction of the effective cross section of the flow
in the upper region. From the principle of the fluid flux conversation it follows that
the fluid velocity V must increase in this region. According to Bernoulli's law for
an inviscid fluid
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