Magnetospheric MHD Resonances and ULF Pulsations - Ultra and Extremely Low Frequency Electromagnetic Fields - page 234

this effect we suppose that 1 2 , and B 1 B 2 . On account of the relation
V 1 V 2 we also assume that there are no plasma motion in the magnetosphere,
i.e., V 2 0. Substituting these values into Eq. ( 6.58 ) yields

V 1 >4V A : (6.59)

The implication here is that if only the plasma flow in the magnetosheath is super-
Alfvénic, then the Kelvin-Helmholtz instability can develop. As alluded to earlier
in Sect. 1.2, the solar wind is supersonic near the Earth orbit. Across the bow shock
shown in Fig. 1.8 , the solar wind density and temperature increase abruptly whereas
the wind velocity decreases, allowing for the presence of subsonic flow around the
Earth magnetosphere. In other words, in the vicinity of local magnetic noon the solar
wind flow stalls and becomes sub-Alfvénic. Toward the flanks of the magnetosphere
the stream accelerates in a such way that the flow velocity becomes super-Alfvénic
again. This implies that the Kelvin-Helmholtz instability may occur at the flanks of
the magnetosphere, i. e., around dusk and dawn.
A number of experimental data is consistent with the solar-wind-related mecha-
nism for excitation of the Kelvin-Helmholtz instability followed by the long-period
ULF pulsations (e. g., see the text by Glassmeier 1995 ). First, it is usually the case
that the Pc5 pulsations are observed at the flanks of the magnetosphere, especially
at the downside, that are in favor of the mechanism of the Kelvin-Helmholtz
instability. Moreover, analysis of the observation shows that the vector of the phase
wave velocity is directed toward the tail of the magnetosphere. Second, the ULF
pulsation activity and polarization characteristics are clearly controlled by the solar
wind.
As discussed above, the instability of the tangential discontinuity may result in
the turbulization of plasma flow followed by generation of a rather broad spectrum
of perturbations. This mechanism is capable of exciting different FLRs, which
may therefore form a continuous spectrum of the resonant field. This conclusion
contradicts with the observations since there usually occurs only one resonance.
To explain this contradiction Kivelson and Southwood ( 1985 ) have suggested that
the Kelvin-Helmholtz instability caused by surface waves first results in excitation
of the fundamental and higher harmonics cavity modes, that is the global poloidal
eigenoscillations of the magnetosphere. As has already been stated, the spectrum of
cavity modes is discrete. When these modes are excited they produce a frequency
filter for wideband spectrum of the initial perturbations. At this point the FLRs
can be excited by virtue of the shear Alfvén mode coupling to the resonant cavity
modes. In other words, the energy of unstable surface waves may transform into the
energy of poloidal oscillations which in turn can propagate across field lines up to
the resonance magnetic shell thereby producing the FLR due to the mode coupling.