Geoscience Reference
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this mode tends asymptotically to the dependence x 0 D k ? L or ! D k ? v AI , which
is typical for the FMS mode in a uniform plasma.
The imaginary part of x 0 or dimensionless attenuation coefficient is displayed
in Fig. 5.5 b,d with solid lines S and F for the shear Alfvén and FMS modes,
respectively. It is obvious from this figure that both modes strongly depend on k ? .
Interestingly enough the absolute value of attenuation factor of the shear Alfvén
mode is much stronger than that of the FMS mode. The behavior of FMS mode is
also distinguished from that of shear Alfvén mode by some oscillations, as seen in
these figures. The small peaks in shown in Fig. 5.5 b,d can be due to interference
of the shear and compression modes because they disappear when Ǜ H D 0, that is,
if the modes are decoupled.
To clarify the mode properties, an analytical solution of the dispersion relation
equation ( 5.36 ) is required. The interested reader is referred to the paper by Surkov
et al. ( 2004 ) for details on the approximate analytical solutions shown in Fig. 5.5
with dotted lines.
It follows from the numerical and analytical studies that the shear Alfvén mode
attenuation is much greater than that of the fast mode especially as k ? > 0:01 km 1 .
It means that the excitation of the FMS mode in the IAR is quite possible and it can
play an important role in the formation of the IAR spectrum. It should be noted
nevertheless that the eigenfrequencies and attenuation factors of the FMS mode
become close to those for the shear Alfvén mode as k ? approaches to zero and
the difference between them disappears as the ground conductivity is neglected.
5.3
Sources of IAR Excitation
5.3.1
Possible Physical Mechanisms for IAR Excitation
Special credit has been paid in the past to the study of the physical mechanisms
for the IAR excitation. It is generally believed that the main mechanism of the
IAR excitation in low latitudes is due to the global thunderstorm activity (Polyakov
and Rapoport 1981 ; Belyaev et al. 1987 , 1990 ; Bösinger et al. 2002 ). From this
viewpoint, the electromagnetic noise energy stemming from the thunderstorms
can excite both the Schumann and IAR resonances. The global thunderstorm
activity includes about 2,000 thunderstorms operating in the atmosphere at the same
time. As we have noted above, the most intensive of them are located in Central
Africa, South America, and South-East Asia. The CG lightning discharges result
in the electromagnetic emission propagating in the Earth-Ionosphere waveguide
predominantly in the form of TM mode. This mode can convert into TE mode,
in part, due to the interaction with gyrotropic E-region of the ionosphere. The
coupling of these two modes caused by Hall conductivity results in the formation of
both shear Alfvén and FMS waves in the bottom E-region ionosphere. The Alfvén
wave energy can get trapped in the F -region ionosphere thereby exciting the IAR
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