Geoscience Reference
In-Depth Information
The practical significance of the TEM-mode in the ULF-range is limited
because it is hard to excite it by incident MHD-waves, its amplitude usually
being small. The matter is that an electric mode must have a large vertical
electric component which cannot be effectively generated by magnetospheric
Alfven waves, since the atmosphere's conductivity is small as compared to
that of the ionosphere.
The TEM-mode can propagate to large distances over the ground sur-
face with practically no damping and at velocities close to the velocity of
light [11]. Therefore, despite the extremely low effectiveness of its excitation,
it may contribute to pulsation field far from the MHD-wave beam incident
on the ionosphere. Note, besides, that this mode can be excited by strong
atmospheric sources like lightning discharge. The wave caused by the light-
ning propagates in the TEM-mode producing Shumann resonance in the at-
mospheric waveguide [12].
Spatial Distributions
Magnetic Mode
Let us return to the analysis of field behavior at large distances from the
beam axis. Assuming the incident beam amplitude is spatially localized, set
the magnetic field distribution in the form of
δ
-function:
=
b
(
i
)
=const
.
b
(
i
)
(
x
)=
b
(
i
)
0
b
(
i
)
0
0
x
b
(
i
)
0
y
δ
(
x
)
,
where
b
(
i
)
is the horizontal magnetic field of the incident wave above the
ionosphere. The incident field spectrum is
b
(
i
)
(
k
)=
b
(
i
)
0
√
2
π
.
The magnetic field on the ground surface
b
(
g
)
(
x
) and above the ionosphere
b
(
r
)
(
x
) can be written as
b
(
r,g
)
(
x
)=
G
(
r,g
)
(
x
)
b
(
i
)
0
,
(8.40)
where
G
(
r,g
)
are the Green matrices for the reflected (
r
) from the ionosphere
and transmitted (
t
) through it to the ground (
g
) wave, respectively. Equation
(8.40) can be rewritten as
b
(
r,g
)
=
G
(
r,g
)
b
(
i
)
0
x
b
(
i
)
0
y
.
G
(
r,g
)
xx
xy
x
b
(
r,g
)
(8.41)
G
(
r,g
)
G
(
r,g
)
y
yx
yy
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