Geoscience Reference
In-Depth Information
Now that we have obtained spatial patterns of the magnetic field on the
Earth for various periods of the FLR oscillations we are in the position to
solve an inverse problem and define the half-width of the resonance shells
using computed ground fields. In order to do this we fit the curves in Figures
8.2a by various curves with different
δ
i
varying them so that the fitting is
to be best. We explored the range
50 km from the spatial maximum for
the fitting and found follow reconstructed values for
δ
i
: 5.4 km for
T
=20s,
33.6 km for
t
= 80 s and 55.6 km for
T
= 210 s. It follows by inspection of
the respective initial values of
δ
i
=8
,
13
.
5
,
and 25 km with the found
δ
i
that
this approach indeed yields rather proper results in the considered case only
for the short-period (low-latitude) FLR oscillations.
±
Synchronous Alfven Wave Beams
Point Source
Suppose an Alfven 2D wave beam is incident on the ionosphere. We assume
that the beam is narrow and describe the distribution of the magnetic field in
it as a
δ
-function. Let the latitudinal distribution of the magnetic component
in the initial incident wave be given by
b
(
i
y
(
x
)=
b
(
i
)
0
L
0
δ
(
x
), where
b
(
i
0
is a
characteristic magnetic amplitude in the beam and
L
0
is its scale-width. The
spectrum of
b
(
i
0
L
0
δ
(
x
)is
L
0
/
√
2
π.
b
(
i
A
(
k
)=
b
(
i
)
(8.27)
0
For the high ground conductivity (
τ
K
1) similar to (8.18), we find
+
∞
b
(
i
0
L
0
exp
ikx
|
dk.
k
√
2
πh
Φ
3
A
=
−
−|
(8.28)
−∞
Substituting it into (8.12) and integrating, we obtain
2
π
Y
sin
I
X
hL
0
b
(
g
)
h
2
+
x
2
b
(
i
0
.
SA
(
x
)=
b
(
g
x
(
x
)=
−
(8.29)
According to (7.28) valid for the high conductive ground, the surface im-
pedance
Z
(
m
g
depends weakly on
k.
As a result, for the vertical magnetic
component we have
∂E
(
g
)
Z
(
m
)
∂b
(
g
x
(
x
)
∂x
1
ik
0
y
∂x
g
ik
0
b
(
g
z
(
x
)=
−
=
−
.
This is combined with (8.29) to give
Z
(
m
)
4
π
Y
sin
I
X
hL
0
x
g
ik
0
(
h
2
+
x
2
)
2
b
(
i
0
.
b
(
g
)
z
−
=
(8.30)
Search WWH ::
Custom Search