Geoscience Reference
In-Depth Information
A similar calculation can be made for the low conductive ground. Then the
horizontal and magnetic fields are given by
1
π
Y
sin
I
X
hL
0
h
2
+
x
2
b
(
i
0
,
b
(
g
x
(
x
)=
−
1
π
Y
sin
I
X
xL
0
h
2
+
x
2
b
(
i
0
.
b
(
g
z
(
x
)=
−
(8.31)
The meridional magnetic component on the ground
b
(
g
x
(
x
)for
x
h
is seen from (8.30), (8.31), diminishes as
x
−
2
, and the vertical component
b
(
g
z
(
x
)as
x
−
3
for the high conductive ground and as
x
−
1
for the low con-
ductive ground. At
x
= 0 under the source, the vertical magnetic component
vanishes (
b
(
g
z
= 0) independently on the ground conductivity value contrary
to a resonance field line in which the vertical component
b
(
g
)
has a maximum
z
under the field line axis.
Note that (8.29), (8.30), (8.31) can be obtained from the Bio-Savart law
by the Hall current which is in turn produced by the horizontal electric field
E
x
of the Alfven wave in the ionosphere
sin
I
X
Σ
H
E
x
L
0
sign
I
=2
Σ
H
L
0
b
(
i
)
j
y
L
0
≈−
.
0
Gaussian Beam
Consider another model of an incident beam: synchronous beam of Alfven
waves comes to the ionosphere with bell-coordinate dependence:
b
y
(
x
)=
b
0
exp
,
x
2
2
l
0
−
(8.32)
where
b
0
=
b
(
i
0
+
b
(
r
0
is the magnitude of the magnetic wave field above the
ionosphere,
l
0
is the beam half-width. Here, we assume that in contrast to
FLR (8.15), various parts of the incident wave come simultaneously onto the
ionosphere. We shall show at a later stage, that presetting the initial wave in
the form (8.32) radically alters the spatial distribution as below the source as
far from it. The spectral expression of
b
y
(
x
) has the form
b
A
(
k
)=
b
y
(
k
)=
b
0
l
0
exp
.
k
2
l
0
2
−
If to consider a high conductive ground, then using (8.14), (8.17) and (8.12)
we obtain
2
π
exp
dk.
+
∞
(
kl
0
)
2
2
Y
sin
I
X
b
(
g
)
SA
(
x
)=
−
b
0
l
0
−
+
ikx
−
h
|
k
|
−∞
Search WWH ::
Custom Search