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In-Depth Information
Using the table integral [1]
∞
k
A
−
s
)
ds
=
i
π
2
k
A
exp (
ik
A
x
)
H
(1)
k
2
m
(
s
)
h
2
exp(
−
−
(
k
A
x
)
,
1
0
where
H
(1
1
(
k
A
x
) is the Hankel function of the first kind. So,
G
m
on the ground
surface at large distances from the incident beam axis (see (8.48)) reduces to
1
k
0
hζ
(0
4
/ζ
(0)
−
G
m
=
τ
K
2
−
3
⎛
⎝
⎞
⎠
k
0
hY
(
m
)
k
A
x
k
0
hY
(
m
)
k
A
x
Y
∆
(0)
A
g
ζ
(0)
3
H
(1)
1
g
ζ
(0)
3
H
(1)
1
sign
I
×
Y
∆
(0)
A
2
,
(8.63)
Y
∆
(0)
A
k
0
hε
a
Φ
k
0
hε
a
Φ
sign
I
where
H
(1)
1
H
(1)
1
Φ
(
k
A
x
).
The horizontal component of the magnetic field on the ground surface
will, in accordance with (8.54), be determined by the sum of integral (8.63)
and discrete (8.56) parts. Comparing the corresponding amplitudes in the
transmitted Alfven wave, we conclude that the ground field in this polarization
is determined basically by the residue in the pole with the minimal imaginary
part. For instance, for the high conductive ground the relation between the
amplitudes of the discrete and integral parts is in the order of
≡
(
k
A
x
), and
Φ
≡
≈
k
0
h
X
3
/
2
G
mAA
G
0
AA
1
/
2
Y
2
|
ε
a
|
|
Φ
|
1
,
≈
k
0
hε
a
X
1
/
2
G
mAS
G
0
AS
|
Φ
|
1
.
d
of
the ground magnetic field. To avoid cumbersome expressions, we restrict our
consideration to analysis of the high conductive ground:
Let us define the spatial distribution on the large distances
x
⎛
⎞
ik
A
H
(1)
H
(1)
1
k
0
h
Y
2
X
ik
A
Y
sin
I
X
i
Y
sin
I
X
1
x
−
S
−
x
−
S
⎝
⎠
G
g
=
,
(8.64)
Y
sin
I
S
−
k
0
h
−
iS
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