Geoscience Reference
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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
|
−∞
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