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2r
c
I
1
2
a
Fig. 6.16
A simplified model used to give simple interpretation and to indicate physical meaning
of the results. The atmospheric current fluctuations are correlated inside each vertical cylinder but
are not correlated with respect to each other
can be considered as the correlated current fluctuations inside the vertical cylinder
with radius of the order of
c
.!/. The net current flowing through the cross-
section of this cylinder is estimated as I
1
D
c
h
ıJ
i
, where
h
ıJ
i
is the mean
amplitude of the current density fluctuations. In the first approximation we neglect
the coupling due to the magnetic field generated by each current cylinder. Dividing
the whole perturbed region into parts/cylinders with radii
c
, as shown in Fig.
6.16
,
we obtain that the number of such “coherent currents” is of the order of N
a
2
=
c
.
Since these currents are uncorrelated, the net amplitude of the electric current
variations is proportional to the square root of the current number, that is I
D
I
1
N
1=2
D
a
c
h
ıJ
i
. At far distances the magnetic field of the vertical current
can be expressed through the current moment Ih. Assuming for the moment that
the non-conductive atmosphere with thickness d is “sandwiched” between two
conductive plates, which approximate the ionosphere and the ground, the solution
of the problem is given by Eq. (
4.40
). Replacing the current moment M .!/ by the
value Ihand taking into account that cot .=2/
2=
2R
e
=r yields
0
Ih
2rd
;
ıB
D
(6.108)
where ıB
denotes the azimuthal magnetic field and r is radial distance to the
vertical current moment. If the exponential atmospheric conductivity [Eq. (
3.1
)] is
allowed for, the parameter d in Eq. (
6.10
) should be replaced by the vertical scale,
H, of the conductivity variations with height. Such a characteristic scale can serve
as an effective thickness of “insulator” layer. Substituting I and H into Eq. (
6.108
),
we obtain
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