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Fig. 6.13 A simplified model of random ionospheric currents that are used to gain better
understanding of the solution with rigorous formulation of the problem. The current fluctuations
are correlated inside each cell with sizes x and y but not correlated with respect to each other. R
is the position vector drawn from the cell to the observation point, and ı B 1 is the magnetic variation
caused by the current element I 1 ıl
6.4.5
Rough Estimate of Spectral Density
To gain better understanding of the results alluded to above, it is necessary to
give a simple interpretation of these results on the basis of a simplified model
of the medium. To be specific, we consider E region of the ionosphere as a thin
isotropically conducting layer, and only the wind-driven current flowing in the
y-direction is taken into account. First, we note that the fluctuations of this current
can be considered as the correlated current fluctuations inside the region with
horizontal sizes of the order of x .!/ and y .!/. Consider such a region as shown
in Fig. 6.13 with the shaded area, as an elementary current element. The magnetic
perturbations, ıB 1 , originated from a solitary current element on the ground surface
can be estimated via Biot-Savart law
0 rI 1 ıl
4 .r 2
ıB 1 D
C y 2 / 3=2 ;
(6.100)
where I 1 ıl denotes the current moment, r D x 2
C d 2 1=2 is the distance shown in
Fig. 6.13 , and d is thickness of the neutral atmosphere. The horizontal component
is related to ıB 1 through ıB 1x D ıB 1 cos ' D ıB 1 d=r. The effective length of the
current element is estimated as follows: ıl y while the current amplitude can be
expressed through the height-integrated wind-driven current density, I . w y ,viaI 1
I . w y x . Dividing the ionosphere into the “coherent” regions with sizes x and y as
shown in Fig. 6.13 , we obtain that the number of such “coherent” currents covering
the area dxdy is of the order of dN dxdy= x y . Since these currents are
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