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uncorrelated, the net amplitude of the magnetic variations is close to zero whereas
the sum of squared amplitudes is proportional to dN; that is, the contribution of the
area dxdy is of the order of d .ıB
x
/
2
D
ıB
1x
dN. Combining above relationships
with Eq. (
6.100
) and integrating gives the amplitude of the net squared magnetic
variations
0
I
.
w
y
2
Z
Z
x
y
dxdy
ıB
x
D
C
d
2
/
3
:
(6.101)
16
2
.x
2
C
y
2
1
1
Performing integration over x and y, taking into account that the power spectrum
of the magnetic noise is proportional to ıB
x
, and replacing
I
.
w
y
2
by the spectral
density of random current fluctuation ‚.!/, we obtain
0
x
.!/
y
.!/‚.!/
32d
2
‰
.B/
xx
.!/
D
:
(6.102)
This rough estimate coincides with Eq. (
6.89
) to an accuracy of the numerical factor
=8. This detailed calculation made in previous sections is totally consistent with
the simple model presented above.
6.4.6
Flicker-Noise of Ionospheric Currents
The ionospheric currents and conductivity are subject to violent changes from
the action of many forces: variations of the solar radiation, MHD waves and
particle precipitation from the magnetosphere, fluctuations of the plasma number
density, turbulence occurring in the plasma and neutral gas flows, and etc. A close
analogy exists with conductivity of the electric devices, in which the low-frequency
current fluctuations are supposed to be due to slow fluctuations of both the medium
resistance and the source emissivity, which are in turn provided by a superposition
of a great number of random processes with different relaxation times. This kind
of electromagnetic noise is termed flicker-noise or 1=f noise since overall the
power spectrum of this noise, F .f /, tends to decrease inversely proportional to
the frequency, i.e.,
m
f
n
;
F .f /
D
K
h
J
i
(6.103)
where
h
J
i
is the mean current density, K, m, and n are the empirical constants,
and f
D
!=.2/ is frequency. The exponent n in Eq. (
6.103
) varies within the
interval 0:8 < n < 1:2, but in most cases n is close to unity while m
2
(Rytov et al.
1978
; Weissman
1988
). This universal dependence has been observed
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