Magnetospheric MHD Resonances and ULF Pulsations - Ultra and Extremely Low Frequency Electromagnetic Fields - page 247

where

3Ǜ 2 H

g 3 C 3g 3 F yy .!/
C 2Ǜ H ǚ F xy .!/ C F yx .!/ :

g 3 C g 3 F xx .!/ C

Ǜ 2 H

‚.!/ D

(6.90)

Within the altitudes of the E-layer the ratio of plasma to neutrals number
densities is 10 7 -10 9 for the day- and night-time conditions, respectively. This
means that the motions of electrons and ions practically have no effect on the pattern
of neutral has flow. In contrast, the moving neutrals drag the ions thereby exciting
the wind-driven ionospheric currents. In our model we leave out of account the
diurnal variations and fluctuation of the ionospheric plasma conductivity due to the
variation of solar radiation and other causes. This implies that the spatiotemporal
distribution of the wind-driven currents is basically governed by the hydrodynamic
processes and fluctuations of the neutrals flow in the ionosphere. Such fluctuations
may propagate with the velocities of acoustic and atmospheric gravity waves, which
frequently occur at the altitudes of the E-layer. In this picture the correlation radius,
c .!/, of the random fields can be roughly estimated as (Surkov and Hayakawa
2007 )

2V a .!/
!

c .!/ V a .!/T D : (6.91)

Here V a .!/ denotes the acoustic wave velocity or the mass velocity of the neutrals
and T stands for a typical period of ionospheric parameter variations.
Finally, using Eq. ( 6.91 ) to estimate the correlation radii, x and y , we obtain
the following rough estimate of the power spectrum

0 2 V a .!/‚.!/
64! 2 d 2

‰ .B/

xx .!/

: (6.92)

In a similar fashion we may examine the 2D field of the electromagnetic
fluctuations that can be expressed via the transfer matrix ( 6.78 ). Using this line
of reasoning, the spectral density of correlation matrix . B /

nm is found to be given by

Eq. ( 6.81 ) where the coefficients M . w /
nl

and M . w /

mp stand for the components of the
matrix ( 6.81 ). The 1D random fields, ı I . w / .x;t/, of the height-integrated currents
is considered to be uniform in the ionosphere in such a way that the spatiotemporal
correlation functions, ‰ . w /

lp , and their linear combinations depend only on the time
difference D t t 0 and relative distance D j x x 0 j . As before we choose
for study the Gaussian-shaped form of the correlation function of the ionospheric
current fluctuations

lp .;!/ D F lp .!/ exp

;

2
c .!/

‰ . w / (6.93)