Geoscience Reference
In-Depth Information
Here ψ ( i ) is the potential of the incident wave, k x and k y are horizontal latitu-
dinal and azimuthal wavenumbers, respectively and θ is the colatitude. Since
the maximum horizontal scale on the ground is the equator length, then for the
typical values of Alfven velocity c A
10 3 km, frequency ω =2 π/T
10 2
6
×
10 4 km 1 the term ω 2 /c 2 A in the expressions
for b x and E y is negligibly small.
Let us assume that the azimuthal dependence is absent in the wave, e.g.,
the azimuthal wavenumber is k y = 0. Then, the electric fields and currents
in the ionosphere are proportional to the frequency for the fixed intensity of
the incident magnetic component. The horizontal magnetic component has a
magnitude discontinuity that depends on the ionospheric current generated
by the wave electric component. When going to lower ω, the value of the
electric field will decrease as long as the magnetic component intensity stays
the same. This leads to a decrease in the ionospheric current. The influence
of the ionosphere on the FMS-wave will also decrease. The FMS-wave electric
field induces both ionospheric and ground currents.
The ground current is concentrated mainly within the skin depth
and horizontal wavenumber k
T
σ g
c
2 π
d g =
The total electric surface current I ( g )
S
driven by the horizontal electric field
E ( g )
S
oftheFMS-waveintheEarthis
2 π g E ( g )
c
I ( g )
S
σ g d g E ( g )
S
=
.
S
The height integrated ionospheric current is
I ( ion )
S
Σ P E ( ion )
S
Hence
I ( ion )
S
I ( g )
S
E ( ion )
S
E ( g )
S
E ( ion )
S
E ( g )
S
Σ P
σ g d g
= Σ P
c
2 π
g
.
(9.30)
For FMS-waves with frequency ω and horizontal wavenumber k (7.16), (7.34)
and (7.113) give
E ( ion )
S
E ( g )
S
ζ 3 (0)
ζ 3 ( h ) =cosh kh
i k 0
k Y ( m )
=
sinh kh.
(9.31)
g
For disturbances with horizontal scales > 100 km the inequality kd g
1
holds almost everywhere (horizontal scale is big in comparison with the skin
depth). So the admittance Y ( m )
= ε g =(1+ i )( k 0 d g ) 1 . Let also kh
1,
g
then (9.31) becomes
 
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