ULF-Sounding of Magnetosphere and Earth - Hydromagnetic Waves in the Magnetosphere and the Ionosphere - page 332

[5]. It may be summarized in a more physical language as follows. If an
Alfven or an FMS wave is incident on the ionosphere both Alfven and
FMS waves are reflected. An Alfven wave has a longitudinal electric cur-
rent. This wave reflects into the same wave with the reflection coecient
(7.126)

− √ ε m sin I
X + √ ε m sin I ,

AA = X

X = 4 π
c

R (0) Σ P . (11.27)

The total electric field of the Alfven wave creates the Pedersen and Hall
current systems. The Pedersen system provides the reflection of the Alfven
wave into another Alfven wave. The Hall current creates a reflected FMS-
wave and a transmitting wave which penetrates into the atmosphere and
into the Earth. The electric current of the wave, penetrated into the Earth,
generates the atmospheric and magnetospheric fields. As a result, the elec-
tric and magnetic field in the reflected FMS-wave depend on the Earth's
conductivity.
Let us estimate the influence of the Earth's conductivity on the longitu-
dinal component of the magnetic field b . Let, as before, z -axes be vertically
upwards so that x -and y - axes are horizontal. The medium is assumed to be
horizontally stratified, which means that the conductivity is function only the
vertical coordinate z . And let any field component F be given by

F = F ( z )exp( ik x x + ik y y )

where k x and k y are horizontal wavenumbers in meridional and longitudinal
directions, respectively. Then the horizonal components E and b in (7.16)
may be written

b x = ik x dΨ
dz

y = ik y dΨ
dz

E x = − k 0 k y Ψ, E y = k 0 k x Ψ, , ,

and (7.80) become

b = − sin I ( k − ik x cot I ) kΨ,

where k = k x + k y . The substitution of (7.148) in the last equation gives

Y
2

b = − exp( iI sign k x )[1 − R g exp( − 2 kh )] E A ,