MHD-Waves in Layered Media - Hydromagnetic Waves in the Magnetosphere and the Ionosphere - page 228

gives inessential contribution into the magnetic field. The reflected magnetic
field, and consequently, magnetic field on the ground and under the ionosphere
are determined first of all by currents inside the ground.
In the Alfven wave the magnetic field under the ionosphere appears to be
due to the ionospheric Hall currents which are the source of the magnetotel-
luric field [4]. Comparing the solid curves in Fig. 7.11b and Fig. 7.10b one
can see that the magnetic field under the ionosphere in this case is greater
approximately by a factor of 1 . 64 than that on the ground. Estimation by
(7.151) gives the same ratio for the field amplitudes.

7.9 Discussion

There are two points that emerge from the theoretical consideration. The
first is that fundamental distinction exists between propagation of vertical
and inclined MHD-waves. The approximation of the normally incident wave
is equivalent to the assumption of independence of the field component on the
transversal coordinate, i.e. the infinite transversal scale is assumed. It is obvi-
ous that there is a natural horizontal scale, the Earth's radius, which defines
the largest transversal wave-scale. A finite horizontal scale or the decline of the
wave-vector results in the total reflection because of the strong discontinuity
of the phase velocities at the magnetosphere-atmosphere boundary. The wave
propagates in the magnetosphere with the Alfven velocity of c A ∼ 10 3 km/s,

10 5 km/s. As a result, the
wave front rotates back to the magnetosphere even for very small inclination
of the wave vector.
Under the ionosphere, the wave field decreases exponentially at the dis-
tances of order of the horizontal wave-scale size. The wave reflected totally
from the ionosphere can be detected at distances from the ionosphere not
larger than the transversal scale of the wave. When oscillations are observed
on the ground it means that these oscillations are in fact a tail of the MHD-
wave exponentially attenuating in the atmosphere.
The second is that only the FMS-mode can penetrate the atmosphere. This
follows directly from the polarization structure of the Alfven wave which con-
tains field-aligned electrical current. This current, meeting on its way the non-
conductive atmosphere, spreads over the ionosphere creating the ionospheric
current system which is the same as large-scale current systems produced
by the magnetospheric processes with the exception of its configuration and
intensity.
Taking into account the finite conductivity of the atmosphere has no influ-
ence on the general conclusion about ionospheric screening of the Earth for the
Alfven waves with the exception of the rather exotic wave-like TEH mode.
For discussion of some features of this wave, regularities of its propagation
and generation refer to Chapter 8.

and in the atmosphere with light velocity c =3 ×