MHD-Waves in Layered Media - Hydromagnetic Waves in the Magnetosphere and the Ionosphere - page 229

The magnetic component of the wave reached the ground rotated on π/ 2
compared to the magnetic component of the initial Alfven wave. One can see at
once that this is defined by the Hall conductivity Σ H . This phenomena occurs
also for stationary influx currents into the ionosphere from the magnetosphere
([8], [9], [10]). The Hall conductivity is of great concern in the penetration of
the MHD-wave to the ground. While Σ H is reduced the amplitude of the
magnetic component on the ground vanishes. This effect is a result of the
total compensation of the magnetic fields caused by the longitudinal current
of the Alfven wave and the Pedersen currents spreading over the ionosphere.
Three key factors define the eciency of the transformation of the Alfven
wave into the ground wave of the FMS polarization: (1) atmosphere does
not let leak the longitudinal current; (2) The Hall conductivity provides the
current system, the magnetic field of which can reach the ground, and (3) a
transversal scale-size of the initial wave. One can assert that only the oscil-
lations of the scale-size of the order of the atmosphere thickness or more can
be seen on the ground.
The FMS-wave in contrary to the Alfven wave does not contain the longitu-
dinal current and delivers to the ionosphere the horizontal electric field. The
ionospheric, atmospheric and the ground electrical currents connected with
this electric field generating corresponding magnetic fields. Magnetic fields
on the ground and under the ionosphere are defined by the resultant action
of these currents and their relative contribution depends on the ionospheric
and ground conductivities. Since the conductivity of the ground is higher in
comparison with the ionospheric one, the influence of the ionosphere on the
propagation of the FMS-mode is rather weak. For instance, a change from
dayside ionosphere to the nightside ionosphere almost has no affects on the
transmission coecient of the FMS-mode.
Comparing propagation mechanisms of the Alfven and FMS-modes, one
can say that penetration to the ground of the incident Alfven wave in the
same mode is defined by the total resistivity of the system: magnetosphere-
ionosphere-atmosphere-Earth because of the longitudinal current. This system
can be considered as an electrical chain with series resistances and, vise versa
for the FMS-mode, this system can be treated as a series which is the same
but parallely connected resistances. The effective conductivity of the system
is defined mainly by the geoelectrical cross-section at the observation point.
As for reflected waves, the essential point is that the reflection coecient
of the A A modes is independent on the horizontal wave-scale. Hence, the

package of the Alfven waves incident onto the ionosphere does not disperse
and goes back to the magnetosphere conserving the shape.
The expression for R AA is independent of the Σ H and it is defined only
by the relative values of the dimensionless terms associated with Pedersen

⇒

conductivity Σ P ( X =4 πΣ P /c ) and the Alfven velocity c A ε m = c 2 /c 2 A .
For the dayside ionosphere X ε 1 / m , the coecient R AA ≈

1 , i.e. the total
magnetic component above the ionosphere tends to 2 as at the surface of a
perfect conductor. At the night ionosphere, relations between X and ε 1 / 2 are

m