ULF-Sounding of Magnetosphere and Earth - Hydromagnetic Waves in the Magnetosphere and the Ionosphere - page 334

10 0

DAY
T = 100 s

10 −1

b SA , ρ g =10 5 Ohm⋅ m

10 −2

b AA

b SA , ρ g =10 4 Ohm ⋅ m

10 −3

0 1000 2000 3000 4000 5000 6000

Distance, km

Fig. 11.9. The horizontal magnetic component b SA ( x ) in the FMS-wave above the
ionosphere. The initial incident wave is an Alfven beam with the horizontal magnetic
component b ( i ) =exp −x 2 / 2 L 2 . Oscillations period is T = 100 s, L = 100 km. The
ground is a homogeneous half-space of the resistivity ρ g . The ionospheric conduc-
tivities were chosen for the dayside conditions and the dip I = π/ 2. The distance is
shown from the axis beam

MHD-Wave Beams

Let us abandon the spectral presentation of fields in favor of a coordinate
presentation for sources of two types: a localized wave bell-beam in the high-
latitude ionosphere and a resonance magnetic shell. The relations for the
ground ( b ( g ) , E ( g ) ) and magnetospheric ( b ( m ) , E ( m ) ) fields are defined by the
inverse Fourier transformation as was discussed in Chapter 8. Assume that an
Alfven monochromatic bell-beam b ( i A ( x ) is incident on the polar ionosphere
with a vertical magnetic field. Coordinate dependence of the intensity in the
beam is

exp

,

x 2
δ i

b ( i )
A

( x ) ∝ −

where δ i a half-width of the beam. It is firstly useful to assume that the
Earth is a homogeneous half-space with finite specific resistivity ρ g . Let the
values of the integral Hall and Pedersen conductivities correspond to dayside
conditions, Σ P =1 . 2 10 8 km/s. Fig. 11.9 shows the

spatial dependencies of horizontal magnetic component b SA ( x ) of the reflected
FMS-wave and the total b AA ( x ) of the Alfven wave. The curves are given for
two values of the resistivity ρ g =10 5 Ohm

10 8 km/s, Σ H =1 . 4

× ×

mand ρ g =10 4 Ohm m. It follows

from the figure that just the reflected FMS-wave is sensitive to the geoelectric
resistivity. The horizontal magnetic field of the reflected FMS-wave roughly
doubles when ground resistivity changes by an order of magnitude.
The longitudinal magnetic component b is a distinctive feature of an FMS-
wave. Figure 11.10 demonstrates the spatial distribution above the ionosphere
of the longitudinal magnetic component for the ground resistivities shown

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