Propagation of MHD-Beams - Hydromagnetic Waves in the Magnetosphere and the Ionosphere - page 263

180

20 s

σ g =1×10 6 s −1

150

120

60 s
100 s

90

20 s

60

60 s

30

600 s

3600 s

100 s

0

−30

0 500 1000 1500 2000 2500 3000 3500

Distance, km

Fig. 8.11. Phase of the horizontal magnetic component b x ( x ) versus distance from
the source for different periods T. Solid lines are for the day ionosphere, dashed lines
are for the night ionosphere

The calculations demonstrate also the change in spatial dependencies at
large distances. For instance, for oscillations with T = 20 s the distance x ,
where the amplitude of b ( g x -component in the magnetic mode is compared
with the amplitude of b ( g x -component in the TEM mode and then remains
practically constant, is about 3000 km.
Another unexpected outcome of the calculations is the spatial dependen-
cies of phases. Figure 8.11 illustrates the dependence of phase on distance.
Numbers near the curves indicate oscillation periods. Solid lines refer to the
dayside ionosphere, dotted lines correspond to the nightside ionosphere. Three
significantly different regions exist in the distribution. The first region is close
to the source where phase shifts are small. The second region is transitional.
Large phase shifts are observed here. The apparent phase velocities turn out
to be 100 km/s for oscillations with T = 100 s. The behavior of phase veloc-

ity in this region is complicated: in going to long periods, regions appear with
inverse phase velocities.
In the model considered, the magnetic field on the ground is the sum of
the 'ground' and 'magnetospheric' waves. The hodographs for each of these
waves presented in Fig. 8.8, demonstrate that the phase of the magnetic field
is also the sum of the phases of both waves. Their phases being almost op-
posite. Therefore situations are possible when at certain distances the am-
plitudes of these waves are significantly different. Generally, field regions can
arise with inverse phase velocities. Figure 8.11 emphasizes that at 'moder-

≈

ate' ground conductivities σ g =10 6 s − 1 such regions can appear at night
for oscillations with T> 20 − 60 s and during the day at T> 600 s. In the