ULF-Sounding of Magnetosphere and Earth - Hydromagnetic Waves in the Magnetosphere and the Ionosphere - page 337

10 5

Day
T = 100 s
FMS 10 4

Σ P =1.1⋅ 10 8 km/s
Σ H =1.4⋅ 10 8 km/s
δ i =20 km

ρ ap = ρ A (x)

10 3

Day
T = 100 s
Alfven mode

model 1
model 2

ρ ap = ρ S (x)

10 4 10 2

−200 0 200 −200 0 200

Distance, km Distance, km

Fig. 11.12. The curves of apparent resistivity versus a distance x from the resonance
beam axis for the Alfven ρ A and FMS ρ S modes. Resistivities and thicknesses for
two geoelectrical models are given in Table 11.2. δ i is the half-width of the FLR.
Solid and dashed lines are ρ A ( x )and ρ S ( x ) for the 1-st and 2-nd geoelectrical cross-
sections, respectively

ρ ap ( x )=0 . 2 T E y ( x )
b x ( x )

2

. (11.28)

The apparent resistivities are different for two MHD-wave modes. Let ρ ap ≡
ρ A ( x ) for the Alfven mode and ρ ap ≡

ρ S ( x ) for the FMS mode. The de-
pendencies of ρ A ( x ) are shown in the left frame of Fig. 11.12 and ρ S ( x )in
the right. The solid line respects to the 1-st and the dashed line to the 2-nd
geoelectrical cross-section (Table 11.2). ρ A ( x ) depends weakly on coordinate
x . It follows from (11.27) that

c
4 πΣ P

ρ A ( x ) ≈ .

The weak dependency of ρ A on the horizontal coordinate and the ground
resistivity can be explained as follows. The longitudinal downgoing and up-
going currents of the Alfven wave cannot penetrate into the highly resis-
tive atmosphere. They spread over the ionosphere and are enclosed in it. So,
ρ A ( x ) is defined by the ionospheric conductivity and magnetospheric wave
conductivity. The influence of Hall currents on the Alfven wave is small (see
Chapter 7).
The apparent resistivity ρ S ( x ) contrary to ρ A ( x ) depends strongly on both
x and on geoelectrical properties. In the vicinity of the FLR-shell there is a
noticeable deep minimum, as shown by the right frame of Fig. 11.12. The north
( x< 0) and south ( x> 0) sides of the curve ρ S ( x ) are asymmetrical, and the
south side is more sensitive to changes of the ground electrical properties. In
the vicinity of the resonance shell, the horizontal scale is of the order of δ i .So,
the small-scale harmonics k − 1 ≈ δ i contribute mostly to the spatial structure