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400
8
350
Σ
P
=1.55× 10
8
km/s
3
1
6
300
250
200
4
6
150
2
2
100
5
50
4
0
1
2
3
4
5
6
L
−
shell
Fig. 6.4.
The FLR-period
T
1
=2
π/ω
A
and relative decrements
γ
1
/ω
A
versus
L-shell. Lines 1
,
2
,
3
,
4 are plotted for the 'thin' model, while 5
,
6 for the 'thick'
ionospheric model. Two models of the equatorial distribution of the cold plasma
were used (see Fig 6.3): the curves 1 and 3 refer to the 1-st magnetospheric model;
the curves 2 and 4 are for the 2-nd model. The 1-st, 2-nd, and 3-rd, 4-th show
T
1
and
γ
1
/ω
A
, respectively, of the first harmonics calculated for the 'thin' ionosphere
with the integral Pedersen conductivity
Σ
P
=1
.
55
10
8
km/s. The curves 5 (
T
1
)
and 6 (
γ
1
/ω
A
) are for a 'real' (i.e. of finite thickness) ionosphere of the same
Σ
P
×
magnetospheric parts. The FLR-period can be estimated roughly as
T
1
2
∼
c
AI
+
l
m
l
I
2
c
Am
where
c
AI
and
c
Am
are typical Alfven velocities in the ionosphere (I) and
magnetosphere (m); respectively,
l
I
and
l
m
are lengths of the ionospheric and
magnetospheric segments of the field-line. Since,
c
AI
<c
Am
(
c
AI
≈
300 km/s
and
c
Am
≈
2
l
I
/c
AI
at the low latitudes
where
l
I
>l
m
c
AI
/c
Am
. It means that at these latitudes the MHD-wave travels
mostly within the ionosphere. In the near equatorial region, the field line is
almost totally immersed into the ionosphere. The resonance period vanishes
near the equator. This latitudinal range is not shown in Fig. 6.4. The length
of the ionospheric field line segment decreases with latitude, therefore the
FLR-period, in turn, decreases.
Approaching the plasmapause, the length of the magnetospheric segments
becomes so large that the inequality
l
m
>l
I
c
Am
/c
AI
is satisfied. So, in this
region the traveling time is determined by the magnetospheric part. The field
line length increases and the
T
1
FLR-period increases with latitude. Behind
1000 km/s), then the FLR-period
T
1
∼
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