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In-Depth Information
F
(
ω
(
n
j
,L
)
∂F
(
ω
(
n
)
j
ω
(
n
+1)
j
(
L
)=
ω
(
n
)
j
(
L
)
−
.
,L
)
∂L
A zero approximation can be calculated from (6.99).
So, the numerical algorithms enabled us
•
to find frequencies and decrements of the FLR for a given
L
-shell and
•
to find the resonance
L
-shell and half-width of the FLR for a prescribed
value of the frequency of the external source.
FLR-Frequencies and Decrements
We explored two ionospheric models. In the first model, we used height de-
pendencies of the ionospheric conductivities (see Chapter 2) computed with
IRI 2000 [5]. We call this model a 'thick' ionosphere in contrary to the 'thin'
ionosphere (the 2-nd model). We used also two models of equatorial distrib-
ution of cold plasma (see Fig. 6.3). Dependencies of the fundamental FLR-
period
T
1
=2
π/ω
A
and relative decrement
γ
1
/ω
A
on McIllwain parameter
L
for the 'thin' and 'thick' ionospheres are given in Figure 6.4. The curves
1 and 3 correspond to the 1-st model; 2 and 4 are for the 2-nd model. The
curves 1, 2 and 3, 4 show
T
1
and
γ
1
/ω
A
, respectively, of the first harmonics
calculated for the 'thin' ionosphere with
Σ
P
=1
.
55
10
8
km/s.
The curves 5 (
T
1
)and6(
γ
1
/ω
A
) are for a 'thick' (i.e. of finite thickness)
ionosphere of the same
Σ
P
with an account taken of the steep growth of
the ion concentration in the
F
-layer. The curves 5 and 6 are shown only for
L<
3
.
5
.
Outside this region the curves for
T
1
and
γ
1
/ω
A
merge with the same
curves calculated for the thin ionospheric model. It can be seen from Fig. 6.4
that resonance periods at
L
×
2 calculated for thin and thick ionospheric
models are almost the same. At
L
2 resonance period
T
1
for the thin
ionosphere decreases monotonously with
L
while the thick ionosphere gives a
minimum of
T
1
≈
1
.
5.
In order to find the decrement
γ
1
and the resonance half-width
δ
L
at
10 s at
L
≈
L
2
.
5, it is sucient to use the 'thin' ionospheric approximation which
gives the same dependencies as the real ionospheric model. As to the inner
regions with
L
2,
γ
1
and
δ
1
are found in the real ionospheric model, to go up
rather steeply, whereas for the 'thin' ionosphere they go down monotonically.
Thus at
L
2, the
Q
-factor of the FLR decreases severely and the resonance
effects become very weak.
One can see that in the
T
1
(
L
) dependency there is a minimum at
L
=1
.
6
in which
T
1
≈
10 s. The FLR-period goes down in the low latitudes to
L<
1
.
6
and then goes up to the plasmapause at
L
=
L
pp
. Behind the plasmapause
T
1
(
L
) decreases steeply and increases smoothly to the large
L
.
The low latitudinal minimum is caused with the fact that the total trav-
eling time between conjugate ionospheres consists of the ionospheric and
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