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1+
α
(0)
,
+
γ
(0)
0
O
2
=
α
(0)
0
(
b
1
cos 2
Ωt
−
a
1
sin 2
Ωt
)+
···
(13.13)
0
2
Ω
+
γ
(0
0
1+
[N
e
]=
α
(0)
0
α
(0)
0
d
1
cos 2
Ωt
1
2
Ω
b
1
+
γ
(0)
0
α
(0
0
a
1
+
γ
(0
0
c
1
sin 2
Ωt
+
,
−
···
(13.14)
where
α
(0)
0
and
γ
(0)
0
are found from the averaged equations (13.6), (13.7):
α
(0)
0
+
γ
(0
0
=0
,
Aα
(0)
0
a
0
α
(0)
I
1
−
−
0
α
(0)
0
+
γ
(0
0
=0
.
I
2
+
Aα
(0)
c
0
α
(0)
−
(13.15)
0
0
Suppose now that the pump wave amplitude is modulated by the harmonic
oscillations sin
Ωt.
Then
T
e
fluctuations are proportional to sin
2
Ωt
. The total
electron temperature
T
e
is given by
T
e
=
T
0
+
T
1
sin
2
Ωt.
We find
α
(0)
and
0
γ
(0)
0
from (13.15), substitute them into (13.13) and (13.14) and obtain the
time dependencies of
O
2
and [N
e
]
.
Figure 13.3 (curves 7 and 8 for periods
τ
T
=10sand
τ
T
= 100 s, respectively) shows the dependence of the depth of
modulation
p
m
=
δN
e
/
[
N
e
(max) +
N
e
(min)] of
N
e
on
T
1
/T
0
.
10
0
5
τ
T
= 100 s
6
2
8
4
1
10
−1
τ
T
= 10 s
3
7
10
−2
0
2
4
6
8
10
T
1
/T
0
Fig. 13.3.
Relative amplitude of oscillations of the electron concentration
p
m
=
δN
e
/
[
N
e
(max) +
N
e
(min)] = [
N
e
(max)
− N
e
(min)]
/
[
N
e
(max) +
N
e
(min)] as a func-
tion of the temperature modulation
T
1
/T
0
for
τ
T
=10and
τ
T
= 100 s. Curves 1,2
correspond to 10/100s minimum solar activity. Curves 3,4 are for maximum activity.
Curves 6 and 5 represent the dependency
p
m
(
T
1
/T
0
) for the long time modulation
(
τ
T
/τ
chem
1) for the minimum and maximum solar activity, respectively. The
dashed lines labeled 7 and 8 respect to the fast modulation (
τ
T
/τ
chem
1) are the
integrand of (13.13)-(13.14) for
τ
T
= 10 and 100
s
correspondingly
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