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10
−
24
g/ cm
3
. Then from (6.102) we have
mass
m
p
=1
.
673
×
166
.
5
106
n
1
/
2
ω
A
(
L
)=
1
.
015
/L
)
1
/
2
,
Ω
=
L
4
,
n
1
/
2
L
4
(1
−
e
e
atanh
0
.
889
n
1
/
2
e
,
1
.
015
/L
)
1
/
2
L
3
γ
j
(
L
)=
0
.
637
j
(1
−
1
X
4
−
3
.
047
/L
94
.
19
LΩX
w
0
1+3
w
0
q
=
.
(6.103)
If the frequencies
ω
A
(
L
) and decrements
γ
L
are found, one can determine the
FLR-half-width
δ
(
j
)
L
in the magnetosphere if we take hold of (6.83) in the form
γ
j
ω
j
(
L
)
,
δ
(
j
)
L
≈
(6.104)
where
ω
j
(
L
)=
dω
j
/dL
. Mapping
δ
(
j
L
onto the ionosphere, one can express
the half-width of the resonance region
δ
(
j
)
i
at the ionospheric height in terms
of
δ
(
j
)
L
6523
L
(4
L
δ
(
j
)
i
3)
δ
(
j
L
(km)
.
≈
(6.105)
−
Since the decrement is small, then from (6.103) follows that
d
ln (
ω
j
(
L
))
dL
4
L
+
1
2
L
(
L
p
2
L
.
≈−
1)
+
(6.106)
−
From (6.105) and (6.106), we obtain for the half-width
δ
(
j
)
L
outside the plas-
masphere:
γ
j
L
γ
j
L
3
δ
(
j
)
L
≈
1) +
p/
2
∼
.
−
4+1
/
2(
L
−
Distribution of the Wave Fields
A field line distribution of the magnetic disturbances is given by
e
j
(
w
)
.
Let
e
j
(
w
) be normalized by conditions
w
0
w
0
ν
j
c
2
Ω
2
ν
−
2
j
e
1
(
w
)d
w
e
2
(
w
)d
w
=1
.
−
(6.107)
−w
0
−w
0
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