Geoscience Reference
In-Depth Information
iǛ
H
x
0
L
Ǜ
P
V
AI
ŒA.0/
D
‰.0/
dž.0/
f
1
;
(5.120)
iǛ
P
x
0
L
Ǜ
H
V
AI
Œ@
z
‰.0/
D
‰.0/
dž.0/
C
f
2
;
(5.121)
where x
0
is a dimensionless frequency defined in Eq. (
5.17
). Here we made use of
the following abbreviations
ǚ
Ǜ
P
.
k
?
v
/
z
C
Ǜ
H
.
k
?
v
/
;
iB
V
AI
k
2
?
f
1
D
(5.122)
ǚ
Ǜ
P
.
k
?
v
/
Ǜ
H
.
k
?
v
/
z
iB
V
AI
k
2
?
f
2
D
(5.123)
Depending on the neutral wind velocity,
v
, the functions f
1
and f
2
play a role of
forcing functions/sources for the IAR excitation.
Now we use Eq. (
5.29
)for‰ in the atmosphere to connect the potential ‰ and
its derivative at the interface
z
D
0 between the atmosphere and the ionosphere
@
z
‰.0
/
D
k
?
‰.0/
C
k
?
tanh .k
?
d/
k
?
C
tanh .k
?
d/
;
(5.124)
where is given by Eq. (
5.30
). Here minus in the argument of the function ‰ in
Eq. (
5.124
) denotes that the derivative should be taken just below the E-layer.
As is seen from Eqs. (
5.120
) and (
5.121
), the boundary conditions at
z
D
0 relate
the jump of values of @
z
‰ and A just above and below the E layer of the ionosphere.
It follows from Eq. (
5.19
) that just above E-layer the function @
z
‰ is
@
z
‰.0
C
/
D
‰.0/
LJ
2
I
L
;
(5.125)
where the function LJ
2
is given in Eq. (
5.22
). Notice that the values of ‰.0/ are
the same in both Eq. (
5.124
) and Eq. (
5.125
) because the function ‰ must be
continuous at
z
D
0. Subtracting Eq. (
5.125
)fromEq.(
5.124
) brings about the jump
of derivative @
z
‰ across the E layer
Œ@
z
‰.0/
D
‰.0/
I
LJ
2
:
C
k
?
tanh .k
?
d/
k
?
C
tanh .k
?
d/
L
k
?
(5.126)
As we have noted above, the potential A
D
0 in the atmosphere, so that the jump
of function A across the E layer equals the value of A just above E-layer, that is
ŒA.0/
D
A.0
C
/. According to Eqs. (
5.80
) and (
5.18
), the jump of A is given by
Œ@
z
dž.0
C
/
i!
D
LJ
1
dž.0/
V
AI
ŒA.0/
D
;
(5.127)
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