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with
X
=
X
+
√
ε
m
|
sin
I
|
. The Hall current caused by this field is
2
Σ
H
sin
I
X
b
(
i
A
.
I
y
≈
Then, the horizontal magnetic components excited by this current are
P
1
R
g
e
−
2
kh
b
(
i
A
b
(
r
)
Sx
≈
−
at
z
=+0
,
P
e
kz
+
R
g
e
−k
(
z
+2
h
)
b
(
i
A
b
Sx
≈−
at
−
h
≤
z<
0
,
b
(
g
)
Pe
−kh
(1 +
R
g
)
b
(
i
)
A
Sx
≈−
at
z
=
−
h,
(7.151)
where
Z
g
k
0
/ik
+
Z
g
.
In the dispersion equation of the FMS-wave,
k
A
can be neglected and
then it is written as
k
x
+
k
z
= 0 (since
y
-component of the wavevector is
neglected). The substitution of
k
z
=
P
=
Y
sin
I
X
R
g
=
k
0
/ik
−
,
±
ik
x
into
∇
·
b
= 0 gives the polarization
b
z
/b
x
=
i
. Hence, the magnetic field of the FMS-wave is circularly polarized
in the meridional plane. For upgoing wave the polarization is +
i
.The
b
x
and
b
z
are in the quadrature and have the same amplitude. Thus, the component
of the magnetic field of the FMS-wave transversal to
B
0
is
b
x
=
i
exp(
iI
)
b
x
.
Then (7.151) may be written (since
R
SA
=
b
x
/b
(
i
A
)as
±
i
exp(
iI
)
P
1
R
g
e
−
2
kh
R
SA
≈
−
(7.152)
Let
Σ
P
>Σ
P
, then (7.152) and
X
≈
X
gives the reflection coecient
1
R
g
e
−
2
kh
.
Y
sin
I
X
R
SA
≈
i
exp(
iI
)
−
≈
√
ε
m
sin
I
and
For
Σ
P
<Σ
P
,
X
√
ε
m
1
R
g
e
−
2
kh
Y
R
SA
≈
i
exp(
iI
)
−
with a weak dependence of the transformation coecient on
I
.
It is seen from Fig. 7.9 that the eciency of FMS-waves excitation by
incident Alfven waves is higher at big magnetic field inclination
I
and high
conductivities.
The electric field in the Alfven wave is the most sensitive to ionospheric
conductivity changes. Component-wise dependencies of the total ionospheric
electric fields on
Σ
P
are shown in Fig. 7.10a. The solid lines correspond to
the initial Alfven wave, and dashed lines to the FMS-wave. The inclination
angle
I
=60
◦
. The intensity of the total electric field is in the inverse pro-
portion to
Σ
A
in the Alfven wave (see (7.150)). The maximum ionospheric
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