Geoscience Reference
In-Depth Information
y/δ
i
−10
−8
−6
−4
−2
0
2
4
6
8
10
East
Fig. 9.1.
The horizontal magnetic polarization ellipses below the FLR-shell versus
meridional coordinate
y.
The ionosphere consists of two half-planes.
Σ
P
and
Σ
H
for
the nightside and dayside ionospheres are given in Table 9.1. The distance is in the
half-width
δ
i
of the shell. Arrows show sense of rotation of the horizontal magnetic
component for
y/δ
i
=
−
2 (nightside ionosphere) and +2 (dayside ionosphere)
Distributed Inhomogeneities
Let the conductivity depend only on
x
and let
Σ
=
Σ
(
x
) be a continuous
function of
x
. Consider an incident wave with the electric field directed along
∇
⊥
Σ
(
x
) and described by the potential
Φ
(
i
)
=
Φ
(
i
)
(
x
). Equation (9.11) en-
ables us to find an analytical solution for the currents on the ionosphere and
for the magnetic field below the ionosphere. Let
E
(
i
)
=
−
∇
⊥
Φ
(
i
)
(
x
)
be the electric field in the incident wave. Then, from (9.11), for components
of the total ionospheric electric field
E
and surface current
I
=(
I
x
,I
y
), we
obtain
E
x
(
x
)=
2
√
ε
m
X
(
x
)
E
(
i
)
(
x
)
,
y
=0
,
E
x
(
x
)=
2
√
ε
m
X
(
x
)
Σ
P
(
x
)
E
(
i
)
(
x
)
,
I
P
(
x
)=
I
x
(
x
)=
Σ
P
(
x
)
·
(9.16)
2
√
ε
m
X
(
x
)
Σ
H
(
x
)
E
(
i
)
(
x
)
,
I
H
(
x
)=
I
x
(
x
)=
−
Σ
H
(
x
)
·
E
x
(
x
)=
−
X
(
x
)=
4
π
c
Σ
P
(
x
)+
√
ε
m
.
It is obvious that the maximum of
I
x
(
x
) and, thus, of
b
y
(
x
) is shifted from
E
(
i
)
(
x
) maximum ([4], [5], [10]).
Table 9.1.
Parameters of dayside and nightside ionospheres utilized for the calcu-
lation of the series of ground horizontal magnetic variation ellipses shown in Fig. 9.1
near a terminator. Subindex '+' refers to dayside ionosphere modeled by a half-plane
and '-' to the nightside
1
.
5
×
10
8
km/s
1
.
5
×
10
7
km/s
Σ
P
+
Σ
P−
1
.
75
×
10
8
km/s
1
.
75
×
10
7
km/s
Σ
H
+
Σ
H−
g
1+
1.1
g
1
−
0.79
g
2+
0
.
83 +
i
1
.
36
g
2
−
0
.
54 +
i
0
.
88
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