Geoscience Reference
In-Depth Information
is continuous. This gives
Φ
n
+1
− Φ
n
Γ
n,n
+1
=2
√
ε
m
X
−
1
1
,n
+1
Φ
(
i
)
Γ
n,n
+1
,
− X
−
1
1
,n
Ψ
n
+1
− Ψ
n
Γ
n,n
+1
=2
√
ε
m
Y
n
+1
X
−
1
1
,n
Φ
(
i
)
Γ
n,n
+1
.
Y
k
X
−
1
1
,n
+1
−
(9.14)
Field Line Resonance and Terminator
Let us assume that we have two half-planes with different conductivities (day-
side and nightside ionospheres)
y>
0
Σ
=
Σ
+
= const
if
Σ
=
Σ
−
= const
if
y<
0
Let us also assume that potential
Φ
(
i
)
describes resonant Alfven oscillations
(the first term of the series in (8.15)). Then horizontal fields under the
ionosphere are
b
x
z
=
−
0
=
A
g
1
±
·
,
δ
i
x
+
iδ
i
g
2
±
·
δ
i
+
x
+
i
(
|
y
|
+
δ
i
)
b
y
z
=
−
0
=
ig
2
±
·
δ
i
±
A
x
+
i
(
|
y
|
+
δ
i
)
Y
±
X
±
g
1
±
=
−
i
1
Y
+
X
+
−
1
X
−
Y
−
X
−
1
X
±
∓
g
2
±
=
−
X
+
−
±
iY
±
−
1
1
X
+
+
iY
±
1
X
−
−
×
+
.
(9.15)
iY
−
where '+' and '
' signs correspond to
y>
0and
y<
0,
δ
i
is the half-width
of the resonance region in the ionosphere,
A
-amplitude factor.
If the ionosphere is homogeneous,
g
2
±
=0
,
and the magnetic vector makes
a
π/
2 turn. Ionospheric inhomogeneities distort the angle from
π/
2. The
ground magnetic field becomes elliptically polarized, even though the initial
field was linearly polarized. A numerical example is shown in Fig. 9.1 and the
chosen parameters are given in Table 9.1
The ellipses are shown for
x
=0and
y/δ
i
=
−
8
,...,
8
,
10
.
The mag-
netic vector rotation sense is opposite on the two sides of
y/δ
i
= 0. Deviation
of the main axis decreases from
−
10
,
−
15
◦
for
y/δ
i
≈
5
◦
for
y/δ
i
≈
≈
1to
≈
10 to
15
◦
the right of the discontinuity. To the left of
y/δ
i
= 0 the main axis is
≈−
5
◦
off for
y/δ
i
≈−
off for
y/δ
i
≈−
1andis
≈−
10. Far from the discontinuity,
the polarization becomes linear.
Search WWH ::
Custom Search