Geoscience Reference
In-Depth Information
450
n
0
=aL
−s
=a cos
−2
Φ
400
10
3
cm
−3
s=1.767
a=3
×
350
300
250
200
o
(geomagnetic latitude)
Φ
150
56
58
60
62
L
3.2
3.4
3.6
3.8
4
4.2
Fig. 11.3.
Equatorial distribution of the plasma concentration
n
0
recalculated to
the geomagnetic latitudes by (11.15). The circles are calculated according to (11.15).
The approximation (11.9) is shown by the line
horizontal homogeneity depends only on the difference between the arguments,
i.e.
|
r
=
R
E
=
G
(
r
r
)[
n
b
τ
(
r
)]
ds
,
E
τ
(
r
)
−
×
(11.19)
where
n
is a unit vector normal to the ground and integrating is over the
ground surface. Kernel
G
is determined from the solution of the electrody-
namic problem for a half-space with the predetermined conductivity.
Applying the spatial
x, y
-Fourier transform to (11.19), we obtain the re-
lation between spectral components of the electric
E
τ
and magnetic
b
τ
fields
on the ground
E
τ
(
ω
;
k
x
,k
y
)=
Z
(
ω
;
k
x
,k
y
)
b
τ
(
ω
;
k
x
,k
y
)
,
(11.20)
where
Z
(
ω
;
k
x
,k
y
) is the spectral impedance matrix. It is convenient to
present the ground and atmospheric fields as a superposition of two modes -
electric (index
e
) and magnetic (
h
) (see Chapter 7). From (7.30) we get
k
x
k
y
(
Z
e
−
,
k
x
Z
e
−
k
y
Z
h
Z
(
ω
;
k
x
,k
y
)=
1
k
2
Z
h
)
−
(11.21)
k
y
Z
e
+
k
x
Z
h
k
x
k
y
(
Z
h
−
Z
e
)
where
Z
h
(
ω
;
k
x
,k
y
)and
Z
e
(
ω
;
k
x
,k
y
) are spectral impedances of the mag-
netic and electric types.
Z
h
and
Z
e
coincide if
k
vanishes
0
Z
e
(
ω
;
k
x
,k
y
)=
Z
0
+0
k
2
,
lim
k
0
Z
h
(
ω
;
k
x
,k
y
) = lim
→
k
→
where
k
2
=
k
x
+
k
y
.
In this case (11.20) yield
E
τ
=
Z
0
(
ω
)
b
τ
(11.22)
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