Geoscience Reference
In-Depth Information
00:55 AST
01:43 AST
500
500
450
450
400
400
350
350
300
300
250
250
200
200
150
150
5.3e5 cm
23
4.75e5 cm
23
N
m
5
N
m
5
100
H
m
5
340 km
H
0
5
49.1 km
100
H
m
5
345 km
H
0
5
49.4 km
50
50
0
2
4
6
0
2
4
6
n
e
(cm
23
)
10
5
n
e
(cm
23
)
10
5
3
3
Figure 5.3b
Two nighttime plasma density profiles along with a fit to an
α
-Chapman
layer.
H
0
is the neutral scale height. (Figure courtesy of Jonathan Makela.)
In the Problem Set, the reader is asked to show that a solution of the form
N
m
e
−
λ
t
exp
1
e
−
z
2
1
n
z
,
t
=
z
−
−
(5.17c)
4
H
2
exists if and only if
λ
=
D
0
/
=
β
0
where
β
0
is the recombination coefficient
at
z
0, the altitude where the Chapman function peaks. Note the similarity
to (5.10). The profile form, because of the factor of 2, is called an
=
α
-Chapman
layer, even though the recombination is due to the parameter
. Diffusion and
recombination thus balance in such a way that the shape of
n
β
z
)
(
is constant
while the decay of the whole layer is determined by
β
0
, the recombination rate
at the F peak. Figure 5.3b shows typical layers measured over Arecibo at night,
along with a fit to an
α
-Chapman layer, which gives credence to this simple
model.
It can be shown that for this solution
W
D
is a constant with altitude and is
equal to
g
/ν
in
evaluated at the F peak. This remarkable result can be explained
as follows. At high altitudes the plasma falls through the F peak and recom-
bines below it. This is clearly a nonequilibrium case because the plasma density
decreases with time, but the layer shape is independent of time. Without any
other forces acting, except for gravity and pressure, the layer would stay at the
same height but steadily decrease in density. This is not quite what happens in the
real ionosphere, though, since neutral winds and electric fields exist and control
the height of the F layer at night. These effects, along with the role of a finite dip
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