Geoscience Reference
In-Depth Information
5.1.4 F-Layer Solutions with Production, Diffusion, and Flux
Consider first the steady-state behavior at high altitudes. Then
∂/∂
t
=
0, both
z
)
z
)
=
l
(
and
q
(
0, and (5.14) becomes
d
2
n
dz
2
+
2
n
1
H
2
3
2
dn
dz
+
1
D
n
=
=
0
z
)
It is straightforward to show that the solutions for
n
(
are of the form
n
z
=
1
2
z
A
2
e
−
z
A
1
e
−
(5.15)
+
The corresponding vertical velocity for each solution is found from 5.13. The
A
1
solution yields
D
a
H
1
2
+
1
2
W
D
=−
−
=
0
which corresponds to the hydrostatic equilibrium with a scale height of 2
H
as
found in section 5.1.1. The
A
2
solution has a vertical velocity given by
D
0
e
z
2
H
D
a
H
1
2
D
a
2
H
=
W
D
=−
−
1
+
=
Thus, for this solution there is a net vertical flux, which is given by
A
2
D
0
2
H
z
)
F
=
n
(
W
D
=
A
2
e
−
z
. With no back pressure from the
which is independent of
z
since
n
z
)
=
(
plasmasphere,
W
D
is always
0. Boundary conditions such as a plasmaspheric
source and low altitude production determine the relative roles of the
A
1
and
A
2
solutions. Note that a nonvanishing
A
2
term modifies the topside scale height.
Consider now a solution to the time independent equation (5.14) without the
recombination term but including production of the form
q
≥
q
0
e
−
z
, which
is the high altitude term in the Chapman function. The solution to this differential
equation is
z
)
=
(
2
q
0
H
2
3
D
0
exp
2
z
)
z
)
=
z
/
z
/
n
(
n
0
exp
(
−
2
)
+
(
−
2
)
−
exp
(
−
exp
z
)
2
FH
D
0
z
/
±
(
−
2
)
−
exp
(
−
(5.16)
where
n
0
is the electron density at the low boundary (
z
=
0) and
F
is the plasma
flux at the upper boundary (“
” correspond to inward and outward
flux, respectively). At high altitudes the electron density distribution for
F
+
” and “
−
=
0
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