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at the rate of
q
O
+
is as follows:
O
+
)
dt
n
O
+
dn
(
O
+
)
−
γ
1
(
O
+
)
−
γ
2
(
=
q
(
N
2
)
n
(
N
2
)
n
(
O
2
)
n
(
O
2
)
(5.7)
=
O
+
)
−
β
O
+
)
q
(
n
(
where the reaction rates have been combined to form
β
=
γ
1
(
N
2
)
n
(
N
2
)
+
γ
2
(
. Although the density of N
2
is about ten times that of O
2
, the
corresponding
O
2
)
n
(
O
2
)
γ
's have the opposite tendency so the two components of
β
are
comparable. In a steady state,
q
O
+
β
n
O
+
=
(5.8)
goes to zero
with altitude, the electron density would go to infinity. Balance is restored by
diffusion, which rapidly increases with altitude. As a rule of thumb, diffusion
dominates above the altitude where the chemical lifetime equals the diffusive
time scale. The chemical time scale is
However, (5.8) cannot be correct as is for the F2 layer since, as
β
τ
ch
=
β
−
1
(5.9)
and the time needed to diffuse one scale height is
H
2
τ
D
=
/
D
a
(5.10)
where
D
a
is the ambipolar diffusion coefficient. The F2 peak thus occurs where
these two time scales are equal:
τ
ch
=
τ
D
(5.11)
For the earth's atmosphere, balance occurs around 300 km. Above this height,
ignoring plasma storage and release from high altitudes, diffusive equilibrium
occurs (see Section 5.1.1).
5.1.3 Equations Including Vertical Flux Without Winds or Electric
Fields
It is instructive first to consider a vertical magnetic field since the equations are
less complex. We finally return to a coordinate systemwith
B
in the
−ˆ
a
z
direction
for the rest of this text. For a stratified ionosphere with
B
a
z
,
the
z
component of the steady state ion and electron momentum equations are
=−
B
0
ˆ
a
z
and
g
=−
g
ˆ
=−
∂(
n
i
k
B
T
i
)
∂
ν
in
V
i
0
+
n
i
eE
z
−
n
i
Mg
−
n
i
M
z
=−
∂
∂
ν
en
V
e
0
z
(
n
e
k
B
T
e
)
−
n
e
eE
z
−
n
e
mg
−
n
e
m
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