Environmental Engineering Reference
In-Depth Information
electrons as a result of photoionization processes occurs at an altitude of about
160 km and is 4
10
15
cm
3
s
1
.
One can obtain rough estimates of the number density of charged particles at
medium altitudes, where the photoionization rate constant is a maximum. The
photoionization cross section is
10
18
10
17
cm
2
, so the number density
σ
ion
10
12
cm
3
at altitudes where photoion-
ization occurs. The number density of molecular ions
N
i
at these altitudes follows
from the balance equation
ion
L
)
1
10
11
of molecules is
N
m
(
σ
is the dissociative recombi-
nation coefficient for processes 13-15 in Table 6.6 and
I
ion
α
N
e
N
i
I
ion
/
L
,where
α
10
10
cm
2
s
1
is
the flux of photons whose absorption leads to photoionization. From this it follows
that
2
r
I
ion
α
10
5
cm
3
.
N
i
L
5
(6.100)
This corresponds to the maximum number density of ions in the atmosphere. The
number density of molecular ions in the lower layers of the atmosphere follows
from the balance equation
wN
i
L
α
N
i
.
This gives the number density relation
N
i
N
m
10
15
cm
6
,where
N
m
is the num-
ber density of nitrogen molecules.
A typical time for establishment of the equilibrium for molecular ions that fol-
lows from the estimate (6.100) is
N
e
)
1
τ
(
α
20 s, whereas a typical ion
rec
drift time for these altitudes is
10
4
s. Therefore, local equilibrium for molec-
ular ions results from the competing ionization and recombination processes. Be-
cause of the short time for establishment of this equilibrium, the number density
of charged particles for daytime and for nighttime atmospheres is different. The
above estimate refers to the daytime atmosphere. The ion number density of the
nighttime atmosphere follows from the relation
τ
dr
α
N
i
t
1, where
t
is the dura-
10
2
10
3
cm
3
tion of the night. This gives the estimate
N
i
for the nighttime
atmosphere.
Atomic ions formed as a result of the photoionization process participate in the
ion-molecule reactions listed as processes 27-30 in Table 6.6. A typical time for
these processes is
(
kN
)
1
10 s, and is small compared with a typical
recombination time. This explains why ions in the ionosphere are molecular ions
(see Figure 6.22). In addition, it shows the origin of NO
C
molecular ions. These
ions cannot result from photoionization because of the small number density of
NO molecules.
Atomic ions are removed from high altitudes because of a short transport time.
One can estimate the maximum number density of atomic oxygen ions by com-
paring a typical drift time
L
/
w
and the characteristic time for the ion-molecule
reactions listed in Table 6.6 and estimated as by (
k
[N
2
])
1
. Assuming the basic com-
ponent of the atmosphere at these altitudes to be atomic oxygen, we find that the
maximum number density of O
C
atomic ions occurs at altitudes where [N
2
][O]
τ
0.01
