Environmental Engineering Reference
In-Depth Information
rate of atom excitation that is determined by the rate of electron energy variation
from zero energy up to the excitation threshold
dN
dt
D
N
e
k
ee
exp
4
p
2
e
4
Δ
ε
T
e
Λ
m
1/
e
T
5/2
Δ
ε
ln
,
k
ee
D
π
,
(3.61)
e
where
k
ee
is the effective rate constant for elastic collisions of electrons due to the
Coulomb interaction of electrons. Formula (3.61) is valid at high number densities
of electrons according to the criterion
N
e
N
a
g
k
q
g
0
k
ee
,
(3.62)
where
g
e
2 is the statistical weight of an electron and
g
is the statistical weight
of excited atoms. If criterion (3.62) hold true, fast establishment of the equilibrium
occurs for the electron velocity distribution. This criterion is analogous to criteri-
on (3.55) for the regime of low electron number density.
We give as a demonstration of these results the boundary degree of ionization of
a plasma of inert gases for transition between (3.59) and (3.61) for the excitation
rate of metastable states. This boundary degree of ionization is determined by
N
e
N
a
D
g
k
q
g
0
k
ee
and is represented in Table 3.2 under typical conditions
T
e
b
D
D
1eVandln
Λ
D
10
together with the rate constant
k
ee
according to (3.61).
In the analysis of the processes of atom excitation in a plasma above, we assumed
that quenching of excited atoms proceeds through other processes rather than elec-
tron impact, as radiation of excited atoms and quenching of excited atoms on the
walls. Let us consider now the quenching regime resulting from collision of excited
atoms with electrons, that is, the equilibrium takes place according to the scheme
e
A
$
A
.
Then the equilibrium for atom excitation and quenching processes in collisions
with electrons requires the equality of the rates:
C
e
C
f
0
(
v
0
)(
v
0
)
2
d
v
0
.
2
d
ν
ex
f
0
(
v
)
v
v
D
ν
q
Ta b l e 3 . 2
The parameters of excitation of metastable inert gas atoms in accordance with (3.61)
and (3.62).
N
e
N
a
b
,10
6
Δ
ε
,eV
k
ee
,10
4
cm
3
/s
Metastable atom
He(2
3
S
)
19.82
5.8
5.4
Ne(2
3
P
2
)
16.62
2.9
0.69
Ar(3
3
P
2
)
11.55
2.0
2.0
Kr(4
3
P
2
)
9.915
1.7
2.0
Xe(5
2
P
2
)
8.315
1.4
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