Environmental Engineering Reference
In-Depth Information
One can see that this limiting case may be realized at low electric field strengths,
which corresponds to
1.
As a demonstration, we apply the above results to the helium case, where the
quenching rate constant is
k
q
γ
10
9
cm
3
/s [43], the rate constant for elastic
electron scattering by a helium atom is
k
ea
D
3.1
10
8
cm
3
/s [44], and we have
D
7.1
10
4
δ
D
0.13 in accordance with the definition. Next,
μ
D
1.4
for the helium
10
3
x
2
,where
x
case, and
E
/
N
a
is the reduced electric field
strength, which is measured in Townsends. In this case
γ
in (3.57) is 4.3
D
μ
and
δ
are fixed, where-
as
varies with variation of the electric field strength. In this case the ratio of rates
according to (3.54) and (3.52) is 8.4/
x
3
, and the boundary of these mechanisms
of atom excitation relates to the electric field strength of
x
γ
2Td. In the same
manner, we find that (3.58) and (3.52) give the identical result at
x
D
D
1.5 Td, and
the excitation rates according to (3.58) and (3.54) are equal at
x
3.1 Td. Thus,
we conclude that the rate of excitation of the metastable He(2
3
S
)atominanion-
ized gas of a low degree of ionization is determined by (3.52) at low electric field
strengths and by (3.54) at high electric field strengths. Formula (3.58) may be used
in a narrow intermediate range of electric field strengths, roughly between 1.5 and
3.1 Td.
Wenowconsideratomexcitationinanionizedgasinanelectricfieldfora
regime of electron evolution that corresponds to the opposite criterion with respect
to (3.30) when the Maxwell distribution function for electrons holds true. The gen-
eral character of atom excitation is the same as in the regime of a low density of
electrons. In the limit when the excitation process does not influences the tail of
the distribution function, the rate of atom excitation is given by (3.54), where
D
'
0
(
v
0
)
is the Maxwell distribution function, and this formula has the form
T
e
Δ
ε
v
0
)exp
3/2
dN
dt
D
4
p
π
m
e
M
T
e
Δ
ε
N
e
ν
(
.
(3.60)
If the electron distribution function decreases sharply near the excitation thresh-
old because of atom excitation, the rate of atom excitation by analogy with (3.53) is
given by
Z
1
dN
dt
D
v
@
f
2
d
4
π
v
@
t
v
0
Z
B
ee
(
v
0
)
1
f
0
T
e
C
df
0
d
4
π
v
0
m
e
2
d
D
4
π
v
I
ee
(
f
0
)
D
,
v
ε
v
0
where the distribution function
f
0
near the excitation threshold has the form
N
e
m
e
2
3/2
exp
exp
T
e
Δ
ε
T
e
f
0
(
v
)
D
,
ε
Δ
ε
.
π
T
e
Using (3.20) for the electron-electron collision integral under assumption the exci-
tation energy exceeds the electron temperature, that is,
Δ
ε
T
e
,wehaveforthe
