Environmental Engineering Reference
In-Depth Information
We solve this equation in the case when the excitation process leads to a sharp
variation of the distribution function with increasing electron energy. Therefore,
we use the quasiclassical method taking the distribution function in the form
f
0
(
v
)
D '
0
(
v
)exp(
S
),
where
) is the electron distribution function in the absence of the excitation
process. The quasiclassical solution requires the validity of the criterion
dS
d
'
0
(
v
2
d
2
S
d
.
2
v
v
In this approximation we obtain
p
3
dS
d
ν
ν
eE
m
e
ex
v
D
,
a
D
,
a
and near the threshold the electron distribution function is
0
@
1
A
Z
v
a
p
3
d
f
0
(
v
)
D '
0
(
v
0
)exp(
S
)
D '
0
(
v
0
)exp
ν
ν
,
ex
v
0
where
v
0
is the threshold electron velocity. Transferring from the excitation rate to
the quenching rate on the basis of (2.57), we have
r
3
g
g
0
ν
ε
Δ
ε
Δ
ε
5/4
2
v
0
5
a
S
D
ν
.
q
We note that we assume the collision parameters, such as the rate of elastic elec-
tron-atom collisions, to be independent of the electron velocity near the excita-
tion threshold. These formulas give the following expression for the rate of atom
excitation by electrons if this process proceeds mostly near the excitation thresh-
old [41, 42]:
dN
dt
D
Z
2
d
4
π
v
f
0
(
v
0
)exp(
S
)
ν
ex
(
v
)
v
ν
1/5
2/5
q
g
a
v
0
2
0
D
4.30
a
v
f
0
(
v
0
) ,
(3.58)
ν
ν
0
g
0
0
where the distribution function
f
0
coincides with
0
in (3.54). It is convenient to
express this rate of atom excitation through the parameters in (3.57), so (3.58) takes
the form
dN
dt
D
'
3
0
3/5
3/5
2/5
.
5.48
v
ν
'
μ
γ
δ
0
Comparing (3.58) with (3.52) and (3.54) for the rate of atom excitation in other
limiting cases, we find that this case is realized under the condition
δ
1,
μγ
δ
3/2
3/5
2/5
3/2
γ
1 .
(3.59)
μ
