Environmental Engineering Reference
In-Depth Information
Because the nonstationarity of the distribution function is determined by its tail
and is relatively small, one can use in the first approximation the stationary expres-
sion for
f
0
that is given by
T
df
0
d
Ma
2
3
C
ε
C
f
0
D
0
ν
2
with the boundary condition
f
0
(
Δ
ε
)
D
0. Its solution has the form
)
1
exp
ε
Δ
ε
T
ef
Ma
2
3
f
0
(
ε
)
D '
0
(
ε
)
'
0
(
Δ
ε
)
D '
0
(
ε
,
T
ef
D
T
C
,
ν
2
where the distribution function
) is determined by (3.27) in ignoring the ex-
citation process. As is seen, because of absorption of fast electrons, the electron
energy distribution function differs from that in the absence of absorption because
atom excitation near the boundary of electron absorption leads to a decrease of the
electron energy by the atom excitation energy.
From the above formulas we obtain for the rate of atom excitation in this limiting
case
'
0
(
ε
dN
dt
D
m
e
M
3
0
4
π
v
ν
(
v
0
)
'
0
(
v
0
) .
(3.54)
This expression does not contain the rate constant for excitation, which is assumed
to be very large. Comparing (3.52) and (3.54), we have that the regime of (3.54) is
realized if the following criterion holds true:
Δ
ε
T
ef
3/2
m
e
M
g
0
ν
g
ν
q
1 ,
(3.55)
where
N
a
k
q
is the rate of quenching of excited atoms by a slow electron.
Let us consider the simple case when the elastic electron-atom collision rate
ν
D
q
(
v
)
is independent of the electron velocity. Then the Maxwell distribution function is
valid for electrons,
ν
N
e
3/2
exp
m
e
T
ef
'
D
0
(
ε
)
,
2
π
T
ef
and for the rate of atom excitation (3.54) gives
Δ
ε
T
ef
3/2
exp
N
e
m
e
Ma
2
3
dN
dt
D
4
p
π
Δ
ε
T
ef
M
ν
(
v
0
)
I
T
ef
D
T
C
.
ν
2
This formula allows us to determine the excitation efficiency
,thatis,thepor-
tion of input electric energy that is consumed in atom excitation. According to the
definition, the excitation efficiency is given by
dN
dt
eEw
e
N
e
D
Δ
ε
,
