Environmental Engineering Reference
In-Depth Information
and the difference between the electron and gas temperatures is [40]
Ma
2
6
2
ν
v
T
e
T
D
.
(3.49)
h
v
2
ν
i
ω
2
C
ν
2
0 (3.48) coincides with (3.34), and (3.47) is trans-
formed into (3.26) if we employ in (3.47) instead of the electric field strength
E
its
In the limit
ω
ν
,at
t
D
effective value
E
/
p
2. In the other limiting case,
, the difference between
the electron and gas temperatures is independent of the collision rate and is
ω
ν
Ma
2
6
T
e
T
D
.
(3.50)
ω
2
3.2.6
Kinetics of Atom Excitation in Ionized Gases in an Electric Field
We now consider the character of atom excitation by electron impact in an ionized
gas subjected to an external electric field. In analyzing atom excitation by electron
impact in a plasma, we are restricted by a lower resonant excited atom state because
in reality this process gives the main contribution to atom excitation. The rate of
atom excitation by definition is given by
Z
1
dN
dt
D
2
d
N
a
k
exc
(
v
)
f
0
(
v
)
4
π
v
v
,
(3.51)
v
0
D
p
2
where
Δ
ε
/
m
e
is the threshold electron velocity, where
Δ
ε
is the atom
v
0
excitation energy,
k
exc
(
) is the rate constant for atom excitation resulting from
collision with an electron of a velocity
v
, and the symmetric distribution function
for electrons is normalized by the condition
1
v
Z
2
d
f
0
(
v
)4
π
v
v
D
N
e
.
0
Formula (3.51) is valid if the electron distribution function above the excitation
threshold is determined by elastic electron-atom collisions and the excitation pro-
cess does not perturb it.
Let us find the rate of atom excitation in an ionized gas on the basis of (3.51)
under the assumption that the excitation process does not change the electron dis-
tribution function above the excitation threshold. Then, the distribution function
above the excitation threshold has the following form according to (3.27):
f
0
(
v
0
)exp
ε
Δ
ε
T
ef
Mu
2
3
f
0
(
v
)
D
,
T
ef
D
T
C
,
and we consider a typical case for a gas discharge plasma when excitation relates to
the tail of the distribution function, that is,
Δ
ε
T
ef
.
