Environmental Engineering Reference
In-Depth Information
Here
v
and
v
0
are the electron velocities before and after atom excitation, and from
the energy conservation we have
v
N
k
q
are the rates of atom excitation and quenching by electron impact, so
N
0
and
N
are the number densities of atoms in the ground and excited states, respectively,
and
k
ex
and
k
q
are the rate constants for the corresponding processes, which are
connected by the principle of detailed balance (2.57). Therefore, we have
2
D
2
Δ
ε
/
m
e
C
(
v
0
)
2
;
ν
D
N
0
k
ex
and
ν
D
ex
q
s
2
f
0
q
0
N
0
g
0
N
g
Δ
ε
m
e
2
f
0
(
v
)
D
2
v
,
v
>
v
0
D
.
v
From this equality we obtain the following relation between the distribution func-
tions for slow and fast electrons:
f
0
(
v
0
)
f
0
q
0
2
v
2
v
f
0
(
v
)
D
.
(3.63)
f
0
(0)
In the case of a Maxwell distribution function for slow electrons (
f
0
(
ε
)
exp(
/
T
e
)), for fast electrons whose energy exceeds the threshold energy of
atom excitation this formula gives
ε
v
0
)exp
ε
Δ
ε
T
e
f
0
(
)
D
f
0
(
,
v
that is, it leads to a Maxwell distribution function for fast electrons. Thus, quench-
ing collisions of electrons with excited atoms restore the Maxwell distribution func-
tion above the threshold of atom excitation.
The above cases of atom excitation by electrons in a plasma show that this pro-
cess depends on the character of establishment of the electron distribution function
near the threshold of excitation. The result depends both on the rate of restoring
the electron distribution function in electron-electron or electron-atom collisions
and on the character of quenching of excited atoms. Competition between these
processes yields different ways of establishing the electron distribution function
and different expressions for the effective rate of atom excitation in a gas and plas-
ma. Thus, the excitation rates depend on the collision processes which establish
the electron distribution function below and above the excitation threshold, and
the equilibrium for excited atoms.
Ionization of atoms in a plasma proceeds similarly to atom excitation, but in
contrast to excitation of the lowest electron level, excitation processes influence
strongly the electron energy distribution function, and this leads to the dependence
of the ionization rate on excitation processes. In the limit of low electron number
density, the rate constant for atom ionization is given by
Z
1
k
ion
D
v
N
a
σ
ion
(
v
)
f
(
v
)
d
v
,
v
0
D
p
2
J
/
m
e
is the threshold electron velocity for atom ionization,
J
is
the atom ionization potential, and
where
v
0
σ
ion
(
v
) is the ionization cross section. A spread
