Environmental Engineering Reference
In-Depth Information
with electrons according to the scheme
A
C
.
e
C
A
$
2
e
C
(3.110)
Evidently, this process is stepwise. As a result, electrons are formed both in colli-
sions of two excited atoms according to process (3.102) and as a result of ionization
of excited atoms by electron impact (process (3.110)). Correspondingly, the balance
equation for the number density of electrons in the first stage of evolution of a
photoresonant plasma takes the form
dN
e
dt
D
k
as
N
2
C
N
e
N
k
ion
,
where
N
e
and
N
are the number densities of electrons and excited atoms,
k
ion
is
the rate constant for ionization of an excited atom by electron impact, and
k
as
is the
rate constant for process (3.104). The solution of this balance equation is
exp(
N
k
ion
t
)
1
.
k
as
N
k
ion
N
e
D
(3.111)
As is seen, the process of associative ionization is of importance in increase of the
electron number density in the first stage of evolution of a photoresonant plasma.
Subsequently, increase of the electron number density is determined by ionization
of atoms by electron impact.
To determine the electron temperature, we use the balance equation for the av-
erage energy of electrons per unit volume that results from processes (3.109):
d
(
N
e
ε
e
)
D„
ω
N
e
(
k
q
N
k
exc
N
0
),
dt
where we assume a Maxwell distribution function for electrons, and
3
T
e
/2 is
the average electron energy,
k
q
is the rate constant for quenching of excited atoms
by electron impact, and
k
exc
is the rate constant for atom excitation by electron
impact. We assume the energy distribution function for electrons to be a Maxwell
distribution function, whereas the electron temperature
T
e
varies in time. Taking
the excitation temperature
T
in accordance with (3.104) and using the principle
of detailed balance that connects rate constants
k
q
and
k
exc
,wereducethisbalance
equation to the form
ε
D
e
1
exp
„
T
„
T
e
dT
e
dt
D
2
„
3
(
T
T
e
)
k
q
N
D
,
τ
T
where we assume the electron and excitation temperatures to be nearby (
j
T
e
T
j
T
), and a typical time for establishment of the electron temperature
τ
T
in
a photoresonant plasma is
3
T
2
τ
D
.
(3.112)
T
2(
„
ω
)
2
k
q
N
