Environmental Engineering Reference
In-Depth Information
In the above regime of evolution of a photoresonant plasma, the energy of inci-
dent radiation is contained in outgoing radiation. We now consider another regime
of evolution of a photoresonant plasma [70], where incident radiation energy is con-
sumed on ionization of excited atoms in accordance with the following processes:
A
!
A
!
A
C
.
e
C
e
C
A
,
e
C
2
e
C
(3.113)
In this regime, electrons obtain energy by quenching of excited atoms and lose the
energy as a result of the ionization process, which leads to the balance equation for
the electron energy [70]:
„
ω
N
N
e
k
q
D
J
N
k
ion
N
e
,
where
k
q
is the rate constant for quenching of a resonantly excited atom by elec-
tron impact,
k
ion
is the rate constant for ionization of an excited atom in collision
with an electron that is assumed to have stepwise character, and
J
is the ioniza-
tion potential of a resonantly excited atom. This gives the equation for the electron
temperature
T
e
:
k
ion
T
e
D
„
J
k
q
T
e
.
(3.114)
From this it follows that the electron temperature is independent of the number
density of atoms, and its values are given in Table 3.4 for an alkali metal photores-
onant plasma. Here (3.69) is used for the rate constant for stepwise ionization of
excited atoms in collisions with electrons, and the values of the rate constants
k
q
for quenching the resonantly excited atom by electron impact are taken from Ta-
ble 2.8. Note that because (3.69) gives overstated values of the rate constant for
stepwise atom ionization, the values of the electron temperature in Table 3.4 are
lower than the real values, but the simplicity of (3.69) allows us to analyze a general
physical picture in this case.
Ta b l e 3 . 4
The electron temperature
T
e
according to (3.104), the equilibrium constant
K
ion
for ionization equilibrium at this temperature, and the intensity of incident radiation
I
ω
if the
excitation temperature is equal to the electron temperature
T
e
.
Vapor
T
e
,eV
K
ion
,10
15
cm
3
τ
,10
8
s
τ
T
,10
9
s
τ
ion
,10
8
s
Li(2
2
P
)
0.31
180
20
1.6
2.7
3.0
Na(3
2
P
0.26
1400
13
1.1
2.6
2.1
K(4
2
P
1/2
)
0.24
440
3.6
1.6
1.6
0.7
K(4
2
P
3/2
)
0.24
440
7.5
1.5
1.6
2.6
Rb(5
2
P
1/2
)
0.23
510
2.9
1.7
1.6
2.8
Rb(5
2
P
1/2
)
0.22
630
5.8
1.6
1.6
2.7
Cs(6
2
P
1/2
)
0.22
270
3.5
1.8
1.1
2.6
Cs(6
2
P
3/2
)
0.21
480
6.0
1.6
1.1
2.4
