Environmental Engineering Reference
In-Depth Information
N
e
has the form
N
B
(2
1
P
)
N
e
N
0
N
(2
1
P
)
D
,
where
N
(2
1
P
)and
N
B
(2
1
P
) are current and Boltzmann number densities of atoms
in this state, and for an optically thick plasma we have
N
0
10
18
cm
3
,where-
as for a real optically thick plasma this value is several times lower. Thus, for the
electron number densities we have
D
1
N
(2
1
P
)
N
B
(2
1
P
).
In the same manner we have
N
B
(2
3
P
)
N
e
N
0
N
(2
3
P
)
D
,
10
13
cm
3
.For
and we have in this formula for optically thick plasma
N
0
D
4
simplicity, we take as in the previous case
N
(2
3
P
)
N
B
(2
3
P
).
In considering the balance for metastable state 2
3
S
involving electron collision
processes, we have from the balance equation
N
(2
1
S
)
N
(2
3
S
)
D
N
B
(2
1
S
)
N
B
(2
3
S
)
1
,
k
(2
1
S
!
2
1
P
)
1
C
k
(2
1
S
!
2
3
S
)
and since the rate constants
k
(2
1
S
2
3
S
) are comparable, the
relative population of the 2
1
S
metastable state with respect to the 2
3
S
metastable
state differs from that for the Boltzmann distribution, but not significantly.
For the lowest metastable state 2
3
S
, we obtain by ignoring the transition from
the 2
1
S
state
2
1
P
)and
k
(2
1
S
!
!
1
N
(2
3
S
)
N
B
(2
3
S
)
D
.
k
(2
3
S
2
1
S
)
k
(2
3
S
2
3
P
)
!
C
!
1
C
k
(2
3
S
!
1
1
S
)
Being guided by electron temperatures in the range
T
e
4 eV, we have that the
rate constants for quenching are comparable with the excitation rate constants for
transitions between excited states. Hence, from this formula we have
D
1
N
B
(2
3
S
)
100
N
(2
3
S
)
.
Thus, we obtain from the above analysis that the population of atom excited
states is lower than that under thermodynamic equilibrium. The reason is that
emission of resonantly excited atoms leads to violation of the thermodynamic pop-
ulation of these levels, and this violation is transferred to metastable states through
electron collision processes. Hence (3.69) for the rate constant for stepwise atom
ionization by electron impact based on thermodynamic equilibrium for excited
states does not work under real conditions where thermodynamic equilibrium is
violated. We add to this that the Maxwell energy distribution of electrons may be
violated in the tail of the distribution function because of inelastic processes involv-
ing electrons. This may enforce this effect.
