Environmental Engineering Reference
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where
σ
0
ω
are the cross sections of absorption and stimulated emission for
propagating resonant photons in accordance with (2.145) and (2.146) and
k
ω
is the
absorption coefficient of the plasma given by (2.149) in the case of thermodynamic
equilibrium between atoms in the ground and resonantly excited states. From this
we find that the photon flux is damped as it penetrates in a plasma and is given as
j
ω
(
z
)
σ
ω
and
1/
k
ω
. We ignore here the reabsorption processes
that hold true for strong fluxes of incident radiation, and this gives
j
ω
exp(
z
/
λ
), where
λ
D
j
0
.
In the above regime of a photoresonant plasma, the equilibrium is supported
between incident radiation and plasma emission at low intensities of incident ra-
diation, which leads to a low number density of electrons. We now analyze an-
other regime of evolution of a photoresonant plasma, where electron processes
determine the energy balance in the plasma. In particular, in the regime of low
intensity of incident radiation, the rate of associative ionization of excited atoms
(process (3.102)) is small compared with the rate of photon departure, that is,
N
τ
N
2
ef
k
as
,
where values of the rates of associative ionization
k
as
aregiveninTable2.14foran
alkali metal plasma. Taking the Lorenz broadening mechanism of spectral lines,
on the basis of (3.85) we obtain this criterion in the form
1
N
N
ef
D
r
k
ion
p
k
0
R
,
(3.108)
τ
where
τ
r
is the lifetime of an isolated atom. Taking typical parameters in this for-
10
8
s,
k
0
10
5
cm
1
,
R
10
12
cm
3
/s, we obtain
mula,
τ
1cm, and
k
as
10
18
cm
3
. This criterion holds true for a weakly
criterion (3.108) as
N
3
excited photoresonant plasma.
3.3.9
Kinetics of Electrons and Ionization Processes in Photoresonant Plasma
In considering the behavior of electrons in a photoresonant plasma, we note that
the strongest processes involving electrons correspond to ground-state excitation
and quenching of excited atoms according to the scheme
A
$
e
C
e
C
A
,
(3.109)
where
A
and
A
represent an atom in the ground and resonantly excited states.
Then, for a Maxwell distribution of free electrons, we find from this equilibrium
the electron temperature
T
e
Δ
ε
ln
N
0
g
N
T
e
D
,
g
0
which coincides with the excitation temperature given by (3.104),
T
e
T
.The
electron number density is determined by ionization of excited atoms in collisions
D
