Environmental Engineering Reference
In-Depth Information
and
is the angle between the photon direction and the direction perpendicular to
the plasma surface (Figure 3.4). Evaluating this integral, we obtain for the photon
flux [34]
θ
0.274
N
d
1/2
k
1/2
0
j
D
.
(3.84)
τ
r
As is seen, the photon flux in an optically thick plasma is lower by (
k
0
d
)
1/2
than
that in an optically thin plasma.
Let us introduce the effective radiative time
τ
ef
of the resonantly excited state as
J
j
D
τ
τ
,
ef
r
where
r
is the radiative lifetime of an isolated atom. The effective radiative life-
time depends both on the geometry of the volume occupied by the plasma and on
the character of broadening of the spectral line. In particular, in the case when an
optically thick uniform plasma is located inside a tube, and the Lorenz type (2.136)
of spectral line broadening occurs, on the basis of the above result we have
τ
r
(
k
0
d
)
1/2
.
τ
D
0.91
τ
(3.85)
ef
3.3.6
Resonant Emission from a Nonuniform Plasma and Self-Reversal of Spectral Lines
Resonant radiation from a plasma containing resonantly excited atoms results from
radiative transitions involving these exited states and ground states, and according
to the above formulas the propagation of resonant photons through an optically
thick plasma is not diffusive in nature. Namely, transport of photons over large
distances compared with the mean free path of photons of the spectral line center
is determined by photons with frequencies in the spectral line wings. The reason
is that a photon emitted far from the center of a spectral line is more likely to
propagate a long distances than is a photon emitted near the center of a spectral
line, where repeated emissions and absorptions will occur with high probability.
As a result, the principal contribution to long-distance propagation of resonant
photons comes from the wings of the spectral line, where the mean free path of
these photons is of the order of the dimensions of the gaseous system through
which the photons propagate.
We now estimate on the basis of the above argumentation the flux of photons
outside a gaseous system assuming that the photon transport process does not
affect the density of excited atoms. We can take the mean free path of photons
corresponding to the center of the spectral line to be small compared with the
size
L
of the system, that is,
k
0
L
1,
where the absorption coefficient
k
0
for line-center photons is
k
0
D
N
0
σ
abs
(
ω
0
)
N
σ
em
(
ω
0
) according to (2.148), where
ω
0
is the central photon frequency. Under
