Environmental Engineering Reference
In-Depth Information
This formula determines the width of the spectral line
of the total radiation.
This means that the radiation flux from a flat layer of a plasma
j
ω
Δ
ω
is equal to the
equilibrium radiation flux according to (1.61) for
j
ω
ω
j
Δ
ω
and is zero outside
0
this range.
In the case of Lorentz broadening of the spectral line we have from (2.136) for
the absorption coefficient at the line wing
2
ν
k
ω
D
k
0
0
)
2
,
(
ω
ω
and the width of the spectral line for the total radiation flux is estimated as
p
k
0
L
,
Δ
ω
ν
k
0
L
1 .
(3.91)
Correspondingly, for the Doppler profile (2.138) of the spectral line of the atom we
obtain the width of the spectral line of total radiation:
D
p
ln(
k
0
L
),
k
0
L
Δ
ω
Δ
ω
1 ,
(3.92)
where
D
is the width of the Doppler-broadened spectral line in the case of a
small optical thickness of the plasma. Thus, resonant radiation from a plasma is
characterized by a broadened spectral line compared with the spectral line from in-
dividual atoms, because the principal contribution to the emergent radiation arises
largelyfromthewingsofthespectraofindividualatoms.
We now consider the profile of the spectral line for resonant radiation that leaves
a nonuniform plasma under real conditions when the temperature at plasma
boundaries is less than it is in the bulk of the plasma. The radiation emanating
from a plasma for frequencies near the center of a spectral line originates in a
plasma region near the boundaries. We use (1.61) for the radiative flux
j
ω
from
the equilibrium plasma, and we substitute in this formula the temperature
T
of
the layer that gives the main contribution to the radiation flux. This layer lies at
distance
x
ω
Δ
ω
from the boundary such that the optical thickness of this region is of
Figure 3.12
Self-reversal of spectral lines. 1 - profile of individual spectral line, 2 - spectral
power of emitted radiation at constant temperature, 3 - spectral power of emitted radiation if
the temperature drops to the boundary temperature.
