Environmental Engineering Reference
In-Depth Information
where R is the solar radius, r is the distance between the Earth and the Sun, and
j ω is the radiation flux at the Sun's surface. As is seen, the spectral distribution for
radiation near the Sun and the Earth is identical.
Let us represent the radiation flux emitted by the solar photosphere on the basis
of (3.76) and (1.61) in the form
Z
Z
1
1
du ω exp
F ( u ω ),
j ω D ω
2
u ω
cos
d cos
θ
2
π
2 c 2
θ
0
0
1 1 . Assuming the dependence F ( u ω )tobeweak,
we expand this function in a series
D exp(
where F ( u ω )
ω
/ T )
1
2 ( u ω
u 0 ) F 0 ( u 0 )
u 0 ) 2 F 00 ( u 0 ).
F ( u ω )
D
F ( u 0 )
C
( u ω
C
u 0 is taken such that the second term is zero after integration. This yields u 0
D
2/3,
and the radiation flux is
( u 0 ) 1
5 F 00 ( u 0 )
18 F ( u 0 )
j (0)
j ω D
,
(3.97)
ω
where j (0)
1 ) 1 is the radiation flux of a blackbody
at a temperature that corresponds to the point with optical thickness u ω D
2 (4
2 c 2 ) 1 ( exp(
ω D ω
π
ω
/ T )
2/3.
The second term in the parentheses in (3.97) allows us to estimate the accuracy of
the operation employed.
We now apply (3.97) to the solar atmosphere assuming the process
H !
ω C
e
C
H ,
(3.98)
where H is a hydrogen atom. The dependence on the photon frequency for the
cross section
det of the process (3.98) of electron photodetachment from the neg-
ative hydrogen ion is given in Figure 3.13, and we below use a simple approxima-
tion [65] for this cross section:
σ
3/2
0
0 ) 3/2
8
ω
(
ω ω
σ
det (
ω
)
D σ
,
(3.99)
max
ω
3
Figure 3.13 The cross section of photodetachment of the negative hydrogen ion. Experiment:
open circles - [62], closed circles and triangles - [63], theory: 1 - [64], 2 - [65].
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