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2.2 Continuum radiation models
2.2.2
25
Special cases
Special cases, in which some additional approximations or some analytical
expressions are considered, are discussed in this section.
2.2.2.1
Photodetachment
Photodetachment transitions are typically modeled with the assumption
that:
1. Only the ground state of the negative ion contributes for the overall absorption coefficient.
2. The negative ions ground state is in a Saha equilibrium with the neutral
species ground state.
The Saha equilibrium equation becomes in this case:
NAB − = 0
2πµkB Tel
h2
3/2
QAB − (T )
NAB
0
h
i Q Q (T )
el AB
exp −1.4388 EAB − − EAB
(2.46)
0
with Qel = 2 and QAB − (T ) = gAB −
0
0
Photodetachment absorption cross-sections are then calculated in the usual
fashion:
hν
α(ν)T = NAB − σ(ν) 1 − exp −
(2.47)
0
kB T
2.2.2.2
Bremsstrahlung
Some analytic expressions for the calculation of the Bremstrahlung emission/absorption cross-sections are available in the literature.
The classical emission coefficient for the Inverse Bremsstrahlung of atomic
ionized species is given by Kramers [26]:
12 α2
6
hc
ν Ne Ni [MKS]
kB Te
(2.48)
Cross-sections for the Inverse Bremsstrahlung of N and O are provided by
Mjolsness and Ruppel [27]:
8
εν [J/m3 s sr Hz] =
3

√ 
σ(ν, Te ) = 8π 2 2π 
2π
3kB Te me
2π
h
hc
√ e
4π0
√ e
4π0
me c3
2  h
 
i2  
√ e
4π0
a0
i2
exp
 23
1 hc
 1 + 2 kB Te ν 5
kB Te 
a 0 σ0
3
(hcν)
(2.49)