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Chapter 11: Plasma physics
59
2. The Doppler broadening is caused by the thermal motion of the particles:
Δ
λ
λ
=
2
c
±
2ln(2)
kT
i
m
i
This broadening results in a Gaussian line proFle:
k
ν
=
k
0
exp(

[2
√
ln 2(
ν

ν
0
)
/
Δ
ν
D
]
2
)
, with
k
the coefFcient of absorption or emission.
3. The Stark broadening is caused by the electric Feld of the electrons:
Δ
λ
1
/
2
=
²
n
e
C
(
n
e
,T
e
)
³
2
/
3
with for the H
β
line:
C
(
n
e
,T
e
)
≈
3
·
10
14
˚
A

3
/
2
cm

3
.
The natural broadening and the Stark broadening result in a Lorentz proFle of a spectral line:
k
ν
=
1
2
k
0
Δ
ν
L
/
[(
1
2
Δ
ν
L
)
2
+(
ν

ν
0
)
2
]
. The total line shape is a convolution of the Gauss and Lorentz proFle
and is called a
Voigt profle
.
The number of transitions
p
→
q
is given by
n
p
B
pq
ρ
and by
n
p
n
hf
±
σ
a
c
²
=
n
p
(
ρ
d
ν
/h
ν
)
σ
a
c
where
d
ν
is the
line width. Then follows for the cross section of absorption processes:
σ
a
=
B
pq
h
ν
/cd
ν
.
The background radiation in a plasma originates from two processes:
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This note was uploaded on 01/30/2011 for the course PHYSICS 208 taught by Professor Ye during the Spring '10 term at Blinn College.
 Spring '10
 Ye
 Plasma Physics

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