Impact of the one-parameter approximation on the shape of optically-thick lines

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Impact of the one-parameter approximation on the
shape of optically-thick lines
D. Karabourniotis University of Crete GREECE
COST-529, Meeting at Mierlo, March 2006
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Plasma spectroscopy an open problem
Diagnosing high-pressure discharges by
optically-thick lines is an asymptotic process
starting somewhere get a first picture, which
gradually refines A correct interpretation of
diagnostics results need an understanding of the
plasma as it helps to improve this understanding
Diagnostics is yet an open problem due to a lack
of fundamental physical knowledge
(understanding) In this sense plasma spectroscopy
is yet an open problem
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Outline
v Expression of line intensity and in terms of
reduced functions for the plasma structure and
the line profile v One-Parameter Approximation
(OPA) for the source function v Validity of OPA
to represent emissivity in case of position
dependent line profile v Numerical examples of
line shapes and optical-depth profiles v
Experimental line shapes and optical-depth
profiles v Numerical tests for the determination
of the inhomogeneity parameter using the OPA
model
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Intensity of a spectral line

• Symmetric plasma layer

I?
xo
-xo
0
x
Emissivity
Planck law
Density of the Upper
Density of the Lower
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Line emissivity in terms of x
Position-dependent line profile
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Case of the Lorentz profile
Relative Lorentz profile
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Line emissivity in terms of y
xo
-xo
0
x
I?
1
0
y
2
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Self-reversed lines
IM
Im
Condition for reversal permits determination of
tst(?0s)
Emissivity at the line maximum
Ks?(?0s) becomes a function of ?(y) and Q (s0
,y)
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One-Parameter Approximation (OPA)
a (alpha) inhomogeneity parameter
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Validity of the OPA to represent Ks

• Case
• Position independent line profile, P(?,?)P(?)
• Position dependent line profile, P(?,?)
• Atomic collision broadening
• Electronic collision broadening

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dc ?
?i/?d1.03
?i/?dlt1.003
Accuracy of the one-parameter approach (OPA) for
representing Ks when P(?,?)P(?) better than 3
Karabourniotis, van der Mullen (2005)
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Atomic collision broadening
Decreasing L(x) Parabolic T(x), a1.62
?s
Without shift
12.6
d c
(i)
(d)
s0s/d0
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Decreasing L(x) Parabolic T(x), a1.62
With shift
?s
d c
(i)
(d)
s0s/d0
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Hollow L(x)
d c
a2.64
?s
(i)
(d)
Increasing L(x)
d c
a6
(d)
(i)
s0s/d0
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Parabolic T(x)
Decreasing L(x), a1.62
?i/?d
Atomic collision broadening
Hollow L(x), a2.64
s0s/d0
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Electronic collision broadening
?i/?d
Decreasing L(x) a1.62
s0s/d0
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Atomic collision broadening
?(?)
t(?)
w(?-?0)/d0?
Decreasing L(x), Parabolic T(x), s0 4, ?
0.73 (a1.62)
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?(?)
t(?)
w(?-?0)/d0?
Increasing L(x), Parabolic T(x), s0 4,
?0.3 (a 4.1)
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Electronic collision broadening
?(?)
t(?)
w(?-?0)/d0?
Decreasing L(x), Parabolic T(x), s0 4, ?
1.74 (a1.62)
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Experimental I(?) and t(?)
Neutr. Filter
Choper
L
M/Chr
Spher. Mir.
Uncertainty Neutral-filter absorbance 90
tNF4.5, ?t/t4.6
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Hg- 5461
PHILIPS R6 mm, Ig18 mm, 7.14 mg Hg, 100mbar
Ar/Kr, 150 W, 2.7A, P3 atm
Karabourniotis, Drakakis, Palladas XX ICPIG, 1991
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Tl- 5350
OSRAM R9 mm, Ig48 mm, 60mg Hg, 6 mg TlI, 30 mb
Ar 300 W, 2.8A, P6atm
Drakakis, Palladas, Karabourniotis J. Phys. D
1992
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Emission line
Na D-lines
PHILIPS R6 mm, Ig18 mm, 5 mg Hg,1.87 mg NaI,
100mbar Ar/Kr, 150 W, 3.65 A,
P2.8 atm
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Absorption profile
Na D-lines

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Experimental observations
v Optical depth at the line center, t0, one order
of magnitude lower than the calculated one on the
basis of the classical theories v Intensity at
the line minimum one to two orders of magnitude
higher than the calculated one on the basis of
the classical theories
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Determination of alpha (a)
Hg-5461, LTE, d c, Lin.(1) T(x), a2.23
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log(IM/Im)
15
7.4
4.2
log(so)
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7.4
D
6
log(IM/Im)
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Na-5890, Hollow L(x), d c, Para. T(x), a 2.18
L
log(IM/Im)
r?
6
log(so)
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6
D
log(IM/Im)
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Tl-5350 Increasing L(x), d c, Constr.
T(x), a 18
log(IM/Im)
22
log(so)
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Conclusions

• For optical depths lt12 the Ks-value is affected
  from the radial change of P(?,x) by less than 2.
• In order to determine Ks one needs to know only
  the a-value instead of the exact plasma
  structure.
• The difference in Ks using the OPA is less than
  5
• The measurements give optical depths at the line
  center less than 6.
• The determination of alpha is proved to be
  possible at these low optical depths using the
  OPA model.

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Sechin, Starostin et al, JQSRT 58, 887
(1997) Resonance radiation transfer in dense
media
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Emission line
Auto-lamp Very high-pressure P 20-40atm
Na D-lines ?D-line
20 Å ----------------
5894
Philips-Dusseldorf
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Hg-5461, LTE, d constant, Para(2) T(x), a1.23
log(IM/Im)
4.5
log(so)