1. Impact of the one-parameter approximation on the shape of optically-thick lines COST-529, Meeting at Mierlo, March 2006 D. Karabourniotis University of Crete GREECE

2. 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

3. Outline √ Expression of line intensity and in terms of reduced functions for the plasma structure and the line profile √ One-Parameter Approximation (OPA) for the source function √ Validity of OPA to represent emissivity in case of position dependent line profile √ Numerical examples of line shapes and optical-depth profiles √ Experimental line shapes and optical-depth profiles √ Numerical tests for the determination of the inhomogeneity parameter using the OPA model

4. Intensity of a spectral line Symmetric plasma layer +xo+xo -xo-xo 0 x IνIν Emissivity Density of the Upper Density of the Lower Planck law

5. : Position-dependent line profile Line emissivity in terms of x

6. Case of the Lorentz profile Relative Lorentz profile

7. Line emissivity in terms of y +xo+xo -xo-xo 0 x IνIν 10 2 y

8. Self-reversed lines Condition for reversal permits determination of τ s =τ(ν 0 +s) K s =Κ(ν 0 +s) becomes a function of Λ(y) and Q (s 0,y) Emissivity at the line maximum ν0ν0 ν 0 +sν Bleu wingRed wing IMIM ImIm

9. One-Parameter Approximation (OPA) α (alpha) = inhomogeneity parameter

10. Validity of the OPA to represent K s Case: Position independent line profile, P(λ,χ)=P(λ) Position dependent line profile, P(λ,χ) Atomic collision broadening Electronic collision broadening

11. Accuracy of the one-parameter approach (OPA) for representing Ks when P(λ,χ)=P(λ) better than 3% Karabourniotis, van der Mullen (2005) Κ i /Κ d ~1.03 Κ i /Κ d <1.003 δ=c →

12. Atomic collision broadening Decreasing L(x) Parabolic T(x), α=1.62 s 0 =s/δ 0 ΚsΚs (i) (d) δ = c 12.6 Without shift :

13. Decreasing L(x) Parabolic T(x), α=1.62 s 0 =s/δ 0 ΚsΚs δ = c With shift : (i) (d)

14. ΚsΚs s 0 =s/δ 0 α=2.64 α=6 δ = c Hollow L(x) Increasing L(x) (i) (d) (i) (d)

15. Atomic collision broadeningΚi/ΚdΚi/Κd s 0 =s/δ 0 Decreasing L(x), α=1.62 Hollow L(x), α=2.64 Parabolic T(x)

16. Electronic collision broadening s 0 =s/δ 0 Decreasing L(x) α=1.62 Κi/ΚdΚi/Κd

17. Atomic collision broadening τ(ν) w=(ν-ν 0 )/δ 0 → Κ(ν) Decreasing L(x), Parabolic T(x), s 0 = 4, η = 0.73 (α=1.62)

18. Increasing L(x), Parabolic T(x), s 0 = 4, η=0.3 (α = 4.1) τ(ν) Κ(ν) w=(ν-ν 0 )/δ 0 →

19. Electronic collision broadening Decreasing L(x), Parabolic T(x), s 0 = 4, η =1.74 (α=1.62) w=(ν-ν 0 )/δ 0 → τ(ν) Κ(ν)

20. Experimental I(λ) and τ(λ) M/Chr L Spher. Mir. Neutr. Filter Choper Uncertainty: Neutral-filter absorbance 90% τ NF =4.5, Δτ/τ=4.6%

21. PHILIPS: R=6 mm, Ig=18 mm, 7.14 mg Hg, 100mbar Ar/Kr, 150 W, 2.7A, P~3 atm Karabourniotis, Drakakis, Palladas XX ICPIG, 1991 Hg- 5461

22. OSRAM: R=9 mm, Ig=48 mm, 60mg Hg, 6 mg TlI, 30 mb Ar 300 W, 2.8A, P~6atm Tl- 5350 Drakakis, Palladas, Karabourniotis J. Phys. D 1992

23. Na D-lines PHILIPS: R=6 mm, Ig=18 mm, 5 mg Hg,1.87 mg NaI, 100mbar Ar/Kr, 150 W, 3.65 A, P~2.8 atm Emission line

24. Na D-lines Absorption profile

25. Experimental observations √ Optical depth at the line center, τ 0, one order of magnitude lower than the calculated one on the basis of the classical theories √ Intensity at the line minimum one to two orders of magnitude higher than the calculated one on the basis of the classical theories

26. Hg-5461, LTE, δ = c, Lin.(1) T(x), α=2.23 log(I M /I m ) log(s o ) 15 4.2 Determination of alpha (α) 23 7.4

27. log(I M /I m ) D 7.4 6

28. log( s o ) Na-5890, Hollow L(x), δ = c, Para. T(x), α = 2.18 r→r→ L log(I M /I m ) 6

29. D 6

30. Tl-5350 Increasing L(x), δ = c, Constr. T(x), α = 18 log( s o ) log(I M /I m ) 22

31. Conclusions For optical depths <12 the Ks-value is affected from the radial change of P(λ,x) by less than 2%. In order to determine Ks one needs to know only the α-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.

33. Sechin, Starostin et al, JQSRT 58, 887 (1997) “Resonance radiation transfer in dense media”

34. Auto-lamp Very high-pressure P: 20-40atm 5894 Na D-lines →D-line Emission line 20 Å ---------------- Philips-Dusseldorf

35. Hg-5461, LTE, δ = constant, Para(2) T(x), α=1.23 log(I M /I m ) log(s o ) 4.5