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Radiation modeling for optically thick plasmas

Radiation modeling for optically thick plasmas. Application to plasma diagnostics. D. Karabourniotis University of Crete GREECE. Plasma Light Model-Inventory workshop , Madeira, April 2005. Outline. General expression of spectral intensity I λ from a plasma layer

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Radiation modeling for optically thick plasmas

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  1. Radiation modeling for optically thick plasmas Application to plasma diagnostics D. Karabourniotis University of Crete GREECE Plasma Light Model-Inventory workshop, Madeira, April 2005

  2. Outline • General expression of spectral intensity Iλfrom a plasma layer • Εxpressionof Iλwith constant line width • Validity of calculating emissivity by means of a simple empirical radiation model based on the “inhomogeneity parameter” • Numerical validation of a method for determining the “inhomogeneity parameter” from line-reversal • Application to the temperature determination in a Hg-NaI lamp

  3. General expression of side-on intensity The equation of radiation transfer Expression for the side-on intensity Because of the plasma symmetry

  4. Expression of Iλ in terms of emissivity Kλ η=n/g,

  5. Relative distribution functions • For the absorbing atoms: • For the emitting atoms: • For the line profile: • Column density:

  6. Expression of Kλin terms of the optical coordinateY • optical coordinate:

  7. Assumption: • Expression of emissivity Kλ • Condition for reversal at line peak, Ks=K(λο±s) at the line peaks becomes a function of Λ(Y)

  8. A simple empirical plasma model for line self-absorption • Source function: • Alpha: inhomogeneity parameter, with Ks=K(λο±s) becomes a function of alpha, α

  9. Relationship between Ks and α Accuracy of the one-parameter approach for representing Ks better than 3% Karabourniotis, van der Mullen (2004)

  10. s0 Imax Imin (λ- λ0)/δ |s|/δ 0 How the alpha can be determined from line contours? • Contour of a self-reversed line and definitions • δ: half-width of a Lorentzian line profileP(λ)

  11. Construction of a discharge model • Absorbing atoms: • Emitting atoms: • Source function:

  12. τ0 Optical depth at λ0 L(r)U(r) total optical depth at λο along a plasma diameter INPUTS: α(y) τ0(y) τs(y) K0(y) Ks(y) OUTPUTS Numerical experiment Inputs and outputs

  13. Example: Decreasing L(r): a =10, b =20, c = 0.5; Parabolic T(r): T0=6000 K, Tw=1000 K; Eul = 3 eV L Λ U

  14. Input: τ0 =10 at y=0

  15. Experimental data –contour characteristics

  16. alpha Contour characteristics calculated from the one-parameter approach for the source function 1.7 1.6 1.5 Karabourniotis, ICPIG-2005 Inputs: α = 1.62 Ks = 0.520 Results: α = 1.64 Ks = 0.514 alpha 1.7 Dexp 1.6 1.5 log(Imax/Imin)exp

  17. Electron temperature in a 12-atm, 150-W Hg-NaI “standard” lamp

  18. T(5461) T(4047) Telectron Telectron ≡ T(63P2,63P0) Karabourniotis, Drakakis, Skouritakis, ICPIG-2005

  19. Summary • The emissivity at the peak of a self-reversed line is readily obtained if the inhomogeneity parameter (alpha) is known. • The alpha-value can be deduced from the line contours. This was proved through plasma numerical-simulation. • The distribution and the electron temperature were determined in 12-atm Hg-NaI lamp.

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