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Data Quality and Needs for Collisional-Radiative Modeling

Data Quality and Needs for Collisional-Radiative Modeling. Yuri Ralchenko National Institute of Standards and Technology Gaithersburg, MD, USA Joint ITAMP-IAEA Workshop, Cambridge MA July 9, 2014. Basic rate equation. Vector of atomic states populations. Rate matrix. autoionizing

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Data Quality and Needs for Collisional-Radiative Modeling

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  1. Data Quality and Needs for Collisional-Radiative Modeling Yuri Ralchenko National Institute of Standards and Technology Gaithersburg, MD, USA Joint ITAMP-IAEA Workshop, Cambridge MA July 9, 2014

  2. Basic rate equation Vector of atomic states populations Rate matrix

  3. autoionizing states Collisional- Radiative Model Continuum ionization limit dielectronic capture autoionization (de)excitation charge exchange rad. transitions recombination ionization Z Z+1

  4. Collisional-radiative models are generally problem-taylored

  5. Atomic states Term Superconfiguration 1P 1224344452 3s23p3d24p 3P 3D3 1D 12283541 3D2 3D 3D1 3S 122836 3s23p34s Average atom Level Configuration 5S BUT: field modifications, ionization potential lowering

  6. How good are the energies? • The current accuracy of energies (better than 0.1%) is sufficient for population kinetics calculations • For detailed spectral analysis, having as accurate as possible wavelengths/energies is crucial(blends) • May need >1,000,000 states

  7. Radiative Autoionization • Allowed: generally very good if the most advanced methods (MCHF, MCDHF, etc) are used • Forbidden: generally good, less important for kinetics • Acceptable for kinetics, (almost) no data for highly-charged ions

  8. Collisions and density limits • High density • Different for different ion charges • LTE/Saha equilibrium • Collisions are much stronger than non-collisional processes • Populations only depend on energies, degeneracies, and (electron) temperature • BUT: need radiative rates for spectral emission • Low density (corona) • All data are (generally) important • Line intensities (mostly) do NOT depend on radiative rates, only on collisional rates pLTE Corona

  9. e-He excitation and ionization • Completeness • Consistency • Quality • Evaluation

  10. Neutral beam injection:Motional Stark Effect W. Mandl et al. PPCF 35 1373(1993) σ Iij,a.u. H π λ(Hα) Displacement of Hα Example: ; /0 = 0.353 0.42

  11. Solution: eigenstates are the parabolic states E = v×B parabolicstatesnikimi  = /2 for MSE Radiativechannelnikimi→ njkjmjπ – componentswithΔm=0σ – componentswithΔm=±1  nilimi– sphericalstates Standard approach: nilimi→ njljmj Only one axis: along projectile velocity There is another axis: along the induced electric field E How to calculate the collisional parameters for parabolic states?

  12. Answer • Express scattering parameters (excitation cross sections) for parabolic states (nkm) quantized along z in terms of scattering parameters (excitation cross sections AND scattering amplitudes) for spherical states (nlm) quantized along z’ O. Marchuk et al, J.Phys. B 43, 011002 (2010)

  13. Collisional-radiative model • Fast (~50-500 keV) neutral beam penetrates hot (2-20 keV) plasma • States: 210 parabolic nkm(recalculate energies for each beam energy/magnetic field combination) up to n=10 • Radiative rates + field-ionization rates are well known • Proton-impact collisions are most important • AOCC for 1-2 and 1-3 (D.R. Schultz) • Glauber (eikonal approximation) for others • Recombination is not important (ionization phase) • Quasy-steady state

  14. Theory vs. JET and Alcator C-Mod E. Delabie et al (2010) I. Bespamyatnov et al(2013)

  15. How important is dielectronic recombination? Fraction

  16. How to compare CR models?.. • Attend the Non-LTE Code Comparison Workshops! • Compare integral characteristics • Ionization distributions • Radiative power losses • Compare effective (averaged) rates • Compare deviations from equilibrium (LTE) • 8 NLTE Workshops • Chung et al, HEDP 9, 645 (2013) • Fontes et al, HEDP 5, 15 (2009) • Rubiano et al, HEDP 3, 225 (2007) • Bowen et al, JQSRT 99, 102 (2006) • Bowen et al, JQSRT 81, 71 (2003) • Lee et al, JQSRT 58, 737 (1997) • Typically ~25 participants, ~20 codes Validation and Verification

  17. EBIT: DR resonances with M-shell (n=3) ions EBIT electron beam 1s22s22p63s23p63dn extracted ions LMN resonances: L electron into M, free electron into N Fast beam ramping ER ER ER time

  18. Strategy Ca-like W54+ • Scan electron beam energy with a small step (a few eV) • When a beam hits a DR, ionization balance changes • Both the populations of all levels within an ion and the corresponding line intensities also change • Measure line intensity ratios from neighbor ions and look for resonances • EUV lines: forbidden magnetic-dipole lines within the ground configuration Ionization potential A(E1) ~ 1015s-1 A(M1) ~ 105-106 s-1 I = NAE (intensity)

  19. [Ca]/[K] THEORY: no DR

  20. [Ca]/[K] THEORY: no DR isotropic DR Non-Maxwellian (40-eV Gaussian) collisional-radiative model: ~10,500 levels

  21. [Ca]/[K] Non-Maxwellian (40-eV Gaussian) collisional-radiative model: ~18,000 levels THEORY: no DR isotropic DR anisotropic DR J m=+J m=-J atomic level degenerate magnetic sublevels Impact beam electrons are monodirectional

  22. Monte Carlo analysis: uncertainty propagation in CR models • Generate a (pseudo-)random number between 0 and 1 • Using Marsaglia polar method, generate a normal distribution • Randomly multiply every rate by the generated number(s) • To preserve physics, direct and reverse rates (e.g. electron-impact ionization and three-body recombination) are multiplied by the same number • Ionization distribution is calculated for steady-state approximation

  23. We think in logarithms… • Sample probability distribution • Normal distribution with the standard deviation  • Normal distribution is applied to log(Rate) • log-normal distribution

  24. Ne: fixed Ion/Rec rates Ne = 108 cm-3 Te = 1-100 eV Ionization stages: Ne I-IX ONLY ground states MC: 106 runs NOMAD code (Ralchenko & Maron, 2001)

  25. Ne: + stdev=0.05

  26. Ne: + stdev=0.30

  27. Ne: + stdev=2

  28. Ne: + stdev=10

  29. Only stdev=10 Structures appear!

  30. Only stdev=10

  31. Lines: two ions populated 1-  Z Z+n n=1, 2, >2

  32. C: 106, 1017, 1019, and 1021 cm-3

  33. Needs and conclusions (collisions) • CROSS SECTIONS, neither rates nor effective collision strengths • EBITs, neutral beams, kappa distributions,… • Scattering amplitudes (off-diagonal density matrix elements) • Also magnetic sublevels • Complete consistent (+evaluated) sets (e.g., all excitations up to a specific nmax) • Do we want to have an online “dump” depository? AMDU IAEA? VAMDC? • Need better communication channels

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