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 2

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

4. Collisional-radiative models are generally problem-taylored Collisional-radiative models are generally problem-taylored

5. Typical sets of atomic data NON-COLLISIONALNON-COLLISIONAL ▫Energy levels, ionization potentials  E/B-field-modified  IP lowering ▫Radiative probabilities  High multipoles ▫Autoionization probabilities  Fields?.. ▫Field-induced processes COLLISIONALCOLLISIONAL ▫Electron impact  Excitation, deexcitation  Ionization, 3-body recomb.  Radiative recomb., photoionization ▫Heavy-particle impact  Excitation, deexcitation  Ionization, 3-body recomb.  Charge exchange

6. Atomic states 6 Average atom 122836122836 12243444521224344452 1228354112283541 Superconfiguration 3s 2 3p 3 4s 3s 2 3p3d 2 4p Configuration 5S5S 3S3S 3D3D 1D1D 3P3P 1P1P Term 3D13D1 3D23D2 3D33D3 Level BUT: field modifications, ionization potential lowering

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

8. 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

9. Collisions and density limits Low density (corona) ▫All data are (generally) important ▫Line intensities (mostly) do NOT depend on radiative rates, only on collisional rates pLTE Corona

10. e-He excitation and ionization Completeness Consistency Quality Evaluation Completeness Consistency Quality Evaluation

11. Motional Stark Effect Neutral beam injection: Motional Stark Effect Displacement of H α I ij,a.u. σ π λ(H α ) W. Mandl et al. PPCF 35 1373 (1993) HH HH 0.42

12. Solution: eigenstates are the parabolic states  n i k i m i parabolic states n i k i m i n i l i m i n i l i m i – spherical states n i k i m i n j k j m j Radiative channel n i k i m i → n j k j m j π – components with Δm=0 σ – components with Δm=±1 n i l i m i n j l j m j Standard approach: n i l i m i → n j l j m j Only one axis: along projectile velocity There is another axis: along the induced electric field E  =  /2 for MSE E = v×B How to calculate the collisional parameters for parabolic states?

13. Answer scattering parameters parabolic states ( nkm ) quantized along z scattering parameters spherical states ( nlm ) quantized along z’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 ( nlm ) quantized along z’ O. Marchuk et al, J.Phys. B 43, 011002 (2010)

14. Collisional-radiative model Fast (~50-500 keV) neutral beam penetrates hot (2-20 keV) plasma n=10States: 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

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

16. Non-statistical populations Boltzmann (statistical): Reduced populations: n i =N i /g i Statistical  equal n i w/o field ionization with field ionization n e = 3×10 13 cm -3 T e = 3 keV E b = 50 keV/u B = 3 T Marchuk, Ralchenko, and Schultz (2012)

17. How important is dielectronic recombination? Fraction

18. How to compare CR models?.. Non-LTE Code Comparison WorkshopsAttend 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 Workshops8 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 18 Validation and Verification

19. EBIT: DR resonances with M-shell (n=3) ions LMN resonances: L electron into M, free electron into N 1s 2 2s 2 2p 6 3s 2 3p 6 3d n EBIT electron beam extracted ions time ERER ERER ERER Fast beam ramping

20. Strategy 1.Scan electron beam energy with a small step (a few eV) 2.When a beam hits a DR, ionization balance changes 3.Both the populations of all levels within an ion and the corresponding line intensities also change 4.Measure line intensity ratios from neighbor ions and look for resonances 5.EUV lines: forbidden magnetic-dipole lines within the ground configuration A(E1) ~ 10 15 s -1 A(M1) ~ 10 5 -10 6 s -1 I = N  A  E (intensity) Ionization potential Ca-like W 54+

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

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

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

24. 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

25. We think in logarithms…

26. Ne: fixed Ion/Rec rates N e = 10 8 cm -3 T e = 1-100 eV Ionization stages: Ne I-IX ONLY ground states MC: 10 6 runs NOMAD code (Ralchenko & Maron, 2001)

27. Ne: + stdev=0.05

28. Ne: + stdev=0.30

29. Ne: + stdev=2

30. Ne: + stdev=10

31. Only stdev=10 Structures appear!

32. Only stdev=10

33. Lines: two ions populated  1-  ZZ+n n=1, 2, >2

34. C: 10 6, 10 17, 10 19, and 10 21 cm -3

35. 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 n max ) “dump” depositoryDo we want to have an online “dump” depository? AMDU IAEA? VAMDC? Need better communication channels