Report

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 ... ˆ N N Z ,i ... Vector of atomic states populations dNˆ t ˆ ˆ A t , N t , N e , N i , Te , Ti ... Nˆ t dt Rate matrix I ij N i Aij Eij 3 autoionizing states CollisionalRadiative Model Continuum ionization limit (de)excitation rad. transitions Z Z+1 Collisional-radiative models are generally problem-taylored 6 Atomic states Term Superconfiguration 1P 1224344452 3s23p3d24p 3P 12283541 Average atom 122836 3D 3 1D 3D 2 3s23p34s Configuration 3S 3D 3D 1 Level 5S BUT: field modifications, ionization potential lowering 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 Radiative • Allowed: generally very good if the most advanced methods (MCHF, MCDHF, etc) are used • Forbidden: generally good, less important for kinetics Autoionization • Acceptable for kinetics, (almost) no data for highlycharged ions Collisions and density limits • High density ▫ Different for different ion charges ▫ LTE/Saha equilibrium Collisions are much stronger than non-collisional processes = 0 −∆0/ 0 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 e-He excitation and ionization • Completeness • Consistency • Quality • Evaluation Neutral beam injection: Motional Stark Effect σ π Iij,a.u. -4 -2 0 2 W. Mandl et al. PPCF 35 1373 (1993) H 4 λ(Hα) Displacement of Hα Example: = ; /0 = 0.353 0.42 Solution: eigenstates are the parabolic states E = v×B E parabolic states nikimi Radiative channel nikimi→ njkjmj π – components with Δm=0 σ – components with Δm=±1 = /2 for MSE v nilimi – spherical states 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? 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 (nlm) quantized along z’ O. Marchuk et al, J.Phys. B 43, 011002 (2010) 2±10 1 1 1 20 2 = 20 + 20 + 2 21 ∓ cos 20 2 2 2 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 Theory vs. JET and Alcator C-Mod E. Delabie et al (2010) I. Bespamyatnov et al (2013) Fraction How important is dielectronic recombination? 18 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 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 Strategy 1. 2. 3. 4. 5. 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 Ca-like W54+ Ionization potential A(E1) ~ 1015 s-1 A(M1) ~ 105-106 s-1 I = NAE (intensity) [Ca]/[K] 54+ 3 2=2 − 3 2=3 55+ 33/2 − 35/2 THEORY: no DR [Ca]/[K] 54+ 3 2=2 − 3 2=3 55+ 33/2 − 35/2 THEORY: no DR isotropic DR Non-Maxwellian (40-eV Gaussian) collisional-radiative model: ~10,500 levels [Ca]/[K] Non-Maxwellian (40-eV Gaussian) collisional-radiative model: ~18,000 levels 54+ 3 2=2 − 3 2=3 55+ 33/2 − 35/2 THEORY: no DR isotropic DR anisotropic DR J atomic level m=+J m=-J degenerate magnetic sublevels Impact beam electrons are monodirectional 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. electronimpact ionization and three-body recombination) are multiplied by the same number • Ionization distribution is calculated for steady-state approximation We think in logarithms… • Sample probability distribution ▫ Normal distribution with the standard deviation ▫ = 1 − − 2 /2 2 2 ▫ Normal distribution is applied to log(Rate) log-normal distribution 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) Ne: + stdev=0.05 Ne: + stdev=0.30 Ne: + stdev=2 Ne: + stdev=10 Only stdev=10 Structures appear! Only stdev=10 Lines: two ions populated 1- Z Z+n =+∙ 1− = − ∙ + − n=1, 2, >2 C: 106, 1017, 1019, and 1021 cm-3 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