1. FAST CODES FOR MODELING THE FUSION PLASMAS RADIATIVE PROPERTIES V.S. Lisitsa IAEA CCN meeting, Vienna, Sept. 27-28, 2010 RRC Kurchatov Institute, Moscow, Russia

2. Why do we need the simplified fast atomic codes? 1) Incorporation as the blocks into integrated plasma modeling (on the basis of transport code ASTRA, B2-EIRENE, etc.) 2) Account of new plasma effects: turbulent fluctuation of plasma parameters (especially for edge and divertor plasmas); 3) Estimation of atomic effects for complex ions (RR and DR for complex ion with account of core polarization effects); 4) Universal representation of plasma radiative properties with multi-electron impurity ions. General approach - quasiclassical methods V.A.Astapenko, L.A.Bureyeva, V.S.Lisitsa Review of Plasma Physics, 2003, v.23, pp.1-206. L.A. Bureyeva et al. Phys. Rev.A, v.65032702 (2002) V.I. Kogan, A.B. Kukushkin, V.S. Lisitsa, Phys. Rep., v.213,1 (1992) A survey of current status and applications of fast codes

3. Goal: Estimation of contribution of heavy atom impurities to the charge exchange recombination spectroscopy (CXRS) in tokamak plasmas (including the CXRS of core plasma in ITER) Motivation: The number of atomic energy states in two dimensional (nl) kinetics is rather large for direct computing of DR and CX spectroscopy, 2D radiative-collisional cascade is well described by quasiclassical kinetic model (without cut-off procedure, typical for numerical solving of kinetic equations system). M.B. Kadomtsev, M.G. Levashova, V.S. Lisitsa, JETP 106 (2008) 635-649 1. nl-KINRYD, n,l collisional-radiative kinetics of Rydberg atomic states

4. Population distribution function of bound atomic electron in С 5+ as a function of principal (n Z ) and orbital (l Z ) quantum numbers for charge exchange of С 6+ on diagnostic beam of Hydrogen atoms per one ion of С 5+ and one atom of Hydrogen N e =10 14 cm -3, T e =15 keV Hydrogen atoms in the ground state H 0 (n = 1) nl -population distribution function in С 5+ ion

5. ElementTransition Excitation rates (n=1) , 10 –14 m 3 /s Excitation rates H(n=2) , 10 –14 m 3 /s DINA [3]ADAS [3]nl-KINRYD He + 4–30.1020.0880.0770.016 C 5+ 8–70.6090.6880.5740.124 O 7+ 10–90.0910.025 S.N. Tugarinov, M.B. Kadomtsev, M.G. Levashova, V.S. Lisitsa, N.N. Nagel, 36th EPS Conference on Plasma Phys. Sofia, June 29 - July 3, 2009 ECA Vol.33E, P-5.214 (2009) Excitation rates for a 100-keV hydrogen beam User: ITER CXRS diagnostics, S.Tugarinov et al. (TRINITI, Russia)

6. ESMEABRR = (Electron + Static Many-Electron Atom) Goals: Estimations of background radiation for Thomson scattering diagnostics in ITER. Estimation of contribution of impurities to continuous spectrum in divertor and edge tokamak plasmas (including ITER divertor diagnostics tasks) Semi-analytic description of Bremsstrahlung and radiative recombination cross sections for collisions of quasiclassical electrons with a static many electron atoms and ions (from neutral atom to fully stripped). Users: ITER Divertor Thomson Scattering diagnostics, E.Mukhin et al. (Ioffe, Russia) ITER Edge Physics and Plasma-Wall Interactions Section (ITER). 2. Fast code for Bremsstrahlung + Radiative Recombination spectra

7. V.I. Kogan, A.B. Kukushkin, Sov. Phys. JETP, 60 (1984) 665. V.I. Kogan, A.B. Kukushkin, V.S. Lisitsa, Phys. Rep., 213 (1992) 1. The universal classical functions g 0 (  ) and g 1 (e) (curves) compared with the corresponding (replotted) results of the numerical quantum calculations s) [Lee C.M., Kissel L., Pratt R.H., Tseng H.K. Phys.Rev., 1976] Thomas-Fermi model Z – nucleus electric charge E- incident electron energy Classical “rotational“ approximation for high  Gaunt factor g for electron Bremsstrahlung on neutral atoms

8. EMEARCP = (Electron + Many-Electron Atom with Core Polarization). Goal: recombination rates of electrons in collision with complex ions (the input atomic data – energy levels and oscillator strengths are needed) Application: ionization balance in divertor and edge plasmas V.A.Astapenko, L.A.Bureyeva, V.S.Lisitsa Review of Plasma Physics, 2003, v.23, pp.1-206. L.A. Bureyeva et al. Phys. Rev.A, v.65032702 (2002) 3. Fast quasiclassical code for radiative and dielectronic recombination rates for many-electron ions with core polarization effects

9. Enhanced factor R averaged over coronal equilibrium for the temperature 500 eV for different heavy ions: 1 – W, 2 – Mo, 3 – Fe. Enhanced R-factor for radiative recombination with core polarization effects

10. Distribution of DR rates (in units 10 - 12 cm 3 /s) over n for the C 3+ ion at the electron temperature T e =10 5 K: solid curve – universal formula; dotted line – calculation [3]; long dashed line- calculation [2] Reference 1. K. LaGattuta and Yu. Hahn, Phys. Rev. Lett. V. 51, 558 (1983) 2. D. R. Rosenfeld, Astroph. J. V. 398, 386 (1992) 3. J. Li and Yu. Hahn, Z. Phys. V. D41, 19 (1997) The ISAN site: http://www.isan.troitsk.ru/ The same but for the Mg1+ ion: solid curve – universal formula; dotted line – calculation [1] DR rates in quasiclassical approximation

11. 1- total recombination rate (close coupling S. N. Nahar, Phys. Rev. A 55, 1980 (1997), 83 atomic states), 2- total radiative recombination rate (quasiclassical method with core polarization effects), 3- radiative recombination rate ( Kramers approx.), 4- recombination rate (static core), 5-dielectronic recombination rate. Recombination rates of Fe 2+ ion vs. electron temperature

12. Unified approach to dynamic and static Stark broadening, strong Zeeman splitting, etc. Goals: isotope composition diagnostics in ITER plasma by Balmer spectroscopic measurements (H-alpha, H-betha spectral lines; estimations of background radiation for Thomson diagnostics in ITER Paschen (e.g. P7) spectral line shape) Method: Fast numerical codes for line shapes in thermonuclear plasmas with strong magnetic fields combined with B2-EIRENE data for plasma parameters distribution along lines of sights. Users: ITER H-alpha diagnostics, A. Medvedev et al. (Kurchatov, Russia) ITER Thomson scattering diagnostics, E.Mukhin et al. (Ioffe, Russia) 4. Line broadening of hydrogen spectral lines in strongly magnetized plasmas

13. H  (B = 2 T and B = 4 T), N e = 10 15 cm −3, T e = 99764 K. H , B = 4 T, N e = 10 14 cm -3, T e = 1 eV Observation angle = 0° Observation angle= 90° Balmer lines spectra in magnetized plasmas S. Ferri, A. Calisti, C. Mosse et al., Contr. Plas. Phys. (2010); Marseille U. + Kurchatov Inst. Diagnostics D/T ratio in divertor plasmas o molecular dynamics _ kinetic method

14. Goal: background for Thomson diagnostics in ITER Users: ITER Divertor Thomson Scattering diagnostics, E.Mukhin et al. (Ioffe, Russia) Line shape calculations with B2-EIRENE code data for plasma parameters distribution

15. Plasma parameters along lines of sight: electron and neutral (Monte-Carlo modeling –B2- EIRENE code) densities and temperatures. LINES OF SIGHT

16. PLASMA PARAMETERS ALONG CHORDS (B2- EIRENE code) TeTe nene

17. Balmer P7 line shapes for ITER TS chord The integral along the chord. Green line is the contribution of continuum. The typical spectral line shape of deuterium Р-7 line across magnetic field in one separate point at the chord, observed under dome ( ~ 10000 A). Blue – static line shape with Zeeman splitting, Red – with addition of ion dynamics (FFM), Green – with addition of electron impact broadening, Magenta – total line shape, with Doppler broadening; Vertical lines mark the position of Zeeman components.

18. (work in progress) Screening constants + quantum defect method = fast code for calculations of radiative energy losses of arbitrary impurities in unstable plasmas et. It was demonstrated the effect of precise kinetics on radiative energy losses at low temperatures (R.E.H Clark, J. Abdallah (Jr.),At. Plasma-Material Int. Data for Fusion, v.11(2003)1). Just for such plasma parameters the turbulent temperature and density fluctuations can change strongly the results. To take turbulent effects into account is more simply by fast kinetics codes with further comparison with precise kinetics. 5. Universal radiative-collisional kinetic code, based on the method of charge screening constants and quantum defect for arbitrary chemical elements

19. Radiative losses of Li-plasma for Ne = 10 13 см -3 : with (solid) and without (dashed) turbulence

20. 1. Fast Quasiclassical Codes (FQC) are effective method for calculations of radiative properties of tokamak plasmas including ITER conditions. 2. These codes need the support of more complex codes both atomic ones (energy levels, oscillator strengths) and plasma modeling codes (B2-EIRENE, transport code ASTRA, etc.) 3. The codes are accessible: - Kurchatov Institute website (next year); - RAS Institute of Spectroscopy website; - semi-analytical formulas from surveys referenced above. 6. Conclusions