Fumihiro Koike, Kitasato University and NIFS

1. Atomic structure and dynamics calculations using the GRASP family of codes, and an introduction of some activities in NIFS Collaborators: Izumi Murakami, NIFS (National Institute of Fusion Science) Daiji Kato, NIFS (National Institute of Fusion Science) Xiaobin Ding, NIFS (National Institute for Fusion Science) Tohru Kawamura, TITECH (Tokyo Institute of Technology) Fumihiro Koike, Kitasato University and NIFS

2. Outline: • Analysis of Visible M1 Lines in Tungsten Ions • Collisional-radiative model for W ions • Code development for single electron capture by H nucleus from metal surface • Ka radiation from low charge chlorine heated by an ion beam for plasma diagnostics • Code Availability • Summary

3. Analysis of Visible M1 Lines in Tungsten IonsExperimental: Komatsu et al, Proceedings of HCI@Shanghai (2010) submitted

4. Magnetic dipole transitions between the W26+ ground state multiplets using GRASP2K MCDF wavefunctions

5. Mean radius of 4l orbital in Cd-like ions • Ground state: • [Kr]4d104f2 • For W26+ ions • <r4f> < <r4p> • Strong correlations between 4p,4d, and 4f orbitals are expected.

6. Identification of the M1 Lines for W26+ • Correlation Models • Active Space: • AS1={4f,5s,5p,5d,5f,5g}, AS2=AS1+{6s,6p,6d,6f,6g} • Valence-Valence Correlation: • 5SD: 4d104f24d10(AS1)26SD:4d104f24d10(AS2)2 • Core-Valence Correlation: • 4p_5SD: 4s24p64d104f24s24p54d104f1(AS1)2 The wavelength (in nm) of the transition [4f-2]4 [[4f-]5/2[4f]7/2]5

7. Collaboration with theoretical group, LHD and EBIT experimental groups EBIT/CoBIT measurements of visible spectra for Wq+ (q=12~30) GRASP calculation for atomic structure. CR model with atomic data from HULLAC code. EUV and visible spectroscopy for LHD plasma. (C. Suzuki) gAr distribution CR model CoBIT experiments W26+(4f25/2)J=4 – (4f5/24f7/2)J=5 l = 3894.1 (experiment) l = 3937 (GRASP2K) l = 4029 (HULLAC) Komatsu et al. (2010) HCI 2010 @ Shanghai

8. Energy Levels of the ground state of W26+

9. Collisional-radiative model for W ions I.Murakami, D. Kato, H. A. Sakaue, N. Yamamoto, C. Suzuki NIFS

10. Measurement and atomic calculations MCDF calculations W 33+ W 34+ Berlin EBIT W 35+ W 36+ ASDEX W39+ - W45+ W 37+ P¨utterich et al.(2005) Rhee and Kwon (2008)

11. recombination Excitation by electron & proton impact Deexcitation by electron & proton impact and radiative decay Ionization Deexcitation by electron & proton impact radiative decay Rate equations • Rate equation of excited level p in steady–state is described asdn(p)/dt = Γin – Γout =0 Excitatiob by electron & proton impact Population density of level p is then obtained as：　 n(p)=n0(p)+n1(p)=R0(p)neni+R1(p)nen(1) wheren0(p): recombining plasma component ∝ni(FeXXII) n1(p): ionizing plasma component ∝n(1)(FeXXI) The plasma considered here is headed by the neutral beam injection (NBI) and the ionizing plasma component is dominant.

12. W ions considered here: • W 37+ (194 levels)4s2 4p6 4d, 4s2 4p6 4f, 4s2 4p6 5l (l=s~g), 4s2 4p5 4d2, 4s2 4p5 4d 4f, 4s2 4p5 4d 5s • W 36+ (213 levels)4s2 4p6 4d2, 4s2 4p6 4d 4f, 4s2 4p6 4d 5l (l=s~g), 4s2 4p5 4d3 • W 35+ (296 levels)4s2 4p6 4d3, 4s2 4p6 4d2 4f, 4s2 4p6 4d2 5s, 4s2 4p5 4d4

13. Electron density effect on the calculated spectra for W35+ CR model calculations Atomic data : HULLAC code 45.12A: 4p54d4 (J=5/2) – 4p64d3 (J=7/2) (45.12A) gA=3.538x1012 4p54d4 (J=9/2) – 4p64d3 (J=7/2) (45.13A) gA=3.33x1012 52.16A: 4p64d24d (J=5/2) – 4p64d3 (J=3/2) (52.11A) gA=1.506x1013 4p64d24f (J=7/2) – 4p64d3 (J=5/2) (52.17A) gA=1.372x1013 53A: 4p64d24f(J=3/2) – 4p64d3 (J=3/2) (52.96A) gA=1.011x1013 4p64d34f (J=5/2) – 4p64d3 (J=3/2) (53.00A) gA=2.493x1011 4p54d4 (J=5/2) – 4p64d3 (J=3/2) (53.02A) gA=5.068x1011 13

14. Code development for single electron capture by H nucleus from metal surface Daiji Kato NIFS IAEA CCN Meeting 2010

15. Features of theoretical methodimplemented with the code • Semi-classical treatment of H nucleus-metal surface collision. • Target surface electrons are represented by degenerate free electron gas in the jellium model. • Static linear density response of target electron gas induced by external nuclear charge (calculated by means of Kohn-Sham DFT in local density approximation). • Direct numerical solution (split-operator-spectral method) of time-dependent Schrödinger equation of electron wave-function. • Adiabatic expansion of wave-function, and B-spline method and discrete-variable-representation of adiabatic state function. • Density matrix formulation of level population. IAEA CCN Meeting 2010

16. Semi-classical method for single electron capture by translating projectile ion outward from metal surface Electronic transition is treated by quantum mechanics Ion motion is represented by classical trajectories De Broglie wavelength of ion << atomic scale （= proton kinetic energy ≥ 1eV） For electrostatic dielectric response of solids, Ion velocity ≤ 10-8 cm × plasma frequency （1016 s-1 for ne=1023 cm-3） （= proton kinetic energy ≤ 25 keV） Electron gas in surface potential well (jellium model) Dielectric response of the electron gas　（Static linear density response theory） Constant velocity classical trajectory IAEA CCN Meeting 2010

17. Classical picture of H atom-metal surface interaction electron image electron VeI VCoul VpI D z nucleus nuclear image ρ= (x2 + y2)1/2 surface vacuum solid IAEA CCN Meeting 2010

18. Effective potential energy of electron near Mo surface Hydrogen nucleus is located at the origin, 10 a.u. above from Mo surface. Cylindrical coordinates are used. 1 au length = 1 Bohr radius. 1 au energy = 27.21 eV. IAEA CCN Meeting 2010

19. Level population created by electron capture from Mo surface Hydrogen atoms translating outward from Mo surface with angle of 60 degree to the surface normal. Hydrogen atoms translating outward from Mo surface to the surface normal direction. Fermi velocity of Mo = 1.19 au = 2.61 x 108 cm/s. IAEA CCN Meeting 2010

20. Status of the code development • The code can be improved substantially (e.g. more realistic target description, beyond jellium model) • Validation of theoretical methods implemented in the code requires more comparison with experimental results. • This code is not ready to open for public. IAEA CCN Meeting 2010

21. Ka radiation from low charge chlorine heated by an ion beam for plasma diagnostics Toru Kawamura, Kazuhiko Horioka Department of Energy Sciences, Tokyo Institute of Technology Fumihiro Koike Physics Laboratory, School of Medicine, Kitasato University

22. Cln+:1s2s22p63l(8-n): (1 ≤ n ≤ 8) with open M-shell Cl(8+m)+:1s2l(8-m) : (1 ≤ m ≤ 7 ) 1.2 with open L-shell grasp, grasp92 calculation Many K lines is distributed over photon energy according to the ionization state. 1.0 0.8 Tokyo Institute of Technology radiative decay rate ( x 1014 sec-1) 0.6 0.4 0.2 0 2.8 2.6 2.65 2.7 2.75 photon energy (keV) Ka photon energies show the characteristic charge state of plasmas , and Ka with M-shell electrons may be useful for lower temperature.

23. 6 6 6 ~10 eV K1 grasp92 calculation Cl+ Cl3+ Cold Ka is mainly composed of the lines from Cl+ ~ 6+, and may be a good candidate for cold plasma diagnostics. Cl5+ Cl7+ K2 4 4 4 Cl4+ Cl6+ Cl8+ Cl2+ 2 2 2 Tokyo Institute of Technology National Astronomical Observatory : http: //www.nao.ac.jp/ K1 : 2622.3 eV K2 : 2620.7 eV 0 Blue-shift of Ka lines by outer-shell ionization is very small. radiative decay rate ( x 1013 s-1) Accuracy of the order of a 1 eV is necessary for cold plasma diagnostics. 0 Calculated by GRASP92 and RATIP: F. A. Parpia et al., CPC, 94, p.249, 1996 S. Fritzsche et al., Phys. Scr. T100, p.37, 2002 0 2610 2620 2625 2630 2635 2615 photon energy (eV)

24. Auger calculation Many Auger channels compete with radiative processes, and are indispensable to estimate Ka yield. Tokyo Institute of Technology Ground states of 1s-vacant Ions (1s2l2l’ and 1s2l3l’ are estimated for Cl14+.) KLL Auger is the most predominant over the competition with Ka transition. Fluorescence yield of low charge state ( Cl+~Cl13+ ) Ka are : 0.05 ~ 0.1 T. Kawamura et al., PRE, 66, p.016402, 2002 Calculated by Auger-code: S. Fritzsche et al., Phys. Scr. T41, p.45, 1992

25. Inner-shell ionization by an ion beam • • >> • • Population Pbulk P1s-vacant 1s-vacant ions are created by inner-shell ionization at low Te . Average Z total is determined by bulk ions due to small population of 1s-vacant ions. modeling of population kinetics bulk ions 1s-vacant ions recombination & ionization Tokyo Institute of Technology Cl3+ : 1s2s22p63s23p3 Cl2+ : 1s22s22p63s23p3 recombination & ionization radiative & auger decays Cl4+ : 1s2s22p63s23p2 Cl3+ : 1s22s22p63s23p2 radiative & auger decays recombination & ionization Cl5+ : 1s2s22p63s23p Cl4+ : 1s22s22p63s23p radiative & auger decays dielectronic capture • •

26. Code Availability • GRASP and GRASP2 • GRASP92 + RATIP • GRASP2K • CR-Model Code based on HULLAC • Code for single electron capture by H nucleus from metal surface

27. GRASP Family of Codes • GRASP and GRASP2-- Very convenient for simple calculation with batch mode user interface • GRASP92 + RATIP-- Interactive user interface that is convenient for sophisticated types of calculations.-- In combination to RATIP code package, several types of transitions such as Auger processes may be calculated • GRASP2K -- Gives wide range of applicability.

28. RATIP Package

29. Others: • CR-Model Code based on HULLAC-- Still under development.-- To make this code open, an agreement for the use of HULLAC is necessary. • Code for single electron capture by H nucleus from metal surface -- Still under development.-- Will be available in not very future.

30. Summary • Several use and development of the codes have been introduced. • GRASP family of codes can be installed in a on line access server. • CR-Model code, and proton-surface charge transfer code may be available in not very future.

31. Thank You

36. Introduction • There are strong needs for atomic and spectroscopic data on Tungsten ions for fusion plasma diagnostics, since Tungsten will be used as a wall material in ITER. • EBIT measurements (NIST, Berlin, LLNL, & Tokyo EBITs, CoBIT) and spectral measurements of laboratory plasmas (ASDEX, JT-60U, LHD) have been done. • Atomic calculations (GRASP, MCDF) and spectral model calculations (Hullac & FAC codes) have been tried: e.g. Rhee & Kwon (2008) MCDF calculation for W33+ - W37+Fournier (1998). CRM for W47+ - W37+ (Hullac code).Ralchenko et al.(2005) CRM for W39+ - W47+ (FAC code)

37. CR model • We have tried to construct a collisional-radiative model for W ions with using atomic data calculated by HULLAC code: - Atomic structure: parametric potential method - Electron impact excitation and ionization cross sections: relativistic distorted wave approximation. • Recombination processes are ignored here. • Rate equations are solved with quasi-steady state assumption (dn(i)/dt = 0). • Ne=3×1013 cm-3, Te= 100 – 1000eV(Ne=1x1010, 1x1020 cm-3)

38. 3．Collisional-Radiative Model • We constructed a set of collisional-radiative models (CR models) for Fe ions from H-like (Fe XXVI) to Ca-like (Fe VII), in which fine structure levels up to n=5 are considered. • Population densities of excited levels are calculated by solving rate equations with assumption of steady-state. • In the rate equations, radiative transitions, electron-impact excitation and deexcitation, proton-impact excitation and deexcitation, electron-impact ionization, radiative recombination, 3-body recombination, and dielectronic recombination processes are considered. • Most of the atomic data are calculated with HULLAC atomic code. • Line intensity is obtained as a product of population density and transition probability: n(p)Ar(p,q)

39. Summary • gA distribution and spectra calculated with the CR model are quite different by excitation effects.When electron density is large, the calculated spectra look similar to gA distribution. • Current CR model can include up to 500 levels, which is not enough for W ions. Needs to tune to have more levels, also needs some method to handle more than millions levels. • Dielectronic recombination rates are needs to obtain to include recombination processes.

40. ５．Discussion • Comparing with the electron temperature distribution, the electron temperature of the emission region is lower than the one for the peak abundance of Fe XXI in ionization equilibrium (Te~1.1keV, for low density limit case). • It could suggest that the equilibrium temperature for the electron density 1012~1014cm-3 would be different from the low density limit case. Due to the density effect (ionization via excited states), effective ionization rate would be larger and the equilibrium temperature could be lower. • Or, we could expect Fe XXI ions would not be in ionization equilibrium. • To prove them we need more detailed analysis and model calculations, such as time dependent evolution of Fe ion densities after the pellet injections with including the effect of diffusion. • To check the CR model, (1) we need independent information of proton density, electron density, and electron temperature for Fe XXI emitting region; and (2) spatial distribution of Fe XXI emitting region will be able to obtain by 2D measurements of EUV spectra in near future, which can be compared with this current method.

41. 3．Collisional-Radiative Model We constructed a set of collisional-radiative models (CR models) for Fe ions from H-like (Fe XXVI) to Ca-like (Fe VII), in which fine structure levels up to n=5 are considered. Population densities of excited levels are calculated by solving rate equations with assumption of steady-state:dn(p)/dt = Γin – Γout =0 Population density of level p is then obtained as：　 n(p)=n0(p)+n1(p)=R0(p)neni+R1(p)nen(1)wheren0(p): recombining plasma component ∝ni(FeXXII)n1(p): ionizing plasma component ∝n(1)(FeXXI) The plasma considered here is headed by the neutral beam injection (NBI) and the ionizing plasma component is dominant. Line intensity is obtained as a product of population density and transition probability: n(p)Ar(p,q) recombination Excitation by electron & proton impact Deexcitation by electron & proton impact and radiative decay Ionization Deexcitation by electron & proton impact radiative decay 41

42. gA and calculated spectrum: W37+ 4d -4f transitions: Effect of excitation processes (⊿λ/λ=0.005 assumed) Fournier (1998)

43. gA and calculated spectrum: W36+

44. gA and calculated spectrum: W35+

45. Electron density effect on the calculated spectra for W35+ 45.12A: 4p54d4 (J=5/2) – 4p64d3 (J=7/2) (45.12A) gA=3.538x1012 4p54d4 (J=9/2) – 4p64d3 (J=7/2) (45.13A) gA=3.33x1012 52.16A: 4p64d24d (J=5/2) – 4p64d3 (J=3/2) (52.11A) gA=1.506x1013 4p64d24f (J=7/2) – 4p64d3 (J=5/2) (52.17A) gA=1.372x1013 53A: 4p64d24f(J=3/2) – 4p64d3 (J=3/2) (52.96A) gA=1.011x1013 4p64d34f (J=5/2) – 4p64d3 (J=3/2) (53.00A) gA=2.493x1011 4p54d4 (J=5/2) – 4p64d3 (J=3/2) (53.02A) gA= 5.068x1011

46. 4.2 Atomic data and CR model for W ions W is one of candidates for plasma wall materials of ITER and a future fusion reactor. But once it is included in a fusion plasma, it will cause large radiation power loss and the accumulation in core plasma and impurity transport is one of big issues to be solved. We need to examine W transport problem and spectroscopy is one of good tools to examine it. Large amount of atomic data are necessary. Many groups are challenging to produce atomic data and construct CR models.

47. Effective potential energy of electron above surface • Coulomb attractive potential of proton: -1/r, • Induced surface dipole layer and exchange-correlation effect (surface potential well): VeI, • A pile of electron density at surface induced by proton (repulsive potential barrier): VpI. IAEA CCN Meeting 2010 IAEA CCN Meeting 2010 47

48. Surface potential well of jellium model Semi-empirical formula proposed by Jennings et al., • z0 is position of image plane. It is given by empirical formula of Ossicini et al. or fitting to potentials of elaborate first-principle calculations. • V0 is given by the sum of Fermi energy and work function. • λrepresents electric field strength of surface dipole. ～1 for many elements. IAEA CCN Meeting 2010 IAEA CCN Meeting 2010 48

49. Static linear density response of electron gas VpI IAEA CCN Meeting 2010 IAEA CCN Meeting 2010 49

50. Adiabatic expansion of electron wave-function in sector Adiabatic expansion to describe electron wave-functions in the rest frame of a moving nucleus, assuming nucleus translation velocities along surface normal is smaller than Fermi velocity of target metals. Adiabatic state functions are solutions for eigen-value problem of adiabatic Hamiltonian at each nucleus-surface distance (D). IAEA CCN Meeting 2010 50