First Step Benchmark of Inelastic Collision Cross Sections for Heavy Ions using Charge State Evolutions via Target Penetration

Transcription

1 First Step Benchmark of Inelastic Collision Cross Sections for Heavy Ions using Charge State Evolutions via Target Penetration Alex M Imai, Viatcheslav P Shevelko Department of Nuclear Engineering, Kyoto University P. N. Lebedev Physical Institute of Russian Academy of Sciences Uncertainty Assessment and Benchmark Experiments for Atomic and Molecular Data for Fusion Applications, Dec. 2016, IAEA, Vienna.

2 σ 10 σ 21 σ 10 σ 21 σ 20 He Ne Ar Kr C r o s s S e c t i o n (cm 2 ) , 2+ (a) Be σ 10 σ 20 σ 21 σ 20 +, 2+ (b) B σ 10 σ 21 σ 20 H 2 CH 4 C 2 H 6 C 3 H 8 CO CO , 2+ (a') Be +, 2+ (b') B 20 theories E n e r g y (kev/u) M. Imai et al., J. Plasma Fusion Res. SERIES Vol.7, pp (2006). 2/26

3 Layton et al. He Ar Kr σ 10 σ 21 C r o s s S e c t i o n (cm 2 ) (a) Fe + σ 10 (b1) Ni + H 2 CH 4 C 2 H 6 C 3 H 8 CO CO 2 N 2 σ 20 (b2) Ni 2+ σ 10 σ 21 σ σ 10 (a') Fe + (b1') Ni + (b2') Ni E n e r g y (ev/u) M. Imai et al., J. Plasma Fusion Res. SERIES Vol.7, pp (2006). 3/26

4 Single-electron capture cross sections for W + ions Single Electron Capture Cross Sections for W + Ions Cross Section (cm 2 ) H 2 D 2 CH 4 C 2 H 6 C 3 H Energy (kev) M. Imai et al., Fusion Science Tech. 63, pp (2013). 4/26

5 Background You require not just accuracy of calculated cross sections but also their completeness. Experimentalists would like the evaluation of theoretical data to be done with experiments, but in many cases, there exist few experiments directly comparable to theories. Experimentalists are able to provide very accurate experimental results in some cases. 5/26

6 Experimental apparatus in Japan Atomic Energy Agency 2.0 MeV/u C q+ (q=2-6), S q+ (q=6-16), 1.0 MeV/u W q+ (q=13,15,28,29,30,38) C 2+ Target C-foil 0.9~200 μg/cm 2 S, W Post-stripper C-foil ~20 μg/cm 2

7 Equilibrium and pre-equilibrium charge-state distributions of 2.0 MeV/u C ions after C-foils M.Imai et al., NIM B 354, 172 (2015). 7/26

8 Equilibrium and pre-equilibrium charge-state distributions of 2.0 MeV/u C ions after C-foils q = qy q q, d = q q 2 y q q, s = q q 3 y q q d 3 M.Imai et al., NIM B 354, 172 (2015). 8/26

9 Computer codes for charge-state evolutions ETACHA: a program for calculating charge states at GANIL energies, (10 80 MeV/u) J.-P. Rozet, C. Stéphan, D. Vernhet, NIM B 107, 67 (1996). Matrix Method: Charge evolution of swift-heavy-ion beams explored by matrix method, O. Osmani, P. Sigmund, NIM B 269, 813 (2011). ETACHA3, ETACHA4: Extention of charge state distribution calculations for ion-solid collisions towards low velocities and many-electron ions, E. Lamour, P. D. Fainstein, M. Galassi, C. Prigent, C. A. Ramirez, R. D. Rivarola, J.-P. Rozet, M. Trassinelli, D. Vernhet, PRA 92, (2015). BEAR (Balance Equations for Atomic Reactions) V. P. Shevelko, N. Winckler, I. Yu. Tolstikhina, NIM B 377, 77 (2016). 9/26

10 Set of cross sections on the cutting-board Case Cross Sections References Accuracy (1)-(3) e-cap. e-loss ex. OBK relativistic Born relativistic Born JPB37,201(2004) JETP119,1(2014) NIMB184,295(2001) dye-cap. relativistic Eikonal PRA32,3291(1985) i e-loss CDW-EIS PMB58,673(2013) (4) dx = y j x σ ji y i x σ ij y j = 1 ex. symmetric Eikonal PRA52,4972(1995) ETACHA4 i j i j i REC Bethe-Salpeter (1957) Cas Calculation rad. & Auger decay Yields Y i JPCRD8,307(1979) Density Effect e (1) (2) (3) Present (4) ETACHA4 PRA92,042703(2015) Charge-State 7(C 0 C 6+ ) CS + n =1,2-state 18(C 0 C 6+ ) CS + nl -substate many(c 0 C 6+ ) Not involved. 50% 30-50% 30-50% Scaling used partly inside. High n states are ionized. JPB38,2675(2005) High n states are ionized. Shorter collision intervals are involved in the RE. 10/26

11 Model calculations using sets of cross sections for 11/26

12 Model calculations using sets of cross sections for 12/26

13 Model calculations using sets of cross sections for 13/26

14 Model calculations using sets of cross sections for 14/26

15 Model calculations using sets of cross sections for 15/26

16 Model calculations using sets of cross sections for 16/26

17 Model calculations using sets of cross sections for 17/26

18 Scores for reproducibility of the equilibrium Case Score1 = Model Cross Section s Score1 Score2 (1) Simple Better (2) Simple Better (3) Intermediate Better (4) Full General i=3,4,5,6 y i eq,cal y i eq,exp 4 σ i eq,exp 2 Score2 = i=q,d,s y i eq,cal y i eq,exp σ i eq,exp /26

19 Shifted model calculations using sets of cross sections for 19/26

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25 Scores for reproducibility of the pre-equilibrium Case pre eq y,cal pre eq,exp 2 i Score = i y i N N = 97 Model Cross Sections Score Score1 Score2 (1) Simple Better (2) Simple Better (3) Intermediate Better (4) Full General /26

26 Summary and outlook You require not just accuracy of calculated cross sections but also their completeness. Experimentalists would like the evaluation of theoretical data to be done with experiments, but in many cases, there exist few experiments directly comparable to theories. Experimentalists are able to provide very accurate experimental results in some cases. It would be possible to evaluate set of calculated cross sections (e-capture, loss, excitation, de-excitation) using charge state evolution data. It would be also possible to reduce the collision energy by using dense gas targets. 26/26

27 Vielen Dank und Frohe Weihnachten! Nakamura Jakuemon V

28 Fraction Mean Charge Distribution Width Charge-state distributions of 2.0 MeV/u C q+ ions after C-foils E (a) Target Thickness (mg/cm 2 ) μg/cm (b) Target Thickness (mg/cm 2 ) E-1 1E-2 1E-3 1E-4 1E M.Imai et al., NIM B 354, 172 (2015). Exit Charge State /26

29 Shifted model calculations using sets of cross sections for 29/26

30 Shifted model calculations using sets of cross sections for 30/26