An automated method to generate the collisional radiative model of multiple charged ions SASAKI Akira, NISHIHARA Katunobu, MURATA Masaki Quan
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1 An automated method to generate the collisional radiative model of multiple charged ions SASAKI Akira, NISHIHARA Katunobu, MURATA Masaki Quantum Beam Science Directorate, Japan Atomic Energy Research Agency 8-1 Umemidai Kizugawa-shi, Kyoto, , Japan Institute for Laser Engineering, Osaka University 2-6 Yamadaoka, Suita-shi, Osaka, , Japan National Institute of Information and Communications Technology Information and Network System Department 3-5 Hikaridai, Kizugawa-shi, Kyoto, , Japan (Received: ) Abstract : 10 4 Kr Keywords:Atomic process, collisional radiative model, multiple-charged ion, plasma spectroscopy, simulation 1 X [1] (collisional radiative model) [2, 3] author s sasaki.akira@jaea.go.jp 1
2 Grasp [4] Hullac [5] FAC [6] [7] (Local Thermodynamic Equilibrium: LTE) Kr 2 LTE i N i,j N i,1 N i,j = g ( i,j N i,1 exp E ) i,j E i,1, (1) g i,1 kt e i i + 1 N i+1,1 = g i+1,1 cte 3/2 N i,1 g i,1 n e ( exp I ) i, (2) kt e g E T e I i i (= E i+1,1 E i,1 ) c i ( gi,j P i = N i,1 exp E ) i,j E i,1 = N ( ) i,1 Ei,1 exp Q i, (3) g i,1 kt e g i,1 kt e Q i i Q i = j g i,j exp ( E ) i,j, (4) kt e i + 1 i R i R i = ct 3/2 e n e Q i+1 Q i, (5) 2
3 R i Q i Q i nmax n=1 g i,n exp j g i,j exp ( ) E i,n kt e ( ) E i,j kt e nmax n=1 g i+1,n exp j g i+1,j exp ( ) E i+1,n kt e ( E i+1,j kt e ), (6) Q i+1 Q i = Q i+1 Q i, (7) (4) Q i nl H He H H 1s 2s 2p 3s... 1s He 1snl He 2s 2p 3s... 2snl 2pnl 3snl... He 1s 2 1s2s 1s2p... Li 1s 2 nl 1s2snl 1s2pnl... LTE [3] 3
4 3 He 1s 2 1s2s 1s2p Li 1s 2 nl 1s2snl 1s2pnl n 3 1s 2 2s, 1s 2 2s, 1s 2 2p, 1s 2 3s, 1s 2 3p, 1s 2 3d, (8) 1s2s 2, 1s2s2p, 1s2s3s, 1s2s3p, 1s2s3d, (9) 1s2p 2, 1s2p3s, 1s2p3p, 1s2p3p, (10) 1s 2 1s2s 1s2p n 3 1s 3 1s2s 1s2p 1s2s2p 1s2p2s (Java) [8] TreeMap TreeMap ASCII Comparator 4
5 2 (l < n) (0 n e 2 (2l + 1)) ( ) s 3 4 Kr 5 Kr 2 1 Ne 2p 5 nl 2s2p 6 nl 2p 4 3snl 2p 4 3pnl 2p 4 3dnl [9] [10] Kr Kr 25+ Kr 26+ 5
6 2p 6 2p 5 3s 2p 5 3s 2p 5 3p 2p 5 3d 2s2p 6 3s Kr 25+ 2p 6 nl 2p 5 3snl 2p 5 3snl 2p 5 3pnl 2p 5 3dnl 2s2p 6 3snl [2, 3] Kr FTU EBIT [11] 2 LTE 8 LTE Kr FTU EBIT 10 L tot Kr (T e ) = P rad n e n Kr, (11) Kr 100eV 10keV LTE T e = 200eV 11(a) s 2 3p 6 3d 2 nl 3s 2 3p 5 3d 3 nl 3s3p 6 3d 3 nl 3s 2 3p 6 3d4fnl 11(b) (7) Fournier[11] 500eV p 6 3l i 3l M 2p 5 3l i+1 Kr 24+ Mg 2p 6 3s 2 + e 2p 5 3s 2 3d, (12) 6
7 1800eV 2p 6 3s 2 + e 2p 6 3s3p, (13) 2p 5 3s3dnl 2p 5 3s3dnl 2p 6 3snl + hν, (14) Fournier L 5 Hullac Java LTE Kr FTU Fournier [12] 7
8 [1] 83, 658 (2007). [2] H. Griem, Principle of plasma spectroscopy, Cambridge University Press, [3] T. Fujimoto, Plasma spectroscopy, Clarendon Press, [4] F. A. Parpia, C. F. Fischer, and I. P. Grant, Comp. Phys. Commun. 94, 249 (1996). [5] A. Bar-Shalom, M. Klapisch, and J. Oreg et al., J. Quant. Spectrosc. Radiat. Transfer 71, 169 (2001). [6] M. F. Gu, Atrophys. J (2003). [7] A. Sasaki, K. Nishihara, M. Murakami, T. Kagawa, T. Nishikawa, K. Fujima, T. Kawamura and H. Furukawa, Appl. Phys. Lett. 85, 5857 (2004). [8] A. Sasaki, M. Murata, T. Kanamaru, T. Shirado, H. Isahara, Y. Ueshima, and M. Yamagiwa, J. Plasma Fusion Res. 81, 717 (2005). [9] K. B. Fournier, D. Apcella, M. J. May, M. Finkenthal, and W. H. Goldstein, Nuclear Fusion, 37, 825 (1997). [10] D. E. Post, ADNDT (1977). [11] K. B. Fouriner, M. J. Jay, D. Pacella, M. Finkenthal, B. C. Gregory, and W. H. Goldstein, Nucl. Fusion 40, 847 (2000). [12] J. G. Rubiano, R. Florido, C. Bowen, R. W. Lee, and Y. Ralchenko, HEDP 3, 225 (2007). 8
9 1: Kr Kr 14+ Kr 15+ Kr 16+ Kr 17+ Kr 18+ Kr 19+ 3s 2 3p 6 3d 3 nl 3s 2 3p 6 3d 2 nl 3s 2 3p 6 3dnl 3s 2 3p 6 nl 3s 2 3p 5 nl 3s 2 3p 4 nl 3s 2 3p 5 3d 4 nl 3s 2 3p 5 3d 3 nl 3s 2 3p 5 3d 2 nl 3s 2 3p 5 3dnl 3s3p 6 nl 3s3p 5 nl 3s3p 6 3d 4 nl 3s3p 6 3d 3 nl 3s3p 6 3d 2 nl 3s3p 6 3dnl 3s 2 3p 4 3dnl 3s 2 3p 3 3dnl 3s 2 3p 6 3d 2 4snl 3s 2 3p 4 3d 4 nl 3s 2 3p 4 3d 3 nl 3s 2 3p 4 3d 2 nl 3s3p 5 3dnl 3p 6 nl 3s 2 3p 4 3d 5 nl 3s 2 3p 6 3d4snl 3s 2 3p 6 4snl 3s3p 5 3d 2 nl 3s 2 3p 3 3d 2 nl 3s3p 4 3dnl 3s 2 3p 6 3d 2 4pnl 3s 2 3p 6 3d4pnl 3s 2 3p 6 4pnl 3s 2 3p 3 3d 3 nl 3p 6 3dnl 3s 2 3p 2 3d 2 nl 3s 2 3p 6 3d 2 4dnl 3s 2 3p 6 3d4dnl 3s3p 5 3d 3 nl 3p 6 3d 2 nl 3s3p 4 3d 2 nl 3p 5 3dnl 3s3p 5 3d 5 nl 3s3p 5 3d 4 nl 3s 2 3p 6 4dnl 3s 2 3p 5 4snl 3s 2 3p 2 3d 3 nl 3s3p 3 3d 2 nl 3s 2 3p 6 3d 2 4fnl 3s 2 3p 6 3d4fnl 3s 2 3p 3 3d 4 nl 3s3p 4 3d 3 nl 3p 5 3d 2 nl 3s 2 3p3d 3 nl 3s 2 3p 5 3d 3 4snl 3s 2 3p 5 3d 2 4snl 3s 2 3p 6 4fnl 3s 2 3p 5 4pnl 3s3p 3 3d 3 nl 3p 4 3d 2 nl Kr 20+ Kr 21+ Kr 22+ Kr 23+ Kr 24+ Kr 25+ Kr 26+ 2p 6 3s 2 3p 3 nl 2p 6 3s 2 3p 2 nl 2p 6 3s 2 3pnl 2p 6 3s 2 nl 2p 6 3snl 2p 6 nl 2s 2 2p 5 nl 2p 6 3s3p 4 nl 2p 6 3s3p 3 nl 2p 6 3s3p 2 nl 2p 6 3s3pnl 2p 6 3pnl 2s 2 2p 5 3snl 2s2p 6 nl 2p 6 3s 2 3p 2 3dnl 2p 6 3s 2 3p3dnl 2p 6 3s 2 3dnl 2p 6 3p 2 nl 2p 6 3dnl 2s 2 2p 5 3pnl 2s 2 2p 4 3snl 2p 6 3p 5 nl 2p 6 3p 4 nl 2p 6 3p 3 nl 2p 6 3s3dnl 2p 6 4snl 2s 2 2p 5 3dnl 2s 2 2p 4 3pnl 2p 6 3s3p 3 3dnl 2p 6 3s3p 2 3dnl 2p 6 3s3p3dnl 2p 6 3p3dnl 2p 6 4pnl 2s2p 6 3snl 2s 2 2p 4 3dnl 2p 6 3s 2 3p3d 2 nl 2p 6 3s 2 3d 2 nl 2p 6 3p 2 3dnl 2p 6 3d 2 nl 2p 6 4dnl 2s2p 6 3pnl 2s2p 5 3snl 2p 6 3p 4 3dnl 2p 6 3p 3 3dnl 2p 6 3s3d 2 nl 2p 6 3s4snl 2p 6 4fnl 2s2p 6 3dnl 2s2p 5 3pnl 2p 6 3s3p 2 3d 2 nl 2p 6 3s3p3d 2 nl 2p 6 3p3d 2 nl 2p 6 3s4pnl 2s 2 2p 5 4snl 2s2p 5 3dnl 2p 6 3s 2 3d 3 nl 2p 6 3p 2 3d 2 nl 2p 6 3d 3 nl 2p 6 3s4dnl 2s 2 2p 5 4pnl 2p 6 3snl 2p 6 3p 3 3d 2 nl 2p 6 3s3d 3 nl 2p 6 3s 2 4snl 2p 6 3p4snl 2s 2 2p 5 4dnl 2p 6 3pnl TreeMap input configuration Comparator 1s 2 2s 2 output configuration 1s 2 2s 2 3p 1 2p 2 2p 2 1s 2 2s 2 2p 2 3p 1 3p 1 1s 2 2s 2 3p 1 2p 2 1: TreeMap Comparator 9
10 input configuration 1s 2 2s 2 2p 6 3s 1 3s-3p -3s +3s excitation 1s 2 2s 2 2p 6 3p 1 ionization 1s 2 2s 2 2p 6 recombination 1s 2 2s 2 2p 6 3s 2 2: closed shell 1s 2s 2p open shell 3p 1 1s 2 2s 2 2p 6 1s 2 2s 2 2p 6 3p 1 upper configuration 1s 2 2s 2 2p 6 3p 1 lower configuration 3s-1 3p 1 3s-3p excitation 1s 2 2s 2 2p 6 3s 1 3: Low excitated states of He-like ion Configurations of Li-like ion 1s 2 1s 3 1s 2 2s 1 1s 2 2s 1 1s 1 2s 2 1s 2 2p 1 1s 1 2s 1 2p 1 1s 1 2s 1 1s 2 2p 1 1s 1 2s 1 2p 1 1s 1 2p 2 1s 1 2p 1 1s 1s 2 3s 1 1s 1 2s 1 3s 1 1s 1 2p 1 3s 1 1s 2 3p 1 1s 1 2s 1 3p 1 1s 1 2p 1 3p 1 2s 2p 3s 1s 2 3d 1 1s 1 2s 1 3d 1 1s 1 2p 1 3d 1 3p 3d TreeSet of electron orbits to be added to the core configuration 4: He Li 10
11 5: Kr Ne Ar H
12 6: Kr 12
13 <?xml version="1.0" encoding="utf-8"?> <!-- averaged energy levels, radiative and autoionization rates calculated by Hullac v94 --> <!-- ionization energy (ionpot) [ev] --> considered --> <data> <atom name="kr"> <ion name="ne" ionpot=" " closed="1s"> <!-- energy levels, energy [ev] --> <configurations name="0" core="2s 2 2p 5"> <conf name="002p" orbs="2p 1" energy=" 0.000" de=" 0.000" gval="1.0"/> <conf name="003s" orbs="3s 1" energy=" " de=" 0.000" gval="12.0"/> <conf name="003p" orbs="3p 1" energy=" " de=" 0.000" gval="36.0"/> <conf name="003d" orbs="3d 1" energy=" " de=" 0.000" gval="60.0"/> <conf name="004s" orbs="4s 1" energy=" " de=" 0.000" gval="12.0"/> <conf name="004p" orbs="4p 1" energy=" " de=" 0.000" gval="36.0"/> <conf name="004d" orbs="4d 1" energy=" " de=" 0.000" gval="60.0"/> <conf name="004f" orbs="4f 1" energy=" " de=" 0.000" gval="84.0"/>... </configurations>... <!-- radiative rates, A coeff [/s], average energy and width [ev] --> <rad_rate> <rad trans="002p-003s" energy=" " de=" " A=" E+12"/> <rad trans="003s-003p" energy=" " de=" 5.490" A=" E+10"/> <rad trans="003p-003d" energy=" " de=" 5.542" A=" E+10"/> <rad trans="002p-003d" energy=" " de=" " A=" E+12"/>... </rad_rate>... </ion> </atom> </data> 7: Ne Kr XML 13
14 8: Kr (a)10 14 /cm 3 (b)10 22 /cm CRE(Collisional Radiative Equilibrium) 9: Kr (a)10 14 /cm 3 (b)10 22 /cm
15 10: Kr FTU EBIT Fournier /cm 3 11: Kr (a) Q i (b) /cm 3 200eV 15
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