N. "Yamamoto

T. Kato

T." Fujimoto

National Institute for Fusion Science (NIFS-Repository)

§16. Populating Mechanism in Dense Plasma for Doubly Excited States Yamamoto, N. (Rikkyo Univ.), Kato, T. (NIFS), Fujimoto, T. (Kyoto Univ.) We study effective rate coefficients using a collisional-radiative model (CRM) including doubly excited states. The effective rate coefficients in dense plasma were studied by Fujimoto and Kato [1]. They examined Is-2s excitation / de-excitation using a CRM including doubly excited states 2snl as well as Is-2p excitation / de-excitation including 2pnl states. They found an enhancement of the excitation and de-excitation rate coefficients with increasing electron density. We also found an enhancement due to different mechanism compared with their found mechanism [2]. In this paper, we present the populating mechanism of doubly excited states 21'nl for effective Is-21 excitation rate coefficients in dense plasma [3]. We constructed a new CRM including singly excited Isnl states and doubly excited 21'nl and 3dnl states. Our model contains a total of 255 states; 1 S2, 1 s, 21, and 31 states, 60 singly excited 1 snl states, 118 doubly excited 21 'nl, and 70 doubly excited 31 'nl states, where n is up to 20. The atomic processes considered in our model are excitation / de-excitation by electron impact, ionization / three-body recombination, radiative transitions, radiative recombination and auto-ionization / dielectronic capture. Atomic data used in our CRM for 1 snl and 21 'nl states are the same as those described in ref.[I]. For 31'nl states we calculated the data using HULLAC code [4]. Indirect contributions to effective 1 s-21 excitation rate coefficients exceed direct excitation rate coefficient at Ne -1019 cm-3 for carbon ions (Z = 6) as shown in Fig.I. Indirect contributions through auto ionization after dielectronic capture, Is -- 3/'nl -- 21, which is a resonance contribution, are important at low density. This resonance contribution decreases with increasing electron density at Ne > 1021 cm-3, as predicted in Ref.[5] by dielectronic ' capture ladder-like (DL) excitation-ionization process Is -- 3/'nl -- 31'n "I" --... -- 31'. With increasing density, indirect contributions through DL excitation-ionization, Is -- 21'nl -- 2/'n "I" --... -- 21' increase. At very high density (> 1021 cm-\ indirect processes 1 s -- 1 snl -- 21 'nl -- 21' increase the effective rate coefficients proportionally to Ne [2]. We also found that for 2s-1 s de-excitation, I-changing transitions, 2snl-2pnl, are important at intermediate densities. Two population mechanisms are considered for doubly excited states at high density in ionizing phase (N1s = 1). The first one is DL excitation-ionization, 1 s -- 21'nl -- 21', where contributes to the increase in the effective excitation / de-excitation. The second one is indirect process 1 s -- 1 snl -- 21'nl -- 21' where the excitation 1 snl -- 2/'nl process is important to produce the population densities of 21 'nl states. At high density, a population density for a high-n doubly excited state q(2/'n!) can be written approximately using the method described in Ref.[ 6], N _ Cq_1,q N Ci,q ~ +--N. q C q-l C I q,q+l q,q+l (1) The excitation rate coefficients are scaled as Cq-1,q ex (n-1)7/n3, Cq,q+! ex n7/(n+ 1)3. The excitation rate coefficents Ci,q for 1 snl-21 'nl do not depend on a principal quantum number 11. We can derive Nq / gq ex n-6 from the first term in eq.(1), as is shown in Ref.[6], where gi is a statistical weight. The second term in eq.(1) corresponds to the second population mechanism, and Nq / gq ex n-4 [3] is derived since Ni ex n2 in LTE. At very high density, the second process has a stronger effect than dose the first. So n-dependence of the population density per statistical weight changes from n-6 to n-4 at very high density as shown in Fig.2. 10-13 ell .... E- 10-14 Is-2s en c: ~ ·u S 10-15 ~ 0 ------------u 2 e 10-16 ~ oti " u ~ "-<+-i 10-17 W 1014 1016 1018 1020 1022 electron density (cm-3) Fig.I. The effective 1 s-2s excitation rate coefficients for Z = 6 at Te = 3.5 x 105 K. Solid lines: indirect contribution including 2/'nl and 3/'nl states, dotted lines: without 31'nl states, dot-dashed line: dielectronic capture resonances through 31'nl states, dot-dot-dashed lines: direct Is-2s. ~ 10-4 " ~- 10-6 1: t:lJ) .Qj 10-8 ~ ~ c.> 10-10 .~ .~ 10-12 .... (!) 0.. .~ 10-14 c: (!) ""0 10-16 c: 0 .~ :; 0.. 0 0.. principal quantum number n Fig.2 population density per statistical weight for doubly excited 2snl states for Z = 6 at Te = 3 .5x 1 05 K. Reference 1) T. Fujimoto and T. Kato, Phys. Rev. A32, (1985) 1663 2) T. Kato et aI., JQSRT 71, (2001) 431 3) N. Yamamoto et aI., J. of Plasma and Fusion Research 78 (2002) 1 4) A. Bar-Shalom et aI., Phys. Rev. A38, (1988) 1773 5) T. Fujimoto and T. Kato, Phys. Rev. A35, (1987) 3024 6) T. Fujimoto, J. Phys. Soc. Jpn. 47, 273 (1979). 377 

Populating Mechanism in Dense Plasma for Doubly Excited States

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