I. "Murakami

K. Moribayashi

T. Kato

U.L." Safronova

National Institute for Fusion Science (NIFS-Repository)

§13. Population Inversion and Gain of X-ray Spectral Lines of Be-like Ions in Recombining Plasmas Murakami, I., Kato, T. Moribayashi, K. (JAERI) Safronova, U.L (Notre Dame University, USA) 'Ve have constructed a collisional-radiative model (CRM) to calculate population densities, n(i), of the excited states of Be-like ions, Fe22+ and Ne6+ in recom-binillg plasma, to calculate population densities and to examine the population inversion and laser gain coef-ficients. 'Ve assume quasi-steady state for solving the rate equations, including radiative transitions, collisional excitation and deexcitation, collisional ionization, ra-diative recombination, dielectronic recombination, and three-body recombination. In the CRM, 2snllevels with n up to 70 (Fe22+) or 20 (Ne6+), and 2pnllevels with n up to nth (11 for Fe22+ and 6 for Ne6+) are included. The populatioll inversions are found in recombining plasma at some electron density and temperature re-gions, for example, between 2s3s 3 Sand 2s3p 3 P levels or between 2s3d 3D and 2s4f 3F levels. Here we focus on 3d-4f transitioll to examine the laser gain coefficients for NeVIl and FeXXIII lines in recombining plasma, since the gain coefficient of AIX 3d-4f transition (I7i.8A) in laser produced plasma has been measured by Hara et al.(I989) to be 3.5 ± 0.5cm- 1 [1]. Figure 1 shows the normalized population density, n(i)/(g(i)'nen+) of 2s3d, 2p3d, 2s4f, and 2p4f levels as a function of electron density in a recombining plasma for NeVIl, where '11+ is ion density of Li-like Ne and g(i) is the statistical weight. The population inversion occurs at ne < I018cm-:1 for Te = 7eV. In Fig. 2 we show the contour maps of the normalized gain coefficient, G' = GI(n+R), of the 2s3d ID - 2s4f 1F transition for NeVIl and FeXXIII at the line center of the Gaussian lille profile in a plane of scaled electron deusity a.nd temperature, i.e. 'neIZ~ff and Tclz~ff' where G is a gain coefficieut with the usual definition and R = AI,6.A, spectral resolving power. Roughly, G' <X z;f f is fouud from the plots, and then G <X z~ f f if n+ = l/,c I Ze f f· If we apply t his scaling law to the AIX 2s3d 1 D - 2s4f 1 F transitioll with plasma parameters Te = GeV amI 'fl' c = 1019 Clll-:1, the gain coefficients is expected to be G rv 4(R/500)cm- 1 ifn+ = uelZeff. This is cOllsistent with the coefficieut measured by Haret et ai. if R rv 500. References [1] Hara T, Ando K, Kusa.kabe N, Yashiro H, and Aoyagi Y 1989 Japanese J. Applied Phys. 28 LIOI0 -20 -20,5 -21 -21.5 . c ~ '5; ~ -22 z 0'1 .Q -22.5 -23 -23.5 -24 NeVil (T.=7eV) 16 17 / .... /;; .. :.: l~~~!-~~--.!.---------·------18 19 log n.(cm -3) 20 21 Figure 1: Normalized population densities, Tt(i)/(g(i)ne'll+), of 2s3d, 2p3d, 2s4f, and 2p4f levels for NeVIl as a fUllction of electron density. -0.5 -1 log T/zA2 (eV) -1.5 -2 -24 -23 NeVil ! i /' ! " ; ,. !: ; / ! !", ;,' /' ,!,:j/l I ;' ;;! .j :' Ilf I~ -25 .'! ': ':' , " i' ,:' :' 2 ", i2~~2}' NeVil boundary ;,' ;' ,f ,/ : ,,/ ,/ /:/ /'~\ -24 -23 -22 -21-2(}19-18 FeXXl1i boundary FeXXll1 7 8 9 10 11 12 13 14 15 16 log rJzA7 (cm-3) Figure 2: Contour map for the normalized gain, G', for 2s3d 1 D - 2s4f 1 F line in normalized electron dellsity nelZ:ff vs normalized electron temperature TelZ;ff plane. Thin lines are for FeXXIII and thick liues for NeVIl labeled with 10gG'. 327 

Population Inversion and Gain of X-ray Spectral Lines of Be-like Ions in Recombining Plasmas

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