HAL Id: jpa-00227457
https://hal.archives-ouvertes.fr/jpa-00227457
Submitted on 1 Jan 1988
HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
C-R MODEL CALCULATIONS IN RECOMBINING PLASMAS : POPULATION INVERSIONS IN Cal7+,
Ti19+ AND Cu26+ LITHIUM-LIKE IONS
A. Sureau, H. Guennou, C. Möller
To cite this version:
A. Sureau, H. Guennou, C. Möller. C-R MODEL CALCULATIONS IN RECOMBINING PLASMAS :
POPULATION INVERSIONS IN Cal7+, Ti19+ AND Cu26+ LITHIUM-LIKE IONS. Journal de
Physique Colloques, 1988, 49 (C1), pp.C1-195-C1-198. �10.1051/jphyscol:1988137�. �jpa-00227457�
JOURNAL DE PHYSIQUE
Colloque C1, Suppl6ment au n 0 3 , Tome 49, Mars 1988
C-R MODEL CALCULATIONS IN RECOMBINING PLASMAS : POPULATION INVERSIONS IN c a 1 7 + ,~i"+ AND C U ~ ~ ' LITHIUM-LIKE IONS
A. SUREAU, H. GUENNOU and C. M ~ L L E R
Laboratoire de S p e ~ t r o s c o p i e Atomique et Ionique, CNRS UA-775, Bat. 350, Universit6 Paris Sud, F-91405 Orsay Cedex, France and GRECO Interaction Laser Matigre. Ecole Polytechnique, F-91128 Palaiseau Cedex, France
RESUME. Dans le cadre des recherches sur les lasers X-UV, ce travail pr6sente les rdsulta obteflyf avec un modele collisionnel-radiatif, qui avait d6ja 6t6 utilisd pour Alf'+et S
..
Ltint6r@t des 616ments plus lourds consid6r6s ici (Ca, Ti, Cu) est multiple. En particulier, les longueurs d'onde de certaines transitions, entre niveaux dont les populations sont inversees, sont situ6es en dessous de la discontinuit6 d'absorption du carbone, ce qui est adapt6 2 l'6tude des mat6riaux organiques. Nos r6sultats apportent des informations sur les inversions de population qui peuvent &re obtenues compte tenu des conditions de densit6 et de temperature dans les plasmas 6tudi6s. Une comparaison avec des r6sultats expsrimentaux existant pour le cuivre est discutCe.ABSTRACT. Related to the investigations on XUV lasers, this wor resentsl,f$sults obtained by a collisional radiative model previously used for A1 and S
.
Theinterest of the heavier elements which are considered here (Ca, Ti, Cu) is manifold.
In particular, the wavelengths of some transitions between the inverted-population levels are below the carbon absorption edge, which is suitable for organic material investigations. Our results give information about the population inversions which may be expected according to the density and temperature conditions of the plasma concerned. Comparisons with existing experimental results are discussed in the copper case.
I-INTRODUCTION :
In the investigations on X-ray lasers, two main schemes arise according as the population inversion is principally due to collisional excitations from the ion ground level, or to recombination cascades from the next-higher ionisation stage. The first scheme occurs in Ne-like and Ni-like ions, the second in hydrogenic and Li-like ions. The Li-like scheme is well suited to the progress towards shorter wavelengths because t e Z-scaling of t e wavelength (where Z is the nuclear charge) is favourable (
, . ,
Z-q.3against x,Z-'in Ne-like and hydrogenic schemes) and it requires a lower plasma temperature at a given wavelength. A recent experiment has thus been performed at Rochester (in association with a NRL group) on a copper target / I / . The authors have observed 26+population Inversion between the 4f and the 3d levels of t$e lithium-like Cu Lon the wavelength of the corresponding transition being 25.6 A.The reduced population ratio 4f/3d is evaluated to be approximately equal to 3 and the authors estimate that this value is accurate to a factorl?$ 2.
We give below the results of calculations concerning the Ca and ~ u ~ ~ + i o n s , carried out with a time-dependent collisional radiative model described previously /2,3,4/.
These results give information about the population inversions which may be expected according to the condit- s of temperature and density of the plasma concerned. The results we obtain for Cera'yu compatible with the experimental observations of Ref .l and a comment on the comparison between observed and calculated results is given.
11-RESULTS AND DISCUSSION :
The method we use to calculate the population densities of the excited levels of Li-like ions in plasmas is described in Ref.3. The atomic data (energy levels,
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1988137
C1-196 JOURNAL
DE
PHYSIQUEtransition probabilities,
...
) (see Table I) are obtained by a modified Hartree-Fock method including the configuration interactions (in the general case) and the spin-orbit interactions, allowing a direct calculation in the intermediate coupling scheme 151. The hydrodynamics data (free-electron density and temperature, total density of Li-like ion, density of He-like ground state, all of them time-dependent) may be provided by the code named FILM /6/, or input as parameters. The collisional radiative model then gives the populayon density of each level individually. The populations of the 21 excited levels 1s n l - 2 ~,
with 2 < n<
5,
are obtained solving a-system of coupled rate equations where a13 electric-dipole radiative decays and e -ion collision induced transitions (deexcitations and excitations) are taken into account.Defining X = N He INLi
,
the plot of the reduced-population density ratios of Ca 17+A
A31.99 682 3d5/2 5f7/2 39.55 477 32.04 727 3d3/2 4f5/2 57.76 1354 46.77 2065 3d5/2 4f7/2 57.86 1448 46.87 2206 4d3/2 Sf512 124.78 253 101.06 386 4f5/2 5g7/2 124.95 431 101.20 657 4d5/2 5f7/2 124.97 271 101.25 414
ls2n'f-2~7/2 over ls2nd- D5/2 (with n'= 4,5 and n= 3,4) versus T 2 for a number of e'
Cu 26+
A
A17.54 2266 17.59 2&13 25.64 6868 25.74 7320 55.41 1284 55.50 2184 55.59 1373 55.59 2260
rent values of X and N
,
are shown in figufg+l for call' and in figure 2 for :?".Analogous results haveseen obtained for Ti.
Figures 1 and 2 show that, for a given value of N
,
the inversion-ratio value at low temperature is independent of X. This is due to %he fact that when the temperature drops, the part of collisional excitations becomes negligible (except between very close levels). The excited levels with quantum number n < 6 are then essentially populated by deexcit.ation cascades from upper levels, in particular those of the thermal band (n>, 6), and their population is proportional to N and independent of .The ratio of population of two excited levels is therefore independent of NHe, He and X at low temperature.Table
zl.
Calculated yave$engths%in A) and spontaneous emission probabilities A (in ns ) for some 1s nl- LJ+ 1s n'l'-2~' J l transitions in Li-like ions.In the series of results presented below, we consider the hydrodynamics data N (free-electron density), NHe (He-like ground-state density) and N (total ~i-likg ion density) as free parameters and we calculate the reduced-po&%ation densities (Nlg) (where g=2J+1, the statistical weight of the level) as functions of the temperature T
.
The Ne, NHe and NLi values are kept within the electro-neutrality limit.Copper case :
In all cases considered here, the 4f/3d reduced population ratio remains lower than 2 (d1.8 at maximum). This is not inconsistent with the experimental result of Ref.1 (see the introduction) but our calculated result is less optimistic. That may be due to the fact that we have not considered any exceptional situation concerning the density and temperature values, and their mutual compatibility. On the other hand, the experimental value is deduced from a set of relative intensities observations with the assumption that the plasma is optically thin for all the spectral lines involved.
The 3d-5f transition is situated at 17.5 A (see Table I) and its spontaneous-emission intensity is much weaker than the 3d-4f one. So, even though a 3d-5f population inversion arises, it cannot be observed in a plasma of smal dimension. A similar situation occurs for aluminium / 4 / where the 36-51 line of Alto+ appears only in the axial spectrum of a plasma column, and not in the transverse spectrum.
It is proved that the Li-like ions offer multiple possibilities in the investigations on X-UV lasers.-For achieving gain at. wavelengths between the absorption edges of oxygen at 23.3 A and carbon at 43.5 A (making it possible
Y,
study organic material without absorption by water),
the 3d-4f transitions in Cu''
may be considered as good candidates. The production of the suitable copper plasma requires huwever a very high power incident laser. It may therefore be advantageous to use rather the 3d-5f transitions of f?yer-Z elezents, in cylindrical plasmas. For example, the 3d-Sf transition in Ca at 39.5 A seems particularly attractive.Figure 1, Reduced population ratios 5f/3d (a), 4f/3d (b) and 5f/4d (c)., versus Te, at different values of N and X = NHe/NLi
,
in Ca.JOURNAL DE PHYSIQUE
Figure 2. Reduced population ratios 5f/3d (left) and 4f/3d (right), versus Te, at different values of N and X =NH,/NLI
,
in Cu.REFERENCES :
/2/ H.GUENNOU, A.SUREAU, Proc.8 th Int.Col1. on EUV and X-Ray Spectroscopy of astrophys. and lab. plasmas. IAU Co11.86. Washington (DC).1984.p.221 G.JAMELOT, A.KLISNICK, A.CARILLON, H.GUENNOU, A-SUREAU, P-JAEGLE J.Phys. B : At. Mol. Phys.
18
(1985) 4647/3/ H.GUENNOU, A.SUREAU,J.Phys. B : At. Mol. Phys.
20
(1987) 919 H.GUENNOU, A.SUREAU, C.M~LLER, J. de Physique67,
C6 (1986) 351151 A.SUREAU, H.GUENNOU, M.CORNILLE,J.Phys. B : At. Mol. Phys.
17
(1984) 541 /6/ J.C.GAUTHIER, J-P-GEINDRE, N.GRANDJOUAN, J.VIRMONT,J.Phys. D : Appl.. Phys. -I& (1983) 321
