Report on Atomic and Molecular Data for Fusion and Propulsion
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§
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K. Katsonis , M. Cornille , G. Maynard , R.E.H. Clark , J. Abdallah Jr.
*
# Laboratoire de Physique des Gaz et des Plasmas, UMR 8578, Université Paris-sud
91405 Orsay cedex, FRANCE.
§ Laboratoire de LUTH, Observatoire de Paris, Meudon, FRANCE
$ IAEA Vienna AUSTRIA.
* LANL Los Alamos USA.
konstantinos.katsonis@pgp.u-psud.fr, tel. 0033169156543, Fax 0033169157844
marguerite.cornille@obspm.fr
gilles.maynard@pgp.u-psud.fr
R.E.H.Clark@iaea.org
abd@lanl.gov
An extensive data collection, production and application effort is in progress in
our laboratory (LPGP) especially within the Atomic and Molecular Data for
Diagnostics and Modeling research group, which enlarges the scope of a previous
LPGP group on Atomic Physics of Fusion Plasmas. This work is developed in
collaboration with other specialized laboratories from allover the world. On this new
project, emphasis is given to fusion oriented data, but data for electric propulsion,
plasma reactors and natural plasmas are also included within the scope. Main
processes studied and methods used are:
1. Ionization and excitation of atoms(ions) in collisions of atoms(ions) with
atomic, ionic and molecular targets. The n-particle Classical Trajectory
Monte Carlo (n-CTMC) method and LCAO method have been used to
obtain the corresponding cross sections (see e.g. Refs. 1, 2).
2. Ionization and excitation of atoms(ions) in collisions of electrons with
atomic, ionic and molecular targets. The n-CTMC method has also been
used to obtain the corresponding cross sections (Ref. 3).
3. Transition probabilities (Aji) of rare gases atoms and ions. Most of the work
is based in the Coulomb approximation (CbA) and concerns evaluation of
Aji in LS and jK coupling between levels ji having energies
experimentally known (Refs. 4, 5). Ab initio quantum methods are
implementing the CbA calculations.
4. Recombination (radiative, di-electronic) and simple photo-ionization (Ref.
6). Evaluations are based in quasi-classical approximation and existing
formulas (Kramers).
Available data on transition probabilities concern the species summarily listed
in Table I. Although transition probabilities can be found in numerous databases
(notably in the database of NIST) these additional data have been used to develop
Collisional-Radiative (C-R) models allowing for the study of rare gas plasmas (Ar,
Xe) in experimental devices, industrial applications and natural plasmas. Such models,
meant for fusion application, have been often made available in the past (see e.g. Refs
7, 8). Theoretical results obtained by our C-R models are compared with those
provided by existing models, whenever they are available. A systematic validation
effort is under way, including comparison of our theoretical spectra with those
obtained experimentally in various plasmas. In fact, this comparison constitutes a
theoretical support to emission spectroscopy, a powerful optical diagnostics tool
largely used in studying and monitoring a multitude of industrial, laboratory and
natural plasmas. In fact, because these plasmas are rarely in Local Thermodynamic
Equilibrium (LTE), a prerequisite of satisfactory plasma electron density n e and
temperature Te evaluation by emission spectroscopy is the existence of a detailed (CR) model, taking into account the main physical processes influencing the plasma
state and the dynamics of its main constituents (Ref. 9). The theoretical spectra which
such a model generates match the experimental ones whenever the experimental
values of ne and Te are introduced. In practice, in validating C-R models,
discrepancies are observed which often are due to the atomic data included in such
models. In generating theoretical spectra pertaining to each atom(ion) multiplet, the
most sensible atomic data are the relevant Aji and the electron collision excitation
cross sections ij. We note that the latter are actually poorly known, especially for
low ionization stages and near the excitation threshold. Although we are working to
obtain an improved set of them we now focus on the evaluation of the former,
especially of the Aji of the Ar(2, 3)+ ions generating the Ar III, IV spectra and of those
of the Xe(2, 3)+ ions, which are evaluated in an analogous way. These Aji have been
used to establish C-R models of Ar and Xe plasmas for electric propulsion (Ref. 6) but
are also needed for optical diagnostics of the Tokamak plasmas near the wall and in
modeling laser-matter interactions.
Extensive studies of the Ar III and Xe III spectra exist, but the present status of
Aji cannot be considered sufficient for generating the theoretical spectra even of the
most prominent visible lines (Ref. 10) coming from the Ar III multiplets 4s  4p, 5p
(corresponding to the well known “red” and “blue” lines of Ar I but somehow shifted
here) 4p  4d, 5d and 3p  4s, 5s (resonant). The analogous Xe III multiplets (which
have principal quantum numbers increased by two) are more dispersed and even more
difficult to reproduce theoretically. In accordance with the gap observed in the
Grotrian diagrams, the resonant lines which belong to the 3p  4s, 5s multiplets (5p 
6s, 7s for Xe III) together with the important metastable levels, give spectra in the UV
region. On the other hand, multiplets corresponding to close-lying terms, result in
lines located in the infrared region. As for the Ar IV and Xe IV data, these are very
badly known.
We are actually involved in evaluating AjI data within the frame of a
Coordinated Research Program (CRP) of the IAEA. Experimental evaluation of the
Aji needed for the considered C-R models is clearly too wide a task, therefore
experiments are mostly reserved for benchmark purposes. Consequently, various
theoretical methods have been developed, for which in our group we are extensively
using the quasi-classical CbA method mentioned in 3., in conjunction with two ab
initio quantum codes (Ref. 11):
(i)
The SUPERSTRUCTURE (SST) package (Ref. 12), developed at
University College (UCL) by Eissner and collaborators and based in a
non-relativistic Hamiltonian using orbitals calculated in scaled
Thomas-Fermi-Dirac-Amaldi (TFDA) potentials and
(ii)
An extension of the H-F RCG Mod 4 program of Cowan given in the
LANL site (http://aphysics2.lanl.gov/tempweb/, also Ref. 13).
The methods in (i) and (ii) are extensively used in laboratories with which we
collaborate in data base development. The Aji obtained in the CbA approximation
whenever experimental values are used for the energy levels are very satisfactory, but
of course restricted only to transitions allowed in the coupling scheme chosen, that is
often LS or jK. The ab initio methods are able to evaluate also forbidden Aji which
become allowed in the context of LSJ, a wide scheme of intermediate coupling. And
also Aji for transitions for which the wavelengths are unknown. Detailed comparison
of the results obtained by CbA, LANL and SST calculations for the 4s  4p multiplet
of Ar III will be given elsewhere (Ref. 14).
As an example of our work on C-R models validation, we report here on the
comparison of the generated theoretical spectra with those obtained for the plasma of
a direct current discharge device with carbon cathode, available at the LPIIM
Laboratory in Marseille (Ref. 15). First, we generate by our C-R model a set of
theoretical spectra, encompassing a sufficiently wide field of n e and Te values for this
experiment. Spectra from this set are compared with the experimental spectra which
are obtained for the DC discharge plasma, for a discharge current within 40 mA and
70 mA and a pressure varying from 0.4 mbar to 0.6 mbar. Once a theoretical spectrum
is found similar with an experimental one, it is leading to the corresponding n e and Te
conditions of the plasma. We obtained by this diagnostic method a plasma T e of the
order of 11000 –12000 °K, varying according to the pressure and discharge current
conditions. Ionic stages included in the model allow for estimations based on the
intensities also of the ionic lines; these are compared with those obtained from the
atomic lines.
A comparison of the experimental and theoretical spectra of part of the “red”
prominent multiplet 4s  4p lines of the Ar I spectrum is given in Figs. 1 and 2. The
experimental spectrum is from an Ar plasma reactor of coaxial microwave type
(RCM) available in our laboratory (see Ref. 16) and the theoretical one from our
model. We are looking forward to replace the Ar working gas by Xenon and to add a
small admixture of Xe in order to obtain a differential diagnostics of the discharge
(Ref. 17) and to further validate our C-R model for Xe plasmas. Such a diagnostics
can be directly used in Tokamak plasmas in the presence of rare gases and adapted to
other elements.
Especially for fusion related data which are of interest in the present meeting, a
selection of the elements of interest to fusion (codename Procrustes) has been made
by IAEA back in 1980 and regularly revised subsequently. This choice include current
constituents of the controlled fusion plasmas, but also impurities and elements as Ge
(ECRII heated reverse sheer) Ar and Xe introduced “ad hoc” by gas puffing or laser
blow off (LBO) for cooling and/or diagnostics. In order to enlarge and validate
accordingly our database we take profit from a considerable number of collaborations
which we have developed.
We are looking forward to enter the described numerical data in the GAPHYOR
database available in our laboratory. Through a connection with the IAEA database
which has been previously established (Ref. 18) these will be available also by the
IAEA.
References
1. Dimitriou K 2001 “Study of ion and electron collisions with atoms and molecules
by the CTMC method” PhD Thesis, Université de Paris-sud, Orsay, France, December
2001
2. Dimitriou K, Aymar F, Katsonis K, Winter HP, Chibishov M I, Janev R K, Urbain
X anf Brouillard F “Atomic Data for H+ + He (NLM) Collisions: Single Ionization,
Excitation and Charge Exchange Cross Sections”, in press.
3. Sattin F and Katsonis K “Electron Impact Ionization Close to the Threshold:
Classical Calculations“ J. Phys. B: At. Mol. and Opt. Phys., 36 L63 2003
4. Bates D R and Damgaard A 1949 Phil. Trans. Roy. Soc. (London) A242, 101
5. Katsonis K and Drawin H W 1976 “Transition Probabilities of Ar I” Rept. EURCEA-FC-835, Fontenay-aux-Roses, also Katsonis K. and Drawin H W 1980 JQSRT
23 1
6. Siskos A “Constantes Atomiques et Modèles C-R pour la Propulsion Ionique”, PhD
Thesis, Université de Paris-sud, Orsay, France, April 2005
7. Katsonis K. 1976 “Statistical and Kinetic Study of Ar non-LTE Plasmas” Doctorat
d’Etat Thesis, EUR-CEA-FC 820, Fontenay-aux-Roses France
8. Griffin D C, Pindzola M S, Show J A, Badnell N R, O’Mullane M and Summers H
P “Electron-impact excitation and ionisation of Ar+ for the determination of impurity
influx in tokamaks” 1997 J. Phys. B 30 3543
9. Katsonis K, Dzierzega K and Pellerin S HTMP 7 559 2003
10. Katsonis K, Clark R E H, Cornille M, Siskos A, Ndiayé A and J. Abdallah Jr.
2005 “Rare Gases Transition Probabilities for Plasma Diagnostics” Plasma
Conference Opole 2005, Opole, Poland
11. Katsonis K, Clark R E H, Cornille M, Abdallah Jr J, Siskos A and Ndiayé A 2005
“Quasi-classical versus quantum evaluation of transition probabilities: The Ar III 4s 
4p case” in prep.
12. Eissner W, Jones M and Nussbaumer H 1974 Compt. Phys.Commun. 8, 270
13. Cowan R D 1981 “The Theory of Atomic Structure and Spectra” Univ. of
California Press, Berkeley Ca
14. Katsonis K, Clark R E H, Cornille M, and Abdallah J Jr. XXIV ICPEAC, Rosario,
2005
15. Katsonis K, Dominique C, Arnas C, Cornille M and Siskos A 2005 “Emission
Spectroscopy of a DC Discharge with Carbon Cathode” Plasma Conference Opole
2005, Opole, Poland
16. Katsonis K, Boisse-Laporte C, Bonnet J, Letout S. and Siskos A 2004 “C-R
Modeling and Spectroscopic Diagnostics of SPT Plasmas” 4th ISPC, 2-9 June,
Sardenia, Italy
17. Malyshev M V and Donnelly V M, Phys. Rev. E 60 6016 1999
18. Humbert D, Ralchenko Y, Clark R E H, Katsonis K, “GENIE and DANSE: Two
atomic and molecular data web search engines for fusion and plasma physics” Proc.
30th European Physical Society Conference on Controlled Fusion and Plasma Physics,
7-11 July 2003, St Petersburg, Russia
Table I
Ar III
123456789101112131415-
3p  4s
4p  5s
4s  4p
3d  4p
3p  3d
3d  4f
3d  5f
4d  4f
4d  5f
4p  4d
3p  4d
3p  5s
5s  5p
3d  5p
4d  5p
Xe III
12345678910111213141516171819-
5p  6s
6p  7s
6s  6p
5d  6p
5p  5d
5d  6f
5d  7f
6d  6f
6d  7f
6p  6d
5p  6d
5p  7s
7s  7p
5d  7p
6d  7p
5d  4f
5d  5f
6d  4f
6d  5f
Forbidden
6s  4f
7s  4f
7s  5f
Ar II
12345678-
3p  4s
4p  5s
4s  4p
3d  4p
3p  3d
3d  4f
3d  5f
4d  4f
Xe II
12345678-
5p  6s
6p  7s
6s  6p
5d  6p
5p  5d
5d  6f
5d  7f
6d  6f
9101112131415-
4d  5f
4p  4d
3p  4d
3p  5s
5s  5p
3d  5p
4d  5p
910111213141516171819-
6d  7f
6p  6d
5p  6d
5p  7s
7s  7p
5d  7p
6d  7p
5d  4f
5d  5f
6d  4f
6d  5f
Forbidden
6s  4f
7s  4f
7s  5f
Ar I
123456789101112131415-
3p  4s
4p  5s
4s  4p
3d  4p
3p  3d
3d  4f
3d  5f
4d  4f
4d  5f
4p  4d
3p  4d
3p  5s
5s  5p
3d  5p
4d  5p
Xe I
12345678910111213141516171819-
5p  6s
6p  7s
6s  6p
5d  6p
5p  5d
5d  6f
5d  7f
6d  6f
6d  7f
6p  6d
5p  6d
5p  7s
7s  7p
5d  7p
6d  7p
5d  4f
5d  5f
6d  4f
6d  5f
70000
811.75
30 mTorr - 500 W
800 - 870 nm
50000
40000
805
810
815
820
825
830
835
840
845
850
867.03 I
852.38
826.68
10000
0
800
841.05
810.59
20000
842.70
30000
800.84
801.70
Nbre de Coups / s
60000
Expérience:
Argon RCM, Pos. 0
855
860
865
870
 (nm)
Fig. 1. Experimental spectrum of RCM plasma reactor in the red region [800-870 nm].
70000
811.754
Intensité [erg cm s ]
60000
-3 -1
Modèle C-R Ar I-III
12
-3
Te = 11 kK ; ne = 5x10 cm
2
=6.24x10
50000
40000
0
800
805
810
815
820
825
830
835
840
845
 (nm)
Fig. 2. Theoretical spectrum in the region of Fig. 1 [800-870 nm].
850
855
867.033 I
852.378
841.052
826.679
800.836
801.699
10000
810.592
Minces
Aij LS
20000
842.694
30000
860
865
870