Measuring DR cross sections
Absolute recombination rate coefficients of tungsten ions
from storage-ring experiments
Stefan Schippers
Institut für Atom- und Molekülphysik
IAM P
JUSTUS-LIEBIGUNIVERSITÄT
GIESSEN
www.uni-giessen.de/cms/iamp
Stefan Schippers, 16th ADAS
Workshop, Cadarache, France,
September 24, 2012
1
Outline
• Motivation
• Atomic data requirements
• Dielectronic recombination data for tungsten ions
• Charge balance of tungsten in a hot plasma
DR of Fe XVIII Fe17+
• Dielectronic recombination measurements @ TSR
• Results for Wq+ ions (q=18-21)
• Atomic structure of open 4f-shell systems
• Comparision with available theoretical results
Stefan Schippers, 16th ADAS Workshop, Cadarache, France, September 24, 2012
2
Ionization balance in a plasma
ionisation
A(q-1)+
Aq+
A(q+1)+
recombination
We need to know rate coeffcients
for
electron-impact ionization
and
electron-ion recombination.
Stefan Schippers, 16th ADAS Workshop, Cadarache, France, September 24, 2012
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Tungsten DR rate coefficients
DR rate coefficient (cm3 s-1)
ADAS
Atomic Data and Analysis Structure
semi-empirical
(based on Burgess formula)
Temperature (eV)
A. Whiteford, PhD Thesis, University of Strathclyde, UK (2004)
http://www.adas.ac.uk
Stefan Schippers, 16th ADAS Workshop, Cadarache, France, September 24, 2012
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Tungsten DR fudge factors
to bring model calculations into agreement with observations
T. Pütterich et al., Plasma Phys. Control Fusion 50 (2008) 085016
Stefan Schippers, 16th ADAS Workshop, Cadarache, France, September 24, 2012
5
Tungsten ionization balance
and cooling factor
T. Pütterich et al., Nuclear Fusion 50 (2010) 025012
Stefan Schippers, 16th ADAS Workshop, Cadarache, France, September 24, 2012
6
The heavy-ion storage ring TSR at the
Heidelberg Max-Planck-Institute
for Nuclear Physics
Heavy-ion storage rings
electron cooler
• Storage of charged particles in
well defined states
 mass
 charge
 velocity
• Electron cooling reduces
 diameter of the ion beam
 velocity spread of the ion beam
 internal energy (molecules)
Control of external and internal degrees of freedom
Stefan Schippers, 16th ADAS Workshop, Cadarache, France, September 24, 2012
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Decay of excited states
Be-like 47Ti18+
-1
Count rate (s )
500
Simply wait until
metastable ions
have relaxed to
their ground state.
2s2p 3P0
decay
400
300
S. Schippers et al.
PRL 98 (2007) 033001
0
2
4
6
8
Storage time (s)
Stefan Schippers, 16th ADAS Workshop, Cadarache, France, September 24, 2012
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Reactions
e.g. charge changing electron collisions
e- beam
Reaction products
• beams of high directionality
• high particle energies in lab frame
100% detection efficiency
collision experiments with dilute ensembles of particles
tunable relative energy: sub meV to sub MeV
electron-ion recombination
electron-impact ionization of ions
Absolute !!! cross sections and rate coefficients
Stefan Schippers, 16th ADAS Workshop, Cadarache, France, September 24, 2012
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Recombination of C3+
Dielectronic Recombination (DR) resonances
-10
mb (10
0
2
C
2+
1s 2p nl
C
3+
8
2
1s 2p
6
1s 2s nl
2
S. Schippers et al.,
ApJ 555 (2001) 1027
5
2
Energy (eV)
2
-1
1
7
6
4
3
cm s )
0
2
1s 2s
-
-2
n=5
-6
2
3
1s 2s 2p P
2
2 1
1s 2s S
3+
2
e + C (1s 2s) 
7
6
-4
-45
4
n=3
2+
2
2+
2
C (1s 2p nl)
2+
2
C (1s 2s nl) 
C (1s 2p n'l')
+ photons
further radiative deexcitation
-50
Stefan Schippers, 16th ADAS Workshop, Cadarache, France, September 24, 2012
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What about more complex ions?
for example: W20+(4d104f8)
one-electron 4d or 4f excitations
Oscillator strength
COWAN code
results
10
7
4d 4f 5g
0.2
9
9
4d 4f
10
7
4d 4f 5d
0.1
0.0
160
180
200
220
240
260
280
300
320
Excitation energy (eV)
Stefan Schippers, 16th ADAS Workshop, Cadarache, France, September 24, 2012
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Fine structure excitations
W20+(4f8 7F6  4f8 2S+1LJ)
1
10
COWAN code
results
293 excited levels
0
longest-lived are
Lifetime (s)
10
3O
-1
10
12 :
7F
0
5L
8
68 000 s
:
8s
:
~2s
-2
10
-3
10
0
S. Schippers et al.,
PRA 83 (2011) 012711
10
20
30
40
50
Excitation energy (eV)
Stefan Schippers, 16th ADAS Workshop, Cadarache, France, September 24, 2012
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Density of doubly excited states
W19+(4f8 nl) states with n  72
7
-1
DOS (10 eV )
5
4
3
2
1
0
0
S. Schippers et al.,
PRA 83 (2011) 012711
10
20
30
40
50
Excitation energy (eV)
Stefan Schippers, 16th ADAS Workshop, Cadarache, France, September 24, 2012
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100
-8
3
-1
Rate coefficient (10 cm s )
DR of Xe-like W20+(4f8)
10
factor of 3000
difference
1.0
1
RR hydrogenic
0.1
energy
range
of 4f8 finestructure
excitations
0.5
-4
-3
-2
-1
0
10
10
10
10
10
40
60
80
100
120
0.0
0
20
S. Schippers et al.,
PRA 83 (2011) 012711
Electron-ion collision energy (eV)
Stefan Schippers, 16th ADAS Workshop, Cadarache, France, September 24, 2012
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W20+ DR rate coefficient in a plasma
TSR
3
-1
Recombination rate coeff. (cm s )
-7
10
factor of 3000
difference
0.1
-9
10
TSR ( E > 47 eV )
RR hydrogenic
factor of 4
difference
ADAS
-10
10
1
10
100
Fractional abundance
-8
10
0.01
Plasma temperature (eV)
S. Schippers et al.,
PRA 83 (2011) 012711
Stefan Schippers, 16th ADAS Workshop, Cadarache, France, September 24, 2012
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New theoretical W20+ DR calculations
statistical approach (full mixing, see also Dzuba et al. PRA 86 (2012) 022714 )
4d4f contribution (IC)
fine structure included (IC)
TSR
TSR
no fine structure
(LS-coupling)
N. R. Badnell, C. P. Ballance, D. C. Griffin, M. O’Mullane, PRA 85 (2012) 052716
Stefan Schippers, 16th ADAS Workshop, Cadarache, France, September 24, 2012
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A simpler system: DR of Au20+(4f13)
TSR
fine structure
included (IC)
TSR
no fine structure
(LS coupling)
C. Ballance et al., JPB 45 (2012) 045001; TSR: S. Schippers et al., Phys. Scr. T144 (2011) 014039
Stefan Schippers, 16th ADAS Workshop, Cadarache, France, September 24, 2012
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18+
10
(4f )
10
-8
1.0
1
RR hydrogenic
0.1
0.5
-4
10
-3
10
-2
-1
10
0
10
10
0.0
10
1.0
1
RR hydrogenic
0.1
0.5
-4
10
50
100
150
200
250
300
0
50
Electron-ion collision energy (eV)
-3
-2
10
-1
10
0
10
10
100
150
200
250
Electron-ion collision energy (eV)
-1
20+
10
8
DR of W (4f )
1.0
-8
PRA 83 (2012) 012711
1
RR hydrogenic
0.1
0.5
100
-4
10
-3
10
-2
10
21+
7
(4f )
TSR February 2012
3
3
-1
100
Rate coefficient (10 cm s )
DR of W
-8
9
(4f )
0.0
0
Rate coefficient (10 cm s )
19+
TSR July 2011
3
3
-8
DR of W
100
-1
TSR June 2011
Rate coefficient (10 cm s )
DR of W
100
-1
Rate coefficient (10 cm s )
Recombination of Wq+ (q=18-21)
-1
10
0
10
0.0
10
1.0
1
RR hydrogenic
0.1
0.5
-4
-3
10
-2
10
10
0.0
0
20
40
60
80
100
Electron-ion collision energy (eV)
120
0
50
100
150
200
250
300
Electron-ion collision energy (eV)
Stefan Schippers, 16th ADAS Workshop, Cadarache, France, September 24, 2012
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Wq+ (q=18-21) recombination in a plasma
18+
W
19+
W
20+
W
21+
W
3
-1
Recombination rate coeff. (cm s )
-7
10
-8
10
TSR
-9
10
-10
10
ADAS
1
K. Spruck et al.
(in preparation)
10
100
Plasma temperature (eV)
Stefan Schippers, 16th ADAS Workshop, Cadarache, France, September 24, 2012
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Conclusions
• Tungsten is used as a plasma facing wall-material in tokamak reactors.
• Quantitative plasma spectroscopy needs accurate plasma models.
• This requires accurate atomic data for tungsten ions.
• We measured dielectronic recombination of tungsten ions with open 4f shell.
• DR rate coefficients are found to be significantly larger than those from ADAS.
• Strong many-body effects make theoretical calculations difficult.
• Even new large-scale calculations do not agree with experiment.
• Novel theoretical approaches are being developed (statistical theory).
Stefan Schippers, 16th ADAS Workshop, Cadarache, France, September 24, 2012
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Collaborators & Funding
ADAS-EU
K. Spruck, D. Bernhardt, A. Müller
IAMP, Justus-Liebig-Universität Giessen
M. Lestinsky
GSI Helmholtzzentrum für Schwerionenforschung
M. Hahn, O. Novotný, D. W. Savin
Columbia Astrophysics Laboratory, Columbia University, New York
A. Becker, M. Grieser, C. Krantz, R. Repnow, and A. Wolf
MPI für Kernphysik, Heidelberg, Germany
Stefan Schippers, 16th ADAS Workshop, Cadarache, France, September 24, 2012
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