measuring dr cross sections absolute recombination rate coefficients of tungsten ions from...

Stefan Schippers, 16th ADAS Workshop, Cadarache, France, September 24, 2012

1

Measuring DR cross sectionsAbsolute recombination rate coefficients of tungsten ions

from storage-ring experiments

JU STU S-LIEBIG - U N IVER SITÄT G IESSEN

I M PAwww.uni-giessen.de/cms/iamp

Stefan Schippers

Institut für Atom- und Molekülphysik

Outline

DR of Fe XVIII Fe17+

• Motivation

• Atomic data requirements

• Dielectronic recombination data for tungsten ions

• Charge balance of tungsten in a hot plasma

• 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

A(q-1)+ Aq+ A(q+1)+

ionisation

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 3

Tungsten DR rate coefficients

A. Whiteford, PhD Thesis, University of Strathclyde, UK (2004)

ADASAtomic Data and Analysis Structure

http://www.adas.ac.uk

Temperature (eV)

DR

rat

e co

effic

ient

(c

m3 s

-1)

semi-empirical (based on Burgess formula)


Tungsten DR fudge factors

T. Pütterich et al., Plasma Phys. Control Fusion 50 (2008) 085016

to bring model calculations into agreement with observations


Tungsten ionization balance and cooling factor

T. Pütterich et al., Nuclear Fusion 50 (2010) 025012


The heavy-ion storage ring TSR at the Heidelberg Max-Planck-Institute

for Nuclear Physics

Heavy-ion storage rings

• 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)

electron cooler

Control of external and internal degrees of freedom


Decay of excited states

Simply wait untilmetastable ionshave relaxed to

their ground state.

0 2 4 6 8

300

400

500

Storage time (s)

Count ra

te (

s-1)

S. Schippers et al.PRL 98 (2007) 033001

2s2p 3P0

decay

Be-like 47Ti18+


Reactionse.g. charge changing electron collisions

Reaction products • beams of high directionality• high particle energies in lab frame

e- beam

100% detection efficiency

electron-ion recombinationelectron-impact ionization of ions

collision experiments with dilute ensembles of particles

tunable relative energy: sub meV to sub MeV

Absolute !!! cross sections and rate coefficientsStefan Schippers, 16th ADAS Workshop, Cadarache, France, September 24, 2012 10

Recombination of C3+ Dielectronic Recombination (DR) resonances

-50

-45

-6

-4

-2

0

2

4

6

8

0 1 2

mb

(10-10 cm3 s-1)

e- + C3+(1s22s) C2+(1s22p nl)

C2+(1s22s nl) C2+(1s22p n'l')+ photons

further radiative deexcitation

C2+

76

n=5

1s2 2s 2p 3P

1s2 2s2 1S

765

1s2 2

s nl

1s2 2

p nl

1s2 2p

En

erg

y (e

V)

1s2 2s

C3+

n=3

4

S. Schippers et al.,ApJ 555 (2001) 1027


What about more complex ions?

160 180 200 220 240 260 280 300 3200.0

0.1

0.2

4d104f7 5g

4d104f7 5d

Osc

illat

or s

tren

gth

Excitation energy (eV)

4d94f9

for example: W20+(4d104f8)

COWAN code results

one-electron 4d or 4f excitations


Fine structure excitations

0 10 20 30 40 50

10-3

10-2

10-1

100

101

Life

time

(s)


W20+(4f8 7F6 ® 4f8 2S+1LJ)

COWAN code results

293 excited levels

longest-lived are

3O12 : 68 000 s7F0 : 8 s5L8 : ~ 2 s

S. Schippers et al.,PRA 83 (2011) 012711


Density of doubly excited states

0 10 20 30 40 500

1

2

3

4

5

DO

S (

107 e

V -

1)


W19+(4f8 nl) states with n £72



DR of Xe-like W20+(4f8)

0 20 40 60 80 100 120

0.0

0.5

1.0

Rat

e co

effic

ient

(10

-8 c

m3 s

-1)

Electron-ion collision energy (eV)

10-4 10-3 10-2 10-1 100

0.1

1

10

100

RR hydrogenic

energy range

of 4f8 fine-structure

excitations


factor of 3000difference


W20+ DR rate coefficient in a plasma

1 10 100

10-10

10-9

10-8

10-7

TSR ( E > 47 eV )

Rec

ombi

natio

n ra

te c

oeff.

(cm

3 s-1)

Plasma temperature (eV)

RR hydrogenic

TSR

ADAS

0.01

0.1

Fractional abundance





New theoretical W20+ DR calculations

N. R. Badnell, C. P. Ballance, D. C. Griffin, M. O’Mullane, PRA 85 (2012) 052716

fine structure included (IC)4d®4f contribution (IC)

no fine structure(LS-coupling)

TSR

TSR

statistical approach (full mixing, see also Dzuba et al. PRA 86 (2012) 022714 )


A simpler system: DR of Au20+(4f13)

C. Ballance et al., JPB 45 (2012) 045001; TSR: S. Schippers et al., Phys. Scr. T144 (2011) 014039

TSR

TSR

fine structureincluded (IC)

no fine structure(LS coupling)


Recombination of Wq+ (q=18-21)

0 20 40 60 80 100 120

0.0

0.5

1.0

Rat

e co

effic

ient

(10

-8 c

m3 s

-1)


10-4 10-3 10-2 10-1 100

0.1

1

10

100

DR of W20+(4f8)

RR hydrogenic

PRA 83 (2012) 012711


0 50 100 150 200 250

0.0

0.5

1.0

Rat

e co

effic

ient

(10

-8 c

m3 s

-1)


10-4 10-3 10-2 10-1 100

0.1

1

10

100

RR hydrogenic

DR of W19+(4f9)TSR July 2011

0 50 100 150 200 250 300

0.0

0.5

1.0

Rat

e co

effic

ient

(10

-8 c

m3 s

-1)


10-4 10-3 10-2 10-1 100

0.1

1

10

100

RR hydrogenic

DR of W18+(4f10)TSR June 2011

0 50 100 150 200 250 300

0.0

0.5

1.0

Rat

e co

effic

ient

(10

-8 c

m3 s

-1)


10-4 10-3 10-2

0.1

1

10

100

RR hydrogenic

DR of W21+(4f7)TSR February 2012


Wq+ (q=18-21) recombination in a plasma

1 10 100

10-10

10-9

10-8

10-7 W18+

W19+

W20+

W21+

Rec

ombi

natio

n ra

te c

oeff.

(cm

3 s-1)

Plasma temperature (eV)

TSR

ADAS

K. Spruck et al.(in preparation)

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).


Collaborators & Funding

K. Spruck, D. Bernhardt, A. MüllerIAMP, Justus-Liebig-Universität Giessen

M. LestinskyGSI Helmholtzzentrum für Schwerionenforschung

M. Hahn, O. Novotný, D. W. SavinColumbia Astrophysics Laboratory, Columbia University, New York

A. Becker, M. Grieser, C. Krantz, R. Repnow, and A. WolfMPI für Kernphysik, Heidelberg, Germany


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