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O. Marchuk 1 , Yu . Ralchenko 2 , D.R. Schultz 3 , W. Biel 1 , T. Schlummer 1 and E. Stambulchik 4 PowerPoint PPT Presentation


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Atomic data for beam-stimulated plasma spectroscopy in fusion plasmas . O. Marchuk 1 , Yu . Ralchenko 2 , D.R. Schultz 3 , W. Biel 1 , T. Schlummer 1 and E. Stambulchik 4. 1 - Institute of Energy and Climate Research, Forschungszentrum Jülich GmbH, 52425 Jülich , Germany

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O. Marchuk 1 , Yu . Ralchenko 2 , D.R. Schultz 3 , W. Biel 1 , T. Schlummer 1 and E. Stambulchik 4

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O marchuk 1 yu ralchenko 2 d r schultz 3 w biel 1 t schlummer 1 and e stambulchik 4

Atomic data for beam-stimulated

plasma spectroscopy in fusion plasmas

O. Marchuk1, Yu. Ralchenko2, D.R. Schultz3,W. Biel1, T. Schlummer1and E. Stambulchik4

1 - Institute of Energy and Climate Research, ForschungszentrumJülich GmbH, 52425 Jülich, Germany

2- Quantum Measurement Division, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA

3 -Department of Physics, University of North Texas, Denton, TX 76203, USA

4 - Weizmann Institute of Science, Rehovot, 76100, Israel

ICAMDATA-2012, NIST, Gaithersburg


O marchuk 1 yu ralchenko 2 d r schultz 3 w biel 1 t schlummer 1 and e stambulchik 4

Contents

  • Overviewofthediagnosticsbased on theinjectionof fast atomsintotheplasma

  • Whytheavailableatomicdatafor beam emissioncan not beused ?

  • Calculationoftheatomicdata in theparabolicrepresentation

  • Comparisonwith experimental data

  • Summary and Outlook

ICAMDATA-2012, NIST, Gaithersburg


Plasma parameters in fusion

Plasma Parameters in Fusion

  • Plasma Temperature ~ 0.2 … 20 keV

  • Plasma Density ~1013…1014 cm-3

  • Magnetic Field ~1.. 7 T

  • In ordertoheattheplasmatotheseconditions

    • Injectionof fast atomsintotheplasma

    • Heatingbytheelectromagneticwaves

Neutrals are also important

for the core plasma!

ICAMDATA-2012, NIST, Gaithersburg


Plasma heating and beams

Plasma Heating and Beams

  • Typical beam parameters (H, D)

  • Energy 30-1000 keV/u

    • ITER heating 500-870 keV/u

    • ITER diagnostic 100 keV/u

  • Current 30-60 A

  • Power < 60 MW

  • Positive ionsource:3 energycomponents

  • Negative ionsource:1 energycomponent

ICAMDATA-2012, NIST, Gaithersburg


Diagnostics based on the injection of fast atoms

Diagnosticsbased on theinjectionof fast atoms

Range ofplasmaparameters:

Beam energy - 20.. 100 keV/u

Plasma temperature - 1..10 keV

Magneticfield – 1..7 T

BES – beam emissionspectra

PCX – passive charge-exchange

ACX – activecharge-exchange

H0 + H+ → H∗ + H+→ ћω (1)

H0 + Xz+1 → H+ +X*z(nl)→ ћω (2)

  • Haspectroscopy on fast hydrogen atoms (BES)

  • sourceofcharge-exchange diagnostic (CXRS)

ICAMDATA-2012, NIST, Gaithersburg


O marchuk 1 yu ralchenko 2 d r schultz 3 w biel 1 t schlummer 1 and e stambulchik 4

Fields „observed“ by fast atom

y

B

Lorentz transformationforthefield:

x

z

(cgs)

v

Beam atom

  • In therestframeoftheatomtheboundelectronexperiencestheeffectofcrossedmagneticandelectricfields

(x´y´z´) isthecoordinatesystem in therestframeof hydrogen atom

(xyz) isthelaboratorycoordinate

system

  • Example: B = 1 T, E = 100 keV/u → v = 4.4·108 cm/s → F = 44 kV/cm

  • Strong electricfield in therestframeoftheatomisexperiencedbytheboundelectron

  • Externalfieldsareusuallyconsideredasperturbationappliedtothefield-freesolution

ICAMDATA-2012, NIST, Gaithersburg


O marchuk 1 yu ralchenko 2 d r schultz 3 w biel 1 t schlummer 1 and e stambulchik 4

Beam-emission of fast atoms in theplasma

  • 3 components in the beam (E/1, E/2, E/3)

  • Ha light fromtheedge

  • Emission of thermal H/D atoms

  • Coldcomponentsof CII Zeeman multiplet

  • Overlappedcomponentsof Stark effectspectra

  • IntensityofMSE (MotionalStark Effect)multipletas a functionofobservation angle θ relative tothedirectionofelectricfield:

ICAMDATA-2012, NIST, Gaithersburg


Linear stark effect for the excited states

Linear Stark effectfortheexcitedstates

  • Hamiltonianis diagonal in parabolicquantumnumbers

  • Sphericalsymmetryoftheatomisreplacedbythe axial symmetryaroundthedirectionofelectricfield

  • Calculationsofthelineintensities, Schrödinger E(1926)

n k |m|

3 2 0

3 1 1

3 0 0

3-1 1

3-2 0

z

„Good“ quantumnumbers:

n=n1+n2+|m|+1, n1, n2 >0 (nkm)

k=n1-n2 – electricquantumnumber

m – z-projectionofmagneticmoment:

n=3

σ0

π4

2 1 0

2 0 1

2 -1 0

n=2

1/2

σ

π

Example: ; /0=0.353


O marchuk 1 yu ralchenko 2 d r schultz 3 w biel 1 t schlummer 1 and e stambulchik 4

Problems withlineintensities

Niisthepopulationofthestatei, Aij-istheradiative rate, 1/s.

  • Statistical assumption:

W. Mandl et al. PPCF 35 1373(1993)

  • Statistical lineintensitiesare not confirmedat JET andotherdevices

  • Plasma codesarebased on thestatisticalassumptionforthe beam excitedstates (n=2, n=3,.. )

Numberofevents

/0

ICAMDATA-2012, NIST, Gaithersburg


O marchuk 1 yu ralchenko 2 d r schultz 3 w biel 1 t schlummer 1 and e stambulchik 4

Major physical processes

  • Radiative decays

    • Well known (Bethe & Salpeter)

  • Field-induced ionization strong for high n’s

  • Electron-impact processes

    • Too high energies => small cross sections

  • Proton-impact processes

    • The strongest but…

Problem: no cross sections/rate coefficients

for transitions between parabolic states

ICAMDATA-2012, NIST, Gaithersburg


Cross sections in parabolic states

Cross sections in parabolicstates

parabolicstatesnikimi

θ

nilimi– sphericalstates

θ=π/2 for MSE

  • Calculationsincludetwotransformationsofwavefunctions

  • Rotation ofthecollisional (z‘) frame on the angle θtomatchzframeEdmonds A R 1957 Angular Momentum in Quantum Mechanics (Princeton, NJ: Princeton University Press)

  • Transformation betweenthesphericalandparabolicstates in the same frame zLandau L D and Lifshitz E M 1976 Quantum Mechanics: Non-Relativistic Theory

ICAMDATA-2012, NIST, Gaithersburg


O marchuk 1 yu ralchenko 2 d r schultz 3 w biel 1 t schlummer 1 and e stambulchik 4

Calculationofthecrosssections in parabolicstates

  • The expressionforthecrosssectioncanbewrittenas:

  • Density-matrix elements

coherenceterms

(off-diagonal elements)

crosssections(diagonal elemens)

ICAMDATA-2012, NIST, Gaithersburg


Calculation of the cross sections in parabolic states n 3

Calculationofthecrosssections in parabolicstates (n=3)

  • Close-couplingcalculations

  • Glauber approximation

  • Eikonal approximation

  • Born approximation

ICAMDATA-2012, NIST, Gaithersburg


Influence of the orientation on the cross sections

Influenceoftheorientation on thecrosssections

  • Energyisvaried in radial direction : 20…200 keV/u

  • Polar angle isthe angle betweenthefielddirectionandtheprojectile. (MSE–/2)

(3,1,1)

?

  • Why do weneedthe angular dependenceif

Cross sectiondepends on therelative velocitybetween beam andplasmaparticles.

relative velocity

-

F

  • The formulasfor rate coefficients beam-Maxwellianplasma must includethe angular dependence.

π/2

Beam direction

ICAMDATA-2012, NIST, Gaithersburg


Effect of the orientation on the h stark multiplet emission

Effectoftheorientation on the Hα Stark multipletemission

F

statisticalcalculations

θ

v

  • The strongestdeviationtothestatisticalcaseisobservedfortheconditionsof Stark effect

  • Increaseofπanddropofσcomponentsas a functionof angle θisobserved

ICAMDATA-2012, NIST, Gaithersburg


Lines ratio of h a stark multiplet

Lines ratioof Ha Stark multiplet

Statistics:

Collisions >>Radiation

n=3

Δn=0

Collisions

Radiation

n=1

O. Marchuk et al. JPB 43 011002 (2010) /theoreticalresults;dashed- Glauber approximation

solid- close-coupling (AOCC) + Glauber approximation/

E. Delabieet al. PPCF 52 125008 (2010) /new experimental data/

ICAMDATA-2012, NIST, Gaithersburg


O marchuk 1 yu ralchenko 2 d r schultz 3 w biel 1 t schlummer 1 and e stambulchik 4

Calculations in strong magneticfield

Plasma parameters:

Magneticfield- 5T

Plasma temperature 20 keVBeam energy:

solid line – 500 keV/udashedline – 100 keV/u

  • The non-statisticalpopulationsinfluencethe Stark effectspectra→Reductionofσ -linesemission

ICAMDATA-2012, NIST, Gaithersburg


O marchuk 1 yu ralchenko 2 d r schultz 3 w biel 1 t schlummer 1 and e stambulchik 4

Populationsofparabolic Stark levels

Beam energy 50 keV/u

Plasma density 3·1013 cm-3

Magneticfieldis 3 T

Field ionizationisexcluded

Field ionizationisincluded

ICAMDATA-2012, NIST, Gaithersburg


O marchuk 1 yu ralchenko 2 d r schultz 3 w biel 1 t schlummer 1 and e stambulchik 4

Deviation from statistical distribution

Does not reach

statistical limit,

primarily due

to collisional

ionization

ICAMDATA-2012, NIST, Gaithersburg

O Marchuk, Yu. Ralchenkoand D R SchultzPPCF 54 095010 (2012)


Summary and outlook

Summary and Outlook

  • The experimental beam-emission spectrademonstrate a significantdeviationfortheσ- andπ- linesratiosforthe Hαlinefromthestatisticalvalues

  • CRM modelin parabolicstatescompletelyresolvedupto n=10 takingintoaccountfieldionizationisdevelopedwithoutanyassumption on thestatisticalequilibrium

  • Densitymatrixelementsfor heavy particlescollisionsplay in thismodelthemajorrole

    • The theoreticaldataare still extremelyrare

ICAMDATA-2012, NIST, Gaithersburg


O marchuk 1 yu ralchenko 2 d r schultz 3 w biel 1 t schlummer 1 and e stambulchik 4

  • The comparisonwiththe experimental data in the Glauber and AOCC demonstrates a verygoodagreementwith JET data.

  • The populationsoftheexcitedlevelsofthe beam do not followthestatisticalassumption

  • The reductionoftheσ- totheπ- components in theemissionofthespectrallinesisobserved.

  • Comparisonofthesimulationswithexperimental datafromotherfusiondevicesisnowongoing

ICAMDATA-2012, NIST, Gaithersburg


Reduction of beam emission rate

Reductionof beam-emission rate

  • Measurementsof CXRS impuritylinesat ITER:

  • Calculations

  • blackline – presentmodel

  • blueline – presentmodelwith infinite collisional rate withinΔn=0 transitions

  • redline – statisticalmodelO. Marchuk et al. Rev. Sci. Instrum. 79 10F532 (2008)*

*- discussion on agreementbetweenstatisticalmodels,Delabie E. et al., PPCF 52 125008 (2010)


Reduction of the beam emission rate coefficients

Reductionofthe beam emission rate coefficients

  • Observation oflong-standing discrepancy on theorderof 20-30% betweenthemeasured (BES) andcalculateddensityof hydrogen beam in theplasmausingstatisticalmodels

  • The non-statisticalsimulationsdemonstrate a reductionofthe beam emission rate relative tothestatisticalmodel on theorderof 15-30% atlowand intermediate density.

E=100 keV/u

T=3 keV


Calculation of the cross sections in parabolic states n 2

Calculationofthecrosssections in parabolicstates (n=2)

s-p

s-p

blue - AOCC (presentresults)

green - Glauber approximation (presentresults)

dashed - Born approximation

orange - CCC Schöller O et al. J. Phys B.: At. Mol. Opt. Phys. 19 2505 (1986)

red – eikonalapproximation, Rodriguez VD andMiraglia JE J. Phys. B: At. Mol. Opt. Phys. 1992 25 2037

black - AOCC (presentresults)

green – Glauber approximation (presentresults)

dashed - Born approximation

blue - SAOCC Winter TG, Phys. Rev. A 2009 80 032701

orange - SAOCC Shakeshaft R Phys. Rev. A 1976 18 1930

red – eikonalapproximation, Rodriguez VD andMiraglia JE J. Phys. B: At. Mol. Opt. Phys. 1992 25 2037

ICAMDATA-2012, NIST, Gaithersburg


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