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

1. 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

2. Contents • Overviewofthediagnosticsbased on theinjectionof fast atomsintotheplasma • Whytheavailableatomicdatafor beam emissioncan not beused ? • Calculationoftheatomicdata in theparabolicrepresentation • Comparisonwith experimental data • Summary and Outlook ICAMDATA-2012, NIST, Gaithersburg

3. 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

4. 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

5. 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

6. Fields „observed“ by fast atom y B Lorentz transformationforthefield: y´ x x´ z (cgs) z´ 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

7. 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

8. 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

9. 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

10. 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

11. 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

12. Calculationofthecrosssections in parabolicstates • The expressionforthecrosssectioncanbewrittenas: • Density-matrix elements coherenceterms (off-diagonal elements) crosssections(diagonal elemens) ICAMDATA-2012, NIST, Gaithersburg

13. Calculationofthecrosssections in parabolicstates (n=3) • Close-couplingcalculations • Glauber approximation • Eikonal approximation • Born approximation ICAMDATA-2012, NIST, Gaithersburg

14. 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

15. Effectoftheorientation on the Hα Stark multipletemission F statisticalcalculations θ v • The strongestdeviationtothestatisticalcaseisobservedfortheconditionsof Stark effect • Increaseofπanddropofσcomponentsas a functionof angle θisobserved ICAMDATA-2012, NIST, Gaithersburg

16. 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

17. 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

18. 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

19. 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)

20. 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

21. 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

23. 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)

24. 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

25. 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