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Progress in the description of Motional Stark Effect in fusion plasmas

Progress in the description of Motional Stark Effect in fusion plasmas. O. Marchuk 1 , Yu . Ralchenko 2 , D.R. Schultz 3 , E. Delabie 4 , A.M. Urnov 5 , W. Biel 1 , R.K. Janev 1 and T. Schlummer 1.

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Progress in the description of Motional Stark Effect in fusion plasmas

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  1. Progress in the description of Motional Stark Effect in fusion plasmas O. Marchuk1, Yu. Ralchenko2,D.R. Schultz3, E. Delabie4,A.M. Urnov5, W. Biel1, R.K. Janev1andT. Schlummer1 1- Institute forClimateandEnergy Research, Forschungszentrum Jülich GmbH, 52425, Jülich, Germany 2- AtomicPhysics Division, NIST, Gaithersburg, MD 20886, USA 3- Physics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6373 4- F.O.M. Institute for Plasma Physics "Rijnhuizen", P.O.Box 1207, 3430 BE Nieuwegein, Netherlands 5- P. N. Lebedev Institute of RAS, Leninskiipr 53, Moscow, 119991, Russia

  2. Principlesofactiveplasmaspectroscopy H0 + {e,H+,Xz} →H∗ + {e,H+,Xz}→ ћω(1) H0 + Xz+1→ H++ X*z(nl) → ћω(2) H++ H0 →H∗ + H+ → ћω(3) beam-emission spectroscopy (BES) sourceofcharge-exchange diagnostic sourceof fast iondiagnosticandmainionratiomeasurements (ACX- activecharge-exchange, PCX- passive charge-exchange) • Plasma parameters: • Density = 1013…1014 cm-3 • Beam energy = 20 .. 200 keV/u • Temperature = 1..15 keV • Magneticfield = 1.. 5 T

  3. Fields „observed“ bytheatom B Lorentz transformationforthefield: y y´ x x´ z z´ v (cgs) Beam atom • In therestframeoftheatomtheboundelectronexperiencestheinfluenceofthecrossedmagneticandelectricfields (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 electricandmagneticfield in therestframeoftheatomisexperiencedbytheboundelectron • Externalfieldsareusuallyconsideredasperturbationappliedtothefield-freesolution

  4. Beam emissionspectrameasuredat JET Hα(n=3 → n=2)Delabie E. et al. PPCF 52 125008 (2010) • 3 components in the beam (E/1, E/2, E/3) • Passive light fromtheedge • Emission of thermal H+and D+ • Coldcomponentsof CII Zeeman multiplet • Overlappedcomponentsof Stark effectspectra • Intensityof MSE multipletas a functionofobservation angle θ relative tothedirectionofelectricfield • Ratiosamongπ-(Δm=0)andσ- (Δm=±1)lineswithinthemultipletarewelldefinedandshouldbeconstant.

  5. „Statistical“ descriptionfortheexcitedstates • The firsttheoreticalmodelsfortheexcitedstatesaresolvedonlyfortheprincipalquantumnumbern • Stark effect was ignoredcompletely, namelyit was observedin fusiona fewyearslater, LevintonFM Phys. Rev. Lett. 63 2060 (1989) • The populationofthefinestructurelevelswithinΔn=0 isassumedtobe proportional totheirstatisticalweights, Isler RC and Olson RE Phys. Rev. A 37 3399 (1988) • The crosssectionsused in these CRM (Δn>0) arebased on thereccomendeddata in sphericalstatesfromthecollisionaldatabases ALLADIN and ORNL, Summers HP 2004 The ADAS User Manual, version 2.6 http://adas.phys.strath.ac.uk • The dominant excitation/ionizationchannelsarecollisionswithions • For heavy particlescollisionsthedataof TDSE, AOCC, DW, EI, … areused

  6. Currentstatusofstatisticalmodels (2011) • Formanyyearsthe different populationsofexcitedstatesof n=2 and n=3 werereportedfrom different models Eb = 40 keV/u Te=Ti= 2 keV Zeff= 1 Solid lineswithpoints – presentcalculations Dashedline - Hutchinson I PPCF 44 71 (2002) Delabie E. et al. PPCF 52 125008 (2010) • Thatisthefirst time thatthepopulationofexcitedstates (n-states) ofthe beam agreewithin 20% forthree different modelsin thedensityrangeof 1013-1014cm-3: • Key component: ionizationdatafrom n=2 and n=3 states

  7. Linear Stark effectfortheexcitedstates • Hydrogen atomplaced in electricfieldexperiences Stark effect • Hamiltonianis diagonal in parabolicquantumnumbers • Sphericalsymmetryoftheatomisreplacedbythe axial symmetryaroundthedirectionofelectricfield. • The energyofthem –levelsis not degeneratedany more in thepresenceofelectricfield (multipletstructure) • The unitarytransformationbetweenthesphericalwavefunctions|nlm>andparabolicwavefunctions|nkm> exists. 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

  8. Calculationofthecrosssections 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

  9. Calculationofthecrosssections in parabolicstates (2) • Transformation betweenthesphericalandparabolicstates 540 • Final expressionforthecrosssectioncanbewrittenas: • The coefficientsciandfinallythecrosssectiondepend on the angle betweenthefieldanddirectionoftheprojectile • This effect was observed in thel - mixingcollisionsof high Rydbergstates (Hickman A P 1983 Phys. Rev. A 28 111; de Prunele E 1985 Phys. Rev. A 31 3593) • Fortheexcitationfromthegroundstatetheexpressionsare still simple:

  10. Influenceoftheorientation on thecrosssections. AOCC calculations. 210 201 • Energyisvaried in radial direction : 20…200 keV/u • Polar angle isthe angle betweenthefielddirectionandtheprojectile. (MSE – π/2) ? • Why do weneedthe angular dependenceif Cross sectiondepends on therelative velocitybetween beam andplasmaparticles. ITER Diagnostic beam: T=20 keV, E=100 keV/u relative velocity - F π/2 θ=π/2± π/6 The simple formulasfor rate coefficients beam-Maxwellianplasma do not workanymore. Beam direction

  11. Populationsofexcitedlevels: pi = Ni/gi/N0 statisticalcasemeans Beam energy 50 keV/u Plasma density 3·1013 cm-3 Magneticfieldis 3 T Ionizationisexcluded Level-crossing + Ionizationbyelectricfield Index ofexcitedlevels

  12. Influenceoftheorientation on the Stark multipletemission statisticalcalculations F θ v • The strongestdeviationtothestatisticalcaseisobservedfortheconditionsofMotional Stark effect • Increaseofπanddropofσcomponentsas a functionof angle θisobserved

  13. Comparisonwith experimental JET data (1993) & (2010) • Points- experimental data E. Delabieet al. PPCF 52 125008 (2010)Error bars- experimental dataW. Mandl et al. PPCF 35 1373 (1993)Dashedline GA O. Marchuk et al. JPB 43011002 (2010) Solid linepresentresults , AOCC + GADashed-point linesdenotestatisticalvalues

  14. Reductionofthe beam emission rate coefficients • Observation oflong-standing discrepancy on theorderof 20-30% betweenthemeasured (BES) andcalculateddensityof hydrogen beam in theplasmausingstatisticalmodels Measured beam emission Calculated beam attenuation • The non-statisticalsimulationsdemonstrate a reductionofthe beam emission rate relative tothestatisticalmodel on theorderof 15-30% atlowand intermediate density. E=100 keV/u T=3 keV

  15. Summary • The completelym-resolvedmodel in parabolicstateupto n=10 was developed. In contrasttothesphericalstatestheparabolicstatesaretheeigenstatesofthe hydrogen beam in theplasma. The modeloperateswitharbitraryorientationbetweenthefieldandprojectiledirection. • The collisionalredistributionamongtheparabolicstates was takenintoaccount in CRM NOMAD • The systematicmeasurementson non-statisticalpopulationsofσ- andπ – componentswereexplainedusingthemodel in parabolicstates. An excellentagreementwith experimental datafrom JET was found. • The assumption on thestatisticaldistributionof m-resolvedstates in the hydrogen beam is not valid in theplasma.

  16. Non-LTE model in parabolicstates • The experimental datafrom JET andotherdevicesclearlydemonstrate a needfor an m-resolvedcollisional-radiativemodel in parabolicstatesforcalculationof: • Line intensitiesfrom m-resolvedlevels • Populationsofexcitedstates • Beam-emission data • Beam attenuation in theplasma • The CRM modelshouldinclude: • Energylevels • Radiativetransitionprobabilities • Cross sectionsamongthe m-resolvedlevels

  17. Statistical intensitiesof Stark effect σ Iij,a.u. • Are theobservedintensitiesof MSE components proportional totheirstatisticalweights ? π • E. Schrödinger, Ann d. Phys. 385(80), 437 (1926) σ1/σ0=0.353 • The experimentsat JET givetheanswer„NO“ σ1/σ0 λ(Hα) Displacementof Hαline W. Mandl et al. PPCF 35 1373(1993)

  18. Ratio betweentheσtoπcomponents • In statisticalcasetheintensityoftheσandπcomponentsisthe same • The ratioisquite sensitive totheplasmadensitywiththesteepgradient in thedensityrangeof 1012-1014 cm-3 • The valuesforthecoronallimitaredeterminedthroughtheexcitationcrosssectionfromthegroundstate

  19. Calculationofthecrosssections in parabolicstates (3) • „The knowledge on the m-resolveddata in sphericalstatesis not enough“ • Off-diagonal elements (coherence) wereobserved in quantumbeatsandpolarizationstudiesof Hαline (H++He) Densitymatrixfor n=2 states • In ordertoachievethe same qualityas in caseofstatisticalmodelsforthecross-sections in parabolicstatesweusedthefollowingmethods: • AOCC calculationsfortheexcitationto n=2 and n=3 states • Glauber approximationforexcitationbetween all otherstates. • Born approximation was usedonlytocontrolthecalculationsat high energies. * H+(E=210 keV/u) + Carbonfoil → H(n=2) Gaupp A. et al. Phys. Rev. Lett. 32268 (1973)

  20. Calculationofthecrosssections in parabolicstates(4) 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 - EA Rodriguez VD andMiraglia JE J. Phys. B: At. Mol. Opt. Phys. 1992 25 2037 black - AOCC (presentresults) blue - SAOCC Winter TG, Phys. Rev. A 2009 80 032701 green – Glauber approximation (presentresults) dashed - Born approximation orange - SAOCC Shakeshaft R Phys. Rev. A 1976 18 1930 red - EA Rodriguez VD andMiraglia JE J. Phys. B: At. Mol. Opt. Phys. 1992 25 2037 • Uptonowtherewereno urgent needsfors-pands-dcoherenceofexcitation

  21. Exampleoftheinfluenceofionization on thepopulationofexcitedstates. ITER Heating beam *For n=5 thestatisticalassumption was assumed

  22. Intensityof CXRS spectrallinesprovides: • Plasma temperature (Doppler broadeningofspectrallines) • Plasma rotation (Doppler shift) • Densityofimpurityions • (posterby T. Schlummer, thisconference) • In ordertoobtainthedensityofimpurityionsoneneedstoknowthedensityofexcitedstatesofthe beam: fisthecalibrationfunction Nz+1isthedensityofimpurity z+1 - isthedensityofthestateofthe beam (=1, 2, etc….)isthe CX rate coefficient cm3/s

  23. PrincipleofLocalThermodynamicEqulibrium (LTE) for H-likeions (gl~2l+1) n, j1 Collisionalchannel • Collisionalchannelswithinthefinestructuredominateradiativedecaysfromthislevel • Heavy particlecollisions(H+,D+) areresponsiblefortheredistributionwithinthe same principalquantumnumber n, j2 Radiativechannel m, j3

  24. Statistical modelsarebased on theatomicdata in sphericalrepresentation • The beam eigenstatesareclosetotheparabolicones ΔE Δn=0,F=0<< ΔE Δn=0,F≠0<< ΔE Δn>0(*) F≠0 F=0 ΔEΔn=0 n2l ΔEΔn=0 n2km ΔE Δn>0 ΔE Δn>0 n1km n1l at (*) • The statisticalresultsare still validifandonlyifthepopulationsofthereal states in theplasmaare proportional tothestatisticalweights

  25. Contents • Principlesofactiveplasmaspectroscopy in fusion • Roleoftheexcitedstatesof hydrogen atoms in plasmadiagnostics • The needsforthe non-LTE models in the atom-plasma interaction • Collisionalatomicdatain different representations • Non-LTE collisional-radiativemodel NOMAD in parabolicstates • Comparisonwith experimental datafor Stark effect • Summary and Outlook

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