Driven Rotation, Self-Generated Flow, and Momentum Transport
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John Rice
Driven Rotation, Self-Generated Flow, and Momentum Transport in Tokamak Plasmas SpringerSeriesonAtomic,Optical, andPlasmaPhysics Volume119 Editor-in-Chief
GordonW.F.Drake,DepartmentofPhysics,UniversityofWindsor,Windsor,ON, Canada
SeriesEditors
JamesBabb,Harvard-SmithsonianCenterforAstrophysics,Cambridge,MA,USA
AndreD.Bandrauk,FacultédesSciences,UniversitédeSherbrooke,Sherbrooke, QC,Canada
KlausBartschat,DepartmentofPhysicsandAstronomy,DrakeUniversity, DesMoines,IA,USA
CharlesJ.Joachain,FacultyofScience,UniversitéLibreBruxelles,Bruxelles, Belgium
MichaelKeidar,SchoolofEngineeringandAppliedScience,GeorgeWashington University,Washington,DC,USA
PeterLambropoulos,FORTH,UniversityofCrete,Iraklion,Crete,Greece GerdLeuchs,InstitutfürTheoretischePhysikI,UniversitätErlangen-Nürnberg, Erlangen,Germany
AlexanderVelikovich,PlasmaPhysicsDivision,UnitedStatesNavalResearch Laboratory,Washington,DC,USA
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DrivenRotation, Self-GeneratedFlow,and MomentumTransportin TokamakPlasmas JohnRice
JohnRice PlasmaScienceandFusionCenter
MassachusettsInstituteofTechnology
Cambridge,MA,USA
ISSN1615-5653ISSN2197-6791(electronic)
SpringerSeriesonAtomic,Optical,andPlasmaPhysics
ISBN978-3-030-92265-8ISBN978-3-030-92266-5(eBook) https://doi.org/10.1007/978-3-030-92266-5
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Preface Examplesofrotationcanbefoundeverywhereinnature,fromwatercirclingthe draintohurricanestospotsonJupitertoentiregalaxies.Rotationisalsoseenin hightemperatureplasmaexperiments,oftenwithnoobviouscause.Thepurpose ofthepresentstudyistodocumentandattempttounderstandtheexperimentally observedrotationintokamaks,toroidal(donutshaped)devicesusedtocontainhigh temperature(afewkeV ≈ 10sofmillionsofdegrees)plasmas.Whilethereare severalexternalmomentumsourceswhichcanbeusedtodriverotationintokamaks, spontaneous,self-generatedflow,upto ∼100km/s,isroutinelyobservedinplasmas withoutexternalmomentuminput.Furthermore,thisintrinsicrotationcanreverse directioninafractionofasecondwithoutanyobviousreason.Thepurposeof tokamakresearchistoprovideanenergysource via controlledthermonuclear fusion,andinordertoachievethisinacosteffectivemanner,itisimportant tounderstandtherichvarietyofphenomenaintokamakplasmas.Whatbetter opportunityistherethanexplainingself-generatedflow?
Theinfluenceofrotationontokamakperformancehasbeenwidelydemonstrated.Forinstancerotationcanstabilizecertaindeleteriousmagnetohydrodynamic (MHD)instabilities,andtherotationgradienthasbeenshowntosuppressturbulence,leadingtotransportbarriersandanenhancementinenergyconfinement.In thisregarditisimportanttounderstandtherotationintokamakplasmas,andtouse thisunderstandingtocontroltherotationspatialprofile.Thereareseveralrecent experimental[1–5]andtheoretical[6–10]surveysonthissubject,andthepresent goalistoupdateandexpandupontheobservationalreviews.
Toroidalvelocityprofileevolutionisgovernedbyabalancebetweenexternal torques(momentumsourcesandsinks)andthemomentumfluxgradient[4]as
wherevφ isthetoroidalvelocity,nisthedensity,mistheparticlemass, φ is themomentumfluxandSext includesexternalmomentumsourcesandsinks.There areseveralmomentumsources,e.g.directdrivefromneutralbeaminjectionorradio frequencywaves,andindirectdrivefromtheelectricfieldcreatedbyorbitshiftsand
losses.Sinksincludeneutraldampingandmagneticbraking(neo-classicaltoroidal viscosity).Sinksandindirectsourcesdependupontheambientplasmaparameters. Themagneticgeometryandsubsequentparticleorbitsmustbeconsideredsince non-ambipolaritywillgiverisetoanelectricfieldwhichentersintotheforcebalance andcollisionsmustalsobetakenintoaccount;thesearetheingredientsforneoclassicaltheory.
ThemomentumfluxisdominatedbythetoroidalReynoldsstress[11]which consistsofthreeparts:
where χφ isthemomentumdiffusivity(orviscosity),Vp isthemomentumpinch(or convection)and res istheresidualstress.Allthreeofthesetransportcoefficients canbedominatedbydifferentcompetingeffectswhichalsodependuponambient plasmaparameters.Thelattercomponent,whichisindependentofboththetoroidal velocityvφ anditsspatialgradient ∂ vφ /∂ r,hastheuniquecharacteristicthatit canfunctionasamomentumsource(andsoappearsonbothsidesoftheforce balance),withtheintrinsictorquedensitygivenby ∇· res [11]. res isgoverned byturbulencewhichisoftendrivenbyspatialgradientsofplasmaparameters. Followingasummaryofrotationvelocitymeasurementtechniques(Chap. 1)willbe anexaminationofmomentumsources(Chap. 2)andsinks(Chap. 3),comparisons withthepredictionsofneo-classicaltheory(Chap. 4),adetaileddiscussionofthe residualstressasamomentumsource(Chap. 5)andareviewofthemomentum transportcoefficients χφ ,Vp and res (Chap. 6).
Itisimportanttounderstandallaspectsofthisproblem,coveredinChaps. 2–6. Eachoftheseeffectshasadifferentplasmaparameterdependence(suchasdensity, temperature,neutraldensity,collisionality)andeachcandominateindifferent regionsofoperationalspace.Itisnecessarytoconsidermagneticgeometry,particle orbits,collisions,electricfields,MHDconstraintsthroughcurrentandpressure gradientsandtheinfluenceofturbulencethroughdensity,temperature,pressureand currentdensitygradients.Furthercomplicatingthisproblemisthatthevelocityisa vector,withdirectionandmagnitude.Thechallengeistoaccountforthismyriadof effectsinacomprehensivemanner.Thisprocesswillbesystematicallyaddressedas follows,afteradiscussionofvelocitymeasurementtechniques.
Themostcommonmethodofvelocitydetermination,fromDopplershiftsof atomictransitions,willbecoveredinSect. 1.1,withareviewofpassive(Sect. 1.1.1) andactive(Sect. 1.1.2)techniques.Directexternalmomentumsourceswillbe consideredinSect. 2.1,includingneutralbeaminjection(NBI)andvariousradio frequencyschemes(ICRF,LHandECH).InSect. 2.2,indirectrotationdrive dueto j×B forcesarisingfromradialorbitshiftsandnon-ambipolareffects, suchastoroidalmagneticfieldrippleloss,willbereviewed.Asummaryof momentumsinkswillbepresentedinChap. 3,includingneutraldamping,magnetic fieldperturbationsandneo-classicaltoroidalviscosity.InChap. 4 comparisonsof observationswithneo-classicalcalculationswillbeshown,includingbothpoloidal andtoroidalrotation.Self-generatedflowarisingfromtheresidualstresswillbe
discussedingreatdetailinChap. 5.Twogeneralcategoriesofintrinsicrotationwill beexamined,thatoccuringintheenhancedconfinementregimes(H-andI-mode) andthatinL-modeplasmas,includingthecuriousrotationreversalphenomenon (anditsconnexionwithconfinementsaturationand“non-local”heattransport cut-off).Chapter 6 willbeconcernedwithdeterminationofmomentumtransport coefficients:themomentumdiffusivity,themomentumpinchandtheresidualstress. AdiscussionofopenquestionswillbethesubjectofChap. 7.Inthefollowing,the toroidalrotationwillbewrittenasvφ orVTor whilethepoloidalrotationwillbe denotedasvθ orVPol .Amajorityofvelocitymeasurementsisofimpurityrotation, whichisoftenusedasaproxyformainionrotation.
Cambridge,MA,USAJohnRice
Acknowledgments EnlighteninginteractionswithClementeAngioni,ManfredBitter,YannCamenen, NormanCao,JonathanCitrin,JohndeGrassie,PeterdeVries,PatrickDiamond, BasilDuval,Lars-GoranEriksson,ChiGao,MartinGreenwald,BrianGrierson, JerryHughes,KatsumiIda,AlexInce-Cushman,DavisLee,EarlMarmar,Rachael McDermott,Yong-SuNa,ArthurPeeters,YuriPodpaly,ThomasPütterich,Matt Reinke,TimothyStoltzfus-Dueck,TuomasTala,SteveWolfe,andMaikoYoshida aregratefullyacknowledged.WorksupportedatMITbyDoEContractNo.DEFC02-99ER54512.
1VelocityMeasurementsinTokamaks
1.1DopplerShiftsofAtomicTransitions
1.1.1PassiveSpectroscopy
1.1.2ActiveSpectroscopy ............................................6
1.2MHDModeRotation ...................................................9
1.3ProbeMeasurements ....................................................10
1.4MicrowaveDopplerReflectometryandScattering
1.5Comments
2MomentumSources
2.1DirectRotationDrive
2.1.1NeutralBeamInjection
2.1.2IonCyclotronRangeofFrequenciesWaves
2.1.2.1IonBernsteinWaves ..................................24
2.1.2.2ModeConversionFlowDrive
2.1.2.3FastMagnetosonicWaves
2.1.3LowerHybridWaves
2.1.4ElectronCyclotronWaves
2.1.5CompactTorusInjection
2.2IndirectRotationDrive .................................................35
2.2.1OrbitShiftj×BForces .........................................35
2.2.2IonandElectronLossDuetoToroidalMagnetic FieldRipple .....................................................39
2.2.3EdgeThermalIonOrbitLoss
2.3Comments
3MomentumSinks
3.1NeutralDamping
3.2ModeLocking,MagneticBrakingandNeo-Classical ToroidalViscosity .......................................................46
3.3EdgeLocalizedModes ..................................................51
3.4Comments ...............................................................51
4ComparisonwithNeo-ClassicalTheory
4.1PoloidalRotationvθ
4.2ToroidalRotationvφ ....................................................54
4.3PoloidalAsymmetriesinEdgeToroidalRotation
4.4Comments ...............................................................60
5IntrinsicRotationandtheResidualStress
5.1EnhancedConfinementRegimes .......................................62
5.1.1OhmicH-Modes ................................................63
5.1.2ICRFH-andI-Modes ..........................................63
5.1.3ECHH-ModesandAddingECH
5.1.4H-ModeswithLH ..............................................77
5.1.5NBIH-Modes ...................................................77
5.1.6PlasmaswithITBs ..............................................82
5.1.7Comments .......................................................83
5.2LowConfinementMode ................................................87
5.2.1MagneticConfigurations
5.2.2CurrentDrivenReversals .......................................92
5.2.3OhmicRotationReversalsandLOC/SOC
5.2.4AuxiliaryHeatedL-Mode ......................................117
5.2.5Comments .......................................................119
6MomentumTransport
6.1MomentumDiffusivity χφ
6.2MomentumPinchV
6.3ResidualStress
7DiscussionandFutureOutlook
Chapter1 VelocityMeasurementsinTokamaks Inordertostudyrotationitisnecessaryfirsttomeasureitreliably.Thereare severaltechniquesinuseontokamakswhichwillbesummarizedanon:Doppler shiftsofatomictransitions,MHDmoderotationfromfrequencyanalysis,probe measurementsandfrommicrowavescattering.Fortheatomictransitions,the populationoftheupperlevelscaneitherbepassive(via collisionalexcitationor radiativerecombinationfromplasmaelectrons)oractive(fromchargeexchange recombinationwithinjectedneutrals).
1.1DopplerShiftsofAtomicTransitions Themostcommonmethodofmeasuringtherotationisfromobservationofthe Dopplershiftsofatomictransitions,eitherinimpurities(intrinsicorextrinsic) orbackgroundions(hydrogen,deuteriumand/orhelium).Dependinguponthe appropriateplasmaconditions,thesemeasurementscanbemadeinthevisible,ultraviolet(UV)orx-raywavelengthranges.
1.1.1PassiveSpectroscopy Earlyvelocitydeterminationintokamakswasfrompassivemeasurementsof intrinsicimpurityionswhoseupperlevelswerepopulatedbycollisionalexcitation.
Thefirstvelocitymeasurement,intheVUVwavelengthrange,wasfromOV (O5+ )emissionintheLT-3device[12].Similarobservationsweresubsequently madeonPLT[13, 14],TorusII[15],PDX[16],TM-4[17],JET[18],TCA[19], COMPASS-D,TEXT[20]andTCABR[21, 22].Mainionvelocitieshavealso beeninferredfromobservationsofDα lightinAUG[23].ThePLTmeasurements
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J.Rice, DrivenRotation,Self-GeneratedFlow,andMomentumTransportin TokamakPlasmas,SpringerSeriesonAtomic,Optical,andPlasmaPhysics119, https://doi.org/10.1007/978-3-030-92266-5_1
Fig.1.1 Schematicofinstrumentationformeasurementofpoloidalortoroidalintensitydistributionswithsimultaneousspectralscanofanemittedline.ReprintedwithpermissionfromFig.1of [13]S.Suckeweretal.‘ToroidalPlasmaRotationinthePrincetonLargeTorusInducedbyNeutralBeamInjection’,Phys.Rev.Lett. 43,207(1979).Copyright(1979)bytheAmericanPhysical Society
[13]werefromacleverspectrometersystem,witharotatingmirrortosamplethe plasmacrosssectionandafastvibratingmirrortoscantheindividuallineshapes, alayoutoverviewofwhichisshowninFig. 1.1.Todemonstratethecapabilities ofthisspectrometer,timehistoriesoftherotationvelocityduringanNBIheated PLTplasmafromthissystemareshowninFig. 1.2.InthecoreofthisTe ∼ 2keV discharge,thetoroidalrotationreachedalevelinexcessof100km/s,asdetermined fromtheDopplershiftofaforbiddenFeXX(Fe19+ )transitionat2665Å.Neutral beampowerwasappliedbetween350and500ms.Emissionlinesfromotherions(C VandHI),whichfellinthespectralrangeofthespectrometershowlowervelocity fromtheperipheralregionsoftheplasma.Aradialvelocityprofileconcoctedfrom thesethreeseparateemissionlinesduringtheNBIphaseforthisplasmaisshown inFig. 1.3.Inthiscasethetoroidalrotationprofilewasstronglypeakednearthe plasmacenter.
OnedrawbackofusingVUVandvisibleemissionlines(whoseupperlevelsare populatedbycollisionalexcitation)isthattheyaretypicallyfromimpuritycharge statesthatexistinnarrowspatialshells,therebyonlyallowingaccesstoonelocation intheplasma.Whileitispossibletocobbletogetheracompleteradialprofileusing avarietyofdifferentimpuritiesandchargestates[13, 18](asinFig. 1.3),itwould bedesirabletoutilizeclosedshellionizationstates(He-likeorNe-like)whichexist overalargerspatialregion.AnotherlimitationofVUVandvisibletransitionsis
Fig.1.2 Timeevolutionofthetoroidalplasmavelocityinducedbytwoco-injectedneutralbeams, withtotalpower1.5MW,inplasmawithcentralelectrontemperatureTe (0) ≈ 2keVanddensity ne (0) ≈ 3–5 × 1019 /m3 .Thedifferentatomsrefertodifferentradiallocationsintheplasma. ReprintedwithpermissionfromFig.3of[13]S.Suckeweretal.‘ToroidalPlasmaRotationin thePrincetonLargeTorusInducedbyNeutral-BeamInjection’,Phys.Rev.Lett. 43,207(1979). Copyright(1979)bytheAmericanPhysicalSociety
thattheyusuallysampleregionsoftheplasmawithlowerelectrontemperature (anotableexceptionistheforbiddenFeXXtransition).Thesetwoshortcomings canbeamelioratedbyusingx-raytransitionsfromHe-likeions.Thefirstx-ray spectrometerintheJohannconfiguration[24]wasinstalledonPLTforviewingHelikeiron[25].AschematicofthissystemisshowninFig. 1.4.Suchaspectrometer requiresalargeareaberylliumwindow,acarefullybentcrystalandalinearposition sensitivedetector.Intheearlymanifestationsofthesespectrometers,varioustypes ofproportionalcounterswereemployed.Johannx-rayspectrometershavebeen usedonPDX[16],TFTR[26, 27],DIII-D[28],JET[18, 29],ToreSupra[30], FTandJIPP-TII.AnexampleofavelocitymeasurementusingtheHe-liketitanium (TiXXIorTi20+ )resonancelineat2.6097ÅfromaneutralbeamheatedTFTR plasma[26]isshowninFig. 1.5.DuringtheNBIpulsefrom2.3to2.8s,thecore toroidalvelocityreached150km/s.OnedrawbackofJohannspectrometersisthat inordertoachievehighwavelengthresolvingpower,theradiusoftheRowland circle,andhencethesystemsize,becomeslarge.Analternativeistousethevon Hamosconfiguration[31],whichallowsforacompactspectrometer.Thelayoutfor
Fig.1.3 Radialdistributionoftoroidalplasmavelocityat100–140msafterbeginningofneutral beaminjection.ReprintedwithpermissionfromFig.4of[13]S.Suckeweretal.‘ToroidalPlasma RotationinthePrincetonLargeTorusInducedbyNeutral-BeamInjection’,Phys.Rev.Lett. 43, 207(1979).Copyright(1979)bytheAmericanPhysicalSociety
thevonHamossystemofAlcatorC[32]isshowninFig. 1.6.Thecylindricallybent crystalisflatinthedispersiveplaneandunliketheJohannsystem,anentranceslit isrequiredforspatiallyextendedsources.ThisallowsforasmallareaBewindow. VonHamostypespectrometershavealsobeenimplementedonAlcatorC-Mod[33] andanexampleofDopplershiftedspectra[34]fromH-likeAr17+ (extrinsically introduced)andNe-likeMo32+ (intrinsic)isshowninFig. 1.7.Thesespectrawere
Fig.1.4 QuartzcrystalspectrometerintheJohannconfiguration.X-raysemittedfromtheshaded areaoftheplasmapassthroughaberylliumwindowintoaheliumfilledtubeandareBragg reflectedbythecrystalontothepositionsensitivedetector.Photonsofdifferentenergiesare focussedtodifferentdetectorpoints.ReprintedwithpermissionfromFig.1of[25]M.Bitteretal. ‘Doppler-BroadeningMeasurementsofX-RayLinesforDeterminationoftheIonTemperaturein TokamakPlasmas’,Phys.Rev.Lett. 42,304(1979).Copyright(1979)bytheAmericanPhysical Society fromtwoOhmicL-modedischargeswiththeplasmacurrentinoppositedirections andexhibitcounter-currentrotationwithmagnitudesof ∼40km/s.
Whileitispossibletoobtainspatialvelocityprofilesbyutilizinganarrayof theindividualspectrometersjustdescribed[33, 35, 36],amoreelegantapproach istouseaspatiallyimagingsystem.Thiscanbeachievedwithasphericallybent crystalintheJohannconfiguration[37, 38]andaschematicofaspectrometersystem isshowninFig. 1.8.Thisarrangementrequiresa2Dx-raydetector:onedirection fordispersion(meridionalplane)andtheotherforspatialimaging(sagittalplane). SuchasystemhasbeenimplementedonAlcatorC-Mod[39]andthelayoutis showninFig. 1.9.Thereareactuallytwospectrometersinthesamehousing,one forviewingHe-likeargonandtheotherforH-like.TheHe-likeargonsystemhas completeup/downcoverageoftheplasmacrosssection,asseeninthebottomframe. Measurementswiththissystemarechordaveraged,soatomographicinversion
Fig.1.5 ToroidalplasmarotationvelocitiesfrommeasurementsoftheDopplershiftoftheTiXXI Kα line.LeftandrightscalesontheordinategivethecenterpositionoftheTiXXIKα lineandthe wavelengthshiftandtoroidalplasmarotationvelocity,respectively,relativetothecenterposition intheOhmicheatingphase.ReprintedfromFig.13of[26]M.Bitteretal.‘Satellitespectrafor heliumliketitanium.II’,Phys.Rev.A 32,3011(1985).Copyright(1985)bytheAmericanPhysical Society
processmustbeusedtodeterminethetruevelocityprofile[39, 40].Thevelocity profileevolution[39]ofanICRFheatedH-modeplasmafromC-Modobtained withthisspectrometerisshowninFig. 1.10.Ascanbeseen,duringtheOhmic phasebefore0.7s,thecorerotationisdirectedcounter-current,becomesweaklycocurrentfollowingapplicationofICRFheatingafter0.7s,andisstronglyco-current duringtheH-modephasefrom1.32to1.52s.SimilarimagingJohannspectrometers havebeeninstalledonKSTAR[41],LHD[42],EAST[43]andW7-X[44],andare beingconsideredforITERandSPARC.
1.1.2ActiveSpectroscopy TheprevioussectionreviewedvelocitymeasurementsfromDopplershiftsofemissionlinespopulatedpassivelybycollisionalexcitationorradiativerecombination fromplasmaelectrons.Anothertechniqueistoutilizetransitionspopulatedby chargeexchangerecombination(CXR)withneutralhydrogenisotopesprovided byactiveneutralbeaminjection(NBI).Advantagesofthismethodarethatthis canprovideaspatiallylocalizedmeasurement(wheretheneutralbeamintersects
Fig.1.6 SchematicofthedispersivecharacteristicsofthevonHamoscrystalspectrometerused. FromFig.2of[32]E.Källneetal.‘HighResolutionX-RaySpectroscopyDiagnosticsofHigh TemperaturePlasmas’,Phys.Scr. 31,551(1985).©IOPPublishing.Reproducedwithpermission. Allrightsreserved
thespectrometersightline)andthatmanytransitionspopulatedthiswayareinthe visiblewavelengthregion,whichallowstheuseofvisiblespectrometers(novacuum required)andfiberoptics.Disadvantagesofthistechniquearethatneutralbeams constituteastrongmomentumsource(andperturbthevelocitybeingmeasured)and thatunfoldingthelineshapetodeterminetheDopplershiftduetothedesiredplasma rotationcanbecomplicated(forexampleduetoenergydependentatomiccross sectiondistortions[45, 46],seeFig. 1.13).AgoodreviewofCXRspectroscopy maybefoundin[47].
EarlyobservationsofCXRpopulation via NBIwerefromH-likeoxygeninT-10 [48]andORMAK[49],andH-likeheliuminPDX[50].Thefirstvelocitymeasurementsusingthistechnique[51]intheUVspectralrangewerefromORMAK usingtheexperimentallayoutshowninFig. 1.11.Thespectrometersystemisvery similartothatshowninFig. 1.1;however,thereissomespatiallocalizationsince CXemissioncanonlyoccurwherethebeamcrossesthespectrometerlineofsight. TheobservedvelocitydeterminedfromthisinstrumentforH-likeOVIII(O7+ )in theUVspectralrangeduetoCXRpopulationfromneutralH/Dinthen = 1level agreesverywellwiththepassivelymeasuredHe-likeNeIX(Ne8+ ),ascanbeseen inFig. 1.12.CXRspectroscopy(CXRS)withNBI(eitherfromheatingordiagnostic beams)wassoonadaptedontokamaksaroundtheworldincludingDoubletIII[52–54],PDX[55],DITE[56],ISX-B[57, 58],ASDEX[59],JET[60]andJIPPTII [61],andisnowthestandardvelocityprofilemeasurementtechnique.Onedrawback withthismethodisthatitrequiresNBI,sothestudyofintrinsicrotationistricky.
Fig.1.7 Thex-rayspectraoftheAr17+ Lyα doubletandofthe2p6 -(2p5 )3/2 4d5/2 transitionin Mo32+ forcounter-clockwise(CCW)Ip (bluedashedcurve)andclockwise(CW)Ip (solidred curve)discharges.TheLyα 1 wavelengthatrestof3731.1mÅisshownbythethinverticalline. ReproducedfromFig.2of[34]J.E.Riceetal.‘X-rayobservationsofcentraltoroidalrotationin ohmicAlcatorC-Modplasmas’,Nucl.Fusion 37,421(1997),withthepermissionoftheIAEA
Awidelyusedtechniqueistoutilizebeamblips,shortdurationpulses,tominimize theinputtorque.
MostapplicationsofCXRSuseintrinsic(carbonfromwallsorboronfrom wallcoating)orinjected(e.g. neon)impuritieswhichyieldstheimpurityrotation (andtemperature).ModernsystemsutilizeCXRfromexcitedneutralhydrogen/deuteriuminthen = 2level,whichpopulatehighn(and l)levels(forexample n = 8inC5+ )whichcascadedowninthevisiblespectralregion.Theimpurity rotationcanbedifferentfromthatofbackgroundions,anditisofinteresttomeasure themainionvelocitydirectly.Thefirstmeasurementsofbackgroundionrotation wereobtainedinDIII-Dheliumplasmas[62].Observationsofmainionrotation inD2 plasmashavealsobeenrealizedinASDEXUpgrade[63].Agoodreviewof importantissuesandcomplicationsofCXRSinhydrogenisotopesmaybefoundin [64].AnexampleofastateoftheartCXRSspectrumofDα isshowninFig. 1.13 whichdemonstratescontributionsfromvariouseffectswithandwithoutNBIina DIII-DH-modeplasma[65].Acomparisonofedgerotationprofilesdetermined fromcarbonanddeuteriumCXRSusingthissamesystemisshowninFig. 1.14 foraDIII-DH-modeplasma[66].Clearlythereisasubstantialdifferencebetween
Fig.1.8 Illustrationofthefocussingpropertiesofsphericallybentcrystals.Reproducedfrom Fig.1of[37]M.Bitteretal.‘Numericalstudiesoftheimagingpropertiesofdoublyfocussing crystalsandtheirapplicationtoITER’,Rev.Sci.Instrum. 66,530(1995),withthepermissionof AIPPublishing
impurityandbackgroundionrotationnearthelastclosedfluxsurface(LCFS),as canbeseeninpanel(d).ThereisanincreaseintheimpurityrotationinthecocurrentdirectionoutsideoftheLCFS;thistopicwillbeexploredinChap. 4 on neo-classicaleffects.
1.2MHDModeRotation Anothermethodofmeasuringthevelocityistoexaminetherotationfrequencyof n = 1pre-andpost-cursorstosawtoothoscillationsusingmagneticpickupcoilsor softx-rayarrays.ThistechniquewasfirstemployedonPLT[16, 67]andhasbeen usedsubsequentlyonISX-B[58],JET[68]andAlcatorC-Mod[35, 36, 69–71].An exampleofthevelocityattheq = 1surfacefromsawtoothpost-cursorscomparedto neighboringx-rayDopplermeasurementsforaC-ModH-modedischargeisshown inFig. 1.15 [35, 36].Whiletherotationofn = 1MHDmodesrelativetoionrotation issubjecttointerpretation[72],theinferredvelocityatthesawtoothinversionradius (r/a ∼ 0.2)fitsnicelybetweentheimpurityrotationatr/a = 0.0andr/a = 0.3 measuredbyDopplershiftsofx-raylines.
Fig.1.9 Topview(a)andsideview(b)ofthespectrometerasinstalledonAlcatorC-Mod. ReproducedfromFig.1of[39]A.Ince-Cushmanetal.‘Spatiallyresolvedhighresolutionxrayspectroscopyformagneticallyconfinedfusionplasmas’,Rev.Sci.Instrum. 79,10E302(2008), withthepermissionofAIPPublishing
1.3ProbeMeasurements ItispossibletoutilizeLangmuirprobepairstoinfertherotationvelocity[73] inthescrapeofflayer(SOL)oftokamakplasmas[74–77].Thelayoutofseveral probesystemsonC-ModisshowninFig. 1.16 [74].TheEASTandWEST tungstenelectrodes,whichareembeddedinanelectricallyfloatingmolybdenum body,sampleplasmafromoppositedirectionsalongthesamefieldline,forming aMachprobepairinwhichtheparallelMachnumbercanbeestimatedfrom theratioofionsaturationcurrentdensities,M = 0.43JEAST /JWEST [73].By fittingpositive-andnegative-goingI-VcharacteristicsfromtheEASTandWEST electrodes,electrondensities,temperaturesandparallelMachnumbersalongthe probe’strajectoryareobtainedevery0.25ms(correspondingto ∼0.25mmofprobe travel).TheNORTHandSOUTHtungstenelectrodeswereoperatedinafloating voltagemode.Theverticalscanningprobeisofsimilarconstructionandisoperated inthesamemanner.ScanningLangmuir-Machprobemeasurementshaveuncovered clearevidenceofstrongballooning-liketransportandassociatedtransportdriven
Fig.1.10 ContourplotshowingtherotationprofileevolvingduringanICRFheatedplasma. Thelineaverageddensity,centralelectrontemperatureandRFheatingpowerarealsoshown. ReproducedfromFig.6of[39]A.Ince-Cushmanetal.‘Spatiallyresolvedhighresolutionx-ray spectroscopyformagneticallyconfinedfusionplasmas’,Rev.Sci.Instrum. 79,10E302(2008), withthepermissionofAIPPublishing
plasmaflowalongfieldlinesintheinnerhighfieldsideSOL.Acompilationof crossfieldplasmaprofiles,includingflowmeasurements,intheinnerandouter SOLregionsforuppersinglenull(USN),doublenull(DN)andlowersinglenull (LSN)equilibriaisshowninFig. 1.17 [75].Thereisaclearchangeinsignofthe innerSOLflowingoingfromUSNtoLSNwhilethekineticprofilesremainthe same.Thisdependenceofrotationonthemagneticequilibriumwillbediscussedin detailinSect. 5.2.1
1.4MicrowaveDopplerReflectometryandScattering TheDopplershiftsofmicrowavesmayalsobeusedtodeterminerotationvelocities [78–80].InDopplerreflectometrytheantennatiltangle θt inducesaDoppler frequencyshiftfD =u⊥ 2sinθt /λ0 inthemeasuredspectrumwhichisdirectly proportionaltotherotationvelocityu⊥ = vExB + vph oftheturbulencemovingin theplasma.Figure 1.18 showsaschematicoftheASDEXUpgrade(AUG)Doppler reflectometerdiagnosticalongwithapoloidalcrosssectionofatypicalLSNplasma
Fig.1.11 Experimentalarrangementformeasuringplasmarotationfromvacuumultravioletlines. Thelaserablationapparatusforinjectingtestimpuritiesisalsoshown.ReproducedfromFig.1of [51]R.C.IslerandL.E.Murray,‘Plasmarotationmeasurementsusingspectrallinesfromcharge transferreactions’,Appl.Phys.Lett. 42,355(1984),withthepermissionofAIPPublishing
[80].Fulldetailsofthediagnosticcanbefoundin[79].Examplesofedgevelocity profilesobtainedwiththissystemforseveralAUGOhmicdischargeswithvarious electrondensitiesandplasmascurrentsareshowninFig. 1.19 [80].Theprofile displaystheusualpeakstructureneartheseparatrixforallcases,buttheinterior rotationswitchesfromtheelectrondriftdirectiontotheiondriftdirectionasthe densityisincreasedforthe0.8MAcases.Thisrotationreversalwillbediscussedin detailinSect. 5.2.3
AnothermethodofvelocitydeterminationreliesoncollectiveThomsonscattering(CTS)ofmicrowaves.Thistechniquehasbeenusedtomeasurethebackground iontemperature[81–83]andmayalsoprovidetherotationvelocity[84, 85].An exampleofthetimehistoryoftherotationvelocitydeterminedbyCTSinanAUG
Fig.1.12 ToroidalrotationvelocitiesmeasuredfromchargeexchangeexcitedlineofOVIIIand fromelectronexcitedlinesofOVIIandNeIX.ReproducedfromFig.3of[51]R.C.IslerandL.E. Murray,‘Plasmarotationmeasurementsusingspectrallinesfromchargetransferreactions’,Appl. Phys.Lett. 42,355(1984),withthepermissionofAIPPublishing
Fig.1.13 (a)BackgroundsubtractedspectrumandfittothespectrumwiththeNBIonandNBI offspectrainset.(b)Residualfromthefitweightedbytheuncertaintyofthemeasuredspectrumat eachpixelbasedonphotonstatistics,darknoise,andreadoutnoise.ReproducedfromFig.3of[65] S.R.Haskeyetal.‘Activespectroscopymeasurementsofthedeuteriumtemperature,rotation,and densityfromthecoretoscrapeofflayerontheDIII-Dtokamak’,Rev.Sci.Instrum. 89,10D110 (2018),withthepermissionofAIPPublishing
discharge,comparedtotheCXRSresult,isshowninFig. 1.20.Ascanbeseen,the valuesfromthetwomeasurementsareinexcellentagreement.
1.5Comments Withtheimprovedtimeresolutioninhighthroughput2Dx-rayarrays,soontobe below1ms,itwillbepossibletomeasurefluctuationsinthecoretoroidalvelocity. ThiswillenabledirectmeasurementintheplasmacoreoftheReynoldsstress, whichisproportionaltothefluctuatingvelocityfields ˜ vr ˜ vφ .TheReynoldsstress intheplasmaboundaryregionhasbeenobserveddirectlyusingprobes[76, 77].
Fig.1.14 H-modepedestalprofilesfromThomsonscattering,impurity,andmainionCXRS. Carbonanddeuteriumrotationfrequencyprofilesareshowninpanel(d).ReproducedfromFig.4 of[66]B.A.Griersonetal.‘Highresolutionmain-ionchargeexchangespectroscopyintheDIII-D H-modepedestal’,Rev.Sci.Instrum. 87,11E545(2016),withthepermissionofAIPPublishing
Fig.1.15 Theplasmastoredenergy(top),impuritytoroidalrotationvelocityatthreeradii(red dots,greenasterisksandpurplediamondsforr/a = 0.0,0.3and0.6,respectively)andmagnetic perturbationrotation(×s)atthesawtoothinversionradius(r/a ∼ 0.2),andtheedgeDα brightness (bottom)foranICRFheatedELM-freeH-modedischarge.ReprintedwithpermissionfromFig.2 of[35]W.D.Leeetal.‘ObservationofAnomalousMomentumTransportinTokamakPlasmas withNoMomentumInput’,Phys.Rev.Lett. 91,205003(2003).Copyright(2003)bytheAmerican PhysicalSociety
Inner Scanning Probe
Electrode, Flush to Probe Body
Coil
Inner Scanning Probe
Top Views of Rotating Probe
Outer Scanning Probe
Axis of Pyramid 19 mm dia.
Outer Scanning Probe
Vertical Scanning Probe
North Flux Surface Probe Body
Electrodes, Flush to Pyramid Magnetic Field
View of Electrodes Along Axis of
Fig.1.16 ScanningLangmuir-Machprobesareusedtoinfersimultaneouslyplasmaprofilesand parallelflowsatthreelocationsintheSOLofAlcatorC-Mod,includingthehighfieldside(inner scanningprobe).Atypicallowersinglenullplasmaequilibriumisshown.ReproducedfromFig.1 of[74]B.LaBombardetal.‘Transport-drivenScrape-Off-Layerflowsandtheboundaryconditions imposedatthemagneticseparatrixinatokamakplasma’,Nucl.Fusion 44,1047(2004),withthe permissionoftheIAEA
Fig.1.17 Scrapeofflayerprofileandflowdataobtainedfromtheinnerandouterscanningprobes. Thefluxsurfacecoordinate ρ isthedistanceintotheSOL,mappedtotheoutermidplane.Shaded regionsindicatewherefieldlinesmaycontactlimitersurfaces.Positivevelocitiescorrespondto flowintheco-currentdirection.Thedashedlinesonthelowerleftpanelshowthemagnitudeof thelocalplasmasoundspeedcs fordeuteriumplasmawithTi =Te .ReproducedfromFig.2of [75]B.LaBombardetal.‘Transport-drivenscrape-offlayerflowsandthex-pointdependenceof theL-HpowerthresholdinAlcatorC-Mod’,Phys.Plasmas 12,056111(2005),withthepermission ofAIPPublishing
Core: ρ < 0.85
Inside pedestal ∇T > ∇n
Mostly Electrostatic ITG, TEM, ETG turb.
(Microtearing: finite β)
Transition: (edge-core)
Pedestal region
∇T dominant
Velocity shear
Edge: 0.85 < ρ < 1
∇P dominant
Electromagnetic Drift-wave turbulence
Scrape-off-layer: ρ > 1
Open field lines, ∇n
Interchange/flute-type turb.
Fig.1.18 PoloidalcrosssectionofatypicalAUGdischargewithaschematicoftheDoppler reflectometer.ReproducedfromFig.1of[80]G.D.Conwayetal.‘Observationsoncoreturbulence transitionsinASDEXUpgradeusingDopplerreflectometry’,Nucl.Fusion 46,S799(2006),with thepermissionoftheIAEA
