DrivenRotation,Self-GeneratedFlow,andMomentum TransportinTokamakPlasmasJohnRice
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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
©SpringerNatureSwitzerlandAG2022
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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
