托卡马克位形优化2

NonlinearityofLHwaveabsorptionTheplasmatemperatureinHL-2Aismuchlowerthanthatinfuturereactor.ToestablishRSconfiguration,theLHdrivencurrentshouldbelocatedoff-axiswheretheplasmatemperatureisevenlower,andtheplasmaabsorptionofhighphasevelocityLHwavesistooweaktoensurethewavesaredampedduringtheirfirstpass.IntheweakelectronLandaudampingconditionLHwaveraysmakemanypassesthroughthewavepropagationdomaininplasmaandundergonumerousreflectionsatthepropagationboundaries.Consideringthepropagationoflower-hybridwavesinatokamak.ThephasespaceenergydensityoftherffieldisdenotedbyU(x,k,t),wherexisthepositionvector,kisthewavevector.UobeystheWKE,AfterdeterminingU(x,k),wecancalculatephysicalquantitiessuchasthe(time-averaged)absorbedpowerdensity,1NonlinearityofLHwaveabsorpTHECYLINDRICALAPPROXIMATIONAppropriatecanonicalcoordinatesintokamakgeometryare(x,k)(r,

,

,kr,m,n).WeconsiderthesourceS=Pin(2)-2(r-ro)(kr–kr0),thesolutionof(1)isThe(time-averaged)energydensityintherfparallelelectricfield,Herefollowsfromthecoldplasmadispersionrelation.Thedampingrate

e

forelectronLandaudampingcanbewrittenasfollows:whereTheabsorbedpowerdensity,,with2THECYLINDRICALAPPROXIMATIONTTheabovesolutionoftheWKEcanbeclassifiedintotwodistinctpara-meterregimes:(i)themultipassregime(for

1),whenUtendstobeuniformalongtheentirerayorbitinthe(r,k)plane,and(ii)thesingle-passregime(for

>5)whennearlyallthepowerisabsorbedbeforetherayreachesthecaustic.Inthemulti-passregime,theabsorptionduetoelectronLandaudampingisstronglypeakedatthecaustic.Fig.10RadialprofilesofPand|E//|2formultipassabsorptionofasinglefieldharmonic(m=100,n=450)inthecylindricalapproximation.3TheabovesolutionoftheWKEInthetokamaktoroidalgeometryintrinsicpoloidalasymmetrybreakstheinvarianceofm,causingformationofathickstochasticlayerintherayphasespace.IntheLHCDdischargesonToreSupra,aregimewithstationaryoscillationbehaviorhasbeenobservedbecauseofthenonlinearlycouplingeffectofbothwave-plasmainteractionandturbulencesuppressionbytheRSqprofile.Itisinterpretedasthatthecurrentdensityandelectrontemperatureprofilesbehaveasapredator-preysystem[Giruzzi,G.,etal.,Phys.Rev.Lett.91(2003)135001].Fig,11Surface-sofsectioninthe(m,

)planefortwoparametersetsonToreSupra.4Inthetokamaktoroidalgeomet556677889910101111Fig.2RegionofLHpowerabsorption(att=1.0s):electronLandaudampinglimit(fullline);n//-upshiftboundary(dottedline);andboundaryofthewavepropagationdomain(dashline).(a)Ip=265KA,(b)Ip=300KAFig.1EvolutionofLHwavedrivencurrentprofileforthecaseoftheLHspectrumproducedwithin(a)theIp=265kAdischarge,and(b)theIp=300KAdischarge

12Fig.2RegionofLHpowerabsoFig.3TimeevolutionoftheLHwavedrivencurrentprofile,andtheregionsofLHpowerabsorptionbystrongelectronLandaudampingattwodifferenttimes:(a)t=1.5s,(b)t=0.8sTheLHwaveabsorptionisboundedintheregiondefinedbythestrongLandau-dampinglimitandtheboundaryofwavepropagationdomain.ThismechanismoftheLHwaveabsorptioncausesinterplayofthedistributionoftheLHwavedrivencurrentwiththemodificationoftheplasmaconfiguration,whichconstitutesnon-linearityintheLHwavedeposition.

Duetonon-linearityoftheLHpowerabsorption,theLHwavedepositionpositionchangesspontaneously,generatingtwodistinctquasi-stationaryreversedmagneticshear(RS)configura-tions.13Fig.3TimeevolutionoftheLHFig.4Timeevolutionof(a)locationofpeakoftheLHdrivencurrentprofile,and(b)locationoftheminimumqintheoscillatingRSdischarge(fullline),thetwo-phaseRSdischarge,andthestationaryRSdischarge(dashedline)InaNBIheatedplasmaofIp=265kA,BT

=2.8T,and,bycontrollingtheradiatedLHspectrum(PLH=0.5MW),quasi-stationaryRSdischarge[Q.Gao,etal.NuclFusion43(2003)982],two-phaseRSdischarge[Q.Gao,etal.PhysPlasmas12(2005)122507]havebeenobtained.When

=60

thelocationofthepeakofLHdrivencurrentpresentsoscillationwithirregularcyclic.non-predator-preyoscillation14Fig.4Timeevolutionof(a)l(a)Profilesoftheiontemperatureatt=1.42s(dottedline),andt=1.69s(fullline)intheoscillatingRSdischarge.(b)Ionthermaldiffusivity

iversus

att=1.42s(dottedline),andt=1.69s(fullline)withthecorrespondingthinlinesindicatingneo-classicalvalue.15(a)ProfilesoftheiontemperOscillationsduringLHramp-upinToreSupra16OscillationsduringLHramp-upLotka-VolterraequationsUsedformodellingpopulationsinecosystems2couplednonlinearequations,periodicsolutionsJ=predator;T=prey?Predator-preysystems17Lotka-VolterraequationsPredatResistivediffusionandheattransportequations:...havesimilaritieswiththeLotka-Volterraequations:18ResistivediffusionandheattOscillationsreproducedbyCRONOS

coupledresistiveandheatdiffusionequations haveperiodicsolutionsif:

jLH(r)j(r)Te(r)

ceisafunctionofj(e.g.,improvedconfinementfornegativeshear)OutputsoftheCRONOScoderesistivediffusionheattransportself-cons.equilibriumjLH(r)j(r)Te(r)19OscillationsreproducedbyCROTheoscillatorybehaviorintheLHCDcontrolleddischargeonHL-2AisinducedbynonlinearcouplingoftheLHpowerabsorptionpositionwiththeplasmaconfiguration.Accordingtotheanalysisbyusingthewavekineticequation,intheweakdampingregimeabsorptionoftheLHwavesduetoELDisstronglypeakedatcaustic.ThepeaklocationofLHdrivencurrentisdeterminedbytheintersectionbetweentheinnerboundary(caustic)ofthepropagationdomainandtheELDlimit.20TheoscillatorybehaviorinthThemechanismofLHpowerdepositionregioncouplingtheqprofile

andTeprofile

isthefollowing:Inthetokamakplasmacondition,theupperboundaryoftheLHwavepropagationdomainisreducedtoInthecentralplasmaregion(

<0.7),isnearlyaconstantapproximatelyequivalentto18becauseitismainlydependentonsquare-rootoftheplasmadensity.Thusisadecreasingfunctionofthemagneticgeometryfactor;TheELDlimitisadecreasingfunctionofTe,andactuallyitisnearlyunchangedintheoscillationsinceitisinverselyproportionaltosquarerootofTe.WhenevertheLHdrivencurrentmovesinwards,decreasesduetothesafetyfactordecreasing,thecausticboundaryiselevated.TheintersectionbetweenthecausticboundaryandtheELDlimit