Modelling of divertor plasma transport in stochastic magnetic boundary

Modelling of divertor plasma transportin stochastic magnetic boundaryM. KobayashiNational Institute for Fusion Science, Oroshi-cho 322-6, Toki city 509-5292, JapanIn acknowledgement of the fruitful discussions and contributions fromY. Feng, S. Morita, K. Ito, S. Masuzaki, T. Morisaki, N. Ezumi, S. Sakakibara, Y.Kikuchi, N. Ohyabu, T. Takizuka, S. Takamura, R. Burhenn, K.H. Finken, M. Lehnen,D. Reiter, S.S. Abdullaev, M.Z. Tokar, Ph. Ghendrih, T. Kobayashi, Y. Narushima, F.Sardei, the LHD experimental groupITER International Summer School 2009, 22-26 June 2009, Aix en Provence, France1

Role of SOL plasma in fusion reactorConfinement region:~10keV, 10 20 m -3 , α-particle confinement/heatingcontrol of pressure/current profile, 500MW fusion power, Q>10Power through LCFSImpurity, fuel influxScrape-off layer:1~few hundreds eV, 10 20 ~10 21 m -3 , balance between // & ltransport, power removal with radiation, impurity transport(material migration), plasma flow distribution, interaction withneutralsPower/particle fluxFuel recycling, impurity sourceMaterial surface: divertor target, first wallplasma neutralization, erosion, deposition, fuel retention,heat removal & fuel/He ash pumpingFirstwallMaterialsurfaceDivertortargetConfinementregionpumpSOL•Mitigation of power load on divertor plate•Reduction of Impurity influx to confinement region•High pumping efficiency of fuel, He ashITER International Summer School 2009, 22-26 June 2009, Aix en Provence, France2

MotivationStochastic field as a tool for controlling edge plasmaRMP for ELMs mitigationRMP reduces pressure gradient, interactswith eigenmode structure of ELMse.g. Ergodic divertor inTEXT, Tore Supra,TEXTOR-DED etc. enhanced radial transport,edge radiation, impurityscreening etc.Intrinsic edge stochastization in Heliotron configurationUnderstanding of plasmatransport characteristics instochastic field is inevitablefor divertor optimizationSymmetry breaking by Resonant Magnetic Perturbation2D axi-symmetric 3D non-axi-symmetricControllability of edge plasma for divertor optimizationITER International Summer School 2009, 22-26 June 2009, Aix en Provence, France3

Study on plasma transport in stochastic fieldMagnetic field structureIsland formaion, overlap (vacuum approximation) plasma response(field amplification, rotational screening, neoclassical effect)Measurements magnetic probe outside plasma, T eprofileIdeal stochastization quasi-linear model, diffusive pictureRealistic field mixture of remnant islands, local ergodicfield, laminar regionContents of the talk1. Formation of magnetic island and stochastic field2. Realistic field structure in devices3. Effects on transport (3D treatment)--- divertor plasma parameters--- SOL impurity transport4. Summary--- further topics to be addressedTransport analysisAnalytical formulae(e.g. R-R model)// & l transport interplay(3D treatment)Time averaged fieldEMC3-EIRENE, E3D, FINDIF etc.Fluctuating fieldElectrostatic/electromagneticturbulence (P. Beyer et al.,DALF3) etc.ITER International Summer School 2009, 22-26 June 2009, Aix en Provence, France4

1. Formation of magnetic island and stochastic fieldITER International Summer School 2009, 22-26 June 2009, Aix en Provence, France5

= rs , ι = n /mFormation of magnetic island : vacuum fieldField lines change their helicity in radialdirection because of magnetic shear.Δθ1 BθR 1ι ≡ = d =2 2∫ φπ π Bφr qd qmagnetic shear: = q 'd rθrProjection ontoresonant surfaceRadial component of RMP B ~ r ( )resonates with field line helicity (m,n).~~ B r∝ cos( mθ − nφ )−5− 4B r/ B t= 10Island width~r q Bw = 4mθ-nφ=const.~ 10s rm , n~ several cmmq'BITER International Summer School θ 2009, 22-26 June 2009, Aix en Provence, FranceB ~ rwrResonantperturbationB ~rField lines wind around original surface.6B ~ r2π/m

Onset of stochastic instability by island overlapping: σ Chir > 1ι = n /( m + 1)Δnι =( m,m + 1)n / mWith increasing B ~ , islandrbecomes large.~w ∝ B r m, n/ ι'“overlap”? ?X-pointO-pointseparatrixσ Chir0.5( w + w2)( n,m)=Δ ( m,m + 1)n1>Island “overlaps”Field lines in overlap region share Bfield with neighboring island, and“forget” from which island come from.1increasesB ~ rw1 ( n,m + 1)w2 ( n,m )Stochastic trajectoriesITER International Summer School 2009, 22-26 June 2009, Aix en Provence, France7K.H. Finken et al., “The structure of magnetic field in the TEXTOR-DED”

Field line structure in stochastic magnetic boundarySchematics of field line structureShort B linesLong B linesPerturbationcoil currentPerturbationfieldPFCsLaminar region(edge surface layers)Connection length (L C) distribution in TEXTOR-DEDrφθRemnant islandsStochasticregionPoloidal turnsLaminar region(edge surface layers)Stochastic regionShort & long L C coexistNo clear separatrix,locally ergodic, remnantislandsITER International Summer School 2009, 22-26 June 2009, Aix en Provence, Franceradialpoloidal8K.H. Finken et al., PRL 98 (2007) 065001.

3. Effects on transport (3D treatment)ITER International Summer School 2009, 22-26 June 2009, Aix en Provence, France9

Magnetic field structure in LHD (Large Helical Device)Connection length (L C) distribution in poloidal cross sectionLHDHelical coils3.9 mITER International Summer School 2009, 22-26 June 2009, Aix en Provence, France10

3D modelling of LHD edge region (EMC3-EIRENE)Computational mesh, configuration and installationsCore, CX-neutral transport, particle sourceSOL, EMC3 simulation domainVacuum of plasma*Physics model•Standard fluid equations of mass,momentum, ion and electron energy•Trace impurity fluid model (Carbon)•Kinetic model for neutral gas (Eirene)Boundary conditions•Bohm condition at divertor plates•Power entering the SOL•Density on LCMS•Sputtering coefficientCross-field transport coefficients•χ e=χ i=3D roughly holds•spatially constant (global transport)•determined experimentallyITER International Summer School 2009, 22-26 June 2009, Aix en Provence, FranceSOLExample of LHDhelical divertorwallLCMSP SOLCore plasmaC 0EMC3H,H 2Divertorlegs11target

Background plasma (fluid):∇⋅∇⋅∇⋅∇⋅UTzIITER International Summer School 2009, 22-26 June 2009, Aix en Provence, FranceModel equations in EMC3-EIRENE( nVi iIIb− Db⊥b⊥⋅∇ni) = Sp( minVi iIIViIIb−ηIIbb⋅∇ViII− mVi iIIDb⊥b⊥⋅∇ni−η⊥b⊥b⊥⋅∇ViII) = −b⋅∇p+ Sm55(2neTeViIIb−κebb⋅∇Te−2TeDb⊥b⊥⋅∇ne− χeneb⊥b⊥⋅∇Te) = −k( Te− Ti) +55( niTVi iIIb−κibb⋅∇Ti− TiDb⊥b⊥⋅∇ni− χinib⊥b⊥⋅∇Ti) = + k( Te− Ti) + SeizIi2Impurities (fluid):∇⋅z z zz( nIVIIIb− DIb⊥b⊥⋅∇nI)zz z( V −V) = −b⋅∇nTIIIb ⋅∇ne= TTieiII+ neeEIIeIeI2=S+ nzI+ n C b ⋅∇Tez−1→zZeE= 0− SNeutrals (kinetic):Boltzmann equation (Eirene code)+ nz→z+1zIZ2+ Rez+1→zC b ⋅∇Te− R+ nPlasma-surface and neutral-surface interaction:Particle and energy reflection, sputtering (Eirene code)IIz→z−1zIC b ⋅∇TiiSee+Simp12

φ=144 0 Vacuum vesselφ=153 0Field line aligned 3D gridsZ (m)Edge plasmaR (m)Z (m)grid verticesφ 1φ 2φ 3φ 4φ 5B field lineITER International Summer School 2009, 22-26 June 2009, Aix en Provence, FranceR (m)13

Fokker-Planck formJump step of Monte Carlo particle: e 3: e 1, e 2( : 1D and 2D random unit vectors)Monte Carloparticlee 2e 1e 3 = bB field lineITER International Summer School 2009, 22-26 June 2009, Aix en Provence, France14

3. Effects on transport (3D treatment)3.1 divertor plasma parametersITER International Summer School 2009, 22-26 June 2009, Aix en Provence, France15

Role of pressure conservation along flux tubes on T div , n divn e, div(10 19 m -3 )Divertor plasma parameter in ASDEXSheath limitedregimeT i, divT e, divhigh recyclingregime~ n−2~ nn e, div3DetachmentT e,i(eV)X-point divertor tokamaksPressure conservation along flux tube,∇// ( nT+ minV//) =gives rise to sensitive divertor parameterdependence on upstream density :High recycling regime (conduction limited regime)ndiv ∝ n up320−2T div∝ n upThe dependence is experimentally confirmed.Stochastic boundaryThe 3D flux tube geometry can introduceperpendicular terms breaking down of thepressure conservation.n e(10 19 m -3 )Y. Shimomura et al., NF 23 (1983) 869.∇2//( nT+ minV//) − ∇⊥(mVi //D⊥∇⊥n+ η⊥∇⊥V//) =0ITER International Summer School 2009, 22-26 June 2009, Aix en Provence, France16

Parallel plasma flow is regulated by remnant island (mode) structureParallel flow distributionnV //10 23 /m 2 /s4.0radialB field lines inmagnetic islandradialEdge surfacelayers2.00.0-2.0Core DivertornVnVnV //-nV //+~toroidal-4.0Flow projection ontopoloidal planepoloidalradialL Cdistributionpoloidal‣The field line structure produces flowalternation.‣Short confinement time in open fieldlines leads to fast parallel flowimpact on impurity transport(discussed later)ITER International Summer School 2009, 22-26 June 2009, Aix en Provence, France17

Parallel plasma flow is regulated by remnant island (mode) structureradialradialEdge surfacelayersParallel flow distributionnV //10 23 /m 2 /s4.0Mach probe scanning path2.00.0-2.0-4.010.50radialCore DivertorB field lines inmagnetic islandnVnVnV //-Flow projection ontopoloidal planenV //+poloidalMach probe measurement~toroidalMach probe #1Mach probe #2Mach probe #33D modellingL CdistributionpoloidalITER International Summer School 2009, 22-26 June 2009, Aix en Provence, France-0.5-1N. Ezumi et al, to appear in PFR.-0.95 -0.90 -0.85 18-0.80Z (m)

Parallel plasma flow is regulated by remnant island (mode) structureradialEdge surfacelayersParallel flow distributionl interactionnV //10 23 /m 2 /s4.02.00.0‣The flow shear momentum loss ofV //via l interaction∇⊥( m iV// D ⊥∇ ⊥n + η ⊥∇ ⊥V//)-2.0-4.0Mach probe measurementn( T + T ) m nVe i+i2//10.5l interactionMach probe #1Mach probe #2Mach probe #33D modelling0-0.5-1N. Ezumi et al, to appear in PFR.l (m)//ITER International Summer School 2009, 22-26 June 2009, Aix en Provence, France-0.95 -0.90 -0.85 19-0.80Z (m)

Two point model with momentum loss in perpendicular direction10 0 -2T d~n uf m0=010 -1nd~nu3Tndd∝∝High recyclingin tokamaks−2uf m0=0 110 1 1.5n ~nd u10 0(b)1 10n u(10 19 m -3 )ITER International Summer School 2009, 22-26 June 2009, Aix en Provence, Francenn3u(1 +(1 +1ffmm)88)2−3Increasing f m0,T d~n u-1(a)fmD 1= ∫ ⊥u2m0//∇ nV//dl ≈ ∝0.5 0.5 22cdsdndcsdTdTdδm( Assumed D=const.)l//δ m−23T d∝ n u nd ∝ n u modest dependence on n uδ m : l characteristic length of the flow alternation: distance along field linel //‣ f m0=0 high recycling in tokamaks‣Strong flux tube deformation large f m0, large momentum lossf m0>>1 −1T d∝ n u1.5nd ∝ n u20M. Kobayashi et al, to appear in JPFR (in Japanese), submitted to FS&T.fl

Divertor probe measurements confirm absence of high recycling regimeprior to detachmentTndd∝∝PP10 / 7SOL−8 / 7SOLnn−2u3u(1 +(1 +ffmm))2,−3High recyclingin tokamaksDetach.‣Moderate dependence of T ed& n edon n u(T>10eV no significant CX loss,ν SOL*=L C/mfp>10)‣n ednever exceeds upstream density‣Both 3D modellings & the two point model(with P SOLvariation due to NBI heatingincluded) reproduce the experimental results. effect of momentum loss via l interactionM. Kobayashi et al, to appear in JPFR (in Japanese),submitted to FS&T.ITER International Summer School 2009, 22-26 June 2009, Aix en Provence, France21

Momentum loss via friction between counter flows in W7-AS/XEMC3-EIRENEδ m ~60 cmn ed 10 19 m -3n ed~n u3δ ml //δ m ~8 cmfm∝Tl//0.5dδ2mn u 10 19 m -3Y. Feng et al., NF 46 (2006) 807, Y. Feng et al., submitted to NF.l //l //W7-AS: ~100 m, δ m ~8 cmW7-X: ~180 m, δ m ~60 cmfm,W 7− AS>>m,W 7−XfField line geometry near divertor, l//, δ m, provides controllability of divertor regime.ITER International Summer School 2009, 22-26 June 2009, Aix en Provence, France22

Summary of 3.1 Divertor plasma parameters1. nV //in stochastic boundary alternating flow regulated by remnant islands2. n div& T divin stochastic boundary of LHD show modest sensitivity to n up, in contrast to thehigh recycling regime in tokamaks.3. Breakdown of parallel pressure conservation via perpendicular frictional interaction of thecounter flows.l//4. The degree of momentum loss can be described as fm∝0.5 2.Tdδm5. The analysis in W7-AS, X controllability of divertor regime:3nd ∝ n u1~1.5nd ∝ n u6. For future devices, l should be optimized for control of divertor plasma with stochastic//,δ mmagnetic field.ITER International Summer School 2009, 22-26 June 2009, Aix en Provence, France23

3. Effects on transport (3D treatment)3.2 SOL impurity transportITER International Summer School 2009, 22-26 June 2009, Aix en Provence, France24

3D impurity transport model : EMC3-EIRENE (fluid approximation)Momentum : // - Classical force balancemz1 Electric field∂ Vz//∂ TinzVi//− Vz//2 ∂ Te∂ T= − ++ ZeE 0.71 2.62 imz//+ Z + Z + ....∂ t n ∂ s τ∂ s ∂ szsτsImpuritypressuregradient forcefriction∂ T∂ sFriction±V Z //?electron & ion temperature gradient force(thermal force)LCFST iThermaldT i/dsMass : | - Diffusion with anomalous coefficientr r r r r∇⋅=S( n V b − D b b ⋅∇n)zz //z−1→znz−1z− S⊥⊥z→z+1nzz+ Rz+1→znz+1− Rz→z−1nzcoreRecyclingFrictionSOLV iIItargetsD z is set to be the same value of bulk plasmathat is deduced from experiments.ITER International Summer School 2009, 22-26 June 2009, Aix en Provence, France25

From thermal-force to friction-dominated impurity transportPlasma ionflow nv II3×10 19Thermal force dominant inward flowCarbon density distributionImpurity flown LCMS=2×10 19 m -3Increase n e(10 18 m -3 )1.00.1Impurity flow4×10 190.01friction dominantITER International Summer School 2009, 22-26 June 2009, Aix en Provence, Franceoutward flow26

Carbon density profiles by 3D model show impurity retention at high density5.03.01.00.800.600.40n LCFS=1.5x10 19 m -32.0x10 193.0x10 196.0x10 1910 21 Impurity ionization (s -1 m -3 )10 190.80.60.40.2Accelerationof //-plasmaflowthermalfriction642Increasing density Enhances friction force in edge surfacelayer with flow acceleration by short flux tubes Stops carbon penetration in edge surface layers Feels more friction Suppresses thermal force in stochasticregion0.60Stochasticregion0.650.70Edge surfacelayersr eff(m)L C/m10 510 410 310 20.00.60 0.65 0.70r eff(m)StochasticEdge surfaceITER International Summer School 2009, 22-26 June 2009, Aix en Provence, France010 110 027

3D code predicts that energy transport follows the remnant island structure strong modulation of Te distributionL C/mT e/eVr 10 5 10 4 10 3 10 2 10 1 10 0eff(m)200 100 00.70Edge surfacelayersEMC3-EIRENE0.650.60StochasticregionInboardOutboardInboardClear mode structure is observed in Teprofiles obtained by Thomson scatteringsystem in good agreement with the code result.ITER International Summer School 2009, 22-26 June 2009, Aix en Provence, FranceT e/ eV* ThomsonEMC3/EIRENEn/m=10/310/510/72.5 2.6 2.7 2.8 2.9 3.028R/m

Key role of remnant islands on impurity transport∂ Ti2.5qr= −nχ⊥ − b ⋅ rκi0Ti∇//∇//Ti∂ r= −nχr⊥rqri0//Θ+ κ T2.5iWith high density & small Θ (~10 -4 in LHD),Θ2Tiκwnχ⊥2.5i0T i>> Θ2l //|-transport dominatesbrr rΘ = b ⋅(Y. Feng NF 46 2006)≈wl //∇//Ti≈ −qrnχΘ⊥∝n−1Increasing density suppresses //-T gradient, i.e.thermal force in the presence of remnant islands.ITER International Summer School 2009, 22-26 June 2009, Aix en Provence, France29M. Kobayashi et al., Proceedings of 22nd IAEA FEC (2008) EX/9-4.

Radial profiles of each charge states of carbon densityImpurity screening shift of impurity density profile to low temperature regionImpurity screening10 18n up=2e19 m -3Z ≥ +4 Z ≤ + 310 18n up=4e19 m -3Z ≥ +4 Z ≤ + 3n z(m -3 )10 17C+6C(all)C+4C+5C+1C+2n z(m -3 )10 17C(all)C+4C+5C+6C+1C+2C+310 16C+310 1610 15 r eff(m)0.60 0.65 0.70r eff(m)10 150.60 0.65 0.70r eff(m)r eff(m)ITER International Summer School 2009, 22-26 June 2009, Aix en Provence, France30

CIII: 977Å, 1S 2 2S 2 -1S 2 2S2P (VUV monochromators)CIV: 1548Å, 1S 2 2S-1S 2 2P (VUV monochromators)CV: 40.27Å, 1S 2 -1S2P (EUV spectrometer)(a)Emission measurements in experiments indicateimpurity retention potential at high densityCIII/neCIV/neCV/ne10 2Viewing areaSpectroscopyAbsolutely calibrated10 1Modelling10 0 0 2 4 6 8CIII radiation distribution in thesame viewing area obtained by3D code.10 -1ExperimentsITER International Summer School 2009, 22-26 June 2009, Aix en Provence, Francen e(e19 m -3 )31

Signature of impurity screening with stochastic boundary various devicesTore SupraY. Corre et al., NF 47 (2007) 119. TEXTOR-DEDG. Telesca et al., JNM 390-391 (2009) 227.Carbon flux and densityC 6+ concentrationwith DEDDEDcurrentwithout DEDHigh densityC 6+ density in confinement regiondecreases with increasing density.time (s)C 6+ concentration in core regiondecreases with DED activation.ITER International Summer School 2009, 22-26 June 2009, Aix en Provence, France32

Summary: SOL Impurity transport1. 3D impurity transport modelling in the stochastic magnetic structure shows impurity screeningeffect at high density :Increasing density Enhances friction force in edge surface layer with flow acceleration by rich ionizationsource Stops carbon penetration in edge surface layers Feels more friction Suppresses thermal force in stochastic regionnχ⊥22. The remnant islands with small Θ ( ≈ w / l ) , >> Θ//2.5and high density κi0T ii.e. suppression of thermal force at high density∇//T∝ n−13. The edge carbon emission measurements agree well with the code results, indicating impurityretention effect of stochastic magnetic boundary.ITER International Summer School 2009, 22-26 June 2009, Aix en Provence, France33

SummaryPlasma transport in stochastic magnetic boundary in LHD is analyzed by the 3D edgetransport code in comparison with experimental results and with other devices.1. Magnetic shear + RMP topological change of field lines (magnetic island), stochastic instability l , // characteristic scale: δ m, w, l//2. Influence on divertor regime:l//high recycling no high recycling with fm∝0.5 2Tdδmnχ⊥3. Impurity screening potential at high density with very small Θ ( ≈ w / l//) ,κi0T and flow acceleration in edge surface layers (laminar region).i2.5>> Θ2These geometrical parameters provide control of edge plasma transport in stochastic SOL.Stochastic magnetic boundariesSymmetry breaking Controllability of edge plasma transportITER International Summer School 2009, 22-26 June 2009, Aix en Provence, FranceFurther topics to be investigatedPower load dispersal on divertor platesPlasma response to RMP.Electric field formation, determination of D,D Z, χ.Quantitative estimation for future devices34

Field lines connect divertor plate with different connection lengths(ranges in two orders, 10 m ~ 1000 m)l0rδ 0‣Magnetic shear + B ~r stretching, bending, compression of flux tubesl (s)Magnetic shearδ (s)B ~ rL C profiles on divertor platesL C (m)The long & short flux tubesare mixed due to thedeformation, creating finestructure.blow upNot only //, BUT l energyexchange between fluxtubes plays important rolein determining wetted area.~4 cmITER International Summer School 2009, 22-26 June 2009, Aix en Provence, France35

3D Modelling : Power deposition profile insensitive to P SOLPROBE10.5U_P02_D0.50_1.50_NUP41.00.8λ p2MW4MW8MW16MW0.60.40.2Δ energy0.00.06 0.08 0.10 0.12 0.14s (m)Maximum power load linearly scales with P SOL,indicating no P SOLdependence of Δ energy.Because of Δ energy>> λ p, change of λ pis negligible.ITER International Summer School 2009, 22-26 June 2009, Aix en Provence, France36

IR camera measurements in TEXTOR-DED:Divertor heat flux is well correlated with L C distributionHeat flux (W/m 2 )Connection length (poloidal turns)M. Jakubowski et al., PPCF 49 (2007) S109.ITER International Summer School 2009, 22-26 June 2009, Aix en Provence, France37

Plasma response to RMP : screening/amplification by current inducedaround resonance surfaceSkin effectPlasmarotationB ~rRMP coilShieldingcurrentI pTearing modeinstabilitycoilB ~r~ plj φcoilB ~ rY. Kikuchi et al. NF 44 (2004) S28.ITER International Summer School 2009, 22-26 June 2009, Aix en Provence, France38

Neo-classical effect : bootstrap current, polarization currentIsland healingIsland healingITER International Summer School 2009, 22-26 June 2009, Aix en Provence, FranceY. Narushima et al., Nucl. Fusion 48 (2008) 075010.N. Ohyabu et al., Phys. Rev. Lett. 88 (2002) 055005.39K. Itoh, S.I. Itoh and M. Yagi, Phys. Plasmas 12 (2005) 072512.

Possibility for stable detachment control with remnant island structureStrong radiation is localized at the remnant island structureY. Feng et al., NF 48 (2008) 024012.ITER International Summer School 2009, 22-26 June 2009, Aix en Provence, France40

Interaction of island chain of different modes at high field region leads to strongflow shear Momentum loss via cross-field friction-4.0 -2.0Helical coilHFRnV // (10 23 1/m 2 /s)0LFR2.04.0radialCore Divertorm=6 mode (even)m=7 mode (odd)poloidalnV //-Flow shearnV //+toroidalHFRHelical coiln( T + T ) m nVe i+i2//ZLFR~ 6cmRITER International Summer School 2009, 22-26 June 2009, Aix en Provence, Francel (m)//41

Parallel plasma flow is regulated by remnant island (mode) structureradialEdge surfacelayersParallel flow distributionnV //10 23 /m 2 /s4.0Mach probe scanning path2.00.0-2.0‣The field line structure produces flowalternation.‣Short confinement time in open fieldlines leads to fast parallel flow,Mach>0.5impact on impurity transport(discussed later)radialCore DivertorpoloidalB field lines inmagnetic islandnVnVnV //-Flow projection ontopoloidal planenV //+poloidal~toroidalITER International Summer School 2009, 22-26 June 2009, Aix en Provence, France-4.010.50-0.5-1Mach probe measurementMach probe #1Mach probe #2Mach probe #33D modellingN. Ezumi et al, to appear in PFR.-0.95 -0.90 -0.85 -0.8042Z (m)

Parallel plasma flow is regulated by remnant island (mode) structureradialEdge surfacelayersParallel flow distributionl interactionnV //10 23 /m 2 /s4.02.00.0‣The flow shear momentum loss ofV //via l interaction∇⊥( m iV// D ⊥∇ ⊥n + η ⊥∇ ⊥V//)-2.0radialpoloidalB field lines inmagnetic island-4.010.5Mach probe measurementl interactionMach probe #1Mach probe #2Mach probe #33D modellingCore DivertornVnVnV //-Flow projection ontopoloidal planenV //+poloidal~toroidalITER International Summer School 2009, 22-26 June 2009, Aix en Provence, France0-0.5-1N. Ezumi et al, to appear in PFR.-0.95 -0.90 -0.85 -0.80Z (m)43

What we have learnedSummary of 3.1 Divertor plasma parameters1. nV //in stochastic boundary alternating flow regulated by remnant islands2. n div& T divin stochastic boundary of LHD show modest sensitivity to n up, in contrast to thehigh recycling regime in tokamaks.3. Breakdown of parallel pressure conservation via perpendicular frictional interaction of thecounter flows.l//4. The degree of momentum loss can be described as fm∝0.5 2.Tdδm5. The analysis in W7-AS, X controllability of divertor regime:3nd ∝ n u6. For future devices, l should be optimized for control of divertor plasma.//,δ me.g. for good neutral compression, f mshould be small.ITER International Summer School 2009, 22-26 June 2009, Aix en Provence, France1~1.5nd ∝ n uWhat we haven’t yet understood1. If D has parameter dependence, f m(n d, T d) ? affects qualitative dependence!!l//2. If l momentum flux is not ∝ ∇ ⊥nV //, but convective one ∝V ⊥ , convV //then fm∝ ?δm affects quantitative dependence!44

What we haven’t yet understoodSummary: SOL Impurity transport1. Parameter & Z dependence of ? affects quantitative dependence!ΘD Z ⊥VZ //+ V Z , conv2. l convective term ? affects qualitative dependence!!Simplified // force balance between frictionand ion thermal force reads,τZi 2VZ //= Vi//+ CiZ ∇//mZTi1D radial continuity,d ⎛⎜ΘnZVdr ⎝∑Z→Z //− DZ ⊥dnd ⎛⎜ΘnIVdr ⎝drZZ //⎞⎟⎠−= −SDZ ⊥Zdndr− RI⎞⎟⎠Z+ S= 0Z −1+RZ + 1Solution for target-released impurities:nItarget⎛⎞⎜ΘVZ//= −⎟, LCMS/ nI, t arg etexp∫ dr⎝ DLCMS Z ⊥ ⎠ITER International Summer School 2009, 22-26 June 2009, Aix en Provence, FrancennI , LCMSI , t arg etLCMSV Z //>V Z //

ITER International Summer School 2009, 22-26 June 2009, Aix en Provence, France46

Simple 1D model~P SOL5/91.03D results0.10 5 10 15 20P SOL(MW)ITER International Summer School 2009, 22-26 June 2009, Aix en Provence, France47