Transport and fluctuations in LHD and comparisons with tokamaks ITPA CDBM and Transport meetings - Spring 2007 at EPFL Lausanne K. Tanaka1), C. Michael1), L.N. Vyacheslavov4), H.Yamada1), M. Yokoyama1) O.Yamagishi1), H. Takenaga2), K. Muraoka3), H.Urano2), S. Murakami5), A. Wakasa6) and LHD Experimental group1) National Institute for Fusion Science, 322-6 Oroshi, Toki, 509-5292, Japan2) Japan Atomic Energy Agency 801-1 Mukouyama Naka Ibaraki, 311-0193, Japan3) School of Engineering, Chubu University, 1200 Matsumoto, Kasugai, Aichi 487-8501 4) Budker Institute of Nuclear Physics, 630090, Novosibirsk, Russia5) Department of Nuclear Engineering, Kyoto University, Kyoto 606-8501, Japan6) Graduate School of Engineering, Hokkaido University, Sapporo, 060-8628, Japan

There is a similarity and dissimilarity between helical/stellarator and tokamakSimilarityBoth global energy confinements scaling (IPB98(y2) for tokamak and ISS04 for helical/stellarator) are similar and are Gyro Bohm like .Dissimilarity Shape of density profile.

The motivation of comparison study between helical/stellarator and tokamak is to understand common underlined physics of transport.

Outline of talk Comparison of global energy confinement scaling between tokamak and helical/stellaratorRole of neoclassical optimization on anomalous transport.Particle transport of LHDExperimental turbulence study in LHD

International sterraltor scaliing 04 (ISS04) is dimensionally similar to IPB98(y,2) on r*. Both are weak Gyro Bohm (H.Yamada N.F.1684 (2005))In Gyro Bohm like transport, transport is turbulence driven, of which wave length is order of ion Larmor radius.H. Yamada, Nucl. Fusion 45 (2005) 1684Tokamak Ip are treated through q2/3 into stellarator scaling.

In LHD, edge (r=0.7~1.1) fluctuation level measured by phase contrast imaging (PCI) increases with increase of edge diffusion coefficient. This is similar to tokamak observation.kperp ri~0.5. This is expected by linear calculation of GOBLIN code. In tokamak, smaller peak wavenumber kperp ri~0.1 was reported anywhere.Edge transport influence global confinement. Similar fluctuation character may results in similar r* scaling K.Tanaka Fusion Sci. Tech. (2007)97

The particularity of helical/stellarator is enhanced neoclassical transport in low collision regime Neoclassical Transport coefficientBanana regimeneiPlateau regime1/n regimeFuture operation regime of reactorAround one orderExperimental De,ceAround one orderhelical/stellaratortokamakFuture operation regime of reactor Neoclassical Transport coefficientPlateau regimeneiExperimental De,ceS. Murakami Nucl. Fusion 42 (2002) L19L22Axis PositionAxis PositionDneo/Dtokamak plateuDneo/Dtokamak plateu1/n regimePlateau regimeIn 1/n, neoclassical transport is minimum at Rax=3.53mIn Plateau, neoclassical transport is smaller at more inward axis.Inward shiftedOutward shiftedInward shiftedOutward shifted

Magnetic axis position change magnetic helical ripple and higher ripple results in larger neoclassical transportFlux SurfaceOrbit of guiding centerHC-IPlasmaHelical coilShifts by external vertical field and Shafranov shiftsB contour

Energy confinement is improved by shift of magnetic axis positionInward shift of Rax Optimization in terms of drift optimizationEffect of neoclassical transport is pronounced in collisionless regime

Confinement improvement by the inward shift of Rax still exists in collisional regimeNeoclassical optimization is successful !Much more than neoclassical theory !?0.60.03Smaller helical rippleSmaller helical ripple

One of the key parameter to determine global energy is eh_eff, which is representative amplitude of magnetic helical rippleH. Yamada, Nucl. Fusion 45 (2005) 1684Representative helical ripple amplitude at r=2/3

Global energy confinements are gyro Bohm character and edge particle diffusion (~edge thermal conductivity ~ global energy and particle transport) are dominated by turbulence (kperpri~0.5) driven transport.With smaller magnetic ripple (inward shifted configuration and smaller neoclassical transport), energy transport is reduced.Reduced neoclassical configuration introduce smaller anomalous transport.Recent non linear gyro kinetic simulation support this. At reduced neoclassical configuration with smaller magnetic helical ripple, zonal flow can be more induced, then turbulence is supressed. (Sugama, Watanabe P.R.L. 94,115001,(2005), Watanabe, Sugama, 21st FEC IAEA-CN-149/EX/5-4)

Summary of global energy confinement in LHD

60U Elmy H modeLHD Rax=3.6m Density scan at PNBI=8-10MW PNBI scan at similar averaged densityDifferent character of density profiles are observed in JT60U and LHD

Magnetic axis position changes density profile as well.Inward shiftedSmall magnetic helical ripple and reduced neoclassical transportOutward shiftedLarge magnetic helical ripple and enhanced neoclassical transport

NBI 11.4MWNBI 1.7MWExample of transport analysisD is anomalous.Vout is comparable Vneo.Impurity may not account for ne profileHigher Te gradient induce outward convection

Density modulation experiments shows Dcore is anomalous, outward Vcore is comparable with neoclassical oneBlank; Experiment, Colored; Neoclassical At lower collisionality Dcore is close toDneo.Dneon*hInward Vcore is not neoclassical.Plateau1/n

Core particle flux is zero. In core region of hollow density profile, outward neoclassical pinch is balanced with inward anomalous diffusion.Outward neoclassical convectionInward anomalous diffusion.Total flux~0-D grad neneVInward directed anomalous flux is predicted by linear theory (O.Yamagishi 14. 012505 (2007) ) G~0 in core (r

Summary of particle transport in LHDOne of the particularity of the helical/stellarator is particle transport. Hollow density profiles are often observed. This is clear contrast that density profile is always peaked in tokamak.Enhanced neoclassical transport introduces hollow density profile.Peaked density profile is obtained at reduced neoclassical configuration and is likely to be driven by anomalous process.Particle diffusion is anomalous, outward convection is comparable with neoclassical value. Inward pinch is against neoclassical prediction.Linear gyro kinetic calculation suggests the balance of turbulence driven flux and neoclassical flux produce hollow density profile.

Top view of integrated fluctuationTop view of upper fluctuationTop view of lower fluctuationPrinciple of 2D PCIUpper fieldLower fieldLaser BeamPropagation direction tells spatial points of fluctuation.

Integrated 2D picture with 8x6=48ch 2D array6.1mm17.5mmSpatial 2D Fourier TransformFluctuation of lower partFluctuation of upper part

Present resolution is a/3~a/5. Signal suffers from cancellation effectsExample signal of 2D PCIA.Sanin et al., Rev. Sci. Instrum., Vol. 75, No.10, (2004) pp.3439-3441C. Michael et al., , Rev. Sci. Instrum. 77, 10E923 (2006) L.N.Vyacheslavov et al.,IEEE special issue of plasma image Vol.33 (2005) pp.464-465

Movie of Fluctuation

Velocity spectrum shows ExB branch and i-diamag branch Core low k and egde e-diamg. high k propagate ExB rotation speed.Edge i-diamg components propagates in i-diamag direction in plasma frameVExBStrong velocity shear in edge may reduce transport.

Edge Ion diamag. components show possible correlation with edge diffusion. Fluctuation level becomes larger at outward shifted configuration

New attempts to measure direct contribution of fluctuation to transportFluctuation induced energy and particle flux is given bySignal is line integrated, but radially dominatedwe tried to estimate fluctuation induced flux from edge PCI signal around r=1.0.2.5

Outward FluxInward FluxWhen NBI power reduced ( transport should have reduced as well), fluctuation induced flux reduced at outside of LCFS1.767sec1.933seckrs~0.2Outside of LCFS, Inside of LCFS

Large amplitude burst take 20% of all time but make 80% of averaged fluxDetail consideration is necessary about integration effects of signal.Bursting signal contributes flux a lot.AmplitudeMean~0

Summary of fluctuation Study2D phase contrast is working to measure fluctuation profile using magnetic shear technique.The results shows different k branch in core and edge.Edge ion diamagnetic components play role on edge particle transport (~global particle transport)Edge velocity shear may play important role on reduced transport Core fluctuation is likely play role on density profile.Preliminary data was obtained to estimate fluctuation induced flux. Fluctuation induced flux is reduced when beam power is reduced and total transport is reduced.

Summary of achieved parameter of LHDAchieved ValueTarget]

Central ion temperature13.5keV at 0.3x1019m-3 Ar plasma) 5keV at 1.2x1019m-3 (H plasma) 10keV at 2x1019m-3 Central electron temperature 10keV at 0.5x1019m-3 10keV at 2x1019m-3 Volume Averaged beta % at 0.425T 5 % at 1~2T Central electron density1x1021m-3 at Te(0)= 0.4keV 40x1019m-3 Stored Energy1.44MJ 4MJ Steady State operation 31min. 45sec 700 kW 1.3GJ 54 min 28sec 500 kW1.6GJ hour (3,000W)]High density and stable operation are advantage

Core fluctuation may play role on density profile shaping.Most of fluctuation components exists in ITG/TEM unstable regionTokamak like. Turbulence transport produce peaked profileHelical particular. Inward turbulence driven flux can be balanced with outward neoclassical

Analysis of fluctuation profiles and phase velocityWhich direction in the plasma frame do fluctuations propagate?Analyze fluctuation phase velocity profileCompare with +NBI CVI CX measurement of vExBCompare with drift velocity

Appear to be 3 fluctuation peaks

Peaks 1 and 2 propagate close to electron drift velocity. Possibly electron drift waves?

Fluctuation amplitude is peaked in regions where Er shear is zero. More than coincidence?

Compare radial profiles of fluctuation amplitude with parameter profiles

Characteristics can vary widely among discharges. This is one example.123#60334 t=2.22sRax=3.6m, B=-2.75T

Spatial profile of k spectrum shows three different branchHigh k (k~0.7mm-1) electron diamag.Low k (~0.3mm-1)High k (k~0.7mm-1) ion diamag.

Rax=3.9m, 1.54T, Dedge=0.57m2/secRax=3.75m, 1.5T, Dedge=0.42m2/secRax=3.6m, 1.49T, Dedge=0.18m2/sec

Turbulence spectrumReal plasma is turbulent. And its spectrum is two dimensionally broad in the cross section perpendicular to B.We measures Fourier components perpendicular to beam axis in broad spectrum Does the measured signal represent local fluctuation?

One of the key parameter to determine global energy and particle confinements is eh_eff, which is representative amplitude of magnetic helical rippleScatter of data suggests there are other hidden parameter.H. Yamada, Nucl. Fusion 45 (2005) 1684helical/stellarator database

The value at r=2/3 is a good approximationof the volume averaged value.Tokamak Ip are treated through q2/3 into stellarator scaling.

Experimental values are compared with neoclassical ones.In the following equation, D1,D2,Er were calculated by GSRAKE and DCOM code. Neoclassical convection term was defined as following.The thermo diffusion term (the second and third term) dominates for electron particle transport in the present experiment regime.

Blank; Experiment, Colored; Neoclassical Dneon*h1/n

The volume averaged value of rotational transform is more appropriate than the surface value.Limiter insertion in LHDJT-60UY.Kamada et al. NF (1993)li dependence in tokamaksJT-60U, TFTRThe value at r=2/3 is a good approximationof the volume averaged value.

Comparison with Tokamak Database : ProvisionalDifferent definition of aReasonable reconsideration ofprofile effect is allowed.Translation of Ip to iTake the value of the rotational transform at r=2/3

Scaling investigations ISS04: renormalizationRef.: H. Yamada et al. NF 45 (2005)

HDLIDHelical Diverter (HD)Local Island Diverter (LID)TemperatureDensityRadial Electric Field By GSRAKE codeClear difference of density profiles are observed between LID and HDHOLLOWFLAT

Enhanced particle transport is observed on LID This is good material to study role of turbulence on particle confinementsLID,HD

Electromagnetic GK mode equation[1] J.B.Taylor, et al., Plasma Physics 10, 479 (1968)[2] G.Rewoldt, et al., Phys. Fluids 25, 480 (1982) Collisionless F0=FM E0=0

(kthi=0.5)ITG results in HD/LID configurationsRelativetemperaturegradientRelativedensitygradient ITG growth rate is larger in LID than in HD, and unstable range is also broader in LID. This is reasonable just because 1/LT is larger in LID. - The value of growth rate can be related to the value of T. - But, the unstable range should be only related to 1/LT, i.e., large f() of T=T0f(), not large T0, is relevant. The effects of 1/Ln or on ITG growth rate seems weak compared to 1/LT.LIDHDa

Neoclassical Er shearing rate is insufficient to suppress the ITG growth rate.Linear growth rate .vs. Er shearing rateHeuristically the condition, lin(Er=0)

Comparison of i-dia branch amplitude and ITG growth rateAmplitude in i-dia branch (edge) scales with calculated ITG growth rate.Profiles of growth rate and observed amplitude are similar.HDLIDLarge particle transportsmall particle transport

Calculation procedure7/15

Dynamics of raw signals of 1-D PCI system5/15