1. Transport and fluctuations in LHD and comparisons with tokamaks ITPA CDBM and Transport meetings - Spring 2007 at EPFL Lausanne K. Tanaka 1), C. Michael 1), L.N. Vyacheslavov 4), H.Yamada 1), M. Yokoyama 1) O.Yamagishi 1), H. Takenaga 2), K. Muraoka 3), H.Urano 2), S. Murakami 5), A. Wakasa 6) and LHD Experimental group 1) National Institute for Fusion Science, 322-6 Oroshi, Toki, 509-5292, Japan 2) Japan Atomic Energy Agency 801-1 Mukouyama Naka Ibaraki, 311-0193, Japan 3) School of Engineering, Chubu University, 1200 Matsumoto, Kasugai, Aichi 487-8501 4) Budker Institute of Nuclear Physics, 630090, Novosibirsk, Russia 5) Department of Nuclear Engineering, Kyoto University, Kyoto 606-8501, Japan 6) Graduate School of Engineering, Hokkaido University, Sapporo, 060-8628, Japan

2. There is a similarity and dissimilarity between helical/stellarator and tokamak Similarity Both 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.

3. Outline of talk 1.Comparison of global energy confinement scaling between tokamak and helical/stellarator 2.Role of neoclassical optimization on anomalous transport. 3.Particle transport of LHD 4.Experimental turbulence study in LHD

4. International sterraltor scaliing 04 (ISS04) is dimensionally similar to IPB98(y,2) on  *. Both are weak Gyro Bohm (H.Yamada N.F.1684 (2005)) LHD tokamak ITER 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) 1684 Tokamak Ip are treated through q2/3 into stellarator scaling.

5. In LHD, edge (  =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. k perp  i ~0.5. This is expected by linear calculation of GOBLIN code. In tokamak, smaller peak wavenumber k perp  i ~0.1 was reported anywhere. Edge transport influence global confinement. Similar fluctuation character may results in similar  * scaling K.Tanaka Fusion Sci. Tech. (2007)97

6. The particularity of helical/stellarator is enhanced neoclassical transport in low collision regime Neoclassical Transport coefficient Banana regime ei Plateau regime 1/ regime Future operation regime of reactor Around one order Experimental D e,  e Around one order helical/stellarator tokamak Future operation regime of reactor Neoclassical Transport coefficient Plateau regime ei Experimental D e,  e S. Murakami Nucl. Fusion 42 (2002) L19–L22 Axis Position D neo /D tokamak plateu 1/ regime Plateau regime In 1/, neoclassical transport is minimum at Rax=3.53m In Plateau, neoclassical transport is smaller at more inward axis. Inward shifted Outward shifted Inward shifted Outward shifted

7. Magnetic axis position change magnetic helical ripple and higher ripple results in larger neoclassical transport Flux Surface Orbit of guiding center H C -I Plasma Helical coil Shifts by external vertical field and Shafranov shifts B contour

8. Energy confinement is improved by shift of magnetic axis position Inward shift of R ax  Optimization in terms of drift optimization Effect of neoclassical transport is pronounced in collisionless regime Confinement improvement by the inward shift of R ax still exists in collisional regime Neoclassical optimization is successful ! Much more than neoclassical theory !? 0.6 0.03 Smaller helical ripple

9. ∝  eff -0.4 One of the key parameter to determine global energy is  h_eff, which is representative amplitude of magnetic helical ripple H. Yamada, Nucl. Fusion 45 (2005) 1684 Representative helical ripple amplitude at  =2/3

10. 1.Global energy confinements are gyro Bohm character and edge particle diffusion (~edge thermal conductivity ~ global energy and particle transport) are dominated by turbulence (k perp  i ~0.5) driven transport. 2.With smaller magnetic ripple (inward shifted configuration and smaller neoclassical transport), energy transport is reduced. 3.Reduced neoclassical configuration introduce smaller anomalous transport. 4.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, 21 st FEC IAEA-CN-149/EX/5-4) Summary of global energy confinement in LHD

11. ＪＴ 60U Elmy H mode LHD Rax=3.6m Density scan at P NBI =8-10MW P NBI scan at similar averaged density Different character of density profiles are observed in JT60U and LHD

12. Magnetic axis position changes density profile as well. Inward shifted Small magnetic helical ripple and reduced neoclassical transport Outward shifted Large magnetic helical ripple and enhanced neoclassical transport

13. NBI 11.4MW NBI 1.7MW Example of transport analysis D is anomalous. V out is comparable V neo. Impurity may not account for n e profile Higher Te gradient induce outward convection

14. Density modulation experiments shows D core is anomalous, outward V core is comparable with neoclassical one Blank; Experiment, Colored; Neoclassical Rax=3.6n, Bt=2.75, 2.8T Rax=3.6n, Bt=1.49T Rax=3.75n, Bt=1.5T Rax=3.9n, Bt=1.54T D core D edge 0.7  V core V edge 0.7  1.0 At lower collisionality D core is close toD neo. D neo * h Inward V core is not neoclassical. Plateau 1/

15. Core particle flux is zero. In core region of hollow density profile, outward neoclassical pinch is balanced with inward anomalous diffusion. Outward neoclassical convection Inward anomalous diffusion. Total flux~0 -D grad n e neVneV Inward directed anomalous flux is predicted by linear theory (O.Yamagishi 14. 012505 (2007) )  ~0 in core (  <~0.9), since source~0, -Dgrad n e ~n e V

16. Summary of particle transport in LHD 1.One 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. 2.Enhanced neoclassical transport introduces hollow density profile. 3.Peaked density profile is obtained at reduced neoclassical configuration and is likely to be driven by anomalous process. 4.Particle diffusion is anomalous, outward convection is comparable with neoclassical value. Inward pinch is against neoclassical prediction. 5.Linear gyro kinetic calculation suggests the balance of turbulence driven flux and neoclassical flux produce hollow density profile.

17. B top B bottom Top view of integrated fluctuation Top view of upper fluctuation Top view of lower fluctuation Principle of 2D PCI Upper field Lower field Laser Beam Propagation direction tells spatial points of fluctuation.

18. Integrated 2D picture with 8x6=48ch 2D array  k(mm -1 ) 6.1mm 17.5mm Spatial 2D Fourier Transform Fluctuation of lower part Fluctuation of upper part Present resolution is a/3~a/5. Signal suffers from cancellation effects Example signal of 2D PCI A.Sanin et al., Rev. Sci. Instrum., Vol. 75, No.10, (2004) pp.3439-3441 C. 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

19. Movie of Fluctuation

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

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

22. New attempts to measure direct contribution of fluctuation to transport Fluctuation induced energy and particle flux is given by Signal is line integrated, but radially dominated we tried to estimate fluctuation induced flux from edge PCI signal around  =1.0. 2.5< <30mm We measure and,then,

23. Outward Flux Inward Flux When NBI power reduced ( transport should have reduced as well), fluctuation induced flux reduced at outside of LCFS 1.767sec 1.933sec k  s ~0.2 Outside of LCFS, Inside of LCFS

24. Large amplitude burst take 20% of all time but make 80% of averaged flux Detail consideration is necessary about integration effects of signal. Bursting signal contributes flux a lot. Amplitude Mean~0 Outward Flux Inward Flux Outward velocity Inward velocty

25. Summary of fluctuation Study 1.2D phase contrast is working to measure fluctuation profile using magnetic shear technique. 2.The results shows different k branch in core and edge. 3.Edge ion diamagnetic components play role on edge particle transport (~global particle transport) 4.Edge velocity shear may play important role on reduced transport 5.Core fluctuation is likely play role on density profile. 6.Preliminary data was obtained to estimate fluctuation induced flux. Fluctuation induced flux is reduced when beam power is reduced and total transport is reduced.

26. Summary of achieved parameter of LHD Achieved Value ［ Target] Central ion temperature 13.5keV at 0.3x10 19 m -3 （ Ar plasma) 5keV at 1.2x10 19 m- 3 (H plasma) ［ 10keV at 2x10 19 m -3 ］ Central electron temperature 10keV at 0.5x10 19 m -3 ［ 10keV at 2x10 19 m -3 ］ Volume Averaged beta ５．０ % at 0.425T ［≧ 5 % at 1~2T ］ Central electron density 1x10 21 m -3 at T e (0)= 0.4keV ） 〔 40x10 19 m -3 〕 Stored Energy 1.44MJ 〔 4MJ 〕 Steady State operation 31min. 45sec （ 700 kW ） 1.3GJ 54 min 28sec （ 500 kW ） 1.6GJ ［１ hour (3,000 ｋ W)] High density and stable operation are advantage

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

28. Analysis of fluctuation profiles and phase velocity Which direction in the plasma frame do fluctuations propagate? –Analyze fluctuation phase velocity profile –Compare with +NBI CVI CX measurement of v ExB –Compare 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 E r 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. 1 2 3 #60334 t=2.22s Rax=3.6m, B=-2.75T

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

30. Rax=3.9m, 1.54T, Dedge=0.57m 2 /sec Rax=3.75m, 1.5T, Dedge=0.42m 2 /sec Rax=3.6m, 1.49T, Dedge=0.18m 2 /sec  ITG by GOBLIN code does not show good agreements with observations yet However Er shearing rate may moderates ITG.

31. Turbulence spectrum Real 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?

32. ∝  eff -0.4 One of the key parameter to determine global energy and particle confinements is  h_eff, which is representative amplitude of magnetic helical ripple Scatter of data suggests there are other hidden parameter. H. Yamada, Nucl. Fusion 45 (2005) 1684 helical/stellarator database

33. The value at  =2/3 is a good approximation of the volume averaged value. Tokamak Ip are treated through q 2/3 into stellarator scaling.

34. 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.

35. Rax=3.6n, Bt=2.75, 2.8T Rax=3.6n, Bt=1.49T Rax=3.75n, Bt=1.5T Rax=3.9n, Bt=1.54T Blank; Experiment, Colored; Neoclassical D core D edge 0.7  V core V edge 0.7  1.0 D neo * h 1/

36. The volume averaged value of rotational transform is more appropriate than the surface value. Limiter insertion in LHD JT-60U Y.Kamada et al. NF (1993) l i dependence in tokamaks JT-60U, TFTR The value at  =2/3 is a good approximation of the volume averaged value.

37. Comparison with Tokamak Database : Provisional Different definition of a Reasonable reconsideration of profile effect is allowed. Translation of I p to  Take the value of the rotational transform at  =2/3 

38. Scaling investigations ISS04: renormalization Ref.: H. Yamada et al. NF 45 (2005)

39. HD LID baffle LID head to pump core plasma LCF S m/n=1/1 island separatrix HD separatrix (disappeared) pum p baffle (plan) LCFS ergodic layer Helical Diverter (HD)Local Island Diverter (LID) TemperatureDensity Radial Electric Field By GSRAKE code Clear difference of density profiles are observed between LID and HD HOLLOW FLAT

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

41. 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 - F 0 =F M - E 0 =0

42. (k ⊥ ρ thi =0.5) ITG results in HD/LID configurations Relative temperature gradient Relative density gradient ITG growth rate is larger in LID than in HD, and unstable range is also broader in LID. This is reasonable just because 1/L T 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/L T, i.e., large f’(ρ) of T=T 0 f(ρ), not large T 0, is relevant. The effects of 1/L n or η on ITG growth rate seems weak compared to 1/L T. LID HD a

43. Neoclassical E r shearing rate is insufficient to suppress the ITG growth rate. Linear growth rate.vs. E r shearing rate Heuristically the condition, γ lin (E r =0) <= ω E can stabilize the modes in finite background E r [Hahm, Burrell, ’95 PoP] a2 GSRAKE (Yokoyama)

44. Comparison of i-dia branch amplitude and ITG growth rate Amplitude in i-dia branch (edge) scales with calculated ITG growth rate. Profiles of growth rate and observed amplitude are similar. HD LID Large particle transport small particle transport

45. Calculation procedure 7/15

46. Dynamics of raw signals of 1-D PCI system 5/15