1. K. Tanaka 1), H. Takenaga 2), K. Muraoka 3), H.Urano 2), C. Michael 1), L.N. Vyacheslavov 4), M. Yokoyama 1) O.Yamagishi 1), 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 Particle transport in LHD and comparisons with tokamaks ITPA CDBM and Transport meetings - Spring 2007 at EPFL Lausanne

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. 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

4. Outline of talk i) The brief overview of density profile of LHD ii) Comparison between experimental particle transport coefficients and neoclassical ones Is particle transport neoclassical or anomalous? iii) Possible modeling and fluctuation behavior iv) Comparison of peaking factor and collisionality dependence between LHD and JT60U

5. These differences are not due to particle fueling but due to transport characteristics. Density profile of LHD changes from peaked to hollow. P NBI = Change of density profile in N-NBI heated plasma Last closed flux surface

6. 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

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. 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.

9. D neo * h D neo ei * h =1.0 3.6 3.75 3.9 3.53 Density profile tends to more peaked for higher collisionality and at more inward shifted configuration (smaller helical ripple)  heff 小 Rax=3.9m Rax=3.75 Rax=3.6m, Rax=3.53m, Bt~1.5T Inward shift Smaller neoclassical Plateau 1/ H C -I Plasma Helical coil B contour Shifting by changing external vertical field Inward Outward Bt~1.5T

10. Is particle transport is neoclassical or anomalous? The answer is Yes and NO.

11. Fuelling rate was controlled to modulate density with constant background. The phase and amplitude was calculated by the FFT correlation analysis after subtracting background density. Frequency signal of modulated components Density modulation was done to study particle transport Measured Cross Section

12. Modulation and equilibrium profiles are characterized by particle transports. D,V are determined to fit both modulation and equilibrium profiles Modulation profile Equilibrium profile Diffusion Convection Analysis results are independent of absolute value of S. Particle flux Particle source rate

13. 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/

14. 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

15. Anomalous dominated outward diffusion Inward anomalous convection Total flux~0 At reduced neoclassical configuration (inward shift configuration), peaked density profile is observed. Density profile can be determined by anomalous process -D grad n e neVneV This is tokamak like.

16. According to gyro kinetic linear theory, the flux direction of quasi linear particle flux changes depending on density profile (Yamagishi, POP 14. 012505 (2007) )  ~0 in core region, where particle source is zero. Outward Inward In hollow density profile, ITG/TEM driven Q.L. flux in core is directed inward. This is consistent with that inward directed diffusion flux is anomalous from modulation experiments. In the peaked density profile, ITG/TEM driven Q.L. flux in core can be zero. This is tokamak like case Strong Hollow Peaking Calculation for LHD Strong Hollow Weak Hollow T e (keV) Q.L. flux  /(  ) 2 n e (x10 19 m -3 ) Weak Hollow ITG/TEM is unstable at calculated data points.

17. For  =0 condition, more peaked ne profile require more peaked Te profile. Hollow ne profile needs additional outward flux to satisfy  =0 Q.L. flux  /(  ) 2 1/Ln=-1/r dn/dr Outward Flux Inward Flux Peaked Density profile Hollow Density profile LHD  =0.8  =0 condition

18. 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

19. At high field (2.8T) inward shifted configuration, peaking factor of lower magnetic ripple in LHD shows similar trends to JT60U data Lower ripple (Lower neoclassical) JT60U; P-NBI, but beam source does not affect peaking. LHD;N-NBI and NNBI+ECH At high field, neoclassical transport becomes smaller

20. At low magnetic helical ripple configuration (reduced neoclassical -> at tokamak like configuration?), Te(0)/Ti(0) does not affects density peaking This is against tokamak prediction (Garbet P.R.L (2003) 35001)

21. Summary 1.Density profile and particle transport in LHD show different characteristics with tokamak ones 2.Peaked density profiles are observed at inward shifted (smaller helical ripple and reduced neoclassical ) configuration and at lower collisionality (weak dependence) 3.Hollow density profiles are observed at outward shifted configuration (larger helical ripple and enhanced neoclassical) and at higher collisionality 4.In LHD, diffusion is anomalous, but outward convection is comparable with neoclassical values. 5.Qausilinear flux is inward directed in positive gradient region of hollow density profile. This can be balanced with outward directed neoclassical convection 6.Quasilinear flux can satisfy  =0 condition for peaked density profile. 7.Fluctuation is dominated in the ITG/TEM unstable region 8.Te/Ti does not influence density profile on LHD at inward shifted reduced neoclassical configuration.

22. Rax=3.5 ｍと Rax=3.6m では磁場の及ぼす影響が大きくことなる。 円柱モデルでのプラトー領域での拡散係数は 磁気軸が違う場合磁場配位 factor （  h,  t など）が入る。 磁場を下げるとホローになるのは新古典の成分が大きくなる （異常輸送の成分が小さくなることも必要）ためか？

23. Gyro kinetic calculation was done for experimental n e and T e profile. In hollow density profile, ITG/TEM Q.L. flux is inward directed and can be balance with outward directed neoclassical convection In peaked profile, inward directed ITG/TEM flux can be balanced with outward directed neoclassical flux at  <0.6. The neutral penetration length are almost identical for both profile,  ~0 condition is same for both profile. i) What flux balance is possible, where ITG/TEM is stable? ii)  ~0 at  <~0.9. Plasma boundary is  ~1.2 due to the ergodic region. Inward directed flux is required for  =0.6~0.9 in peaked profile. iii) Can we rely one Q.L. flux. Turbulence is non linear status Rax=3.53m, Bt=1.45T, P NBI =11.3MW, PNBI=11.3MW

24. Rax=3.5 ｍと Rax=3.6m では磁場の及ぼす影響が大きくことなる。 円柱モデルでのプラトー領域での拡散係数は 磁気軸が違う場合磁場配位 factor （  h,  t など）が入る。 磁場を下げるとホローになるのは新古典の成分が大きくなる （異常輸送の成分が小さくなることも必要）ためか？

25. Particle balance for equilibrium Particle balance for modulation Analytical Formula of density modulation

26. Discrepancy of modulation and equilibrium coefficients If flux is non linear, D eq,V eq are different from D inc,V inc Equilibrium flux Modulated flux D eq =D inc V eq =V inc D inc V inc D eq V eq Increment value and equilibrium value can be different.

27. Radial Integral Equilibrium Fitting Criteria Presently simultaneous fitting is used This is because modulation fitting is unstable due to localized amplitude at 10Hz. However, th え discrepancy between modulation and equilibrium coefficients should be examined.

28. Comparison of  2 mod_int fitting and  2 total fitting Modulation fitting Equilibrium fitting Blue; Both modulation and equilibrium fitting Green; Only modulation fitting 1MW 5.2MW 1MW 5.2MW

29. Fitted results Blue; Both modulation and equilibrium fitting Green; Only modulation fitting 1MW 5.2MW 1MW 5.2MW

30. At similar Te profile and By, density profile becomed more peaked at more inward shifted configuration Inward shifted Small ripple Reduce neoclassical Outward shift Large ripple Enhanced neoclassical

31. Magnetic axis position changes density profile as well.

32. For tokamak configuration similar results are obtained (Yamagishi, POP 14. 012505 (2007) )  ~0 in core region, where particle source is zero. Outward Inward Strong Hollow Peaking Calculation for tokamak Strong Hollow Weak Hollow T e (keV) Q.L. flux  /(  ) 2 n e (x10 19 m -3 ) Weak Hollow ITG/TEM is unstable at calculated data points. For the modeled profile, flux is non zero for pealed profile. For more peaked density profile, flux can be zero.