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Particle transport in LHD and comparisons with tokamaks

Particle transport in LHD and comparisons with tokamaks. ITPA CDBM and Transport meetings - Spring 2007 at EPFL Lausanne.

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Particle transport in LHD and comparisons with tokamaks

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  1. Particle transport in LHD and comparisons with tokamaks ITPA CDBM and Transport meetings - Spring 2007 at EPFL Lausanne K. Tanaka1), H. Takenaga2), K. Muraoka3), H.Urano2), C. Michael1), L.N. Vyacheslavov4), M. Yokoyama1) O.Yamagishi1), S. Murakami5), A. Wakasa6) 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. The motivation of comparison study between helical/stellarator and tokamak is to understand common underlined physics of transport. 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.

  3. Different character of density profiles are observed in JT60U and LHD LHD Rax=3.6m ＪＴ60U Elmy H mode Density scan at PNBI=8-10MW PNBI scan at similar averaged density

  4. Outline of talk i) The brief overview of density profile of LHD ii) Comparisonbetween 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. Density profile of LHD changes from peaked to hollow. Change of density profile in N-NBI heated plasma PNBI= Last closed flux surface Last closed flux surface These differences are not due to particle fueling but due to transport characteristics.

  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 Helical coil Plasma B contour HC-I Shifts by external vertical field and Shafranov shifts Flux Surface Orbit of guiding center

  8. The particularity of helical/stellarator is enhanced neoclassical transport in low collision regime tokamak helical/stellarator Future operation regime of reactor Future operation regime of reactor Experimental De,ce Experimental De,ce Around one order Around one order Neoclassical Transport coefficient Neoclassical Transport coefficient 1/n regime Banana regime Plateau regime Plateau regime nei nei Plateau regime 1/n regime S. Murakami Nucl. Fusion 42 (2002) L19–L22 In 1/n, neoclassical transport is minimum at Rax=3.53m In Plateau, neoclassical transport is smaller at more inward axis. Dneo/Dtokamak plateu Dneo/Dtokamak plateu Axis Position Axis Position

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

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

  11. Density modulation was done to study particle transport 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. Measured Cross Section Frequency signal of modulated components

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

  13. Density modulation experiments shows Dcore is anomalous, outward Vcore is comparable with neoclassical one 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 Dedge Vcore Dcore 1.0 r 0.7 r Vedge 0.7 Dneo 1/n Plateau n*h Blank; Experiment, Colored; Neoclassical Inward Vcore is not neoclassical. At lower collisionality Dcore is close toDneo.

  14. Core particle flux is zero. In core region of hollow density profile, outward neoclassical pinch is balanced with inward anomalous diffusion. neV Outward neoclassical convection -D grad ne Inward anomalous diffusion. Total flux~0

  15. At reduced neoclassical configuration (inward shift configuration), peaked density profile is observed. Density profile can be determined by anomalous process Anomalous dominated outward diffusion -D grad ne neV Inward anomalous convection Total flux~0 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) ) G~0 in core region, where particle source is zero. Calculation for LHD Strong Hollow Weak Hollow Peaking Weak Hollow Outward ne(x1019m-3) Q.L. flux G/(df)2 Te(keV) Te(keV) Peaking Inward Strong Hollow ITG/TEM is unstable at calculated data points. 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

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

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

  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) At high field, neoclassical transport becomes smaller JT60U; P-NBI, but beam source does not affect peaking. LHD;N-NBI and NNBI+ECH

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

  22. Rax=3.5ｍとRax=3.6mでは磁場の及ぼす影響が大きくことなる。Rax=3.5ｍ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（eh,et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 ne and Te profile. In hollow density profile,ITG/TEMQ.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 r<0.6. Rax=3.53m, Bt=1.45T, PNBI=11.3MW, PNBI=11.3MW The neutral penetration length are almost identical for both profile, G~0 condition is same for both profile. i) What flux balance is possible, where ITG/TEM is stable? ii) G~0 at r <~0.9. Plasma boundary is r~1.2 due to the ergodic region. Inward directed flux is required for r=0.6~0.9 in peaked profile. iii) Can we rely one Q.L. flux. Turbulence is non linear status

  24. Rax=3.5ｍとRax=3.6mでは磁場の及ぼす影響が大きくことなる。Rax=3.5ｍ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（eh,et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. Analytical Formula of density modulation Particle balance for equilibrium Particle balance for modulation

  26. Discrepancy of modulation and equilibrium coefficients Increment value and equilibrium value can be different. Deq Veq Equilibrium flux Modulated flux Deq=Dinc Veq=Vinc Dinc Vinc If flux is non linear, Deq,Veq are different from Dinc,Vinc

  27. Fitting Criteria Radial Integral Equilibrium 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 c2mod_int fitting and c2total fitting Modulation fitting Equilibrium fitting 5.2MW 1MW 5.2MW 1MW Blue; Both modulation and equilibrium fitting Green; Only modulation fitting

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

  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) ) G~0 in core region, where particle source is zero. Calculation for tokamak Strong Hollow Weak Hollow Peaking Weak Hollow Outward ne(x1019m-3) Q.L. flux G/(df)2 Te(keV) Te(keV) Peaking Inward Strong 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.

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