Inter-linkage of transports and its bridging mechanism

Transcription

1 Interlinkage of transports and its bridging mechanism Katsumi Ida National Institute for Fusion Science 17 th International Toki Conference 1519 October 27, Toki

2 OUTLINE 1 Introduction 2 particle pinch and impurity exhaust 3 spontaneous rotation 4 T and T dependence of heat transport 5 Nonlocal transport phenomena 6 Summary

3 Transport in plasma Plasma Fueling, drive, heating 1 Radial Fluxes particle fluxes 2 momentum fluxes 3x2=6 heat fluxes 2 r flux Diffusive process flux density profile Velocity profile Temperature profile r Radial flow is negligible V re = V ri = equilibrium ( ) j B= p + p Am bipolar condition Γ =Γ i e i e 6 radial fluxes are determined by transport

4 Transport matrix particle Γ D n e NonDiffusive toroidal momentum P φ μ φ nm i V φ NonDiffusive Poloidal momentum ion heat P θ Q i, = μ θ nm i nχ i, V θ T i Diffusive electron heat Q e, nχ e T e Diffusive 6 radial fluxes are expressed by 5 x 5 transport Matrix + Current diffusion equation 5 Diagonal coefficients are determined by turbulence Γ = D n P φ /(m i n i ) = μ φ V φ P θ /(m i n i ) = μ θ V θ Q e /n e = χ e T e Q i /n i = χ i T i

5 particle, momentum and heat transport simplified There is no need for plasma physicist because physics is simple 1 Linear + diffusive + local transport model (simple!) unrealistic Γ = D n P/(n i m i ) = μ V Q/n = χ T 2 Add Nonlinearity Γ = D(n, n) n Q/n = χ(t, T) T Nonliner dependence stiffness 3 Add Nondiffusivity (interlinkage between flux) Γ = D(n, n) n + D N (n/t) T+ Nondiffusive term particle inward/outward pinch P φ /(n i m i ) = μ φ ( E) V φ + μ N (V th /T) T+ Nondiffusive term spontaneous rotation 4 Add nonlocality (inter linkage in space) Γ = D (n, n ) n + D N (n/t) T + f(n, n, T,,, )dρ + complicated Nonlocal term unrealistic

6 Particle flux Diffusive and nondiffusive transport Diffusive term Nondiffusive term = Diffusion + Nondiffusive term coefficient Ware pinch ( E ) Thermodynamic force ( T) Radial electric field ( Φ) + Turbulence driven Magnetic field curvature ( q) momentum flux Perpendicular = + Nondiffusive term viscosity + Convective term : Γ(nmV) + damping term E r and E r shear Magnetic shear Parallel viscosity Heat flux = thermal conductivity +? + Convective term : (3/2)ΓT T dependence T 3/2 {1+(R/L T κ c ) σ } T T dependence L T = T/ T

7 Particle transport Ware pinch ( E ) Particle flux = diffusion + Nondiffusive term 1. T dependence 2. Thermodynamic force ( T) Radial electric field ( Φ) Turbulence driven 3. Magnetic field curvature ( q) Convective term Convective term

8 Particle transport diffusive term D (m 2 /sec) Exp. Neo..5 1 ρ Diffusion coefficient is much larger than the neoclassical values and particle transport is dominated by turbulent transport. It has temperature dependence of T α where α ~ 1. 1 LHD D (m 2 /sec).1.1 exp edge core 1. T e 2.7 T e edge (ρ >.7) NC.9 T e 2.5 T e core (.4 < ρ <.7) T e (kev) K.Tanaka Nucl. Fusion 46 (26) 11

9 Nondiffusive term of particle flux Diffusion pinch Thermo diffusion Wendelstein 7AS Thermo diffusion term is comparable to diffusion term D 12 /D 11 =1.4 Inward Pinch term is significant u/d 11 = 12.5 m 1 U.Stroth Phys. Rev. Lett. 82 (1999) 928

10 Magnetci field curvature pinch Thermo diffusion flux Magnetic field curvature Inward pinch ρ <.3 : inward.35 < ρ <.6 : outward T term changes it sign between in and core Particle pinch due to magnetic shear is observed G.T.Hoang, Phys. Rev. Lett. 93 (24) 1353

11 Impurity hole evidence of strong outward flux due to Ti gradient? Intensity (a.u.) t=.95s T i (kev) t=.95s t=1.35s LHD Carbon profile becomes hollow associated with the peaking of ion temperature profile.2 t=1.35s 1 V (m s 1 ) R (m) t=1.45s. 5. D (m 2 /s) R (m) 1. t=1.45s The transport analysis shows strong outward convective flow and low diffusivity in the core region R (m) R (m) Impurity hole is observed in the plasma with peaked ion temperature Suggest a strong coupling between Ti gradient and impurity outward flux

12 Momentum transport Particle flux 2. Radial electric field ( Φ) 3. + Turbulence driven Magnetic field curvature ( q) momentum flux Perpendicular = + Nondiffusive term + Convective term viscosity E r and E r shear Magnetic shear + damping term 1. Parallel viscosity

13 Parallel and perpendicular viscosity (diffusive term) v // (km/s) Γ Μ = m i n i [ μ D dv φ /dr + μ N (v th /T i )(ee r ) μ v φ ] μ // +μ (3.5m 2 /s) Anomalous perpendicular viscosity μ // =.3μ // NC μ (18m 2 /s) ρ.8 1. μ eff 1 (1 3 s) NC 89.9 NC+AN Nondiffusive term μ = μ = 2m 2 /s γ (ρ=.2) (m 1 ) 3D Neoclassica l parallel viscosity ρ.8 1. Small ripple configuration Large ripple configuration V mes << V cal(nc) V mes ~ V cal(nc) In the configuration of small ripple the anomalous perpendicular viscosity is dominant in the plasma core ( ρ <.6) even in helical plasmas v // (km/s) μ (18m 2 /s) μ // =.3μ // NC μ // +μ (3.5m 2 /s) K.Ida Phys. Rev. Lett. 67 (1991) 58

14 Physical mechanism determining spontaneous flows T i T e n e Turbulence Nonambipolar flux suppression E r E r shear Helical plasma has additional knob to control radial electric field radial force balance Symmetry braking Spontaneous perpendicular flow and its shear Parallel and perpendicular viscosity Spontaneous parallel flow and its shear

15 Nondiffusive momentum transport in tokamak Momentum Flux Γ Μ = m i n i [ χ φ dv φ /dr +V inward V φ ] μ φ D (m 2 /s) Γ Μ = m i n i [ μ D dv φ /dr + μ N (v th /T i )(ee r ) ] diffusive (shear viscosity) (a) co to ctr ctr to co ρ nondiffusive (driving term) μ φ Ν (m 2 /s) ee r = dti/dr (b) co to ctr ctr to co ρ Finite dv φ /dr can be nonzero for Γ M = because of the existence of nondiffusive term Spontaneous rotation was observed as a nondiffusive term of momentum transport. K.Nagashima, Nucl Fusion 34 (1994) 449 K.Ida, Phys Rev Lett 74 (1995 ) 199, J.Phys.Soc.Jpn 67 (1998) 489

16 Spontaneous toroidal at edge and core edge V t (km/s) core V t (km/s) Ion Root 1.x1 19 m 3 (Ctr) Electron Root.55x1 19 m 3 (Co with ECH) R(m) ECH ON 1.3s 1.8s 1.65s 1.45s 1.25s 2.5s Near Zero.45x1 19 m 3 (Co) V p (km/s) Electron Root.55x1 19 m 3 (Co with ECH) Near Zero.45x1 19 m 3 (Co) Ion Root 1.x1 19 m 3 (Ctr) R(m) V t (km/s) E r (kv/m) R=4.4m t=1.5s NBI 1 and 2 Coupling between poloidal and toroidal rotaion is observed Edge (helical symmetry dominant) ctr rotation for E r > Core (toroidal effect dominant) co rotation for E r > R(m) M.Yoshinuma ITC17 O 12 Friday

17 Sign of nondiffusive viscosity δv φ (km/s) (ρ=.4) paralle to <E r xb θ > neoitb Heliotron Tokamak antiparalle to <E r xb θ > E /B (ρ=.4) (km/s) r θ Helical (external current system) v θ poloidal Helical symmetry Tokamaks (internal current system) v θ poloidal Toroidal symmetry E r < helical effect toroidal effect E r > E r > toroidal E r < toroidal B v φ B v φ Tokamak : negative E r counter spontaneous flow V=1.3E r /B θ Helical : positive Er counter spontaneous flow V=.16E r /B θ K.Ida, Plasma Phys. Control. Fusion 44 (22) 362

18 Why the spontaneous rotation depends on E r in tokamak Why the nondiffusive terms has E r dependence? Γ Μ = m i n i [ μ D dv φ /dr + μ N (v th /T i )(ee r ) ] = (1/r) f φ r dr Nondiffusive term can be expressed as toroidal force which proportional to E r shear μ N = c sym (1/B θ )= c sym qr/(rb φ ) f φ spon = (c sym eqr/b φ )(v th /T i )(1/r)(dE r /dr) ~ (c sym eqrv th /T i )(dω ExB /dr) In tokamak Toroidal momentum is produced by symmetry breaking of nonzero <k >. In stellarator Because of the asymmetry of magnetic field, E r and spontaneous flow are produced by ripple loss too. O.D.Gurcan Phys. Plasmas 14 (27) 4236

19 Evidence of turbulence driven perpendicular and parallel Reynolds stress Radialpoloidal component of the Reynolds stress due to turbulence is observed in JET In TJII stellarator, significant radialparallel component of the Reynolds stress, which drives spontaneous parallel flow is observed C.Hidalgo, Plasma Phys. Control. Fusion 48 (26) S169 B.Concalves, Phys. Rev. Lett. 96 (26) 1451

20 Heat transport Particle flux = diffusion + Nondiffusive term 1. E r and E r shear Zonal flow (Itoh s talk) Magnetic shear Energy flux = thermal + Convective term diffusivity T 3/2 (1+(R/L T κ c ) σ ) T 3. T dependence 2. T dependence

21 T e and gradt e dependence of transport in axisymmetric and nonaxisymmetric system (m 2 /s/kev 3/2 ) χ pb / T e 3/ n ρ e =1.62.5x1 19 m 3 I p =.8MA B ax = 2.27T x.1 JT6U x1 (m 2 /s/kev 3/2 ) χ pb / T e 3/ n e =.83x1 19 m 3 R ax = 3.5m B ax = 2.829T LHD ρ R ax /L T JT6U tokamak W7AS helical LHD Helical R ax /L T Clear scale length threshold No clear T e dependence No scale length threshold clear T e dependence Gyro Bohm type T e 1.5 in Lmode Q T 3/2 {1+(R/L T κ c ) σ } T Electron ITB appears below the scale length threshold in LHD F Ryter et. al., Plasma Phys. Control. Fusion 48 (26) B453 χ pb (m 2 /s) LHD.9 1 3/2 T.8 e.7 5/2.6 T e T e (kev) S.Inagaki, Nucl. Fusion 46 (26) 133

22 Bifurcation of transport between week and strong T e dependence GyroBohm T e dependence 1.4 Q/n = 2.49 T (dte /dr) 1.1 e Weak T e dependence.4 Q/n = 1.23 T (dte /dr).9 e Contour of χ 2 α β ( Q / n T T ) 2 e e e e 2 χ = T e dependence changes but no change in gradt e dependence K.Ida, Phys. Rev. Lett. 96 (26) 1256

23 nonlocal transport Hear flux Diffusive term Additional term Q = χ (T, T) T + f( T,,, ) dρ + local phenomena δq e /n e (kev m/s) LHD #49718 ρ =.19 δq e /n e (kev m/s) Nonlocal phenomena LHD #4978 ρ = dδt /dr (kev/m) e dδt /dr (kev/m) e Nonlocal transport can be expressed as additional flux contributed by the T at different radii Suggest strong coupling of turbulence between at the two location separated through mesoscale flow N.Tamura,, Nucl. Fusion 47, (27) 4495

24 Summary The transport between particle, momentum and heat fluxes are liked through the nondiffusive term of transport 1 Nondiffusive term of particle transport is driven by Te, T i (with strong relation with E r ) and magnetic field curvature. 2 Nondiffusive term of momentum transport, which drive spontaneous rotation, is driven by E r shear and viscosity tensor. Therefore the direction of spontaneous flow depends on sign of E r, magnetic field symmetry and type of responsible turbulence 3 Diffusive term of heat transport is affected by E r shear and E r itself in stellarator (through the reduction of collisional flow damping of Zonal flow). It mainly depends on T e rather than T e in LHD (because of the formation of ITB below the threshold) The transport between different location are liked through mesoscale flow and causes nonlocal transport phenomena 4 Nonlocal transport is characterized as additional flux due to the gradient of different radii

25 Remarks Good news 3N (nonlinearity, nondiffusivity, nonlocality) of transport give us interesting physics to be investigated (and gave me a chance for tutorial talk in this conference) Bad news Because of the recent significant progress of transport study in experiment and in theory, the Xday (all the transport physics will be understood and all the transport physicist will lose their job) is coming soon.

26 Comparison of radial structure of electron ITB between axisymmetric and nonaxisymmetric devices T e (kev) (a) P ECH /n e =4.4 P ECH /n e =3. P ECH /n e =1.5 P ECH /n e = T e (kev) Flattening (b) P ECH /n e =4.1 P ECH /n e =3. P ECH /n e =2. P ECH /n e =.9 P ECH /n e = /B 2 ) (m 2 s 1 kev 3/2 T 2 ) χ e /(T e 3/ (c) ITB LHD ITB JT6U ρ ρ LHD (nonaxisymmetric field) ρ reduction of χ e is extended to the plasma core (weak E r hear) JT6U (axisymmetric field) reduction of χ e is localized in the narrow E r shear region K K.Ida, Plasma Phys. Control. Fusion 46 (24) A45

27 Role of mean ExB flow on turbulence transport Lmode small Er large ZF damping small zonal flow large turbulence Electron ITB large Er small ZF damping large zonal flow small turbulence Thermal diffusivity is reduced in the region with small E r shear by ZF effect K.Itoh, Phys. Plasmas 14 (27) 272