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TCV & fast probe ESEL simulation based on interchange motions

Workshop on Edge Transport in Fusion Plasmas, 11-13.9.2006, Kraków, Poland.

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TCV & fast probe ESEL simulation based on interchange motions

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  1. Workshop on Edge Transport in Fusion Plasmas,11-13.9.2006, Kraków, Poland Understanding SOL plasma turbulence by interchange motions J. Horacek1, O.E. Garcia2, R.A. Pitts3, A.H. Nielsen2, W. Fundamenski4, J.P. Graves3, V. Naulin2, J.J. Rasmussen21 Institute of Plasma Physics, Prague, Czech Republic 2 Risø National Laboratory, Roskilde, Denmark 3 CRPP EPFL, Lausanne, Switzerland 4 UKAEA, Abingdon, United Kingdom • TCV & fast probe • ESEL simulation based on interchange motions • Statistics of density, temperature, flux and potential • Conclusions J. Horacek: Interchange turbulence simulation describes experiment

  2. Vfl1 Is,Te B-field 4mm Vfl4 Experimental set-up for diagnosing edge turbulence in tokamak TCV Map SOL 3D →1D • Reciprocating Langmuir probe • Pins measure at 6MHz sampling • floating potential Vfl=f-3Te potential f • temperature Te (1-120kHz) • ion saturation current IsatneTe1/2 density ne • Radial particle flux: Gr(Vfl1-Vfl4)Isat • Assuming dTe/Te is small 2-3 cm Probe head J. Horacek: Interchange turbulence simulation describes experiment

  3. Density statistics • [Graves PPCF 2005] • [J. Horacek CJP 2004] • Various discharges (ne,B<>0,Ip, L/H-mode, D/He) • Statistics confirms many observations by others e.g. [Boedo] • Fixed-shape PDF not possible • Found some universalities but it is impossible to understand without a model A=m/s saturates J. Horacek: Interchange turbulence simulation describes experiment

  4. Sinks Parallel damping Diffusion - Particle conservation n Energy conservation Vorticity conservation Curvature operator, Advective derivative, x=rs/R0, e=a/R0. The ESEL model • Electrostatic 2D fluid (n*>>10) model solves selfconsistently turbulence in n,Te,W. No neutrals. • Simplifications: parallel losses by linear damping, drift approximation, finite rLi effects neglected, thin layer approximation (dn/n<<1,dT/T<<1), only LFS. A.H. Nielsen, Monday 16:10. O.E. Garcia, Tuesday 14:40 J. Horacek: Interchange turbulence simulation describes experiment

  5. Dissipation and parallel loss estimates • Just 5 scalar measurable inputs: TLCFS,nLCFS,BLCFS,R+a,L|| determine the simulation [Fundamenski, Phys. Plasmas 2006]: • neo-classical collisional perpendicular transport: D┴n~D┴T~D┴W~f(n,T)~10-3m2s-1. • classical parallel transport determines parallel particle loss-time: sT~sn=sW~Lc/cs~1/250ms • Taken as constants in space and time with abrupt changes at LCFS and wall J. Horacek: Interchange turbulence simulation describes experiment

  6. ESEL simulation geometry J. Horacek: Interchange turbulence simulation describes experiment

  7. Outer boundary Flat n and T profiles No poloidal velocity W=0 => no boundary convection ESEL simulation geometry assuming statistical homogeneity in poloidal direction => Periodic r=0 r=1 Linear damping s Poloidal Radial ~3cm Innerboundary constant level of n, T and f W=0 => no boundary convection edge LCFS SOL wall shadow J. Horacek: Interchange turbulence simulation describes experiment

  8. Poloidal Radial 2~3cm J. Horacek: Interchange turbulence simulation describes experiment

  9. 30mm LCFS wall 30mm ESEL simulation ESEL 116, particle density • rvpol generated at LCFS due turbulence itself (via Reynolds stress=Tilting instability) • Blobs are generated at LCFS (due rvpol and rp ?) • Blobs then propagate due (rBxB)xB • Qualitatively consistent with all experimental observations and theoretical concepts. O+ X * S.J. Zweben et al, Nucl. Fusion 44,134 (2004) J. Horacek: Interchange turbulence simulation describes experiment

  10. Density fluctuations in the SOL r = -0.2 r = +0.6 J. Horacek: Interchange turbulence simulation describes experiment

  11. Te correlated with ne at a fixed position Density Temperature Gamma PDF match best TCV & ESEL Functional dependence of statistical moments defines a particular PDF. A = <n>/sn AT = <T>/sT Skewness Kurtosis Gamma: S=2/A Log-Normal S=3/A+A-3 BHP: S=0.9 Gumbel: S=1.14 Gaussian: S=0 [Graves PPCF 2005], [J. Horacek CJP 2004] [J. Horacek EPS Tarragona 2005] J. Horacek: Interchange turbulence simulation describes experiment

  12. t- t+ Coherently averaged density bursts match • Isolate large bursts, normalize, average them and fit by exp(-t/t+-) • Time-scales and asymmetry match • Inter-burst period match => even blob generation is well modelled => no additional mechanism needed  • BTW, [Kirnev Tuesday 11:40] sees 100ms. J. Horacek: Interchange turbulence simulation describes experiment

  13. Density • Gradients, time-scales, turbulence levels and statistical moments match • [O.E. Garcia, PPCF L1 2006] J. Horacek: Interchange turbulence simulation describes experiment

  14. Inside LCFS experiment not reliable due pins separation too large Flux • Cross-field turbulence-driven ExB particle flux • Gradients, turbulence levels and statistical moments match for flux • In absolute levels! • [O.E. Garcia, PSI, China, 2006] J. Horacek: Interchange turbulence simulation describes experiment

  15. Potential structure amplitude and dimension • Correlation on 2 pins poloidally separated is a measure of structure dimensions • Level of potential fluctuations much stronger in ESEL • Potential profile J. Horacek: Interchange turbulence simulation describes experiment

  16. Turbulence-driven (ballooning) flow • Idea: radially propagating blob generates localised pressure increase, i.e. ||p which drives M|| [Fundamenski, Nucl. Fusion 2006] • Turbulence-driven flow given by relative time proportion of high pressure events • In ESEL: p=nT. For TCV: assuming nT, p Isat4/3 • Compare with B-field-independent flow measured by Mach probe • Conclusion: absolute magnitudes roughly match J. Horacek: Interchange turbulence simulation describes experiment

  17. Summary • We demonstrated that a 2D fluid turbulence simulations quantitatively agree with a high-density TCV discharge everywhere in midplane SOL in nearly all studied statistical characteristics • => interchange motions driven by (BxB)xB drifts in p at LFS, dominated by rare convective blobs of ~2cm size and vr~2km/s [J. Horacek, PhD-thesis, EPFL, Switzerland, 2006] • In progress: • ESEL density scan • Varying damping and diffusion coefficients in space and time Thanks for your attention! J. Horacek: Interchange turbulence simulation describes experiment

  18. Reserve slides J. Horacek: Interchange turbulence simulation describes experiment

  19. Density scan • Matched one discharge, what about others? • Confirmed square dependence of ne and Gr at wall [LaBombard, IAEA Sorrento, 2000] • Simulations on the way J. Horacek: Interchange turbulence simulation describes experiment

  20. Motivation • Turbulence is claimed to be responsible for anomalous transport but no model was demonstrated yet to really quantitatively agree with experiment, or even have a predictive capability for radial transport J. Horacek: Interchange turbulence simulation describes experiment

  21. ESEL does describe the anomalous transport, on question over decades! • Why now? • Gradual development of models based on better experimental observations • Analytic treatment (Endler) in 1995 but due to poor computers, only orders of magnitude predictions • The Danes picked up the right physics, e.g. no sheath dissipation • Good quality diagnostic, fast data acquisition, removing properly noise • Close collaboration between theorists, modellers and experimentalists J. Horacek: Interchange turbulence simulation describes experiment

  22. Gr Gr Ez Interchange turbulence Curvature and BxB drift  vertical charge separation (Ez)  EzxB drift outwards  Unstable at LFS due p 2D fluid ESEL model [Garcia Tuesday 14:40] based on interchange motions. Risø run the simulations, CRPP the experiment. + + - - B J. Horacek: Interchange turbulence simulation describes experiment

  23. r = -0.2 r = +0.6 Detail temporal characteristics • Autocorrelation function ACF(tc,b). Time-scales match • Self-organized critical system yields self-similar power spectra f –b, b well defined only in wall shadow. J. Horacek: Interchange turbulence simulation describes experiment

  24. Temperature statistics J. Horacek: Interchange turbulence simulation describes experiment

  25. Gamma distribution describes density PDF Two-parameter Gamma PDF: <n> and A = <n>/sn A determines the shape Graves et al., PPCF 47, L1 (2005) J. Horacek et al. CJP (2004) TCV experiment ESEL model J. Horacek: Interchange turbulence simulation describes experiment

  26. Various analytical distributions determined by mean and STD • Gamma: in systems with clustering, e.g. sand-piles with avalanches [Graves PoP 2002] • Lognormal: for Boltzmann-distributed electrons, neexp(-f/Te) and Gaussian f[Sattin, PoP 2004] • BHP: describes self-organized critical systems [van Milligen, PoP 2005] • Gumbel: PDF of extreme value systems • Gaussian: most frequent in nature, sum of independent random processes A=m/s Gamma Lognormal J. Horacek: Interchange turbulence simulation describes experiment

  27. density radial Analogy with a sandpile • Two-parameter Gamma PDF: • mean <n> • fluctuation level A = <n>/sn • A determines the shape • Gamma distribution describes • Sandpile [Graves, PoP’02] • Density PDF in experiment • Density PDF in ESEL everywhere in tokamak edge • Horacek et al. Czech J. Phys. (2004) • Graves et al. PPCF 47, L1 (2005) J. Horacek: Interchange turbulence simulation describes experiment Local sandpile height

  28. Edge turbulence terminology Too many terms for those coherent structures, perhaps result of a unique phenomena! What phenomena? J. Horacek: Interchange turbulence simulation describes experiment

  29. Absolute level of flux match • Perfect match, independent from normalisation • Large blobs (>m+2.5s) with velocity ~1km/s are rare (6%). With average flux ~200m/s, these blobs carry large part (75%) of all particles J. Horacek: Interchange turbulence simulation describes experiment

  30. a=1.5 a=2.0 a=1.0 Turbulence-driven (ballooning) flow • Idea: radially propagating blob generates localised pressure increase, i.e. ||p which drives M||. [Fundamenski, Nucl. Fusion 2006] • Jhfund.m J. Horacek: Interchange turbulence simulation describes experiment

  31. r=0.8 r=0 Explaining overestimation of Te from swept Langmuir probe? • Use the fluctuating f(r,t), Te(r,t), ne(r,t) to generate swept VI-characteristics of a Langmuir probe in the experimental bandpath < 125kHz. • Fit it in the way the experimental data are fitted. #24530 Collected Current [A] . ESEL data - Quiet plasma - Fit Applied Voltage [V] J. Horacek: Interchange turbulence simulation describes experiment

  32. Effect of fluctuations • profiles well reproduced inside LCFS • Fast sweep is better • Te is indeed overestimated which might explain the experiment! Run 129 J. Horacek: Interchange turbulence simulation describes experiment

  33. Potential profile matches • Vf from the swept lower than from DC Vf-measurement as expected • Profiles correspond well to ESEL J. Horacek: Interchange turbulence simulation describes experiment

  34. m s Basic characteristics of SOL Various discharges (ne,B<>0,Ip, L/H-mode,Z, D/He) J. Horacek: Interchange turbulence simulation describes experiment

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