J. Horacek: Interchange turbulence simulation describes experiment 1 Understanding SOL plasma turbulence by interchange motions J. Horacek 1, O.E. Garcia 2, R.A. Pitts 3, A.H. Nielsen 2, W. Fundamenski 4, J.P. Graves 3, V. Naulin 2, J.J. Rasmussen 2 1 Institute of Plasma Physics, Prague, Czech Republic 2 Risø National Laboratory, Roskilde, Denmark 3 CRPP EPFL, Lausanne, Switzerland 4 UKAEA, Abingdon, United Kingdom 1.TCV & fast probe 2.ESEL simulation based on interchange motions 3.Statistics of density, temperature, flux and potential 4.Conclusions Workshop on Edge Transport in Fusion Plasmas, , Kraków, Poland

J. Horacek: Interchange turbulence simulation describes experiment 2 Reciprocating Langmuir probe Pins measure at 6MHz sampling –floating potential V fl =  -3T e potential  –temperature T e (1-120kHz) –ion saturation current I sat  n e T e 1/2 density n e –Radial particle flux:  r  (V fl 1 -V fl 4 )I sat –Assuming  T e /T e is small Map SOL 3D →1D Probe head 4mm B-field V fl 1 V fl 4 Is,TeIs,Te 2-3 cm Experimental set-up for diagnosing edge turbulence in tokamak TCV

J. Horacek: Interchange turbulence simulation describes experiment 3 Density statistics [Graves PPCF 2005] [J. Horacek CJP 2004] Various discharges (n e,B<>0,I p, 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=  saturates

J. Horacek: Interchange turbulence simulation describes experiment 4 The ESEL model Electrostatic 2D fluid ( *>>10) model solves selfconsistently turbulence in n,T e, . No neutrals. Simplifications: parallel losses by linear damping, drift approximation, finite  Li effects neglected, thin layer approximation (  n/n<<1,  T/T<<1), only LFS. Curvature operator, Advective derivative,  s /R 0,  =a/R 0. Particle conservation n Energy conservation Vorticity conservation Sinks Parallel damping Diffusion - 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: T LCFS,n LCFS,B LCFS,R+a,L || determine the simulation [Fundamenski, Phys. Plasmas 2006] : neo-classical collisional perpendicular transport: D ┴n ~D ┴T ~D ┴  ~10 -3 m 2 s -1. classical parallel transport determines parallel particle loss-time:  T ~  n =   ~L c /c s ~1/250  s 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 ESEL simulation geometry Linear damping  edge LCFS SOL wall shadow Periodic  assuming statistical homogeneity in poloidal direction => Inner boundary constant level of n, T and   =0 => no boundary convection Outer boundary Flat n and T profiles No poloidal velocity  =0 => no boundary convection Radial ~3cm Poloidal

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

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

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

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

J. Horacek: Interchange turbulence simulation describes experiment 12 Coherently averaged density bursts match Isolate large bursts, normalize, average them and fit by exp(-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 100  s.    

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 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] Inside LCFS experiment not reliable due pins separation too large

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  I sat 4/3 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 v r ~2km/s [J. Horacek, PhD-thesis, EPFL, Switzerland, 2006]J. Horacek, PhD-thesis, EPFL, Switzerland, 2006 In progress: –ESEL density scan –Varying damping and diffusion coefficients in space and time

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 n e and  r 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 Interchange turbulence Curvature and  BxB drift  vertical charge separation (E z )  E z xB 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B EzEz + - rr rr

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

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

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

J. Horacek: Interchange turbulence simulation describes experiment 26 Various analytical distributions determined by mean and STD 1.Gamma: in systems with clustering, e.g. sand-piles with avalanches [Graves PoP 2002] 2.Lognormal: for Boltzmann-distributed electrons, n e  exp(-  /T e ) and Gaussian  [Sattin, PoP 2004] 3.BHP: describes self-organized critical systems [van Milligen, PoP 2005] 4.Gumbel: PDF of extreme value systems 5.Gaussian: most frequent in nature, sum of independent random processes Gamma Lognormal A= 

J. Horacek: Interchange turbulence simulation describes experiment 27 Analogy with a sandpile Two-parameter Gamma PDF: mean fluctuation level A = /  n A determines the shape radial density Local sandpile height SandpileTokamak edge Sandpile slope rprp Sand grainsIndividual ions on Larmor orbits Force of gravity Curvature and  r BxB Static frictionThreshold to start an instability (Kelvin-Helmholtz?) Dynamic frictionDissipation at small scales and velocity shear Gamma distribution describes 1.Sandpile [Graves, PoP’02] 2.Density PDF in experiment 3.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 28 Edge turbulence terminology DimensionNameObservationCharacteristic 0D (+ time)Intermittent event, burst Langmuir probeNon-Gaussian 1D radialAvalanche, streamer, density finger Sandpile model fluid model (Sarazin, Ghendrih) Clustering, SOC, self- similarity, marginal stability (Hidalgo) 1D parallelFilamentsLangmuir probe and camera Long correlations (>20m, Endler ) 2D poloidal x radial Theory Blob, eddy (vortex)Models of isolated blobs (Krasheninnikov, Bian, Garcia) Propagation dynamics due (  BxB)xB 2D Experimentplasmoid, avaloid, IPO Fast cameras, LP matrix (CASTOR, DIII- D) 1x2cm 2, 1km/s, … 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 (>  ) 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  =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  =1.5  =2.0

J. Horacek: Interchange turbulence simulation describes experiment 31 Explaining overestimation of T e from swept Langmuir probe? Use the fluctuating  ( ,t), T e ( ,t), n e ( ,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. Applied Voltage [V] Collected Current [A]  =0.8  =0 # ESEL data - Quiet plasma - Fit

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

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

J. Horacek: Interchange turbulence simulation describes experiment 34 Basic characteristics of SOL  Various discharges (n e,B 0,I p, L/H-mode,Z, D/He)