TORPEX: experiments and theory Ivo Furno Past and present: A. Burckel, A. Diallo (PPPL), L. Federspiel (TCV), A. Fasoli, E. Küng, D.Iraji, B.Labit (TCV), S.H.Müller (UCSD), G. Plyushchev, M. Podestà (PPPL), F.M. Poli (Warwick), P. Ricci, B.Rogers (Dartmouth), C. Theiler Centre de Recherches en Physique des Plasmas (CRPP) École Polytechnique Fédérale de Lausanne, Switzerland (EPFL)

The TORPEX device A. Fasoli, et al., Phys. Plasmas 13, (2006) Major radius1 m Minor radius0.2 m Magnetic field B  0.1 T Pulse duration  1 s Neutral gas pressure mbar Injected 2.45GHzP RF < 20 kW Plasma densityn ~ m -3 Electron temperature Ion temperature T e ~ 5-15 eV T i ≤ 1 eV Gas Ion sound Larmor radius H, D, Ar, He, Ne  s /a ~ 0.02 I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12 th March

Flexible magnetic configuration 28 water cooled toroidal coils  |B  |<0.1 T 4 poloidal field coils:  |B z |<5 mT  Tokamak-like (V loop ~3-10V, 50ms, I p <5kA)  Cusp field + strong OH (V loop ~120V, 3ms) for magnetic reconnection studies EC resonant 2.45 GHz I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12 th March

4 Simple magnetized torus: a paradigm for tokamak SOL Parallel losses  B, curvature Source (EC and UH resonance) Plasma gradients B tor BzBz I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12 th March 2010

TORPEX diagnostics I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12 th March 2010 Fast ion source GEA 5

66 A turbulent plasma H 2 plasma P f = 400 W B tor =76mT on axis; B z =2.1mT p gas = 6.0 x mbar Source-free region Main plasma region I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12 th March 2010

Questions addressed on TORPEX  What kind of modes are responsible for turbulence and intermittency?  How are macroscopic structures (blobs) generated?  How do blobs propagate? Can their dynamics be influenced/controlled?  Do the observed fluctuations and structures have a universal character?  What are the consequences, in terms of Plasma flow/rotation? Transport for thermal plasma ? Transport for non-thermal plasma particles (fast ions) ? 7 I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12 th March 2010

 What kind of modes are responsible for turbulence and intermittency?  How are macroscopic structures (blobs) generated ?  How do blobs propagate? Can their dynamics be influenced/controlled ?  Do the observed fluctuations and structures have a universal character ?  What are the consequences, in terms of Plasma flow/rotation ? Transport for thermal plasma ? Transport for non-thermal plasma particles (fast ions) ? 8 Questions addressed on TORPEX I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12 th March 2010

Nature of instabilities: exp. dispersion relation 9 k II ~ 0 k II ≠ 0 N = number of field line turns  = vertical distance between field line return points ex. N = 2  Statistical analysis of 2-points correlations f [kHz] k II [m -1 ] Ex. of k II spectrum kzkz k II I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12 th March 2010

Fluid model ρ i << L,  << 1 ω << Ω ci Braginskii model Electrostatic Drift-reduced Bragiskii equations Collisional Plasma Parallel dynamics Magnetic curvature Source Diffusion Convection + similar equations for T e, Ω (vorticity = ) + parallel momentum balance for V ||e, V ||I source profile from measurements 10 I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12 th March 2010

3D Global simulation, N=2 r z z’ r’ r 11 λ z = , k  = k toroidal ≠ 0, k || = 0 (except sheath effects)  II r z’ z r’ r I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12 th March 2010

r z z’ r’ r 3D Global simulation, N=16 12 λ z = N  largest available scale), k  = k toroidal = 0, k || ≠ 0   r z’ z r’ r I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12 th March 2010

Turbulence phase space Ideal Interchange Resistive Interchange Drift k || =0, λ v =L v /N k φ =0, λ v =L v Interchange drive not important I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12 th March P. Ricci and B.N. Rogers, accepted in PRL

Interpretation of measured dispersion relation f 14 Ideal interchange Resistive interchange k // ~ 0 k // ≠ 0 l z = D I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12 th March 2010

 What kind of modes are responsible for the turbulence? Ideal interchange, resistive interchange or drift waves, depending on pressure gradient and vertical magnetic field 15 F. M. Poli, et al., PoP (2006); PoP (2007); PoP (2008); PhD Thesis A. Diallo et al., PoP (2007) L. Federspiel et al., PoP (2009); Master Thesis P. Ricci et al., PoP (2009); Phys. Rev. Lett. (2008) Questions addressed on TORPEX I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12 th March 2010 From now on we will concentrate on ideal interchange modes (k II ≈0)

 What kind of modes are responsible for the turbulence ?  How are macroscopic structures (blobs) generated ?  How do blobs propagate? Can their dynamics be influenced/controlled ?  Do the observed fluctuations and structures have a universal character ?  What are the consequences, in terms of Plasma flow/rotation ? Transport for thermal plasma ? Transport for non-thermal plasma particles (fast ions) ? 16 Questions addressed on TORPEX I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12 th March 2010

17 Dynamics of blob ejection  Time resolved 2D profiles of n e, T e, V pl from conditional sampling  Ideal interchange mode moves upwards with v ExB  A radially elongated structure forms from a positive cell  The ExB flow shear shears the structure  The structure breaks into two parts in ~100 μs ⇒ formation of the blob I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12 th March 2010

 How are macroscopic structures (blobs) generated ? Strong ExB shear flow breaking interchange wave crest Energy is transferred from shear flow to blobs 18 S. H. Müller, et al., PoP (2007); PhD Thesis I. Furno et al., Phys. Rev. Lett. (2008) ; PoP (2008) C. Theiler et al., PoP (2008) A. Diallo et al., Phys. Rev. Lett. (2008) Questions addressed on TORPEX I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12 th March 2010

 What kind of modes are responsible for the turbulence ?  How are macroscopic structures (blobs) generated ?  How do blobs propagate?  Do the observed fluctuations and structures have a universal character ?  What are the consequences, in terms of Plasma flow/rotation ? Transport for thermal plasma ? Transport for non-thermal plasma particles (fast ions) ? 19 Questions addressed on TORPEX I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12 th March 2010

Study of filaments/blobs in simple geometry 20  Steel limiter on low-field side, defining region with Constant curvature along field lines Nearly constant connection length (~2  R) Near-perpendicular incidence of magnetic field lines No magnetic shear r z Probe tips Region where limiter intercepts both ends of field lines I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12 th March 2010

Vertical cut 21 Analysis of filament/blob motion  Blobs identified by pattern recognition  Automated evaluation of Radial velocity v Vertical size a Density  n, n r [m] z [m] S. H. Müller et al., POP (2006) C. Theiler et al., PRL 103, (2009) I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12 th March 2010

22 Joint probability of blob velocity – size Range of blob sizes below diagnostic resolution Similar sizes in all gases Similar values of  n/n Mean velocity of blobs over their entire trajectory Significant differences in the typical velocity, ranging from 500 m/s (Ar) to 2000 m/s (He) I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12 th March 2010

23 Comparison with existing 2D scaling laws Experimental data in normalized units Damping due to ion-polarization currents Damping due to parallel currents He H 2 Ar Ne I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12 th March 2010 Normalization: L: connection length R: major radius

24 Generalization of 2D blob models and scaling laws Vorticity equation C. Theiler et al., Phys. Rev. Lett. 103, (2009) Fig. from Krasheninnikov et al. I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12 th March 2010

25 Agreement with generalized 2D blob model I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12 th March 2010 Damping due to ion-polarization currents Damping due to parallel currents

 How do blobs propagate? Agreement between data and a generalized 2D model for blob velocity  Parallel currents to the limiter, cross-field ion polarization currents, and ion- neutral collisions 26 C. Theiler et al., Phys. Rev. Lett. 2009; PhD Thesis Questions addressed on TORPEX I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12 th March 2010

 What kind of modes are responsible for the turbulence ?  How are macroscopic structures (blobs) generated ?  How do blobs propagate? Can their dynamics be influenced/controlled ?  Do the observed fluctuations and structures have a universal character ?  What are the consequences, in terms of Plasma flow/rotation ? Transport for thermal plasma ? Transport for non-thermal plasma particles (fast ions) ? 27 Questions addressed on TORPEX I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12 th March 2010

28  ~10000 signals of I sat  H 2, He, Ar  Pressure scan  B z scan  1% < ñ / n < 95%  In TORPEX  ~30% of signals with S<0  In tokamaks  SOL: S>0  S<0 when LCFS is crossed Relation between moments of PDF kurtosis I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12 th March 2010

29 Universal statistical properties of fluctuations  Unique relation Kurtosis vs. Skewness  Measured S vs. K curve and PDF are described by the Beta distribution  ~ 800 signals from TCV edge / SOL plasmas (L-mode) give similar results: statistics associated with interchange OE Garcia et al., PPCF (2006) h ol es TCV: courtesy of J. Horacek K = 1.5 S  Sandberg, PRL 103, (2009)  Process described by quadratic polynomial of Gaussians processes I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12 th March 2010

 Do the observed fluctuations and structures have a universal character ? Unique S vs. K relationship, Beta PDF  Common to a variety of phenomena with convection  E.g. surface T fluctuations in ocean waves, x-ray fluctuations in accretion disks Similar scaling and PDF found in TCV edge data 30 B. Labit et al., Phys. Rev. Lett. (2007); PPCF (2007) Questions addressed on TORPEX I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12 th March 2010

 What kind of modes are responsible for the turbulence ?  How are macroscopic structures (blobs) generated ?  How do blobs propagate? Can their dynamics be influenced/controlled ?  Do the observed fluctuations and structures have a universal character ?  What are the consequences, in terms of Plasma flow/rotation ? Transport for thermal plasma ? Transport for non-thermal plasma particles (fast ions) ? 31 Questions addressed on TORPEX I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12 th March 2010

n e (m -3 ) B z > 0 B z < 0 blob detected  [  s] v  (km/s) B z > 0 B z < 0 32 Effect of blobs on plasma flow / rotation Ref. probe  = 90° vv 1 0  (  s) [km/s B z > z (cm)  Measured with Mach probe along vertical chord in blob region  When blob passes by probe, sudden change in toroidal rotation (not simply due to T e effect on Mach number through c S ) is detected  2D profile shows positive and negative fluctuations of v  I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12 th March 2010

 Same trend for opposite B z signs, though time averaged profiles are very different  Symmetry in fluctuations of v  (skewness ~0) 33 Scaling of blob induced flow with blob amplitude B z > 0 B z < 0 v ,max (km/s) v ,min (km/s) ~ ~ I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12 th March 2010

 What are the consequences, in terms of Plasma flow/rotation ?  Toroidal velocity blobs or holes are associated with density blobs  The variations of toroidal rotation increase (nonlinearly?) with blob amplitude 34 B. Labit et al., RSI (2008); paper in preparation Questions addressed on TORPEX I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12 th March 2010

 What kind of modes are responsible for the turbulence ?  How are macroscopic structures (blobs) generated ?  How do blobs propagate? Can their dynamics be influenced/controlled ?  Do the observed fluctuations and structures have a universal character ?  What are the consequences, in terms of Plasma flow/rotation ? Transport for thermal plasma ? Transport for non-thermal plasma particles (fast ions) ? 35 Questions addressed on TORPEX I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12 th March 2010

36 Mode region: Fluctuation-induced particle flux  Time domain, 2D flux pattern from CAS consistent with Fourier analysis  Heat is convected by particle flux (  T,  are in phase) I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12 th March 2010

37 Blob region: structure related particle flux Instantaneous structure related flux Fraction of positive structures  Time domain, 2D flux pattern from CAS inconsistent with Fourier analysis, but consistent with structure analysis I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12 th March 2010

 What are the consequences, in terms of Plasma flow/rotation ? Transport for thermal plasma ?  Two different mechanisms  Fluctuation-induced flux ( quasi-coherent e.s. instabilities)  Blob-related flux (d ominant in source-free region, depending on instantaneous ExB pattern) 38 M.Podestà et al., Phys. Rev. Lett. (2007); PhD Thesis Questions addressed on TORPEX I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12 th March 2010

 What kind of modes are responsible for the turbulence ?  How are macroscopic structures (blobs) generated ?  How do blobs propagate? Can their dynamics be influenced/controlled ?  Do the observed fluctuations and structures have a universal character ?  What are the consequences, in terms of Plasma flow/rotation ? Transport for thermal plasma ? Transport for non-thermal plasma particles (fast ions) ? 39 Questions addressed on TORPEX I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12 th March 2010

Fast ion source and detector  Collaboration CRPP - UCI  Miniaturized Li 6+ ion emitter  Thermo-ionic effect (~1200 o )  Ion energies: 100ev – 1keV Alumino-silicate coating Tungsten body 1 cm 40 I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12 th March 2010 First grid Second grid Collector 6 mm BN casing Ion emitter Acc. grid Screaning grid 4 cm 2 cm Heating wires (30W)

41 E fast = 300eV Experimental fast ion current density profiles Without plasma With plasma  r =1.5cm  z =2.0cm  r =1.8cm  z =3.2cm  Fast ion current density profiles are broadened (both radially and vertically) by the plasma r (cm) I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12 th March 2010 r (cm) z (cm)

42 Simulated fast ion motion in turbulent E-field Source with realistic spread in energies (10%) and in angular distribution (0.2rad)  Motion of tracer particles in turbulence calculated by 2D fluid simulations Periodic boundary conditions k || =0 2D simulation z (mm) r (mm) I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12 th March 2010

43 Simulated fast ion current density profiles Without plasma With plasma 300eV, blob region 300eV, mode region  Simulation qualitatively explains the shape of the experimental profiles Elongated profiles can be explained by spread in velocity distribution Radial broadening, due to fluctuations and blobs, is consistent with experiments z (cm) z (cm) z (cm) z (cm) r (cm) I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12 th March 2010

 What are the consequences, in terms of Plasma flow/rotation ? Transport for thermal plasma ? Transport for non-thermal plasma particles (fast ions) ?  First experiments reveal effects of plasma turbulence on fast ion profiles  Radial spreading due to fluctuations and blobs in simulation and experiment 44 G. Plyushchev, RSI (2007); PhD Thesis; A.Burckel, Master Thesis Questions addressed on TORPEX I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12 th March 2010

Summary  The results obtained on the TORPEX simple toroidal plasma device enable a quantitative model validation for building blocks the problem of intermittent transport in edge plasma Nature of the underlying instabilities Turbulence local statistical properties Turbulence spatio-temporal structures (blobs) Transport of thermal and suprathermal particles, heat and momentum  More results and details at 45 I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12 th March 2010

Outlook  Studies on blob physics Control of blob dynamics with various limiter configurations E.m. effects  Full code validation project  Change in magnetic topology, in particular for fast ion physics studies Ohmic discharges  Fast ions Development of a large source - collaboration with group in Stuttgart Energy resolved measurements Full 3D particle motion solver  Extensive use of non-perturbative optical diagnostics Laser Induced Fluorescence for ion velocity resolution Imaging with fast framing camera + intensifier, with and without GPI 46 I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12 th March 2010

47 Idea: control of blob velocity via wall tilt Design By pivoting the limiter around a vertical axis, we can achieve |  |~10 o Limiter à configuration variable Schematic top view   Parallel electron current should depend on angle  between B-field lines and wall R. H. Cohen and D. D. Ryutov, PoP 1995; CPP 2006 I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12 th March 2010

48 Preliminary results Average blob dynamics in H 2 shows no significant difference for different  Problem with geometry (e.g. current closure on several plates)? I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12 th March 2010

49 E.M. effects I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12 th March 2010 Multi Bdot array First current meas. inside a blob

50/50 I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12 th March First Ohmic experiments on TORPEX  Ohmic phase: I p  1kA I p duration ~ 2ms V loop ~ 8V  V loop duration ~ 4ms Stable profiles for ~ 1.2ms Plasma current is reproducible within 20% from shot-to-shot Ohmic transformer Closed field lines 50