Transport in the Scrape-off Layer of Tokamak plasmas

Transcription

1 U. Stroth, Tutorial on Drift Waves, DPG Jena

2 Transport in the Scrape-off Layer of Tokamak plasmas Contributions from Gregor Birkenmeier, Daniel Carralero, Golo Fuchert, Peter Manz, Bernhard Sieglin and the ASDEX Upgrade team Max-Planck-Institut für Plasmaphysik D Garching U. Stroth, , École de Physique des Houches, France

3 Or Transport in the No Man s Land (Anne White, yesterday) U. Stroth, , École de Physique des Houches, France

4 Outline Introduction Magnetic configuration of a tokamak Parameters of the plasma edge Parameters of the scrape-off layer (SOL) A simple model for the SOL plasma parameters Edge turbulence SOL turbulence and transport Experimental observations Blobs and models Blob observations and comparison with models Transition to high density and divertor detachment U. Stroth - Les Houches

5 Magnetic configuration of a tokamak U. Stroth, , École de Physique des Houches, France

6 Magnetic configuration of a tokamak (AUG)

7 Magnetic configuration of a tokamak (AUG)

8 Parameters of the plasma edge U. Stroth, , École de Physique des Houches, France

9 Edge pedestal determines plasma performance High confinement (H)-Mode edge transport barrier steep gradients in narrow zone Profile pedestal Large fraction of the confinement is made within 5 % of the radius Steep edge pressure gradient drives cyclic relaxation instability: Edge Localised Modes - ELMs [T. Pütterich et al., PRL 2009] U. Stroth - Les Houches

10 The edge determines the core parameters Stiff temperature gradients in the core 5.0 ASDEX Upgrade ECH T e [kev] Ohmic 0.8 MW ECH 1.6 MW ECH ρ [F. Ryter PPCF 2001] U. Stroth - Les Houches

11 The edge radial electric field and neoclassical theory Radial electric field from CXRS Is consistent with neoclassical theory [E. Viezzer et al. NF 2013] U. Stroth - Les Houches

12 Profile evolution during ELM cycle [E. Wolfrum] during ELM T e is small initial recovery of T e T e recovery stalled n e recovers T e recovery continues T e exhibits large fluctuations

13 Parameters and model of the scrape-off layer (SOL) U. Stroth, , École de Physique des Houches, France

14 Heat flux on divertor target [Sieglin, EFPW 2014] Strike line: λ int = λ q S [Makowski et al., PoP 2012] λ q : Exponential power fall-off length in SOL S: Diffusive broadening between X-point and divertor U. Stroth - Les Houches

15 Scaling of λ q from infrared measurements Power fall-off length shows no dependence on major radius R Divertor broadening shows no dependence on major radius R λ q = Btor qcyl PSOL Rgeo [Eich et al., NF (2013) ] S reg [ mm] = 0.09 n B [Sieglin et al., EPS 2013] e pol U. Stroth - Les Houches

16 The two-point model for SOL transport U. Stroth - Les Houches

17 The two-point model for SOL transport Parallel heat conduction Constant pressure Upstream temperature (100 ev) U. Stroth - Les Houches

18 Natural ExB-flow shear layers in edge and SOL U. Stroth - Les Houches

19 Turbulent transport in the plasma edge U. Stroth, , École de Physique des Houches, France

20 Why wind-tunnel experiment to study edge plasma Use reduced plasma parameters With similar values of the dimensionless parameters And larger characteristic scales Allows the use of Langmuir probes in the plasma edge Compare with fluid code DALF U. Stroth - Les Houches

21 A low-temperature toroidal plasma experiment TJ-K stellarator Reynolds stress array (128 probes) Zonal flow arrays (2x64 probes) U. Stroth - Les Houches

22 Structure of drift-wave turbulence Density structure are elongated along B and slightly tilted Correlations in a parallel distance of > 3 m TJ-K DALF DALF TJ-K [Mahdizadeh et al. PPCF 2007] U. Stroth - Les Houches

23 Structure of drift-wave turbulence Parallel dynamics governed by high electron mobility Potential and density fluctuations are in phase TJ-K DALF [Stroth et al, PoP 2004] U. Stroth - Les Houches

24 Structure of drift-wave turbulence Perturbations drift in electron-diamagnetic direction and scale with ρ s Hydrogen Argon [Lechte PhD 2004] U. Stroth - Les Houches

25 Structure of drift-wave turbulence Radial currents due to polarization drift couple to Alfvén wave [Rahbarnia et al., PPCF 2008] U. Stroth - Les Houches

26 Detailed knowledge about the turbulent dynamics [Birkenmeier et al., PRL 2008]

27 Detailed knowledge about the turbulent dynamics [Birkenmeier et al., PRL 2008]

28 Detailed knowledge about the turbulent dynamics [Birkenmeier et al., PRL 2008]

29 Scrape-off layer (SOL) transport and plasma blobs U. Stroth, , École de Physique des Houches, France

30 Structures after an ELM crash ELM crash leads to filamentary structures Asymmetric and locally enhanced power deposition Fast camera measurement on MAST [Kirk et al. PRL 92 (2004)] Infrared measurements on divertor tile in ASDEX Upgrade [Eich et al, PRL 91 (2003)] U. Stroth - Les Houches

31 L-mode and inter-elm filaments in H-mode Inter-ELM and L-mode filaments are similar to ELM filaments but smaller Fast camera measurement on MAST [Ben Ayed et al., PPCF (2009)] U. Stroth - Les Houches

32 In a poloidal cut, filaments are observed as Blobs Blobs propagate radially Gas-puff imaging on NSTX [Maqueda et al. J. Nucl. Mater. (2011)] Radial velocity increases with density Fast camera measurement on MAST [Ben Ayed et al., PPCF (2009)] U. Stroth - Les Houches

33 Langmuir probes on ASDEX Upgrade Ion saturation current Floating potential [Nold et al. PPCF 2010] U. Stroth - Les Houches

34 Transport across the separatrix on ASDEX Upgrade #22505 holes blobs [Nold et al. PPCF 2010] 34

35 Blobs are intermittent and the PDF is skewed Blobs appear as spikes in the ion-saturation current I sat blobs PDF blobs time (µs) I sat (σ) The skewness increases with the distance from the separatrix Probe measurements on ASDEX Upgrade [B. Nold et al. PPCF 2010] U. Stroth - Les Houches

36 Ions inside blobs are warm Retarding field analyzer on AUG Background temperatures: T e = 10 ev T i = 30 ev Filament temperatures: T i = 100 ev T e = 30 ev Impact of warm ions on blob dynamics and main chamber wall erosion! [M. Kocan et al., PPCF (2012) ] U. Stroth - Les Houches

37 Blob models U. Stroth, , École de Physique des Houches, France

38 Properties of blob model Blobs propagate radially outwards up to the main chamber wall are elongated along the fieldlines are hot and dense contribute significantly to SOL transport and can damage the wall B [B. Nold, PhD thesis] U. Stroth - Les Houches

39 A basic 2D model for radial blob propagation (T i = 0) Divergence free current yields vertical electric field ExB drift accelerates blob radially characteristic size a and time t U. Stroth - Les Houches

40 Fundamental blob model (cold ions) Vorticity equation ( j = 0): Generalized polarization current Curvature drive Parallel [Krasheninnikov et al. J. Plasma Physics (2008) ] U. Stroth - Les Houches

41 Including currents parallel to the magnetic field Inertial regime (collisional) [Garcia et al. Phys. Plasma (2006) ] Sheath connected regime (collisionless) [Krasheninnikov et al. J. Plasma Physics (2008) ] Resistive and electromagnetic regimes Resistivity [P. Manz et al., Phys. Plasmas (2013)] U. Stroth - Les Houches

42 Velocity-size relation for sheath-connected blobs Polarization Blob correspondence principle: Curvature drive Sheath dissipation Analytical velocity-size relation for stationary case: U. Stroth - Les Houches

43 General case (cold ions) Velocity-size relation Compare with TORPEX data Sheath dissipation Neutral friction Polarization currents To be added: X-point geometry Ion temperature [Theiler et al., PRL (2010) ] U. Stroth - Les Houches

44 There is a most stable blob size Blob too small: Mushroom shape (Kelvin-Helmholtz instability) Blob too large: Ballooning fingers (Rayleigh-Taylor instability) Most stable size [Krasheninnikov, et al. J. Plasma Physics 2008] [Aydemir, Phys. Plasmas (2005)] U. Stroth - Les Houches

45 Effect of warm ions from DALF equations Vorticity equation with warm ion effects (τ = T i /T e > 0): Additional factor for most stable blob size: Additional factor for velocity-size relation in sheath-connected regime: [P. Manz et al., Phys. Plasmas (2013)] U. Stroth - Les Houches

46 Blob scaling regimes in the warm-ion model [P. Manz et al., Phys. Plasmas (2015)] U. Stroth - Les Houches

47 Blob observations and comparison with models U. Stroth, , École de Physique des Houches, France

48 Lithium-beam emission spectroscopy (Li-BES) Separatrix Li-BES Flux surfaces Blobs are visible in raw data (~n e ) signal exceeds 2.5σ propagates radially amplitude background U. Stroth - Les Houches

49 Radial profiles of blob properties (Li-BES) Blob width: Few cm Increasing towards wall Maximum radial velocity Between 200 and 1000 m/s Decreasing towards wall Blob frequency: Several hundreds per second [Birkenmeier et al., PPCF (2014)] U. Stroth - Les Houches

50 Comparison of blob sizes with models B-field scan and variation in L : Ohmically heated L-mode Low density n e = m -3 Predicted blob width with cold ions too small Better agreement for warm ion model with additional factor [Birkenmeier et al., PPCF (2014)] U. Stroth - Les Houches

51 Comparison of blob velocity with models Slower velocity of larger blobs as in sheath-connected regime [Krasheninnikov et al., J. Plasma Physics (2008)] Warm ion scaling fits better [P. Manz et al., Phys. Plasmas (2013)] [Birkenmeier et al., PPCF (2014)] U. Stroth - Les Houches

52 Compare with gas-puff imaging (GPI) [Fuchert et al., PPCF 2014] U. Stroth - Les Houches

53 Comparison of blob sizes with models Velocimetry of GPI data Size scaling agrees with sheathconnected warm ion scaling [Fuchert et al., PPCF 2013] U. Stroth - Les Houches

54 Comparison of blob velocity with models Velocimetry of GPI data Size scaling agrees with sheathconnected warm ion scaling Velocities predicted slightly larger [Fuchert et al., PPCF 2013] U. Stroth - Les Houches

55 Blob generation mechanisms U. Stroth, , École de Physique des Houches, France

56 Blobs close to separatrix: drift-wave-like phase relation Plasma potential measured by emissive and swept probes on AUG [Nold et al., NJP (2012)] U. Stroth - Les Houches

57 SOL turbulence from Langmuir probes and GEMR Plasma potential measured by two techniques (emissive, cond. sampling) Experiment Gyro-fluid code GEMR All parameters are in phase drift-wave turbulence Consistent with data from synthetic Langmuir probes in GEMR At larger distance from separatrix blobs become more interchange like U. Stroth - Les Houches 2015 Nold et al., NJP 2011

58 In simulations blobs are ejected across the separatrix Hot and dense blobs are generated intermittently around the last closed flux surface Main activity at the low-field side Convective propagation towards the wall GEMR simulation: Circular limiter plasma, poloidal cross section U. Stroth - Les Houches

59 Blobs in TJ-K are drift-wave like Conditional averaging of Langmuir probe data Generated at the same rate as drift waves appear [Happel et al, PRL 2008] [Fuchert et al, PPCF 2013] U. Stroth - Les Houches

60 Blob generation in simulations (GEMR) Seems consistent with theory Interchange instability generates radially extended streamers Shear flow breaks streamers up into blobs [D Ippolito et al. Phys. Plasmas 2011] Conditional average from GEMR simulations [Nold et al. Phys. Plasmas 2014] U. Stroth - Les Houches

61 Blob generation in simulations (GEMR) The full history shows structures merge exchange particles and energy break up again Turbulence spreading [Gürcan et al. Phys. Plasmas 2005] Conditional average from GEMR simulations [Nold et al. Phys. Plasmas 2014] U. Stroth - Les Houches

62 Drift-wave interact with conducting wall instability? Drift-wave like temperature-potential phases can be expected U. Stroth - Les Houches

63 Shear layers seem to play a role in blob generation Cross-correlation of Langmuir probes in AUG

64 Plasma blob trajectories from GEMR simulations Identify blobs at every time step: density perturbations > 2.5σ Fulfilled over a connected extent of 11 grid points ( 5 mm) track blobs for a least 50 time steps ( 25 µs) [Manz et al. Phys. Plasmas 2015] U. Stroth - Les Houches

65 Statistics of blob trajectories Blob generation outside separatrix blob trajectory density (a.u.) [Manz et al. Phys. Plasmas 2015] U. Stroth - Les Houches

66 Turbulence spreading model Mean free energy Turbulent energy Local turbulence drive Turbulence spreading [Manz et al. Phys. Plasmas 2015] U. Stroth - Les Houches

67 Local drive vs. turbulence spreading In AUG sheath connected conditions, most blobs are generated outside the separatrix local drive turbulence spreading Turbulence spreading could play a role for turbulence in the far- SOL where background gradient is small [Manz et al. Phys. Plasmas 2015] U. Stroth - Les Houches

68 Transition to high density and detachment U. Stroth, , École de Physique des Houches, France

69 Flattening of the SOL density profile at higher density [LaBombard et al., PoP (2001)] [Rudakov et al., Nucl. Fus. (2005)] [Garcia et al., Nucl. Fus. (2007)] Observed in many tokamaks Points to increased convective transport Temperature profiles almost unchanged U. Stroth - Les Houches

70 Changes in blob dynamics with increasing density Sheath connected regime Λ < 1 Resistive or electromagnetic regime Λ > 1 Increasing density Resistivity parameter [Myra et al, PoP (2006)] U. Stroth - Les Houches

71 Blob transport is increased at higher densities (AUG) Langmuir probe measurements of blob transport Transition to increased blob transport regime at higher densities [D. Carralero et al., Nucl. Fusion (2014)] U. Stroth - Les Houches

72 Effect of parallel resistivity At higher densities: Parallel resistivity dominates due to collisions for Λ > 1: Resistivity inhibits short cut more interchange like blobs propagate faster Velocity-size relation: Strongest effect expected in the divertor U. Stroth - Les Houches

73 Blob transport is related to divertor detachment Transition to increased transport regime in line with transition to collisional regime Λ > 1 : Possibly related to divertor detachment measured by degree of detachment (DoD) [Carralero et al., Nucl. Fusion (2014)] U. Stroth - Les Houches

74 Blob transport is related to divertor detachment DoD, LFS divertor f GW ρ I sat, LFS divertor Filament size (cm) ρ f GW [Carralero et al., Nucl. Fusion (2014)]

75 Blob transport is related to divertor detachment DoD, LFS divertor f GW ρ I sat, LFS divertor Filament size (cm) ρ f GW [Carralero et al., Nucl. Fusion (2014)]

76 Blob transport is related to divertor detachment DoD, LFS divertor f GW ρ I sat, LFS divertor Filament size (cm) ρ f GW [Carralero et al., Nucl. Fusion (2014)]

77 Blob transport is related to divertor detachment Degree-of-Detachment at JET and AUG correlates with profile flattening, blob size and transport f GW [Carralero et al., JNM (2014)] U. Stroth - Les Houches

78 The H-mode density limit is related to blob transport 1 Stable H-mode: 2 Degraded 3 H-Lt rans. 4 L-mode [Bernert et al., PPCF (2014)]

79 Increased power transported by blobs at high densities Missing power in main chamber Increased blob transport in the far SOL [Bernert et al., PPCF (2014)] U. Stroth - Les Houches

80 Concluding remarks Perpendicular transport in the SOL is dominated by blobs Dynamics of blobs can be understood in terms of analytical models Blobs are generated drift-wave like and then devlope interchange characteristics 3-wave-coupling and turbulence spreading could be important to understand blob generation Blob transport communicates divertor conditions to the plasma edge and to global confinement In the future full-f simulations are needed including X-point geometry U. Stroth - Les Houches