Turbulence and Transport in Magnetically Confined Plasma Jens Juul Rasmussen Jens Madsen, Volker Naulin, Anders H. Nielsen Association EURATOM – DTU, Department of Physics, Technical University of Denmark, DTU Risø Campus, DK-4000 Roskilde Odd Erik Garcia Department of Physics and Technology, University of Tromsø, N-9037 Tromsø jjra@fysik.dtu.dk Department of Physics Technical University of Denmark
Outline/Motivation • Turbulence and transport in plasma – particularly in the edge region of magnetically confined plasma • Results from numerical modelling with comparison with experimental observations • In magnetically confined plasmas the anomalous – turbulent - transport is the dominant mechanism for transport of particles and energy across the confining magnetic field – orders of magnitude higher than classical collisional transport • Understanding and predicting the transport is essential for the viable operation of fusion power plants 2 DTU Physics SCT-2012 05-06-2012
Tokamak configuration – edge/SOL Conditions at the edge determine plasma performance SOL 3 DTU Physics SCT-2012 05-06-2012
Turbulence and transport Cross field transport of particles and heat in magnetically confined plasmas is dominated by anomalous - turbulent - transport! In the edge/scrape-off-layer (SOL) region transport is strongly intermittent and characterized by: large-amplitude, radially propagating blob-like structures of particles and heat, generated close to the last closed flux surface results in localized power loads at plasma facing components lasting influence on the chamber wall and other plasma facing components strong demands on materials Observed under a variety of conditions: e.g., Zweben Phys. Fluids 28 974 (1985); Boedo et al PoP 10 , 1670 (2003); Zweben et al . Nucl. Fus. 44 , 134 (2004); Grulke et al PoP 13 , 012306 (2006); Garcia et al. PPCF 48 , L1 (2006); Garcia et al. PPCF 49 , B47 (2007); Xu et al Nucl. Fus. 49, 092002 (2009); Nold et al. PPCF 52, 065005 (2010). ... Reviews : Zweben et al Plasma Physics Control Fusion 49 , S1 (2007); D’Ippolito et al. Phys Plasmas 18, 060501 (2011) 4 DTU Physics SCT-2012 05-06-2012
Intermittent density fluctuations In the SOL Inside last closed flux surface Typical density fluctuations in JET – Joint European Torus G. Xu et al Nucl Fusion 49 , 092002 (2009) 5 DTU Physics SCT-2012 05-06-2012
Blob propagation, example from NSTX Plasma blobs – field Separatrix 2cm 2cm aligned filaments - Antenna limiter detaches from shadow confinement region and propagate into the SOL, where the plasma can flow towards material surfaces. Zweben et al. Phys. Plasma 13 , 056114 (2006); PPCF 49 , S1 (2007). D’Ippolito et al. Phys. Plasmas 18, Shot 118152 208.853 ms 060501 (2011) Maqueda et al. IEA Workshop Edge Transport in Fusion Plasmas, Sept. 11 – 13, 2006, Krakow, Poland 6 DTU Physics SCT-2012 05-06-2012
Blob: parallel structure Blobs are filaments stretched long the magnetic field lines Magnetic field line Grulke et al Phys. Plasma 13 , 012306 (2006). Alcator C-Mod Quasi 2D dynamics 7 DTU Physics SCT-2012 05-06-2012
Propagation of a blob of plasma Toroidal magnetic field curved and weaker on the outboard side Consider a localized perturbation of the plasma density/pressure at the outboard side Charge separation by gradB and curvature drifts sets up a vertical E- field, resulting in a radial ExB velocity Radially propagating filament 8 DTU Physics SCT-2012 05-06-2012
Blob propagation Density Vorticity Initially a density perturbation and there is no flow; this arises by vertical charge polarization An isolated blob/filament accelerate and propagate a large radial distance Eventually the blob decelerates and disperses Garcia et al. Phys. Plasmas 12, 090701 (2005); 13 , 082309 (2006) 9 DTU Physics SCT-2012 05-06-2012
2D Equations for convection – fluid model “effective gravity” Rayleigh-Taylor type instability Ω – vorticity φ - stream function θ - electron pressure (cold ions) “Minimal” model! 10 DTU Physics SCT-2012 05-06-2012
Finite ion temperature – finite ion Larmor radius effect Important when blob size σ < 10 ρ T ion Larmor radius Ions then responds to a potential averaged over the fast gyro motion: resulting in a different ExB velocity than the electrons. ρ T leads to the derivation of the Gyro- fluid model – “lowest order kinetic effects” 11 DTU Physics SCT-2012 05-06-2012
Gyro-fluid simulation of blob propagation T i /T e = 0 T i /T e = 3 Propagation of density blob with finite ion temperature effects – compact density blob – like experiments - Madsen et al Phys. Plasma 18 , 112504 (2011) 12 DTU Physics SCT-2012 05-06-2012
Finite ion temperature blob propagation Blob size σ <5 ρ i ion Larmor radius : concentrated blobs Thermal energy I C carried by blob Finite ion temperature structures travel further and live longer. Broaden energy deposition (good), but may run into vessel wall (bad). Madsen et al Phys. Plasma 18 , 112504 (2011) 13 DTU Physics SCT-2012 05-06-2012
Blobs in turbulence – the ESEL model A self-consistent description of fluctuations and intermittent transport in the edge/SOL by employing the ESEL ( Edge SOL Electrostatic) model for interchange dynamics. 2D model perpendicular to magnetic field – dynamics/losses along magnetic field are parameterized • include separate plasma production ``edge'' and loss region ``SOL'', • allow self-consistent flows and profile relaxations, • profiles and fluctuations are NOT separated, • conserve particles and energy in collective dynamics. Results agree very well with experimental observations! Being applied at many laboratories. Garcia, Naulin, Nielsen, Rasmussen, PRL 92 165003 (2004); Phys. Plasma 12 , 090701 (2005); Physica Scripta T122 , 89 (2006). 14 DTU Physics SCT-2012 05-06-2012
Model domain: ESEL Slab domain at outboard midplane B B Local slab 2D geometry, (x,y) Including edge and SOL Global model with self-consistent profiles 15 DTU Physics SCT-2012 05-06-2012
Energy evolution and transfer 16 DTU Physics SCT-2012 05-06-2012
Spatial structure during burst - developing blob structure Particle density (left) and vorticity (right) during a burst ( Δ t = 500) Blob like-structure in plasma density and dipole structure in vorticity 17 DTU Physics SCT-2012 05-06-2012
Single point PDF, density fluctuations Scaled probability density distribution functions, PDF, of density fluctuations at P i . i > 2 – inside SOL - exponential tails, indicating strong blob structures. – Fit a Gamma distribution i >2 Skewness, S, and flatness, F, factors for the density fluctuations 18 DTU Physics SCT-2012 05-06-2012
Particle density flux Turbulent particle density flux : Γ = n v x = n v ExB Re-scaled PDF of particle density Re-scaled PDF of the flux measured at the probes, P i . turbulent radial ExB-velocity, Exponential tails: flux dominated v x , recorded at the probes P i . by strong bursts. Transport is NOT diffusive 19 DTU Physics SCT-2012 05-06-2012
Density fluctuations statistics and wave form Direct comparison with experimental results from the TCV- Tokamak, Lausanne: excellent quantitative agreement Conditionally averaged density Rescaled PDFs of density wave form in far SOL fluctuations in far SOL Characteristics of blob propagation Skewed to the positive side. Fits and fits well simulation results well simulation results. Garcia et al. PPCF 48 , L1 (2006); Nucl. Fusion 47, 667 (2007) 20 DTU Physics SCT-2012 05-06-2012
Particle density flux statistics Particle density flux: Γ = n v x = n v ExB Rescaled PDF of particle flux in far SOL at TCV Tokamak. Almost independent of n e . Flux dominated by strong bursts and agreement with simulation results. Exponential tail -- mean value only contain limited information Transport is NOT diffusive! No simple parameterization in terms of an effective diffusivity and a convection velocity Garcia et al., Nucl. Fusion 47, 667 (2007) 21 DTU Physics SCT-2012 05-06-2012
Parametrization of density flux? Scatter plot for the flux-gradient relation. TCV ESEL Naulin, J. Nucl. Mater. 263-265, 24 (2007) Garcia et al., J. Nucl. Mater. 263-265, 575 (2007) Transport modelling: linear combination of convection and diffusion: Transport cannot be parameterized by an effective diffusivity and a convection velocity 22 DTU Physics SCT-2012 05-06-2012
Summary Transport of particles and heat in the edge region of magnetically confined plasmas is dominated by large- amplitude, radially propagating blob-like structures of particles and heat No parameterisation of transport; not Fickian diffusion . The flux is given by its PDF, characterized by “fat” tails Experimental results well described by the ESEL-model Blob structures give rise to localized power loads on plasma facing components Strong demands on the materials and sets engineering limits to power plant operation For ITER, events with power loads of several MW/cm 2 are expected and control will be essential 23 DTU Physics SCT-2012 05-06-2012
Thanks for your attention 24 DTU Physics SCT-2012 05-06-2012
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