Turbulence and Transport in Magnetically Confined Plasma Jens Juul - - PowerPoint PPT Presentation

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Turbulence and Transport in Magnetically Confined Plasma Jens Juul - - PowerPoint PPT Presentation

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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 Ris Campus, DK-4000 Roskilde

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Department of Physics Technical University of Denmark

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

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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

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Tokamak configuration – edge/SOL

SOL Conditions at the edge determine plasma performance

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Turbulence and transport

  • 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)

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:

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Typical density fluctuations in JET – Joint European Torus

  • G. Xu et al Nucl Fusion 49, 092002 (2009)

In the SOL Inside last closed flux surface

Intermittent density fluctuations

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Blob propagation, example from NSTX

2cm

2cm 208.853 ms

Separatrix Antenna limiter shadow

Shot 118152

Plasma blobs – field aligned filaments - detaches from 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, 060501 (2011) Maqueda et al. IEA Workshop Edge Transport in Fusion Plasmas, Sept. 11 – 13, 2006, Krakow, Poland

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Blob: parallel structure

Magnetic field line

Blobs are filaments stretched long the magnetic field lines

Quasi 2D dynamics

Grulke et al Phys. Plasma 13, 012306 (2006). Alcator C-Mod

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Propagation of a blob of plasma

Consider a localized perturbation of the plasma density/pressure at the

  • utboard side

Charge separation by gradB and curvature drifts sets up a vertical E- field, resulting in a radial ExB velocity Toroidal magnetic field curved and weaker on the outboard side Radially propagating filament

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Blob propagation

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 Density Vorticity

Garcia et al. Phys. Plasmas 12, 090701 (2005); 13, 082309 (2006)

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2D Equations for convection – fluid model

“effective gravity” Ω – vorticity φ- stream function θ- electron pressure (cold ions)

Rayleigh-Taylor type instability

“Minimal” model!

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Finite ion temperature – finite ion Larmor radius effect

Important when blob size σ< 10ρT ion Larmor radius Ions then responds to a potential averaged over the fast gyro motion: ρT resulting in a different ExB velocity than the electrons. leads to the derivation of the Gyro- fluid model – “lowest order kinetic effects”

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Madsen et al Phys. Plasma 18, 112504 (2011)

Gyro-fluid simulation of blob propagation

Ti/T

e = 0

Ti/T

e = 3

Propagation of density blob with finite ion temperature effects – compact density blob – like experiments -

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Finite ion temperature blob propagation

Thermal energy IC 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)

Blob size σ<5 ρi ion Larmor radius : concentrated blobs

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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 ScriptaT122, 89 (2006).

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Slab domain at

  • utboard midplane
  • Local slab 2D geometry, (x,y)
  • Including edge and SOL
  • Global model with self-consistent profiles

B 

B 

Model domain: ESEL

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Energy evolution and transfer

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Spatial structure during burst - developing blob structure

Particle density (left) and vorticity (right) during a burst (Δt = 500) Blob like-structure in plasma density and dipole structure in vorticity

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Single point PDF, density fluctuations

Scaled probability density distribution functions, PDF, of density fluctuations at Pi . 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

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Particle density flux

Re-scaled PDF of particle density flux measured at the probes, Pi. Exponential tails: flux dominated by strong bursts. Re-scaled PDF of the turbulent radial ExB-velocity, vx, recorded at the probes Pi .

Turbulent particle density flux : Γ = n vx = n vExB

Transport is NOT diffusive

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Density fluctuations statistics and wave form

Conditionally averaged density wave form in far SOL Characteristics of blob propagation and fits well simulation results Rescaled PDFs of density fluctuations in far SOL Skewed to the positive side. Fits well simulation results.

Garcia et al. PPCF 48, L1 (2006); Nucl. Fusion 47, 667 (2007)

Direct comparison with experimental results from the TCV- Tokamak, Lausanne: excellent quantitative agreement

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Particle density flux statistics

Rescaled PDF of particle flux in far SOL at TCV Tokamak. Almost independent of ne. 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)

Particle density flux: Γ = n vx = n vExB

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Scatter plot for the flux-gradient relation.

Parametrization of density flux?

Transport cannot be parameterized by an effective diffusivity and a convection velocity

Garcia et al., J. Nucl. Mater. 263-265, 575 (2007) Naulin, J. Nucl. Mater. 263-265, 24 (2007)

TCV ESEL

Transport modelling: linear combination of convection and diffusion:

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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/cm2 are

expected and control will be essential

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Thanks for your attention