Kursus i Plasmafysik, OPL, Risø Juni 6 - 24, 2005Turbulence, mixing and transport, June 21, 2005

Turbulence, mixing and transport Turbulence, mixing and transport

in magnetized plasmas in magnetized plasmas

Ultimate goal: Predictive modelOdd-Erik Garcia, Odd-Erik Garcia, Volker NaulinVolker Naulin, , Anders H.Anders H. NielsenNielsen,, Jens Juul Rasmussen Jens Juul Rasmussen

Turbulence is found to dominate the transport of plasma across the confining Turbulence is found to dominate the transport of plasma across the confining magnetic field.magnetic field.In the edge region turbulent transport is order of magnitude stronger than In the edge region turbulent transport is order of magnitude stronger than classical – collision dominated – transport.classical – collision dominated – transport.

All lost plasma must go through the edge region!All lost plasma must go through the edge region!

Numerical and theoretical studies of turbulence and transport!Numerical and theoretical studies of turbulence and transport!Purpose:Purpose:Understanding turbulence and the associated anomalous Understanding turbulence and the associated anomalous transport in magnetized plasmastransport in magnetized plasmas

Kursus i Plasmafysik, OPL, Risø Juni 6 - 24, 2005Turbulence, mixing and transport, June 21, 2005

Content:Content:

A general description of turbulence Turbulence in fluids Turbulence and mixing/transport Turbulence in plasmas, quasi 2-dimensional Vortex structures Vortex structures and transport Plasma edge turbulence: modelling comparison

with experiments Transport of impurities.

Kursus i Plasmafysik, OPL, Risø Juni 6 - 24, 2005Turbulence, mixing and transport, June 21, 2005

Turbulence?Turbulence?

Every day phenomena: nature --- administration

Leonardo da Vinci : 1452 –1519 van Gogh

Turbolenza

Kursus i Plasmafysik, OPL, Risø Juni 6 - 24, 2005Turbulence, mixing and transport, June 21, 2005

Turbulence? Turbulence?

Irregularity and randomness

Fluctuations on all scales

E(k) ~ k-5/3

”Unpredictability”

Diffusivity, rapid mixing

Energy cascade, input at large scales – dissipation at small scales

Nonlinearity dominates

A.N. Kolmogorov A.N. Kolmogorov 1903 - 19871903 - 1987

Kursus i Plasmafysik, OPL, Risø Juni 6 - 24, 2005Turbulence, mixing and transport, June 21, 2005

Turbulence: effective mixerTurbulence: effective mixer

Turbulence Laminar

Kursus i Plasmafysik, OPL, Risø Juni 6 - 24, 2005Turbulence, mixing and transport, June 21, 2005

Turbulence in a magnetized plasmaTurbulence in a magnetized plasma

ITER

Kursus i Plasmafysik, OPL, Risø Juni 6 - 24, 2005Turbulence, mixing and transport, June 21, 2005

Plasma turbulencePlasma turbulence The turbulence degrades the confinement:

Turbulent transport is the main cause for loosing plasma across the magnetic field lines

Numerical Tokamak, Dorland et al.

Our turbulence studies are concentrated on edge turbulence

Lost plasma has to go through the edge!

Kursus i Plasmafysik, OPL, Risø Juni 6 - 24, 2005Turbulence, mixing and transport, June 21, 2005

Plasma Turbulence is ”2-Dim”Plasma Turbulence is ”2-Dim”

Inverse cascade: energy concentrate at large scales.

Vortical structures dominate the dynamics

VortexVortex

Kursus i Plasmafysik, OPL, Risø Juni 6 - 24, 2005Turbulence, mixing and transport, June 21, 2005

Self-organisation Coherent Self-organisation Coherent structuresstructures

Kursus i Plasmafysik, OPL, Risø Juni 6 - 24, 2005Turbulence, mixing and transport, June 21, 2005

Dipole vorticesDipole vortices

Vortices of opposite Vortices of opposite vorticity do vorticity do notnot cancel cancel

RedRed : positive vorticity : positive vorticity

BlueBlue : negative vorticity : negative vorticity

Kursus i Plasmafysik, OPL, Risø Juni 6 - 24, 2005Turbulence, mixing and transport, June 21, 2005

Vortex mergerVortex merger

Like signed vortices Like signed vortices mergemerge

Kursus i Plasmafysik, OPL, Risø Juni 6 - 24, 2005Turbulence, mixing and transport, June 21, 2005

Vortices trap particlesVortices trap particles

Dipole vorticesDipole vortices

RedRed : positive vorticity : positive vorticity BlueBlue : negative vorticity : negative vorticity

Passive tracer Passive tracer fieldfield

Vortices : transport Vortices : transport barriersbarriers

Kursus i Plasmafysik, OPL, Risø Juni 6 - 24, 2005Turbulence, mixing and transport, June 21, 2005

3-Dimentional vortices3-Dimentional vortices

Kursus i Plasmafysik, OPL, Risø Juni 6 - 24, 2005Turbulence, mixing and transport, June 21, 2005

Vortex ringVortex ring

Vortex ring Vortex ring bubblebubble

Silver ringSilver ring

Kursus i Plasmafysik, OPL, Risø Juni 6 - 24, 2005Turbulence, mixing and transport, June 21, 2005

Particle dispersion Particle dispersion

Potential

Density

Drift-wave turbulenceDrift-wave turbulence

Kursus i Plasmafysik, OPL, Risø Juni 6 - 24, 2005Turbulence, mixing and transport, June 21, 2005

Turbulent flux:Turbulent flux:

Particle flux: Γ = n v = n vExB

Flux PDFFlux PDF

The probability distribution function for the plasma flux across the magnetic field is strongly non-Gaussian, i.e., strong bursts are dominating!

Kursus i Plasmafysik, OPL, Risø Juni 6 - 24, 2005Turbulence, mixing and transport, June 21, 2005

Modelling turbulence at the edgeModelling turbulence at the edge

Two-dimensional dynamics: outboard midplaneTwo-dimensional dynamics: outboard midplane

Kursus i Plasmafysik, OPL, Risø Juni 6 - 24, 2005Turbulence, mixing and transport, June 21, 2005

Modelling turbulence at the edge Modelling turbulence at the edge

Global model 2D: self consistent evolution of pressure profile

The source region is separated from the loss region, SOL

Kursus i Plasmafysik, OPL, Risø Juni 6 - 24, 2005Turbulence, mixing and transport, June 21, 2005

Particle flux at the edgeParticle flux at the edge

Strong possitive flux events!

Pdf of edge particle fluxPdf of edge particle flux

Kursus i Plasmafysik, OPL, Risø Juni 6 - 24, 2005Turbulence, mixing and transport, June 21, 2005

Edge turbulence transport in JETEdge turbulence transport in JET

-20 -10 0 10 20 3010-4

10-3

10-2

10-1

JET #54271

PD

F

ExB / <

ExB>

Large intermittent burstLarge intermittent burst

65.5255 65.5260 65.5265-10

0

10

20

ExB

/ < E

xB>

time (s)

JET #54271

B. Gonçalves: 11th European Fusion Physics Workshop, Heraklion, Crete 8-11 Dec. 2003

. .

Pdf of fluxPdf of flux

Kursus i Plasmafysik, OPL, Risø Juni 6 - 24, 2005Turbulence, mixing and transport, June 21, 2005

Edge transport eventsEdge transport events

Bursts of density and heat are released and propagate far out in the SOL

Strong lasting effect on plasma facing components

Kursus i Plasmafysik, OPL, Risø Juni 6 - 24, 2005Turbulence, mixing and transport, June 21, 2005

Blobs in ExperimentBlobs in ExperimentAlcator C-Mod (Alcator C-Mod (O. Grulke et al 2004)O. Grulke et al 2004)

H-alpha light: proportional to density. CCD: Looking along B-fieldH-alpha light: proportional to density. CCD: Looking along B-field

Kursus i Plasmafysik, OPL, Risø Juni 6 - 24, 2005Turbulence, mixing and transport, June 21, 2005

Blobs aligned with B-fieldBlobs aligned with B-fieldMast, Culham UK Mast, Culham UK (Kirk et al 2005)(Kirk et al 2005)

H-alpha light,H-alpha light,

Kursus i Plasmafysik, OPL, Risø Juni 6 - 24, 2005Turbulence, mixing and transport, June 21, 2005

Impurity transport.Impurity transport.

3-Dim simulations, full geometry, flux-tube coordinated

Global variations self-consistent profiles

Turbulent transport statistics; transport barriers

Impurities are also transported by the turbulence.

Modelled by passive tracer transport: e.g., trace tritium experiments

Poloidal projection of 3-D turbulent field

Kursus i Plasmafysik, OPL, Risø Juni 6 - 24, 2005Turbulence, mixing and transport, June 21, 2005

Dynamics of impurity densityDynamics of impurity density

Projected from a 3D fluxtube simulation onto a poloidal cut

Timespan: 120 μs

Poloidal Asymmetry in transport, pinch

Kursus i Plasmafysik, OPL, Risø Juni 6 - 24, 2005Turbulence, mixing and transport, June 21, 2005

Film blobs:Film blobs:Summary:Summary:

We are approaching models with results that can be compared directly with experiments!

In hot plasmas: Dynamics of fast ions, alphas etc. Confinement!

-------------------------------------------------- Spændende Eksamensprojekter og PhD

Projekter. Med ITER mange nye udfordringer.