2. Kursus i Plasmafysik, OPL, Risø Juni 6 - 24, 2005 Turbulence, mixing and transport, June 21, 2005  Turbulence, mixing and transport in magnetized plasmas Ultimate goal: Predictive model Odd-Erik Garcia, Volker Naulin, Anders H. Nielsen, Jens Juul Rasmussen Turbulence is found to dominate the transport of plasma across the confining magnetic field. In the edge region turbulent transport is order of magnitude stronger than classical – collision dominated – transport. All lost plasma must go through the edge region! Numerical and theoretical studies of turbulence and transport! Purpose: Understanding turbulence and the associated anomalous transport in magnetized plasmas

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

4. Kursus i Plasmafysik, OPL, Risø Juni 6 - 24, 2005 Turbulence, mixing and transport, June 21, 2005 Turbulence? Every day phenomena: nature --- administration Leonardo da Vinci : 1452 –1519van Gogh Turbolenza

5. Kursus i Plasmafysik, OPL, Risø Juni 6 - 24, 2005 Turbulence, mixing and transport, June 21, 2005 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 1903 - 1987

6. Kursus i Plasmafysik, OPL, Risø Juni 6 - 24, 2005 Turbulence, mixing and transport, June 21, 2005 Turbulence: effective mixer Turbulence Laminar

7. Kursus i Plasmafysik, OPL, Risø Juni 6 - 24, 2005 Turbulence, mixing and transport, June 21, 2005 Turbulence in a magnetized plasma ITER

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

9. Kursus i Plasmafysik, OPL, Risø Juni 6 - 24, 2005 Turbulence, mixing and transport, June 21, 2005 Plasma Turbulence is ”2-Dim” Inverse cascade: energy concentrate at large scales. Vortical structures dominate the dynamics Vortex

10. Kursus i Plasmafysik, OPL, Risø Juni 6 - 24, 2005 Turbulence, mixing and transport, June 21, 2005 Self-organisation Coherent structures

11. Kursus i Plasmafysik, OPL, Risø Juni 6 - 24, 2005 Turbulence, mixing and transport, June 21, 2005 Dipole vortices Vortices of opposite vorticity do not cancel Red : positive vorticity Blue : negative vorticity

12. Kursus i Plasmafysik, OPL, Risø Juni 6 - 24, 2005 Turbulence, mixing and transport, June 21, 2005 Vortex merger Like signed vortices merge

13. Kursus i Plasmafysik, OPL, Risø Juni 6 - 24, 2005 Turbulence, mixing and transport, June 21, 2005 Vortices trap particles Dipole vortices Red : positive vorticity Blue : negative vorticity Passive tracer field Vortices : transport barriers

14. Kursus i Plasmafysik, OPL, Risø Juni 6 - 24, 2005 Turbulence, mixing and transport, June 21, 2005 3-Dimentional vortices

15. Kursus i Plasmafysik, OPL, Risø Juni 6 - 24, 2005 Turbulence, mixing and transport, June 21, 2005 Vortex ring Vortex ring bubble Silver ring

16. Kursus i Plasmafysik, OPL, Risø Juni 6 - 24, 2005 Turbulence, mixing and transport, June 21, 2005 Particle dispersion Potential Density Drift-wave turbulence

17. Kursus i Plasmafysik, OPL, Risø Juni 6 - 24, 2005 Turbulence, mixing and transport, June 21, 2005 Turbulent flux: Particle flux: Γ = n v = n v ExB Flux PDF The probability distribution function for the plasma flux across the magnetic field is strongly non-Gaussian, i.e., strong bursts are dominating!

18. Kursus i Plasmafysik, OPL, Risø Juni 6 - 24, 2005 Turbulence, mixing and transport, June 21, 2005 Modelling turbulence at the edge Two-dimensional dynamics: outboard midplane

19. Kursus i Plasmafysik, OPL, Risø Juni 6 - 24, 2005 Turbulence, mixing and transport, June 21, 2005 Modelling turbulence at the edge Global model 2D: self consistent evolution of pressure profile The source region is separated from the loss region, SOL

20. Kursus i Plasmafysik, OPL, Risø Juni 6 - 24, 2005 Turbulence, mixing and transport, June 21, 2005 Particle flux at the edge Strong possitive flux events! Pdf of edge particle flux

21. Kursus i Plasmafysik, OPL, Risø Juni 6 - 24, 2005 Turbulence, mixing and transport, June 21, 2005 Edge turbulence transport in JET Large intermittent burst B. Gonçalves: 11 th European Fusion Physics Workshop, Heraklion, Crete 8-11 Dec. 2003. Pdf of flux

22. Kursus i Plasmafysik, OPL, Risø Juni 6 - 24, 2005 Turbulence, mixing and transport, June 21, 2005 Edge transport events Bursts of density and heat are released and propagate far out in the SOL Strong lasting effect on plasma facing components

23. Kursus i Plasmafysik, OPL, Risø Juni 6 - 24, 2005 Turbulence, mixing and transport, June 21, 2005 Blobs in Experiment Alcator C-Mod ( O. Grulke et al 2004) H-alpha light: proportional to density. CCD: Looking along B-field

24. Kursus i Plasmafysik, OPL, Risø Juni 6 - 24, 2005 Turbulence, mixing and transport, June 21, 2005 Blobs aligned with B-field Mast, Culham UK (Kirk et al 2005) H-alpha light,

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

26. Kursus i Plasmafysik, OPL, Risø Juni 6 - 24, 2005 Turbulence, mixing and transport, June 21, 2005 Dynamics of impurity density Projected from a 3D fluxtube simulation onto a poloidal cut Timespan: 120 μs Poloidal Asymmetry in transport, pinch

27. Kursus i Plasmafysik, OPL, Risø Juni 6 - 24, 2005 Turbulence, mixing and transport, June 21, 2005 Film blobs: 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.