1. Summary on transport IAEA Technical Meeting, Trieste Italy Presented by A.G. Peeters

2. Contents Toroidal momentum transport (S. Newton, A.G. Peeters, G. Falchetto [other session]) Gyro-kinetic calculations (Y.A. Sarazin, V. Grandgirard, G. Rewoldt, B. Scott) The Edge (M. Tokar, N. Kasuya, N. Bisai, J.J. Ramussen, V.I. Maslov, S. H. Mueller) Stabilization of turbulence P.K. Kaw

3. S. Newton Redistribution of impurities changes toroidal momentum tranport Restricted to subsonic rotation to calculate neoclassical terms Z eff = 1 - recover Braginskii, Hinton & Wong results Most experimentally relevant limit: conventional aspect ratio,      << 1, strong impurity redistribution

4. Numerical evaluation using magnetic surfaces of MAST -  = 0.14 N EOCLASSICAL C OEFFICIENTS 0.10.20.30.40.5 0.005 0.010 0.015 ion Mach number 0.00024 Transport ~ 10 times previous predictions - increase with impurity content - increase with Mach number as impurity redistribution increases previous level

5. Main Conclusions At conventional aspect ratio, with impurities pushed towards outboard side, angular momentum flux seen to increase by a factor of  -3/2  now typical of banana regime Radial bulk ion pressure and temperature gradients are the primary driving forces, not rotation shear  strong density and temperature gradients sustain strongly sheared E r Spontaneous toroidal rotation may arise in plasmas with no external angular momentum source

6. Anomalous transport

7. Gyro kinetic simulations

8. (analogous to "Dimits graph" with the same code) Y.A. Sarazin – 2D interchange turbulence (kinetic as well as fluid description) Transition in kinetic simulations not well understood (Same zonal flows) Zonal flows do not explain the whole difference between kinetic and fluid simulation

9. 2 fluid moments are not enough Ortho-normal basis L p   Slow convergence towards 0 Suggest any fluid description of the problem should account for high order moments M k (k>2) Αlternative closure motivated by entropy production rates – Works well in the linear regime (nonlinear ??)

10. V. Grandgirard Interplay of density profile and zonal flow in slab ITG turbulence Semi Lagrangian method (Good energy conserv.) Currently 4D slab ITG Zonal flows are strongly connected with the background density gradient Density gradient both linearly as well as non- linearly stabilizing Extremely nice picture

11. G. Rewoldt – Progress in the development of the GTC code ETG studies (reviewed by T.S. Hahm?) General geometry Parallel velocity nonlinearity Electromagnetic effects Neoclassical studies

14. B.D. Scott, Edge turbulence

16. The Edge

17. M. Tokar – Density limits in tokamaks Alternative Mechanism for MARFE Formation: instability of plasma recycling on inner wall Plasma Flows  B Plasma flows ||B Heat flux to the edge Charged particle losses to wall: Energy losses with particles: Neutrals

18. Model for edge anomalous transport Linearized parallel Ohm’s, Faraday’s and Ampere’s law, ion momentum balance, quasi-neutrality, ion continuity equation  Eigen function equation for electric potential perturbation of Mathieu’s type: DADRB MARFE at HFS: result of recycling instability at high heating when Shafranov shift dominates poloidal asymmetry Detachment at LFS: develops at lower heating power because of transition to anomalous transport driven by DRB- modes

19. N. Kasuya – Poloidal shock formation And particle transport in the H-mode

21. N. Bisai and J.J. Rasmussen (2 independent papers) – 2D SOL turbulence Formation of density blob Fig. From Bisai (2D cold ions, edge and SOL) Density blob forms near edge-to-SOL regions by the detachment from density streamer. In the SOL structures move mostly radially and eventually die out (small structures live shorter, not all move)

22. From J.J.Rasmussen (2D SOL turbulence warm ions)

23. V.I. Maslov Density transport due to convection and diffusion Equation for density evolution due to convective cells (finite lifetime) combined with diffusive regions Also propagation of the cells due to electric field was studied

24. S. H. Mueller – Experiments on TORPEX Important Parameter: The Vertical Magnetic Field B z B BB v  B,e v  B,i E Toroidicity drifts lead to charge separation and electric fields F = -eE || Generation of Parallel flows  „Short circuiting“ of electric field Collisions inhibit parallel motion  Equilibrium  B cscs Sheath parallel loss  sin  E ExB loss  1/sin 2  Competition between two basic loss channels: Implications for confinement Important mechanism Theory and measurement of confinement time: S. H. Müller et al, PRL 2004  Important role of B z for basic confinement

25. Profiles as a Function of B z 1 Shot = 1 Profile = 1 Movie Frame

26. P.K. Kaw – Stabilization of turbulence with RF waves Use of the ponderomotive force of the wave field to compensate the unfavourable curvature force Stabilization of turbulence (over a region of the size of the skin depth) for ITER like parameters is possible using 10 MW RF Reduction due to the change of chaotic behaviour through the introduction of small perturbations in the electric field