1. Chalmers University of Technology Simulations of the formation of transport barriers including the generation of poloidal spinup due to turbulence J. Weiland 1,, T. Tala 2, V. Naulin 3, K. Crombe 4 and P. Mantica 5 and the JET-EFDA contributors 1. Department of Radio and Space Science, Chalmers. University of Technology and Euratom-VR Association, S41296 Gothenburg, Sweden 2 Association Euratom-Tekes, VTT, P.O. Box 1000, FIN-02044 VTT, Finland 3. Association Euratom-Risø DTU, Denmark 4. Association Euratom-Belgian State Department of Applied Physics, Ghent University, Rozier 44 B-9000 Ghent Belgium 5.Istituto di Fisica del Plasma CNR-EURATOM, via Cozzi 53, 20125 Milano, Italy ITPA Transport and Confinement meeting Culham March 22 – 25 2010

2. Chalmers University of Technology Contents We have simulated the formation of a transport barrier in four channels, Ion and Electron temperatures and Toroidal and Poloidal momentum simultaneously. The transport barrier is formed due to simultaneous pinches in toroidal and poloidal momenta A spinup in the poloidal momentum with the same location and approximate magnitude as in the experiment is generated Density is kept fixed as experimental. However there are no traces of barrier in the density profile. Poloidal spinup is due to Zonal flows. The q dependence of these is changed by the parallel perturbed heatflow now added to the model

3. Chalmers University of Technology New fluid model for convective toroidal momentum transport (J. Weiland, R. Singh, H. Nordman. P.K. Kaw, A. Peeters and D. Strintzi Nuclear Fusion 49, 065033 (2009)) We use the ExB flux of this quantity The poloidal flux is as before

4. Chalmers University of Technology Inclusion of reactive parallel heatflow This is a purely reactive term which modifies the effects of parallel ion motion in the model. Thus it influences the q scaling. It is usually somewhat stabilizing but can sometimes be destabilizing. We continue to use one parameter dependent correlation length. It is different for ITG and TE modes. The most recent is that for the TE mode which is: where is the trapped fraction

5. Chalmers University of Technology Simulation of JET69454 As seen in the initial profiles there was no initial trace of a barrier. The density was kept fixed and did not show any sign of barrier.

6. Chalmers University of Technology Simulation of JET69454 without initial barrier without parallel heatflow ____________ Start profile ………………… Simulation

7. Chalmers University of Technology Simulation of JET69454 without initial barrier and without parallel heatflow ___________ Initial condition …….……….. Simulation -- -- -- -- -- -- -- -- -- -- -- Neoclassical 16

8. Chalmers University of Technology Simulation of JET69454 with parallel heatflow ____________ Start profile ………………… Simulation

9. Chalmers University of Technology Simulation of JET69454 cont ___________ Initial condition …….……….. Simulation -- -- -- -- -- -- -- -- -- -- -- Neoclassical

10. Chalmers University of Technology What determines the location of the barrier? The barrier is formed where the heatflux is large and the magnetic shear still is small

11. Chalmers University of Technology Simulation of JET69454 with increased q minimum q = 3 Zonal flow increases with q!

12. Chalmers University of Technology Mechanism of poloidal spinup

13. Chalmers University of Technology Electrostatic model No poloidal spinup Almost no barrier in Vtor but the toroidal momentum pinch leads to strong central rotation

14. Chalmers University of Technology Electrostatic model No well defined barrier. However still high central Ti due to toroidal momentum pinch

15. Chalmers University of Technology Electrostatic model without trapping Electrostatic model without trapping Here transport is reduced so much that we can see a tendency for an edge barrier in Vtor

16. Chalmers University of Technology Electrostatic model without trapping No sharp barrier without poloidal spinup but high central Ti due to toroidal rotation

17. Chalmers University of Technology Simulation of JET72746 The almost flat q profile does not give a well defined location of a barrier

18. Chalmers University of Technology JET72746 Exp. prof. T=45.05 After increase in Vpol but before barrier

19. Chalmers University of Technology Simulation of JET72746 including parallel heatflow ____________ Start profile ………………… Simulation

20. Chalmers University of Technology Simulation of JET72746 cont No data for Vpol but graph as a function of R indicates a barrier around r/a = 0.4 ___________ Initial condition Vtor reversed! …….……….. Simulation -- -- -- -- -- -- -- -- -- -- -- Neoclassical

21. Chalmers University of Technology Directions of rotation The poloidal and toroidal rotations shown here are for the main ion species (Deuterium) while the rotation is measured for impurities. Since the Reynolds stress is symmetric with respect to direction of rotation it is actually the neoclassical rotation that gives the initial ”push” and thus determines the direction of rotation. The neoclassical rotation usually has opposite signs for deuterium and impurities, thus the measured poloidal rotation is usually in the opposite direction to the simulated. The toroidal rotation is not directly influenced by neoclassical effects and here the measured and simulated rotations are generally in the same direction. This is, however, not so for 72746. Of course the rotation is still measured for impurities and the only apparent reason for reversal would be the symmetry breaking effect of the gradient of the poloidal rotation on the average K_parallel.

22. Chalmers University of Technology Summary Previous results on the formation of a transport barriere have been confirmed using a refined model Tests of convergence with up to 99 gridpoints have been performed The q dependence has changed when the parallel heatflow was included. The poloidal spinup increases with higher q. Good agreement with experiment also in steady state A poloidal spinup occurs only in transport barriers. However, sometimes the toroidal momentum pinch alone can give a transport barrier.arriers The ITG mode is stable and the TE mode marginally unstable in

23. Chalmers University of Technology Summary cont The poloidal spinup seems to require both electron trapping and electromagnetic effects. The location of the barrier is due to a combination of small shear large flux