1. Chalmers University of Technology Simulation of toroidal and poloidal momentum including symmetry breaking toroidal effects J. Weiland 1, P. Mantica 2, T. Tala 3, V. Naulin 4, K. Crombe 5, A.G. Peeters 6 and D. Strinzi 7 1. Department of Radio and Space Science, Chalmers. University of Technology and Euratom-VR Association, S41296 Gothenburg, Sweden 2. Istituto di Fisica del Plasma CNR-EURATOM, via Cozzi 53, 20125 Milano, Italy 3. Association Euratom-Tekes, VTT, P.O. Box 1000, FIN-02044 VTT, Finland 4. Association Euratom-Risø DTU, Denmark 5. Association Euratom-Belgian State Department of Applied Physics, Ghent University, Rozier 44 B-9000 Ghent Belgium 6. Center for Fusion, Space and Astrophysics, Physics department, University of Warwick, CV4 7AL, Coventry UK 7. Department of Electrical and Computer Engineering, National Technical University of Athens, GR-157 73 Athens, Greece, Association Euratom –Hellenic Repuplic ITPA Naka March 31 – April 2 2009 1

2. Chalmers University of Technology Contents 3. Simulation of spinup of poloidal rotation. These simulations now also include toroidal momentum. The growth of a barrier, including toroidal and poloidal momentum spinup has been simulated by starting from a situation without barrier. 4. Stiffness in the presence of rotation. The effect of rotation has been studied for increasing temperature gradient. The stiffness is somewhat reduced due to rotation. Also zonal flows were included but did not make a difference 2. Simulation of toroidal momentum with torq modulation. Improvements with the new model 1. New fluid model for convective parts of toroidal momentum transport including toroidal symmetry breaking effects. (J. Weiland, R. Singh, H. Nordman. P.K. Kaw, A. Peeters and D. Strintzi IAEA TH/P8.29) In the new version the transport coefficients are averaged over the modeprofile 2

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 IAEA TH/P8.29) Using the direct method (Taylor and Wilson PPCF 38, 1999 (1996) and the solution for ITG modes (Davydova and Weiland PoP 7, 243 (2000)) we obtain the parallel mode number : 3

4. Chalmers University of Technology Averaging of transport over modeprofile The trend for cancellation of the real part is increased by introducing an averaging of the Doppler shift over the mode profile. This increases the transport. Assuming the correlation length to follow the fastest growing mode we also introduce: 4 where is the trapped fraction

5. Chalmers University of Technology Simulation of JET66128 In order to get a more accurate evaluation of the Prandtl number, a flux surface averaging has now been made also of χ i. This increases χ i somewhat because of non- Markovian resonance effects ____________ Experiment ………………… Simulation 5

6. Chalmers University of Technology JET66128 with no nonlinear averaging ____________ Experiment ………………… Simulation 6

7. Chalmers University of Technology Torqmodulation Amplitudes and phases of Vtor modulation. Points from exp. Thick lines from sim. 7

8. Chalmers University of Technology Diffusivities Transport coefficients 8 From best fit of exp data (empirical)

9. Chalmers University of Technology Prandtl number The diagonal curvature term here has a factor 2 Taking the ratio of χ φ and χ i (diagonal) we find Since at ITG marg. stab, which typically occurs near the axis, we initially get a growing Pr as a function of r/a 9

10. Chalmers University of Technology Prandtl number cont The figure shows Pr as a function of x=r/a for JET 68128. 10

11. Chalmers University of Technology Simulation of JET69454 with initial conditions from the exp. ____________ Experiment ………………… Simulation 11

12. Chalmers University of Technology Simulation of JET69454 with initial conditions from the exp. ____________ Experiment ………………… Simulation -- -- -- -- -- -- -- -- -- -- -- Neoclassical 12

13. Chalmers University of Technology Simulation of JET 69454 with Vtor frozen ____________ Experiment ………………… Simulation 13

14. Chalmers University of Technology Simulation of JET 69454 with Vtor frozen ____________ Experiment ………………… Simulation -- -- -- -- -- -- -- -- -- -- -- Neoclassical The sign of sim Vpol is for D, Experimental is for Carbon ! Thus sign is OK! 14 The anomalous rotation is symmetrical. The direction is determined by initial neoclassical push!

15. Chalmers University of Technology Simulation of JET69454 without initial barrier ____________ Start profile ………………… Simulation 15

16. Chalmers University of Technology Simulation of JET69454 without initial barrier and without smoothing ____________ Initial profile ………………… Simulation -- -- -- -- -- -- -- -- -- -- -- Neoclassical 16

17. Chalmers University of Technology Stiffness in the presence of rotation Weiland: Grey norot, Green Wexb=1.110^4, Purple Wexb = 2.1 10^4, Dimits shift included in calc. but no effect 17

18. Chalmers University of Technology Summary A new model for toroidal momentum transport systematically derived from fluid equations has been tested Good agreement with experiment in steady state In the latest version also reasonable agreement for modulations inside r/a = 0.5 Diffusivities need to be larger outside r/a = 0.5 However, so far (for JET66128) results are close to those obtained by the previously used Hahm model 18

19. Chalmers University of Technology Summary cont The averaging of diffusivities over modeprofiles has a significant effect in increasing transport. However, at least for JET 66128 the new physics effects, not included in the Hahm model, have only a minor impact. We can now simulate the formation of a transport barrier from the start, including also poloidal and toroidal momentum. 19

20. Chalmers University of Technology Summary cont. We have found a rather moderately reduced stiffness when we increase rotation. It appears to be of the magnitude we expect from using the Walts rule in a situation when transport scales as the square of the growthrate i.e. χ≈(γ- ω exb ) 2 The Dimits shift, which is included in our calculations, does not have an effect in our case. However, it does for the GS2 results. This means that there is a significant difference although the graphs are quite similar. 20