1. 1 Peter de Vries – ITPA T meeting Culham – March 2010 P.C. de Vries 1,2, T.W. Versloot 1, A. Salmi 3, M-D. Hua 4, D.H. Howell 2, C. Giroud 2, V. Parail 2, G. Saibene 5, T. Tala 6 and JET EFDA Contributors § JET-EFDA Culham Science Centre, Abingdon, OX14 3DB, UK. 1 FOM institute for Plasma Physics Rijnhuizen, Association EURATOM-FOM, Netherlands 2 EURATOM/CCFE Association, Culham Science Centre, Abingdon, OX14 3DB, UK. 3 Association Euratom-Tekes, Helsinki University of Technology, P.O. Box 4100, 02015 TKK, Finland. 4 Imperial College, SW7 2BY, London, UK. 5 Fusion for Energy Joint Undertaking, 0819 Barcelona, Spain. 6 Association Euratom-Tekes, VTT, P.O. Box 1000, 02044 VTT, Finland. § Annex to F. Romanelli, Fusion Energy 2008 (Proc. 22nd IAEA Conf., Geneva, 2008) IAEA Vienna. Momentum transport studies in JET H-mode discharges with an enhanced toroidal field ripple

2. 2 Peter de Vries – ITPA T meeting Culham – March 2010 Why study plasma rotation?  Plasma rotation provides stability and rotational shear may suppress turbulence.  In order to accurately predict ITER performance, one should understand the impact of rotation and be able to predict rotation profiles Is momentum transport related to energy transport  Hence, previously it was often assumed that rotation profiles follow those of the temperature  But are the momentum and heat sources the same?  How effective is the momentum pinch  visible impact on profiles?

3. 3 Peter de Vries – ITPA T meeting Culham – March 2010 Global Momentum Confinement Rotation Database 1 with predominantly NBI heated plasmas  Database has >500 entries from various scenarios  Momentum confinement time scales with energy confinement time [1] P.C. de Vries, et al. Nucl. Fusion 48 (2008) 065006.

4. 4 Peter de Vries – ITPA T meeting Culham – March 2010 Global Momentum Confinement Rotation Database 1 with predominantly NBI heated plasmas  Database has >500 entries from various scenarios  But the ratio can vary between 0.8 and 1.6 [1] P.C. de Vries, et al. Nucl. Fusion 48 (2008) 065006.

5. 5 Peter de Vries – ITPA T meeting Culham – March 2010 Momentum Transport A detailed look shows that the effective momentum diffusivity in the core is much lower than the ion heat diffusivity 1.  Turbulent theory predicts that they should be the same (as a fluid)  Prandtl number is the ratio of viscosity and heat diffusivity [1] P.C. de Vries, et al. PPCF 48 (2006) 1693.

6. 6 Peter de Vries – ITPA T meeting Culham – March 2010 Momentum Pinch Theory and experiments have shown the existence of inward momentum convention  momentum pinch 1,2 Is the lower effective Prandtl number due to this pinch? Will the gradient of the rotation be affected by the rotation in the outer part of the plasma? What is the magnitude of the pinch in standard H-mode discharges? (Is it relevant?) [1] A.G. Peeters, Phys. Rev. Lett. 98 (2007) 265003. [2] T. Tala, et al. Phys. Rev. Lett. 102 (2009) 075001.

7. 7 Peter de Vries – ITPA T meeting Culham – March 2010 Effect of TF ripple [1] P.C. de Vries, et al. Nucl. Fusion 48 (2008) 035007. A toroidal field ripple breaks the toroidal symmetry  The TF ripple at JET can be varied from 0.08% up to 1.5%  At JET rotation with co-current NBI was found to decrease with increasing TF ripple 1  Effect larger with normal NBI

8. 8 Peter de Vries – ITPA T meeting Culham – March 2010 Effect of TF ripple Tuning the TF ripple allowed us to change the rotation independently from its gradient Hence TF ripple experiments could be used to decouple the diffusive and convective terms in the momentum balance equation (from discharge to discharge).

9. 9 Peter de Vries – ITPA T meeting Culham – March 2010 How does TF ripple affect rotation? Fast particle orbits in a ‘ripple’ toroidal magnetic field can be calculated by the Orbit Following Monte Carlo code ASCOT 1  Determine induced toroidal torque density.  For a small TF ripple  Similar to TRANSP torque density  All applies for small TF ripple amplitudes (  BT <1%) [1] A. Salmi, et al., Contributions to Plasma Physics 48 (2008) 77. Total Net torque near zero

10. 10 Peter de Vries – ITPA T meeting Culham – March 2010 TF ripple experiments and Pinch TF ripple affects the toroidal rotation  When the TF ripple is increased, the toroidal rotation profile is affected but torque flux (  =0.5) is not  This suggests momentum transport is altered. ASCOT torque depositionIon Temperature Toroidal Rotation

11. 11 Peter de Vries – ITPA T meeting Culham – March 2010 TF ripple experiments and Pinch Increasing TF ripple reduces the rotation/momentum in the outer part of the plasma, yielding a smaller effect of pinch  Hence, less peaked rotation profiles and larger effective Prandtl nr.

12. 12 Peter de Vries – ITPA T meeting Culham – March 2010 Magnitude of the Pinch What is the magnitude of the momentum pinch to explain these observations? Averaged over discharges

13. 13 Peter de Vries – ITPA T meeting Culham – March 2010 Profile shape The previous results are averaged over the central region of the plasma  What if the same analysis is done for different regions?  Outer: 0.65<  <0.90 RV p /  = 7.5   =4 m 2 /s  Inner: 0.10<  <0.45 RV p /  = 1.6   =1.3 m 2 /s  Normalised Pinch higher in outer part !

14. 14 Peter de Vries – ITPA T meeting Culham – March 2010 Estimated pinch from Database Assuming that the momentum diffusivity is equal to the ion heat diffusivity one could estimate the magnitude of the pinch for all entries in the database.  Scales with R/L n 1  For H-modes: 2<RV p /  <10 [1] A.G. Peeters, Phys. Rev. Lett. 98 (2007) 265003.

15. 15 Peter de Vries – ITPA T meeting Culham – March 2010 TF ripple experiments and Pinch Increasing TF ripple reduces global momentum confinement time with respect to that of the energy  At small TF ripple:   ~  E but   eff <  i (significant inward convection)  At large TF ripple:   <  E but   eff =  i (small inward convection)  What determines edge rotation?

16. 16 Peter de Vries – ITPA T meeting Culham – March 2010 Discussion The magnitude of the momentum pinch found in this study agree with earlier experiments and with theoretical predictions.  Scales with the gradient length of density The momentum pinch is a relevant factor in JET standard H- modes  Depending on the edge rotation it has a significant impact on the gradient of the rotation profile  Values of 2 < RV p /  <10 are found. In order to predict the magnitude and gradient of the rotation in ITER one has to know what the momentum in the outer part of the plasma (top of H-mode pedestal) will be.