1. 1 Plasma Rotation and Momentum Confinement – DB ITPA - 1 October 2007 by Peter de Vries Plasma Rotation and Momentum Confinement Studies at JET P.C. de Vries 1, M.-D. Hua 2,3, D.C. McDonald 1, M. Janvier 4, M.F. Johnson 1, C. Giroud 1, T. Tala 5, K.-D Zastrow 1, TFT rotation and momentum transport working group and JET EFDA Contributors § 1 EURATOM/UKAEA Fusion Association, Culham Science Centre, OX14 3DB, Abingdon, UK 2 Imperial College, SW7 2BY, London, UK. 3 Ecole Polytechnique, Route de Saclay, 91128, Palaiseau, France. 4 Institute National Polytechnique de Grenoble, Grenoble, France. 5 Association Euratom-Tekes, VTT,, P.O. Box 1000, 02044 VTT, Finland. § See Appendix of M.L. Watkins, et al., Fusion Energy 2006 (Proc. 21th Int Conf. Chengdu) IAEA (2006)

2. 2 Plasma Rotation and Momentum Confinement – DB ITPA - 1 October 2007 by Peter de VriesIntroduction Rotation of Tokamak plasmas is thought to play an important role in plasma stability and the suppression of turbulence. It is therefore important to understand the scaling of plasma rotation and momentum confinement, in order to accurately predict ITER performance. In order to study trends and scaling of plasma rotation and momentum transport and extensive databases has been set up at JET. This presentation will: –present the rotation database at JET –discuss scaling of rotation of JET plasmas –Analysis of momentum and energy transport

3. 3 Plasma Rotation and Momentum Confinement – DB ITPA - 1 October 2007 by Peter de Vries Rotation Database at JET The rotation database is built up of 7 subsets, each for a distinct JET operation scenario. There is overlap between the rotation database and existing JET databases for most of the entries. The database contains a large number of parameters describing the plasma properties, rotation and confinement characteristics How well defined the database is depends on the number of entries, the accuracy of each parameter and the independence of each entry or parameter.

4. 4 Plasma Rotation and Momentum Confinement – DB ITPA - 1 October 2007 by Peter de Vries Database parameters Creating a large database of means a compromise between accuracy and the number of entries/parameters.

5. 5 Plasma Rotation and Momentum Confinement – DB ITPA - 1 October 2007 by Peter de Vries Parameter correlation Correlation between entries and parameters can compromise (regression) analysis. For many H-mode entries:

6. 6 Plasma Rotation and Momentum Confinement – DB ITPA - 1 October 2007 by Peter de Vries Mach numbers Mach numbers are dimensionless parameters which enables an easy comparison between various JET scenarios and other devices. Thermal Mach number: Alfvén Mach number:

7. 7 Plasma Rotation and Momentum Confinement – DB ITPA - 1 October 2007 by Peter de Vries Scaling of averaged rotation in JET Regression analysis has been carried out to find the scaling of Mach numbers. Scales with the ratio of torque and input power, inversely with q and weakly negative with n e. Off-set ?

8. 8 Plasma Rotation and Momentum Confinement – DB ITPA - 1 October 2007 by Peter de Vries Type I and III EMLy H-mode Average Mach number is smaller for type III ELMy H-modes compared to those with type I ELMs.

9. 9 Plasma Rotation and Momentum Confinement – DB ITPA - 1 October 2007 by Peter de Vries The scaling of Mach number profile peaking has been analysed. Positive scaling with magnetic field and an inverse scaling with the density. (The last effect could be due to off-axis torque deposition at high density. Hollow Mach profiles for dominant ICRH and counter NBI entries. Scaling of rotation profile peaking

10. 10 Plasma Rotation and Momentum Confinement – DB ITPA - 1 October 2007 by Peter de Vries Momentum and energy confinement In many devices a link between momentum and energy transport has been observed. Such a link is predicted by ITG turbulence theory from which one finds that the momentum and heat diffusivity are equal. The database finds that the global momentum and energy confinement times scale. However individual cases can differ significantly!

11. 11 Plasma Rotation and Momentum Confinement – DB ITPA - 1 October 2007 by Peter de Vries Although there is a rough trend between momentum and energy confinement, individual cases can differ significantly:a Although there is a rough trend between momentum and energy confinement, individual cases can differ significantly: The ratio of energy and momentum confinement can be: 0.5 <  E /   < 1.8 The ratio scales inversely with rotation (for example ) Confinement ratio

12. 12 Plasma Rotation and Momentum Confinement – DB ITPA - 1 October 2007 by Peter de Vries Regression analysis Reasonable fits were obtained with fitting the energy confinement time to a non- linear model depending on n e, I p, B T and P in. However, this model did not give satisfactory results for the momentum confinement time –This suggests again a difference between the energy and momentum confinement The best results were found when rotation or torque information was added to both models: The regression analysis on the global energy and momentum confinement times suffered from a coupling between torque and power. This coupling was especially strong for the H-mode only subset of the data.

13. 13 Plasma Rotation and Momentum Confinement – DB ITPA - 1 October 2007 by Peter de Vries Although there is a rough trend between momentum and energy confinement, individual cases can differ significantly The effective momentum diffusivity was found to be smaller than the heat diffusivity in the core of the plasma (0.2<  <0.7). P r <1. Difference between core and edge confinement?Differences

14. 14 Plasma Rotation and Momentum Confinement – DB ITPA - 1 October 2007 by Peter de Vries Core and edge confinement The core and edge/pedestal confinement times for momentum and energy can be compared. The pedestal energy and momentum are less accurately determined than the total values, which are given by the integration of profiles. Works for JET but Ill-defined? W ped L  ped W core L  core Energy or momentum density r n ped T ped l  ped

15. 15 Plasma Rotation and Momentum Confinement – DB ITPA - 1 October 2007 by Peter de Vries Momentum pedestal The pedestal momentum scales with the pedestal energy. –For H-mode entries only one finds: [kg m 2 s -1, MJ] –For most H-mode entries:

16. 16 Plasma Rotation and Momentum Confinement – DB ITPA - 1 October 2007 by Peter de Vries Core and edge confinement The core and edge confinement of energy and momentum differ. The edge/pedestal momentum confinement is smaller than that of the energy! For many H-mode cases the core momentum confinement is better than that of the energy. High density counter NBI discharges were an exception. pedestal/edge core

17. 17 Plasma Rotation and Momentum Confinement – DB ITPA - 1 October 2007 by Peter de Vries Type I and III EMLy H-mode Average Mach number is smaller for type III ELMy H-modes compared to those with type I ELMs The difference is caused by a degraded pedestal momentum confinement.  E (type I)=180ms  E (type III)=160ms drop of 12%   (type I)=120ms   (type III)=85ms drop of 30%   ped (type I)=83ms   ped (type III)=49ms drop of 40%   core =36ms unchanged

18. 18 Plasma Rotation and Momentum Confinement – DB ITPA - 1 October 2007 by Peter de Vries Scaling of core confinement The ratio of total energy and momentum confinement decreased with M –The ratio of the pedestal energy and momentum confinement did not depend on M –But the core ratio did: The core momentum confinement may be affected by an inward pinch 1,2. [1] A.G. Peeters, Phys. Rev. Lett. 98 (2007) 265003 [2] T. Tala, et al., Plasma Phys. Control. Fusion (2007)

19. 19 Plasma Rotation and Momentum Confinement – DB ITPA - 1 October 2007 by Peter de Vries Conclusions (1) A extensive database has been built at JET to study the scaling of plasma rotation and momentum transport. Thermal and Alfvén Mach numbers proved to be useful (dimensionless) parameters to compare rotation properties between various JET scenarios. General scalings for the thermal and Alfvén Mach number in predominantly NBI heated JET discharges have been found. The peaking factor of the Mach number or plasma rotation profile may be affected by the NBI torque deposition profile. –Information related to the torque deposition profile is relevant to understand the scaling of rotation and momentum transport.

20. 20 Plasma Rotation and Momentum Confinement – DB ITPA - 1 October 2007 by Peter de Vries Conclusions (2) The global momentum and energy confinement times are not identical in JET plasmas and can differ substantially in individual discharges (> factor 2). The scaling of both energy and momentum confinement times was found to depend on the rotation (i.e. Alfvén Mach number). The confinement of momentum by the pedestal was found to be worse than its energy confinement. The core momentum confinement for many H-mode discharges was often found to be better than that of the core energy confinement. The core momentum confinement could be improved compared to the energy confinement by the presence of an inward non-diffusive transport (pinch). TF Ripple …