1. Carlos Hidalgo Laboratorio Nacional de Fusión CIEMAT Madrid, Spain
Role of turbulence on momentum transport: experiments in stellarators and tokamaks
Carlos Hidalgo
Laboratorio Nacional de Fusión
CIEMAT
Madrid, Spain

2. Outline
Motivation: evidence of anomalous poloidal and toroidal momentum transport
The concept of negative viscosity and development of sheared flows:
Measurements of <vi vj>
Why edge sheared flows?
The importance of diagnostic development: 2-D visualization
Why configuration windows for H mode transition in stellarators?
Joint experiments in stellarators and tokamaks: actions to be taken

3. Outline
Motivation: evidence of anomalous poloidal and toroidal momentum transport
The concept of negative viscosity and development of sheared flows:
Measurements of <vi vj>
Why edge sheared flows?
The importance of diagnostic development: 2-D visualization
Why configuration windows for H mode transition in stellarators?
Joint experiments in stellarators and tokamaks: actions to be taken

4. Anomalous toroidal momentum transport Alcator C-mod [Lee et al. , Phys
Anomalous toroidal momentum transport Alcator C-mod [Lee et al., Phys. Rev. Lett. (2003) / J. Rice et al., Nuclear Fusion 44 (2004) 379
In Alcator C-mod, following the H-mode transition toroidal momentum (anomalous) is observed to propagate in from the plasma edge, although there is no external source
[Lee et al., Phys. Rev. Lett. 91 (2003) ].
This redistribution is clearly linked with an edge physics phenomenon
[J. Rice et al., Nuclear Fusion 44 (2004) 379]
Why edge momentum source?
Role of electric fields?

5. ANOMALOUS POLOIDAL PLASMA ROTATION IN DIII-D
V.M. Solomon et al PoP- June 2006
DIII-D QH-mode
Similar results in JET: Anomalous poloidal rotation in JET
K. Crombe, Y. Andrew et al., PRL-2005 (JET)

6. Outline
Motivation: evidence of anomalous poloidal and toroidal momentum transport
The concept of negative viscosity and development of sheared flows:
Measurements of <vi vj>
Why edge sheared flows?
The importance of diagnostic development: 2-D visualization
Why configuration windows for H mode transition in stellarators?
Joint experiments in stellarators and tokamaks: actions to be taken

7. Eddy (positive) viscosity
The tendency of sheared motion to be reduced with the passage of time, if no other forces are at work to maintain it, leads to the concept of (positive) coefficient of viscosity
The eddy momentum flux is directed from regions of larger values of mean flow toward regions of smaller values.

8. Negative viscosity
The eddy momentum flux is directed from regions of smaller values of mean flow toward regions of larger values.
This effect has a direct impact in the development of differential rotation
The subject of negative eddy viscosity has its origins from the calculation of Reynolds stresses from observed data mainly concerning earth’s atmosphere.
Physics of negative viscosity phenomena
(with applications to earth and solar atmospheres, spiral galaxies, oceanic circulations)
V. P. Starr , Earth and planetary science series, McGraw-Hill (1968).

9. Negative viscosity: geometrical interpretation
Flow having a momentum transport into the central portion of the channel.
The essential features are the elliptical circulations and the systematic tilts of their major axes.

10. Negative viscosity physics
Key ingredients:
The eddies which transport momentum contrary to the gradient of mean flow must have a supply of eddy kinetic energy.
Eddy tilting (symmetry breaking)
Turbulent “irregulaties”
The mean flow must be subject to some form of braking action so as not to increase without limit (e.g. positive viscosity). But, also this braking should be low enough to allow flow development.
Sustained negative viscosity effects are to be found in systems with great complexity (especially where eddy forcing takes place from the outside):
atmosphere, galaxies, starts,……fusion plasmas

11. Physics of negative viscosity (poloidal/toroidal)
Turbulent anisotropy (Eddy tilting)
Poloidal
DC rotation
Positive viscosity (e.g. Neoclasical,…)
Turbulent irregularities
Parallel
B. Gonçalves et al., PRL 2006 (TJ-II stellarator)

12. Outline
Motivation: evidence of anomalous poloidal and toroidal momentum transport
The concept of negative viscosity and development of sheared flows:
Measurements of <vi vj>
Why edge sheared flows?
The importance of diagnostic development: 2-D visualization
Why configuration windows for H mode transition in stellarators?
Joint experiments in stellarators and tokamaks: actions to be taken

13. Biasing improved confinement regimes (stellarators)
n/Hincreases and edge turbulence decreases (biasing inducced improved confinement regime)
Perperdicular velocity and edge potential are controlled by external biasing.
C. Hidalgo et al., PPCF-2004
Better understanding of the underlying physics
which may link electric fields, turbulence and parallel dynamics
(J. Rice et al., Alcator Cmod / O. Gürcan, P. Diamond et al., PoP-2007,…..)

14. Biasing, electric fields and parallel flows
SOL
EDGE
TJ-II
Alonso et al.,
EPS-2007

15. Radial-parallel Reynolds stress and flows (TJ-II)
Turbulence driven flows (via RS) can play a role
TJ-II
Alonso et al.,
EPS-2007

16. Outline
Motivation: evidence of anomalous poloidal and toroidal momentum transport
The concept of negative viscosity and development of sheared flows:
Measurements of <vi vj>
Why edge sheared flows?
The importance of diagnostic development: 2-D visualization
Why configuration windows for H mode transition in stellarators?
Joint experiments in stellarators and tokamaks: actions to be taken

17. Why edge sheared flow development: neoclassical and turbulent mechanisms (interplay ?)
There is a coupling between the onset of sheared flow development and the level of turbulence. Sheared flows and fluctuations in TJ-II appear to be organized near marginal stability. The universality of this property is easily understood assuming that edge sheared flows are controlled by turbulence.
C. Hidalgo et al., Phys Rev. E / M.A. Pedrosa et al., PPCF 2005
TJ-II results are consistent with a second order phase transition model (negative viscosity)
B.A. Carreras et al., Phys. of Plasmas December (2006)
In LHD the radial electric field can be controlled by the magnetic configuration (ripple). Results are consistent with NC calculations
K. Ida et al., Nuclear Fusion 2005

18. Outline
Motivation: evidence of anomalous poloidal and toroidal momentum transport
The concept of negative viscosity and development of sheared flows:
Measurements of <vi vj>
Why edge sheared flows?
The importance of diagnostic development: 2-D visualization
Why configuration windows for H mode transition in stellarators?
Joint experiments in stellarators and tokamaks: actions to be taken

19. Edge sheared flows can be 2-D visualized with fast cameras: they are developed in a time scale of tens of s
Fieldlines
Poloidal limiter
View plane
View cone
Alonso et al.,
PPCF-2006

20. n < nth n ≈ nth n > nth
Edge sheared flows can be 2-D visualized with fast cameras: they are developed in a time scale of tens of s
n < nth
n ≈ nth
n > nth
Fieldlines
Poloidal limiter
View plane
View cone
Alonso et al.,
PPCF-2006

21. Outline
Motivation: evidence of anomalous poloidal and toroidal momentum transport
The concept of negative viscosity and development of sheared flows:
Measurements of <vi vj>
Why edge sheared flows?
The importance of diagnostic development: 2-D visualization
Why configuration windows for H mode transition in stellarators?
Joint experiments in stellarators and tokamaks: actions to be taken

22. Does the relaxation time of flows depend on magnetic configuration ?
Configuration effects on improved confinement regimes (W7-AS, Heliotron J, TJ-II). Role of neoclassical viscosity and turbulence on H-mode transition
W7-AS
F. Wagner et al., Phys of Plasmas 12 (2005)
Does the relaxation time of flows depend on magnetic configuration ?
How important is to reduce neoclassical viscosity to get L-H transition (in stellarator)?

23. Damping physics: neoclassical vs anomalous
Stellarator (TJ-II) vs Tokamak (Castor)
HSX
Experimental results show decay times in the range 10 – 50 microseconds in the plasma boundary of stellarator (TJ-II) and tokamak(CASTOR) plasmas. These results can shed some light to test critically neoclassical and anomalous damping mechanisms in fusion plasmas.
M.A. Pedrosa et al., EPS-2007
Floating potential decay rates in HSX. The radial profiles are plotted in a) for the QHS and Mirror configuration. The density scaling in the QHS configuration is shown in b).
HSX team PoP 205

24. Conclusions
Momentum transport physics is an important issue in magnetically confined plasmas (ITER relevant) and it should be considered as an important element in the stellarator / tokamak research programme.
Joint (and well-defined) experiments in stellarators and comparison with tokamaks should be encouraged:
Visualization of flows (e.g. during transition to improved confinement regimes)
Damping physics and iota window for H-mode development.
Measurements of driving forve of turbulence driven flows (<vivj>).
………