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Momentum Transport Studies at JET by Peter de Vries

Momentum Transport Studies at JET by Peter de Vries H.C.M. Knoops 4 , K.M. Rantamäki 2 , C. Giroud 1 , E. Asp 3 , G. Corrigan 1 , A. Eriksson 3 , M. de Greef 4 , I. Jenkins 1 , P. Mantica 5 , H. Nordman 3 , P. Strand 3 , T. Tala 2 , J. Weiland 3 , K.-D Zastrow 1 and JET EFDA Contributors §

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Momentum Transport Studies at JET by Peter de Vries

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  1. Momentum Transport Studies at JET by Peter de Vries H.C.M. Knoops4, K.M. Rantamäki2, C. Giroud1, E. Asp3, G. Corrigan1, A. Eriksson3, M. de Greef4, I. Jenkins1, P. Mantica5, H. Nordman3, P. Strand3, T. Tala2, J. Weiland3, K.-D Zastrow1 and JET EFDA Contributors§ 1EURATOM/UKAEA Fusion Association, Culham Science Centre, Oxon. OX14 3DB, UK. 2VTT Technical Research Centre of Finland, EURATOM-Tekes, Espoo, Finland. 3Chalmers University of Technology, EURATOM/VR Association, Göteborg, Sweden. 4Eindhoven University of Technology, Dept. of Applied Physics, Eindhoven, The Netherlands. 5Istituto di fisica del plasma, Associazione Euratom-ENEA-CNR, Milan, Italy. §See Appendix of J.Pamela et al., Fusion Energy 2004 (Proc. 20th Int Conf. Vilamoura) IAEA, Vienna (2004)

  2. Outline • Plasma Rotation and Momentum Transport at JET • Introduction • Rotation and ion temperature Ti profiles • Relationship between v (or ) and Ti profiles • Gradient lengths of v (or ) and Ti profiles • Mach number of JET plasmas • Momentum and ion heat transport • Torque and power deposition profiles • Local momentum and ion heat i diffusivities • The ratio of momentum and ion heat diffusivity (Prandtl number) • Global momentum confinement • Conclusions (and further work)

  3. Introduction • Coupling of momentum and ion energy confinement • Theory • Viscosity and heat diffusion are coupled in turbulent fluids (Prandtl) • ITG turbulence theory for Tokamak plasmas predicts that = i • Experimental observations • Many devices report profile consistency: v(r) Ti(r) • Many devices have shown that   E • Experimental study of momentum and ion heat transport • Profile analysis: v(r) (or ) Ti(r) • Momentum confinement data-base • Global confinement / Scaling • Local transport properties and i • Determine Prandtl number: Pr = / i

  4. Rotation and temperature profiles • CXRS determines the rotation and ion temperature profile • In case of profile consistency (r)/ Ti(r) cnst • Ratio for 7 CXRS channels (omit 2 outer most channels) • Statistics for all 2000-2003 pulses • No consistency is found for high density H-mode JET discharges H-mode OS/ITB

  5. Rotation and temperature profiles • Behaviour of v(r) Ti(r) during L to H-mode transition

  6. Rotation and temperature profiles • Behaviour of v(r) Ti(r) during an ITB formation • Complication with the determination of v(r) in the presence of an ITB. M increases at ITB formation

  7. ITB Mach numbers of JET plasmas • Mach number • Definition: • Because (r)/ Ti(r) cnst: Mscales with Ti (higher Ti larger M) Type I H-mode Type III H-mode

  8. Gradient Lengths • Relationship between R/Lv and R/LT: • For H-mode discharges only: R/LT > R/Lv flatter v(r) • Similar observation in ASDEX* • More relevant for momentum transport: R/L * D. Nishijimi, et al., Plasma Phys. Control. Fusion 47 (2005) 89

  9. Transport studies in H-modes at JET • Discharge selection • Steady state (part of confinement database) • Predominantly NBI heated discharges (PICRH 0-0.2 PNBI) • ELMy H-mode with high density n > 11020 m-2 • ITG dominated: Te=Ti and flat density profile (R/Ln< 2) • Some discharges at ITG threshold (R/LT 5) show Ti profile stiffness • Transport properties • Profiles are averaged over a time interval (0.2-0.4s) • Properties determined in the gradient region: 0.3<<0.7 • Careful mapping and profile fit for T and  (or v) • NBI Torque and heat sources determined from PENCIL • Interpretative JETTO calculations

  10. Gradient Lengths • Normalised inverse gradient lengths • R/LT < R/L (Remember R/LT > R/Lv) • Ion temperature profile stiffness observed (R/LT 5)  larger ieff • However, no threshold found for the velocity / momentum density profile Increasing 

  11. NBI energy and momentum deposition • Different NBI energy and torque deposition differ • A smaller fraction is transferred to the ions at higher density (or lower T) • More NBI energy to the ions, less to the electrons, in the core • Torque deposition is more off-axis than NBI ion heat deposition

  12. Energy and momentum deposition • Different NBI energy and torque deposition differ • A smaller fraction is transferred to the ions at higher density (or lower T) • More NBI energy to the ions, less to the electrons, in the core • Torque deposition is more off-axis than NBI ion heat deposition • ICRH heat deposition on-axis for these discharges • Ratio of normalised sources • Less torque and a larger ion heat flux • Ratio of normalised gradients • Limited ion temperature gradient

  13. Diffusivities and Prandtl numbers • Effective diffusivities (0.3<<0.7) • Effective diffusivities: include convective transport • Analysis with ‘Weiland-model’ with  = c i  best match c = 0.2 • Trends in Prandtl number: smaller for ITG dominated discharges

  14. Global Confinement • Ratio of energy and momentum times • Analysis of all 2000-2004 discharges (PNBI>6MW, IP>2MA, ‘steady state’) • At high density: E and at low density:  < E • Global Prandtl number  ratio of ion energy and momentum confinement All = L-mode, OS/ITB, Hybrid, H-mode

  15. c t ion f º µ E P r c t f i W t º ion ion E P ion Global ion confinement • Ion energy confinement time • Momentum confinement time scales with ion energy confinement time • Confinement time is a global parameter /and diffusivity a local parameter • Effective diffusivities depends on local profile gradients: R/LT < R/L • Edge confinement (Pedestal: momentum confinement worse ?)

  16. Conclusions • Plasma Rotation and Momentum Confinement • Rotation and temperature profiles • Profile consistency between v and Ti breaks down at high density • At high density: ion heat deposition (NBI+ICRH) more on-axis. • Profile stiffness for Ti but no threshold for the v profile • Torque and heat deposition • At high density: torque deposition (by NBI) in JET is off-axis • But the ion heat deposition (NBI/ICRH) peaks on axis • Global confinement • At high(er) densities:   E but at low density  < E • Momentum confinement time scales with ion energy confinement time ! • Momentum diffusivities for JET H-mode discharges • The effective Momentum diffusivity scaled with the ion heat diffusivity • But Prandtl numbers significantly less than unity: Pr = / i = 0.18-0.35 • Eventhough   ionE • Off-axis momentum source sustained a significant gradient  pinch ? • The edge Prandtl number is expected to be above unity

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