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Stellarator tools for neoclassical transport and flow interpretation in helical RFP plasmas

Stellarator tools for neoclassical transport and flow interpretation in helical RFP plasmas. presented by. M. Gobbin. Consorzio RFX, Associazione Euratom-ENEA sulla fusione. RFX-mod Programme Workshop 2011, February 7-9, Padova, Italy. Outline. Transport and flow in 3D systems

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Stellarator tools for neoclassical transport and flow interpretation in helical RFP plasmas

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  1. Stellarator tools forneoclassicaltransport and flow interpretation in helical RFP plasmas presented by M. Gobbin Consorzio RFX, Associazione Euratom-ENEA sulla fusione RFX-mod Programme Workshop 2011, February 7-9, Padova, Italy

  2. Outline • Transport and flow in 3D systems • 3D tools from stellarators: DKES/PENTA • Er and flow computation in RFX-mod • Open issues RFX-mod Programme Workshop 2011, February 7-9, Padova, Italy

  3. 1 Transport and flow in 3D systems

  4. neoclassical transport dominant in the core and near internal transport barriers (ITB); Helical RFP and STELLARATORS share common topics on neoclassical transport neoclassical fluxes determine Erand averaged flows in non axisymmetry systems. ANOMALOUS TRANSPORT = EXPERIMENTAL – NEOCLASSICAL Neoclassical transport in 3D systems RFX-mod Programme Workshop 2011, February 7-9, Padova, Italy

  5. Tokamaks described by ~ 5 parameters Stellarators described by ~ tens of parameters (aspect ratio, ellipticity, triangularity…) HELICAL RIPPLE TOROIDAL RIPPLE Role of magnetic field configuration RFX-mod Programme Workshop 2011, February 7-9, Padova, Italy

  6. HELICAL RIPPLE TOROIDAL RIPPLE |B| LHD HSX NCSX Quasi Axi. Quasi Helical +eh parallel flow <v· b> strongly depends on the particular configuration Role of magnetic field configuration Tokamaks described by ~ 5 parameters Stellarators described by ~ tens of parameters (aspect ratio, ellipticity, triangularity…) RFX-mod Programme Workshop 2011, February 7-9, Padova, Italy

  7. RFX-mod HSX eh And in eh et et RFX-mod ? higher ehin the core r/a r/a Helical ripple and |B| modulation RFX-mod Programme Workshop 2011, February 7-9, Padova, Italy

  8. RFX-mod HSX eh And in eh et et RFX-mod ? higher ehin the core r/a r/a q~1 q < 0.13 No 1/n regime in helical rfp plasmas: weak |B| modulation in the edge. |B| Gobbin,Spizzo PRL 106 125001 (2011) Helical ripple and |B| modulation RFX-mod Programme Workshop 2011, February 7-9, Padova, Italy

  9. 3D tools from stellarators : DKES/PENTA 2

  10. Transport codes adapted from stellarators community HELICAL EQUILIBRIA By VMEC Monoenergetic coefficients at each magnetic surface DKES - a linearized drift kinetic equation is solved with pitch angle scattering collision operator (NO MOMENTUM CONSERVATION) DKES Hirshman, Phys. Fluids 29 (1986) RFX-mod Programme Workshop 2011, February 7-9, Padova, Italy

  11. Transport codes adapted from stellarators community HELICAL EQUILIBRIA By VMEC Monoenergetic coefficients at each magnetic surface DKES - a linearized drift kinetic equation is solved with pitch angle scattering collision operator (NO MOMENTUM CONSERVATION) - from the resulting distribution function: D11,12,21,22 radial transport D13, 23, 31, 32 bootstrap current D33 parallel transport …used for viscous and friction-flow relations DKES Hirshman, Phys. Fluids 29 (1986) RFX-mod Programme Workshop 2011, February 7-9, Padova, Italy

  12. PENTA computes the ambipolar radial field and neoclassical flow, including correction for the momentum conservation Absolutely required forQuasi Symmetric systems!! #27730@64ms • Experimental Thomson scattering profiles are mapped on helical flux coordinates • No measures of Ti radial profile: guess and sensivity studies PENTA D.A.Spong PoP 12 (2005) RFX-mod Programme Workshop 2011, February 7-9, Padova, Italy

  13. INTRODUCTION to HELICAL RFP REGIMES 3 Erand flow computation

  14. no impurity, ne=3·1019m-3, Ti=0.7Te particle fluxes Solution for ambipolar Er RFX-mod Programme Workshop 2011, February 7-9, Padova, Italy

  15. no impurity, ne=3·1019m-3, Ti=0.7Te particle fluxes Stellarator Ion root: small negative solution reduces the ion flux Electron root: large positive solution both fluxes are reduced improved confinement Er (kV/m) Solution for ambipolar Er RFX-mod Programme Workshop 2011, February 7-9, Padova, Italy

  16. Gi-Ge contour of Gi-Ge as function of Er and r/a Er (kV/m) zoom 0 Gi>Ge Gi=Ge 0 0 Gi<Ge Gi=Ge r/a 0 Er (kV/m) 0 point of minimum Er≈-2kV/maround the ITB ITB r/a Solution for ambipolar Er in RFX-mod RFX-mod Programme Workshop 2011, February 7-9, Padova, Italy

  17. Gi=Ge Er (kV/m) 0 no impurity, ne=3·1019m-3, Ti=0.7Te 0 r/a RFX-mod r/a=0.35 - in the helical core region (red/black lines) ion root solution at Er~-2kV/m Gi eh>>et - |Er| decreases moving towards the quasi-axisymmetric edge Ge at r/a>0.8|Er |≤ 0.1kV/m et>>eh Solution for ambipolar Er RFX-mod Programme Workshop 2011, February 7-9, Padova, Italy

  18. Effect of assumptions on the Ti profile heat fluxes Er ≈ -1.6kV/m Er depends on Ti profile Gi=Ge -ions -electrons Qi/Ti Qe/Te ce,eff ≈ 1.5-3m2/s<10m2/s (experiment) (ITB region) RFX-mod Programme Workshop 2011, February 7-9, Padova, Italy

  19. INTRODUCTION to HELICAL RFP REGIMES 3 Er and flow computation(in progress)

  20. Flow velocity given by: // B B diamagnetic part flow velocity // field (parallel viscous stress tensor) Pfirsch-Schluter flow velocity for RFP also dynamo could play a role: not included now Flow computation RFX-mod Programme Workshop 2011, February 7-9, Padova, Italy

  21. Magnetic surface averaged contravariant flow components computed at the ITB for RFX-mod Experimental estimates ≈ 3km/s (poloidal) RFX-mod Ti=0.7Te - <vq> <v·b> - <vz> q’~0 (ITB region) Flow components in RFX-mod RFX-mod Programme Workshop 2011, February 7-9, Padova, Italy

  22. HSX (ECH) ~30km/s pol. tor. ~-5km/s HSX (ICH) ~0.5km/s tor. pol. ~-6km/s Flow components in RFX-mod Magnetic surface averaged contravariant flow components computed at the ITB for RFX-mod Experimental estimates ≈ 3km/s (poloidal) RFX-mod Ti=0.7Te - <vq> <v·b> - <vz> q’~0 (ITB region) from D.A.Spong PoP 12 (2005) RFX-mod Programme Workshop 2011, February 7-9, Padova, Italy

  23. (ITB region) - <vq> <v·b> - <vz> lower ion temperature gradient  decreasing v values Effect of Ti profile on flow components RFX-mod Programme Workshop 2011, February 7-9, Padova, Italy

  24. (ITB region) (ITB region) + <vq> - <vq> - <v·b> <v·b> - <vz> + <vz> lower ion temperature gradient  decreasing v values flow has opposite sign for zero ion temperature gradient (as Er ) comparison with exp. data in progress:(Boozer coordinates in PENTA) Effect of Ti profile on flow components RFX-mod Programme Workshop 2011, February 7-9, Padova, Italy

  25. ELECTRONS with secondary modes pure helical Effect of residual chaos at the eITB (ORBIT) • experimental transport exceeds the neoclassical one: effect of secondary modes? • Di,e computed locally near ITB by ORBIT with secondary modes too ( at Er=0) RFX-mod Programme Workshop 2011, February 7-9, Padova, Italy

  26. ELECTRONS with secondary modes pure helical low Er required for ambipolarity for small level of secondary modes? What about the predicted flows? runs with helical Er≠0 in progress Effect of residual chaos at the eITB (ORBIT) • experimental transport exceeds the neoclassical one: effect of secondary modes? • Di,e computed locally near ITB by ORBIT with secondary modes too ( at Er=0) RFX-mod Programme Workshop 2011, February 7-9, Padova, Italy

  27. Next steps New version of PENTA released by J.Lore: benchmark on going simpler inclusion of impurity profiles in the new PENTA version a, all species comparison with experiment in the right coordinate system. evaluation of the single terms to the total flows, bootstrap current application to more experimental scenarios (pellet, higher density, higher helical deformation …) RFX-mod Programme Workshop 2011, February 7-9, Padova, Italy

  28. Thanks for your attention Ceterum censeo Chartaginem esse delendam!

  29. RFX-mod r/a=0.35 Gi Ge Solution for ambipolar Er no impurity, ne=3·1019m-3 particle fluxes HSX From J.Lore talk RFX-mod Programme Workshop 2011, February 7-9, Padova, Italy

  30. Transport optimization in Stellarators Subjects of active research for TRANSPORT OPTIMIZATION in Stellarators particle trajectories momentum transport when a “straight” helical system is bent into a torus, ripple trapped particles acquire non zero bounce averaged radial drift asymmetry  damping of plasma rotation both in poloidal and toroidal directions; flow shear and rotation allow : reducing micro-turbolence preventing island formation superbananas losses studying impurity transport …. RFX-mod Programme Workshop 2011, February 7-9, Padova, Italy

  31. RFX-mod eh et Ripples in RFX-mod And RFX-mod ? HSX eh et r/a r/a on the contrary of Stellarators, in helical RFX-mod plasmas eh is much higher in the core and very low at the edge RFX-mod Programme Workshop 2011, February 7-9, Padova, Italy

  32. RFX-mod: effect of configuration on particle orbits HSX RFX-mod q~1 q < 0.13 |B| in helical rfp plasmas: weak |B| modulation at the edge, stronger in the core. no 1/n regime by ORBIT simulations (Er=0):only for higher deformation of the helical surfaces losses due to superbana particles become important. Gobbin,Spizzo PRL 106 125001 (2011) RFX-mod Programme Workshop 2011, February 7-9, Padova, Italy

  33. Flow components in RFX-mod Contravariant flow components computed at the ITB for RFX-mod NCSX (ECH) ~100km/s tor. Experimental estimates ≈ 3km/s (poloidal) pol. RFX-mod Ti=0.7Te ~5km/s poloidal NCSX (ICH) ~-10km/s parallel tor. pol. toroidal ~-30km/s (ITB region) from D.A.Spong PoP 12 (2005) RFX-mod Programme Workshop 2011, February 7-9, Padova, Italy

  34. ITB surface Er/v=0 Er/v=10-3 Er/v=1 Er/v=0.1 Radial transport coefficients D11≈ 0.5-1m2/s: good agreement with ORBIT estimates (Er=0) in experimental condition of density and temperature DKES fails at low collisionality: locality assumption not valid in RFX-mod RFX-mod Programme Workshop 2011, February 7-9, Padova, Italy

  35. Bootstrap current computation evaluation of bootstrap current: IONS very small contribute with ordinary temperature and density experimental profiles ELECTRONS TOTAL ~10-4-10-3Johmic RFX-mod Programme Workshop 2011, February 7-9, Padova, Italy

  36. ITB surface Er/v=0 Er/v=10-3 Er/v=1 Er/v=0.1 Radial transport coefficients D11≈ 0.5-1m2/s: good agreement with ORBIT estimates (Er=0) in experimental condition of density and temperature DKES fails: at low collisionality locality assumption not valid in RFX-mod

  37. TOP VIEW Toroidal precession Helical flux coordinate c z Y(cm) time (a.u.) time (a.u.) X(cm) Following a trapped particle with its helical flux coordinate: the banana orbit is only slightly modified by the presence of the helix, since |B| is essentially still axisymmetric only for Bh/B > 60 % superbananas can reach the wall

  38. SHAx = helical equilibrium with 1,7 periodicity helical magnetic surfaces onset of internal electron transport barriers low level of residual chaos

  39. n=7 n Helical rfp plasmas At high plasma current a SINGLE saturated resistive kink mode drives most of the self organization process and gives the plasma a global helical symmetry. • Helical equilibrium • helical core • quasi-axisymmetric edge • Low residual magnetic chaos RFX-mod mode spectrum • Neoclassical effects may become relevant 52° APS Conference, 8-12 November 2010, Chicago, USA

  40. TOKAMAK STELLARATOR Bq ≈ Bf RFP RFP HELICAL STATES contribute to 3D physics studies in unexplored regions of the plasma parameter space RFP safety factor is lower than in stellarators and tokamaks q DEVICE adapted from Fujisawa, PPCF,2001

  41. RFX-mod eh et RFP helical states features TOROIDAL RIPPLE HELICAL RIPPLE HSX eh et radial coordinate radial coordinate 52° APS Conference, 8-12 November 2010, Chicago, USA

  42. RFX-mod device: main features Largest RFP R0 = 2 m a = 0.459 m Max Ip = 2 MA Now achieved! (still not optimized) tE up to 5 ms 52° APS Conference, 8-12 November 2010, Chicago, USA

  43. RFX-mod device: main features • plasma current up to 2MA (1,-7) (1,n <-7) • mode (1,-7) is dominant for most of the discharge: Quasi Single Helicity (QSH) • low secondary modes • electron density : 3-6·1019m-3 Back transitions from QSH to MH, related to reconnection events, under investigation 52° APS Conference, 8-12 November 2010, Chicago, USA

  44. RFX-mod device: active control • RWM control both in RFP and Tokamak configuration • control of the internally resonant tearing modes • control of helical magnetic field reinforces persistency of 3D shaping ACTIVE COILS 192 independently feedback controlled coils covering the whole torus. Digital Controller with Cycle frequency of 2.5 kHz. 52° APS Conference, 8-12 November 2010, Chicago, USA

  45. #28218 IP (MA) 1/-7 br(a)/B (%) 1/-8 to -15 1/-7 phase (rad) n/nGW neTe (kPa) time (s) Active control with finite references • Experiments with br(a) ≠0 on the 1/-7 mode: br1/-7(a)≠0 rotating br1/-7(a)≠0 static br1/-7(a)=0 - long, rotating but also static, QSH obtained - high record values for br1,-7(a) - secondary m=1 modes amplitude does not vary significantly 52° APS Conference, 8-12 November 2010, Chicago, USA

  46. Thermal evidences of 3D topology Temperature and SXR emissivity are helical flux function Te • high Te in the helical core • steep gradients SXR 52° APS Conference, 8-12 November 2010, Chicago, USA

  47. Electron Internal Transport Barriers remapping on square root of helical flux r electron Internal Transport Barrier (eITBS) region : link with magnetic topology? In Tokamak or Stellarators ITBs are associated to shear flows weak/negative s= (r/q) dq/dr • suppression of microinstability induced transport by sheared E×B flows • effect of low shear on microinstability growth rates or in reducing their radial extent. Connor et al. 1994 52° APS Conference, 8-12 November 2010, Chicago, USA

  48. DAx and SHAx states in RFX-mod br1,-7(a)/B0(a)>4% br1,-7(a)/B0(a)<4% Depending on the amplitude of the (1,-7) mode, two QSH configurations : DAx Double Axis Separatrix expulsion Single Helical Axis SHAx 52° APS Conference, 8-12 November 2010, Chicago, USA

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