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Transport in the Helical Core of the RFP

RFX-mod Programme Workshop 2009, January 20-22, Padova, Italy. Transport in the Helical Core of the RFP. M.Gobbin , G.Spizzo, L.Marrelli, L.Carraro, R.Lorenzini, D.Terranova and the RFX-mod team. Consorzio RFX, Associazione Euratom-Enea sulla Fusione, Padova, Italy. Contents.

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Transport in the Helical Core of the RFP

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  1. RFX-mod Programme Workshop 2009, January 20-22, Padova, Italy Transport in the Helical Core of the RFP M.Gobbin,G.Spizzo, L.Marrelli, L.Carraro, R.Lorenzini, D.Terranova and the RFX-mod team Consorzio RFX, Associazione Euratom-Enea sulla Fusione, Padova, Italy RFX-mod Workshop, Padova 20-22/01/ 2009

  2. Contents Introduction: helical states in RFX-mod high current plasmas. Diagnostics and numerical tools to investigate the energy/particle transport in helical-shaped plasmas. Particle transport for the main gas: diffusion coefficients from numerical simulations pellet experiments Diffusion of impurities in MH and QSH plasmas. Comparison between LBO experiments and numerical simulations. Energy transport in helical plasmas. Summary and conclusions RFX-mod Workshop, Padova 20-22/01/ 2009

  3. Helical structures in RFX-mod plasmas In high current RFX-mod plasmas, the magnetic topology is not anymore axisymmetric but helically deformed1. Evidencesfrom: • Thomson scattering (TS) -radiation distribution from bolometry • SXR diagnostics • magnetic signals  topology reconstructions (ORBIT and FLiT codes) SXR TS POINCARE’ d d=20-30 cm The (1,-7) mode is not anymore just a small perturbation. A helical geometry in the core must be considered while studying the particle and energy transport in RFX-mod. [1]Lorenzini et al., Phys. Rev. Lett. 101, 025005 (2008) RFX-mod Workshop, Padova 20-22/01/ 2009

  4. EXPERIMENT THEORY PELLET INJECTION IN THE HELICAL STRUCTURES TEST PARTICLE APPROACH by NUMERICAL SIMULATIONS (ORBIT) Laser Blow Off (LBO) – IMPURITIES TRANSPORT EXPERIMENT THEORY Data from THOMSON SCATTERING, BOLOMETRY and other diagnostics Development of new numerical tools to solve the heat balance equations in helical RFP plasmas. Transport in the helical core Particle transport (main gas and impurities): D values prediction for main gas and impurities in helical states Energy transport: RFX-mod Workshop, Padova 20-22/01/ 2009

  5. Test particle approach in helical RFX-mod plasmas Up to now a test particle approach has been used by the code ORBIT to obtain an estimation of the particle diffusion coefficients in many experimental RFX-mod plasmas2. secondary modes HELICAL EQUILIBRIUM FROM MAGNETIC TOPOLOGY collisions with plasma background mode (1,-7) + B0 [2]Gobbin et al., Phys. Plasmas 14, (072305), 2007 RFX-mod Workshop, Padova 20-22/01/ 2009

  6. IONS ELECTRONS Di in SH and QSH De in SH and QSH x10 Test particle approach in helical RFX-mod plasmas Up to now a test particle approach has been used by the code ORBIT to obtain an estimation of the particle diffusion coefficients in many experimental RFX-mod plasmas2. secondary modes HELICAL EQUILIBRIUM FROM MAGNETIC TOPOLOGY collisions with plasma background mode (1,-7) + B0 @Ti = 500-1000 eV Di,QSH2Di,SH Di,QSH1.5-4 m2/s De in the helical core show a very different behavior in SH and QSH regimes: De,QSH10·De,SH but: De,QSH 2-3 m²/s Di,QSH [2]Gobbin et al., Phys. Plasmas 14, (072305), 2007 RFX-mod Workshop, Padova 20-22/01/ 2009

  7. Ns  De> 10m2/s De m²/s Di De< 0.1m2/s (SH: Ns=1) Ns Diffusion coefficients depend on… ..the level of secondary modes: De fastincreases as Ns becomes greater than 1 while Di is nearly constant. We expect from experimental data a dependence of the global D on the secondary modes amplitude. RFX-mod Workshop, Padova 20-22/01/ 2009

  8. v Ns  q De> 10m2/s B De m²/s Di l~1 De< 0.1m2/s (SH: Ns=1) Ns l ~0.1 Diffusion coefficients depend on… ..the level of secondary modes: De fastincreases as Ns becomes greater than 1 while Di is nearly constant. We expect from experimental data a dependence of the global D on the secondary modes amplitude. …the particles pitch angle! pitch: TRAPPED particles diffuse rapidly across the helical structure PASSINGions well confined in the high T helical structure Dpas~0.02-0.1 m²/s Dtrap~2-6 m²/s RFX-mod Workshop, Padova 20-22/01/ 2009

  9. Di,QSH~ 2.5 – 4 m2/s Di,MH~ 20m2/s Experimental data: pellet injection in helical structures Injection of pellet in the helical structures can give informations on particles transportfor the main gas to be compared with the predictions from ORBIT numerical simulations. - density refuelling in the hot helical structure - estimate of the particle confinement time in MH and QSH/SHAx regimes PELLET: ORBIT: tQSH/tMH~2-3 RFX-mod Workshop, Padova 20-22/01/ 2009

  10. Di,QSH~ 2.5 – 4 m2/s Di,MH~ 20m2/s Experimental data: pellet injection in helical structures Injection of pellet in the helical structures can give informations on particles transportfor the main gas to be compared with the predictions from ORBIT numerical simulations. - density refuelling in the hot helical structure - estimate of the particle confinement time in MH and QSH/SHAx regimes PELLET: ORBIT: tQSH/tMH~2-3 More experiments in QSH/SHAx plasmas are required to obtain D values considering an helical geometry while analyzing the pellet ablation and diffusion mechanisms. Experimental estimates of D with different plasma temperature, density and level of perturbations to test the theoretical results on particle transport. -pellet trajectory and ablation - magnetic field structure Fast CCD camera can provide informations on: RFX-mod Workshop, Padova 20-22/01/ 2009

  11. D(m²/s) 20 0 v(m/s) r/a DQSH~20m²/s very close to the one typical of MH regimes. Impurities diffusion: laser blow- off with Ni Experiments of laser blow-off have been recently performed to study impurities diffusion in the helical core of RFX-mod high current plasmas. Emission lines Ni XVII 249 Å and Ni XVIII 292 Å have been observed, indicating that the impurity reached the high temperature regions inside the helical structure3. 1D collisional-radiative impurity transport code reproduces the emission pattern. D and v radial profiles While hydrogen injection by pellet shows an improvementof confinement inside the island, this is not observed for Ni impurities. [3] Carraro et al., submitted to Nucl. Fusion RFX-mod Workshop, Padova 20-22/01/ 2009

  12. Ni ions diffusion in the helical core by ORBIT Investigation by ORBIT both in MH and QSH regimes: Collisions: Test particles: Ni ions RFX-MOD @ 600eV Ni: 25/toroidal transit 0.1/toroidal transit H+: Dominance of collisional effects on magnetic topology in determining the diffusion properties of Ni impurities. D (m²/s) Banana regimes Fully Collisional Plateau MH: DNi~ 0.4-2m²/s QSH: DNi~ 0.1-1.5m²/s Collisions per toroidal transit Ni diffusion coefficients from numerical simulations are nearly the same in QSH and MH plasmas. Qualitative agreement between experiment and simulations. RFX-mod Workshop, Padova 20-22/01/ 2009

  13. Other analysis on impurities diffusion More LBO tests are required to investigate on the quantitative discrepancy between ORBIT results and the experimental data. DNi (ORBIT) < DNi (EXP) Use of different impurities at more plasma temperatures: D increases with ion temperature but the general behavior is still the same; Ni-Hsimulations @ 1200eV other impurities could allow to test different regions of collisionality; Ne: 2 colls / tor. transit Ar: 1.5 colls / tor. transit Ne, Ar, Al Al: 2.3 colls / tor. transit The propagation of cold pulses after the LBO could be analyzed to evaluate the perturbed electron energy diffusion coefficient ce4. [4] M.W.Kissick et al., Nucl.Fusion 34,1994 RFX-mod Workshop, Padova 20-22/01/ 2009

  14. helical flux Energy transport: in progress... Plasmas with large helical structures are characterized by: - a reduction of the energy transport and an increase of the confinement time (about a factor 2-4); - low residual magnetic chaos drift modes of electrostatic nature in helical structure may become important for transport5; - isothermal helical flux surfacesTe=Te(r); [5] Guo S.C., submitted to Phys. Rev. Lett. (2008) RFX-mod Workshop, Padova 20-22/01/ 2009

  15. helical flux The heat diffusion equation must be solved in a helical geometry in order to evaluate the energy diffusion coefficients. r h (r, h, f) Energy transport: in progress... Plasmas with large helical structures are characterized by: - a reduction of the energy transport and an increase of the confinement time (about a factor 2-4); - low residual magnetic chaos drift modes of electrostatic nature in helical structure may become important for transport5; - isothermal helical flux surfacesTe=Te(r); HELICAL EQUILIBRIUM DESCRIPTION Metric tensor gij Semi-analytical and numerical approaches; Adaption of stellarator codes (VMEC…) [5] Guo S.C., submitted to Phys. Rev. Lett. (2008) RFX-mod Workshop, Padova 20-22/01/ 2009

  16. MONO-ENERGETIC Di,j particles flux density energy flux density current density A more complete description of transport Numerical methods to study the neoclassical transportin realistic 3-D magnetic topologies, by solving a linearized drift kinetic equation. Transport coefficients can be obtained as flux-surface-averaged by an adaptation of existing codes for stellarators, but a good description of the helical equilibrium is first required. (by Monte-Carlo, full-f or df schemes, variational approach DKES) Dij integration over energy (Maxwellian distribution) allows to obtain informations on flux-surface-averaged flows: RFX-mod Workshop, Padova 20-22/01/ 2009

  17. Summary and conclusions The presence of an helical core in high current RFX-mod plasmas requires to perform energy/particles transport analysis in a helically-shaped geometry. RFX-mod Workshop, Padova 20-22/01/ 2009

  18. Summary and conclusions The presence of an helical core in high current RFX-mod plasmas requires to perform energy/particles transport analysis in a helically-shaped geometry. Particle transport simulations in helical states by ORBIT: Di,QSH De,QSH 2.5-4m2/s  1/5 DMH (@ T=600eV –1keV) Strong dependence of De on NS and a better confinement for passing particles Qualitative agreement with pellet experiments RFX-mod Workshop, Padova 20-22/01/ 2009

  19. Summary and conclusions The presence of an helical core in high current RFX-mod plasmas requires to perform energy/particles transport analysis in a helically-shaped geometry. Particle transport simulations in helical states by ORBIT: Di,QSH De,QSH 2.5-4m2/s  1/5 DMH (@ T=600eV –1keV) Strong dependence of De on NS and a better confinement for passing particles Qualitative agreement with pellet experiments Nichel diffusion coefficients in QSH and MH are about the same. Dominance of collision mechanisms on magnetic perturbations effect. DNi,QSH DNi,MH Qualitative agreement between theory and experiments. More investigation is required to understand the quantitative discrepancy. RFX-mod Workshop, Padova 20-22/01/ 2009

  20. Summary and conclusions The presence of an helical core in high current RFX-mod plasmas requires to perform energy/particles transport analysis in a helically-shaped geometry. Particle transport simulations in helical states by ORBIT: Di,QSH De,QSH 2.5-4m2/s  1/5 DMH (@ T=600eV –1keV) Strong dependence of De on NS and a better confinement for passing particles Qualitative agreement with pellet experiments Nichel diffusion coefficients in QSH and MH are about the same. Dominance of collision mechanisms on magnetic perturbations effect. DNi,QSH DNi,MH Qualitative agreement between theory and experiments. More investigation is required to understand the quantitative discrepancy. Energy transport and heat balance in helical geometry is still under study: a complete description of the helical equilibrium is first required. RFX-mod Workshop, Padova 20-22/01/ 2009

  21. Summary and conclusions The presence of an helical core in high current RFX-mod plasmas requires to perform energy/particles transport analysis in a helically-shaped geometry. Particle transport simulations in helical states by ORBIT: Di,QSH De,QSH 2.5-4m2/s  1/5 DMH (@ T=600eV –1keV) Strong dependence of De on NS and a better confinement for passing particles Qualitative agreement with pellet experiments Nichel diffusion coefficients in QSH and MH are about the same. Dominance of collision mechanisms on magnetic perturbations effect. DNi,QSH DNi,MH Qualitative agreement between theory and experiments. More investigation is required to understand the quantitative discrepancy. Energy transport and heat balance in helical geometry is still under study: a complete description of the helical equilibrium is first required. Numerical methods adopted in the stellarator community to study global neoclassical transport could be applied also to helical RFP plasmas. RFX-mod Workshop, Padova 20-22/01/ 2009

  22. Thanks for your attention RFX-mod Workshop, Padova 20-22/01/ 2009

  23. RFX-mod Workshop, Padova 20-22/01/ 2009

  24. MORE.... RFX-mod Workshop, Padova 20-22/01/ 2009

  25. Magnetic flux from Poincaré: yM/yMloss A dl C S Helical magnetic flux definition Helical flux contour on a poloidal section : test particles deposited in the o-point yMo-point= 0 loss surface yMloss RFX-mod Workshop, Padova 20-22/01/ 2009

  26. Banana orbits size increases with their energy Passing ion orbit in a QSH (1,-7) Trapped ion orbit 0.2 cm(800 eV) Poloidal banana width: Colors of the trajectories are relative to different helical flux values. 0.5 - 5cm 300 – 1200eV Helical banana size: Electrons experience very small neoclassical effects : their banana orbits are less than few mm still at 800 eV. For a given energy E the banana size of an impurity with atomic mass A is proportional to : v (E/A)1/2 RFX-mod Workshop, Padova 20-22/01/ 2009

  27. (Dr)² (cm²) t(ms) Local diffusion coefficient evaluation Di is evaluated locally too because: -it may vary inside the helical domain -the approximations due to the non linear density distribution are avoided particles deposition Almost constant inside the helical structure: 1-5m²/s Dloc (m²/s) Trapped, passing, uniform pitch particles show different slopes for the relation Dr² versus time t. yM RFX-mod Workshop, Padova 20-22/01/ 2009

  28. Energy transport is still under study ... A first step required to write the heat balance equations in the RFX-mod QSH plasmas is the complete description of the helical equilibrium: yM Z mode (1,-7) + B0 h R (R,Z,f) (yM, h, f) Once defined the change of coordinates, the metric tensor can be computed and so energy transport equations can be written for quantities as function of the helical flux. Semi-analytical from the knowledge of the (1,-7) eigenfunction and of the equilibrium poloidal and toroidal fluxes (E.Martines) Numerical reconstruction of the helical flux and helical angle (from magnetic topology) Adaptation of codes such as VMEC and TRANSP (see Marrelli’s talk) RFX-mod Workshop, Padova 20-22/01/ 2009

  29. Effect of secondary modes on De The level of secondary modes significantly affects the diffusion of electrons in high temperature QSH. De> 10m2/s De Input to ORBIT m²/s Di De< 0.1m2/s Ns n=8-24 x k Secondary modes spectrum is multiplied by a constant k; this changes the Ns parameter: De increases rapidily as Ns becomes greater than 1 while Di is nearly constant. Ns  We expect from experimental data a dependence of the global D on the secondary modes. (SH: Ns=1, k=0) RFX-mod Workshop, Padova 20-22/01/ 2009

  30. Correlation of D with experimental magnetic perturbations Di,QSH (m²/s) Di,QSH (m²/s) Correlations between the magnetic energy of the dominant (1,-7) mode and of the secondary modes with the ion transport properties in the analyzed experimental shots. (mT) Di,QSH (m²/s) Di,SH/Di,QSH Best QSH are very close to the corresponding SH case for ions (mT) RFX-mod Workshop, Padova 20-22/01/ 2009

  31. a main gas ions electrons CVI OVII impurities rL B b nttor H+ RFX-mod >1.2MA e- va va q b B E(eV) Interaction of test particles with the plasma background test particlea backgroundb: aare mono-energetic and energy is conserved during collision mechanisms aparticles change their guiding center position randomly by a gyroradius [3] aparticles change randomly also their velocity direction with respect to B pitch angle: 5 [3] B.A.Trubnikov, Rev. Plasma Phys. 1, (105), 1965 RFX-mod Workshop, Padova 20-22/01/ 2009

  32. v q B l~1 follow helical field lines small thermal drift Trapped and passing ions in helical structures The pitch angle of the particle is an other key parameter in the determination of particles diffusion coefficients. pitch: PASSINGions with l 1arewell confined in the high T helical structure TRAPPED particles diffuse rapidly across the helical structure Dpas~0.02-0.1 m²/s Dtrap~2-6 m²/s poloidal and helical trapping low collisionality and residual chaos banana orbits Dtrap/Dpas ~ 100 !! width: 0.5 - 5cm @ (300 – 1200eV) l ~0.1 RFX-mod Workshop, Padova 20-22/01/ 2009

  33. D(m²/s) simulated v(m/s) experiment r/a Impurities diffusion: LBO in QSH and MH plasmas Experiments of laser blow-off have been performed recently to study impurities diffusion in the helical core of RFX-mod high current plasmas. Emission lines Ni XVII 249 Å and Ni XVIII 292 Å have been observed, indicating that the impurity reached the high temperature regions inside the helical structure.[3] D and v radial profiles to be implemented in the code for a good matching with experimental data: 20 0 with DQSH~20m²/s very close to the one typical of MH case. t(s) While hydrogen injection by pellet shows an improvementof confinement inside the island, this is not observed for impurities. 1D collisional-radiative impurity transport code reproduces the emission pattern. [3] L.Carraro, submitted to Nucl. Fusion RFX-mod Workshop, Padova 20-22/01/ 2009

  34. p Electrons are confined in the magnetic island Ns~1 (pure SH case): De<<Di De and Di are of the same order (at 700eV) 1.03<Ns<1.1: De~Di De rapidly increase with the level of secondary modes De>>Di Ns>1.1: Ratio of Di and De at several level of secondary modes and more temperatures: De/Di (m²/s) 1keV 0.7keV 0.4keV Ns RFX-mod Workshop, Padova 20-22/01/ 2009

  35. De m²/s Di Ns Effect of secondary modes on De The level of secondary modes significantly affects the diffusion of electrons in high temperature QSH: MH De> 12m2/s Typical RFX-mod QSH De(m²/s) n=8-24 x k De~ 3m2/s De< 0.1m2/s SH k The ion diffusion coefficient depends slightly on the level of secondary modes… … but experimentally the global ambipolar D will be a function of the Ns parameter: Ns RFX-mod Workshop, Padova 20-22/01/ 2009

  36. Test particle approach in helical RFX-mod plasmas Up to now a test particle approach has been used by the code ORBIT to obtain an estimation of the particle diffusion coefficients in many experimental RFX-mod plasmas, considering the real helical geometry. 1.Helical flux used as new radial flux coordinate 2.Transport inside the helical structure with: secondary modes y M collisions with plasma background Source n G 3.Evaluation of a diffusion coefficientD particles distribution over the helical domain is recorded helical magnetic flux yM(X,Z,f) associated to each point inside the helix (1,-7) [2] [2]Gobbin et al., Phys. Plasmas 14, (072305), 2007 RFX-mod Workshop, Padova 20-22/01/ 2009

  37. Ion and electron diffusion coefficients in SH and QSH Ion Di in SH and QSH Electron De in SH and QSH x10 Electron diffusion coefficients inside the helical core show a very different behavior in SH and QSH regimes: The effect of residual chaos in QSH does not affect dramatically Di @Ti = 500-1000 eV De,QSH10·De,SH Di,QSH2Di,SH Note that in QSH (@Te>800eV): Di,QSH2.5-4 m2/s De,QSH 2-3 m²/s Di,QSH RFX-mod Workshop, Padova 20-22/01/ 2009

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