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Numerical studies of particle transport mechanisms in RFX-mod low chaos regimes

13rd RFP Workshop, 2008 October 9-11, Stockholm, Sweden. Numerical studies of particle transport mechanisms in RFX-mod low chaos regimes. M.Gobbin , L.Marrelli, L.Carraro, G.Spizzo. Consorzio RFX, Associazione Euratom-Enea sulla Fusione, Padova, Italy. R.B. White.

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Numerical studies of particle transport mechanisms in RFX-mod low chaos regimes

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  1. 13rd RFP Workshop, 2008 October 9-11, Stockholm, Sweden Numerical studies of particle transport mechanisms in RFX-mod low chaos regimes M.Gobbin, L.Marrelli, L.Carraro, G.Spizzo Consorzio RFX, Associazione Euratom-Enea sulla Fusione, Padova, Italy R.B. White Princeton Plasma Physics Laboratory, Princeton, NJ, USA RFP Workshop, Stockholm 9-11 /10/ 2008

  2. Contents High-current RFX-mod plasmas: main parameters, thermal structures and magnetic topology. Particle transport by the ORBIT[0] code in the helical geometry of QSH regimes: the method. Ion and Electron diffusion coefficients in QSH regimes: discussion on the ambipolar electric field implementation. Different trapped and passing particles contribution to the diffusion coefficents in high temperature helical structures. Diffusion of impurities in MH and QSH states. Summary and Conclusions. 1 [0] R. B. White and M. S. Chance, Phys. Fluids 27, 2455 1984. RFP Workshop, Stockholm 9-11 /10/ 2008

  3. Contents High-current RFX-mod plasmas: main parameters, thermal structures and magnetic topology. Particle transport by the ORBIT code in the helical geometry of QSH regimes: the method. Ion and Electron diffusion coefficients in QSH regimes: discussion on the ambipolar electric field implementation. Different trapped and passing particles contribution to the diffusion coefficents in high temperature helical structures. Diffusion of impurities in MH and QSH states. Summary and Conclusions. RFP Workshop, Stockholm 9-11 /10/ 2008

  4. Ns Helical structure in RFX-mod plasmas Main parameters range Large helical structures appear in high current RFX-mod plasmas: Ip 1.21.5 MA F  - 0.02 1.5MA Ns 1.05 ne 1 4·1019m-3 Ip(MA) QSH b1,7 bf(mT) b1,8 b1,9 F (ms) 2 RFP Workshop, Stockholm 9-11 /10/ 2008

  5. Ns Helical structure in RFX-mod plasmas Main parameters range Large helical structures appear in high current RFX-mod plasmas: Ip 1.21.5 MA F  - 0.02 1.5MA Ns 1.05 ne 1 4·1019m-3 Ip(MA) 1keV QSH b1,7 bf(mT) b1,8 b1,9 F Significant electron temperature radial profile in the plasma core: 25-50% of plasma volume (ms) 2 RFP Workshop, Stockholm 9-11 /10/ 2008

  6. Magnetic topology related to QSH states Plasma magnetic topology: Poloidal Poincarè d p d=20-30 cm Ip=1.5MA 3 RFP Workshop, Stockholm 9-11 /10/ 2008

  7. Magnetic topology related to QSH states Plasma magnetic topology: Small thermal structures: Poloidal Poincarè Peaked Te profiles d Smaller helical structures: -reduced stickyness -localized magnetic island -common at low Ip p d=20-30 cm Ip=1.5MA 3 RFP Workshop, Stockholm 9-11 /10/ 2008

  8. Magnetic topology related to QSH states Plasma magnetic topology: Small thermal structures: Poloidal Poincarè Peaked Te profiles d Smaller helical structures: -reduced stickyness -localized magnetic island -common at low Ip p d=20-30 cm Ip=1.5MA m=1 spectrum SH Poincarè SH (1,-7) SHAx states for high values of the dominant mode [1]. • Need to perform particle and energy transport simulations in a helical shaped geometry: • helical equilibrium magnetic field • - superimposition of the residual chaos helical field 3 [1]Lorenzini et al., Phys. Rev. Lett. 101, 025005 (2008) RFP Workshop, Stockholm 9-11 /10/ 2008

  9. Contents High-current RFX-mod plasmas: main parameters, thermal structures and magnetic topology. Particle transport by the ORBIT[0] code in the helical geometry of QSH regimes: the method. Ion and Electron diffusion coefficients in QSH regimes: discussion on the ambipolar electric field implementation. Different trapped and passing particles contribution to the diffusion coefficents in high temperature helical structures. Diffusion of impurities in MH and QSH states. Summary and Conclusions. [0] R. B. White and M. S. Chance, Phys. Fluids 27, 2455 1984. RFP Workshop, Stockholm 9-11 /10/ 2008

  10. Particle transport simulation: the method 1.Helical geometryreconstruction: 2.Transport inside the helical structure 3.D estimation y M Source n ions and electrons G in SH and QSH Loss Surface different energy test particles deposited in the o-point stationary regime achieved impurities transport inclusion of collisions with the background helical magnetic flux yM(x,z,f) associated to each point inside the helix (1,-7) [2] particle distribution on helical domain 4 [2]Gobbin et al., Phys. Plasmas 14, (072305), 2007 RFP Workshop, Stockholm 9-11 /10/ 2008

  11. rL B b va va q b B 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 aparticles change randomly also their velocity direction with respect to B pitch angle: 5 RFP Workshop, Stockholm 9-11 /10/ 2008

  12. 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 RFP Workshop, Stockholm 9-11 /10/ 2008

  13. Contents High-current RFX-mod plasmas: main parameters, thermal structures and magnetic topology. Particle transport by the ORBIT code in the helical geometry of QSH regimes: the method. Ion and Electron diffusion coefficients in QSH regimes: discussion on the ambipolar electric field implementation. Different trapped and passing particles contribution to the diffusion coefficents in high temperature helical structures. Diffusion of impurities in MH and QSH states. Summary and Conclusions. RFP Workshop, Stockholm 9-11 /10/ 2008

  14. Particles distribution inside the helical core Transport simulations for ions at different temperatures in QSH: Flux of ions and electrons at different energy D=const assumes a linear trend for density as function of yM 6 RFP Workshop, Stockholm 9-11 /10/ 2008

  15. Particles distribution inside the helical core Transport simulations for ions at different temperatures in QSH: Flux of ions and electrons at different energy D=const assumes a linear trend for density as function of yM no linear distribution in helical flux above 500 eV reduction of collisionality reduced secondary modes 6 RFP Workshop, Stockholm 9-11 /10/ 2008

  16. Particles distribution inside the helical core Transport simulations for ions at different temperatures in QSH: Flux of ions and electrons at different energy Estimate of a range values for D no linear distribution in helical flux above 500 eV reduction of collisionality reduced secondary modes 6 RFP Workshop, Stockholm 9-11 /10/ 2008

  17. The effect of residual chaos in QSH does not affect dramatically Di A decrease of Di is expected at higher temperatures inside the helical core both in SH and QSH Ion and electron diffusion coefficients in SH and QSH Ion Di in SH and QSH <500eV dominance of drift effects  T >500eV strong collisionality reduction  1/T3/2 7 RFP Workshop, Stockholm 9-11 /10/ 2008

  18. The effect of residual chaos in QSH does not affect dramatically Di A decrease of Di is expected at higher temperatures inside the helical core both in SH and QSH Ion and electron diffusion coefficients in SH and QSH Ion Di in SH and QSH Electron De in SH and QSH x10 Electron diffusion coefficient inside the helical core show a very different behavior in SH and QSH regimes: De,QSH10·De,SH Note that in QSH (800eV): <500eV dominance of drift effects  T Di,QSH1-1.5 De,QSH >500eV strong collisionality reduction  1/T3/2 7 RFP Workshop, Stockholm 9-11 /10/ 2008

  19. Is the ambipolar electric field important in QSH? Transport simulation performed for different level of secondary modes: n=8-24 x k MH Typical RFX-mod QSH De(m²/s) SH k 8 RFP Workshop, Stockholm 9-11 /10/ 2008

  20. Ambipolar transport in high temperature QSH plasma Transport simulation performed for different level of secondary modes: Ratio of Di and De at several level of secondary modes and more temperatures: De/Di (m²/s) 1keV 0.7keV n=8-24 x k 0.4keV MH k Ambipolar transport would take to: De/Di=1 Typical RFX-mod QSH De(m²/s) For typical QSH in RFX-mod (k1) De and Di are about the same even without the implementantion of an ambipolar electric field in the code SH At lower k electron diffusion is strongly reduced while at higher k strongly enhanced k Dependence on temperature 8 RFP Workshop, Stockholm 9-11 /10/ 2008

  21. 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: Ambipolar transport in high temperature QSH plasma Transport simulation performed for different level of secondary modes: Ratio of Di and De at several level of secondary modes and more temperatures: De/Di (m²/s) 1keV 0.7keV n=8-24 x k 0.4keV MH Ns Typical RFX-mod QSH De(m²/s) SH k 8 RFP Workshop, Stockholm 9-11 /10/ 2008

  22. Contents High-current RFX-mod plasmas: main parameters, thermal structures and magnetic topology. Particle transport by the ORBIT code in the helical geometry of QSH regimes: the method. Ion and Electron diffusion coefficients in QSH regimes: discussion on the ambipolar electric field implementation. Different trapped and passing particles contribution to the diffusion coefficents in high temperature helical structures. Diffusion of impurities in MH and QSH states. Summary and Conclusions. RFP Workshop, Stockholm 9-11 /10/ 2008

  23. Ion orbits in helical structures Passing Ion l~1 Poloidal Trapping l0.4 Banana width: 0.2 cm (800 eV) Helical Trapping l0.4 0.5 - 5cm (300 – 1200eV) (from Predebon et al., PRL 93 145001, 2004) Dynamic of trapped and passing ions in helical structures PITCH ANGLE DISTRIBUTION Dpas/Dtrap~0.01 Only trapped ions in the tail of the density distribution [5] Banana width: 9 [5] M.Gobbin et al., poster ICPP Conf. 2008 RFP Workshop, Stockholm 9-11 /10/ 2008

  24. Ion orbits in helical structures Passing Ion l~1 Poloidal Trapping l0.4 Banana width: 0.2 cm (800 eV) Helical Trapping l0.4 0.5 - 5cm (300 – 1200eV) (from Predebon et al., PRL 93 145001, 2004) Dynamic of trapped and passing ions in helical structures PITCH ANGLE DISTRIBUTION Dpas/Dtrap~0.01 Only trapped ions in the tail of the density distribution Simulations at 800 eV using only passing or only trapped ions. PASSINGparticles with l 1well confined TRAPPED particles diffuse across the helical structure Helical trapping follow helical field lines Poloidal trapping SMALL THERMAL DRIFT Main contribution to D Few Losses because of (few) collisions Banana width: 9 RFP Workshop, Stockholm 9-11 /10/ 2008

  25. Effect of the particles pitch angle on density distribution Simulations with selected values of pitch angle range have been recently performed, with the following plasma parameters: Ti~800eV n~0.7kHz ne~3·1019m-3 TRAPPED PASSING No significant dependence on l +l almost linear ions distribution for low pitch angle values as lapproaches to 1, ions are gradually less moved from their initial helical flux location 10 RFP Workshop, Stockholm 9-11 /10/ 2008

  26. Effect of the particles pitch angle on density distribution Simulations with selected values of pitch angle range have been recently performed, with the following plasma parameters: Ti~800eV n~0.7kHz ne~3·1019m-3 TRAPPED PASSING Note that: Electrons experience very small neoclassical effects : their banana orbits are less than few mm still at 800 eV. No significant dependence on l For a given energy E the banana size of an impurity with atomic mass A is proportional to : +l v (E/A)1/2 almost linear ions distribution for low pitch angle values as lapproaches to 1, ions are gradually less moved from their initial helical flux location 10 RFP Workshop, Stockholm 9-11 /10/ 2008

  27. Contents High-current RFX-mod plasmas: main parameters, thermal structures and magnetic topology. Particle transport by the ORBIT code in the helical geometry of QSH regimes: the method. Ion and Electron diffusion coefficients in QSH regimes: discussion on the ambipolar electric field implementation. Different trapped and passing particles contribution to the diffusion coefficents in high temperature helical structures. Diffusion of impurities in MH and QSH states. Summary and Conclusions. RFP Workshop, Stockholm 9-11 /10/ 2008

  28. D(m²/s) simulated v(m/s) experiment r/a Impurities transport in QSH and MH Experiments of laser blow off in QSH plasmas have been performed recently. 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.[5] 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. 11 [5] L.Carraro, submitted for IAEA Conf. 2008 RFP Workshop, Stockholm 9-11 /10/ 2008

  29. ne=nH+=3·1019m-3 Te=800eV TNi=600eV=Ti nNi=0.1% ne nOVI=nCVI=1% ne TOVI=600eV=TCV QSH MH DNi~ 0.5-2m²/s DNi~ 0.5-2m²/s DH+~ 0.4-1.5m²/s DH+~ 20m²/s Impurities transport : a test particle approach Investigation by ORBIT both in MH and QSH regimes: RFX-MOD @ 600eV D (m²/s) Banana regimes Fully Collisional Collisions: Plateau Ni: 25/toroidal transit 0.1/toroidal transit H+: Collisions for toroidal transit Qualitative agreement between experiment and simulation. Differences on the order of DNi to be further investigated. 12 RFP Workshop, Stockholm 9-11 /10/ 2008

  30. Conclusions and future work Strong reduction of the diffusion coefficients for the main gas in the large helical structure of high current RFX-mod plasmas. Transport simulations are performed in a helical geometry defined by the dominant tearing mode m=1,n=-7 by using mono-energetic test particles. 13 RFP Workshop, Stockholm 9-11 /10/ 2008

  31. Conclusions and future work Strong reduction of the diffusion coefficients for the main gas in the large helical structure of high current RFX-mod plasmas. Transport simulations are performed in a helical geometry defined by the dominant tearing mode m=1,n=-7 by using mono-energetic test particles. • Full radial profiles of temperature and density to be implemented • Collisionality depending on particle position Future Work 13 RFP Workshop, Stockholm 9-11 /10/ 2008

  32. Conclusions and future work Strong reduction of the diffusion coefficients for the main gas in the large helical structure of high current RFX-mod plasmas. Transport simulations are performed in a helical geometry defined by the dominant tearing mode m=1,n=-7 by using mono-energetic test particles. The residual magnetic chaos and collisions are enough to ensure an ambipolar transport in QSH at high current between 400 and 1000 eV (Ns~1.05). 13 RFP Workshop, Stockholm 9-11 /10/ 2008

  33. Conclusions and future work Strong reduction of the diffusion coefficients for the main gas in the large helical structure of high current RFX-mod plasmas. Transport simulations are performed in a helical geometry defined by the dominant tearing mode m=1,n=-7 by using mono-energetic test particles. The residual magnetic chaos and collisions are enough to ensure an ambipolar transport in QSH at high current between 400 and 1000 eV (Ns~1.05). Future Work To higher NS values and for NS=1 the ambipolar field should be implemented. (In the range ~ 400-1000eV) 13 RFP Workshop, Stockholm 9-11 /10/ 2008

  34. Conclusions and future work Strong reduction of the diffusion coefficients for the main gas in the large helical structure of high current RFX-mod plasmas. Transport simulations are performed in a helical geometry defined by the dominant tearing mode m=1,n=-7 by using mono-energetic test particles. The residual magnetic chaos and collisions are enough to ensure an ambipolar transport in QSH at high current between 400 and 1000 eV (Ns~1.05). In high temperature low magnetic chaos QSH: passing ions well confined, trapped ions mostly contribute to transport. An opposite behavior respect to a MH scenario. 13 RFP Workshop, Stockholm 9-11 /10/ 2008

  35. Conclusions and future work Strong reduction of the diffusion coefficients for the main gas in the large helical structure of high current RFX-mod plasmas. Transport simulations are performed in a helical geometry defined by the dominant tearing mode m=1,n=-7 by using mono-energetic test particles. The residual magnetic chaos and collisions are enough to ensure an ambipolar transport in QSH at high current between 400 and 1000 eV (Ns~1.05). In high temperature low magnetic chaos QSH: passing ions well confined, trapped ions mostly contribute to transport. An opposite behavior respect to a MH scenario. Nichel diffusion coefficients in QSH and MH are about the same. Dominance of collision mechanisms on magnetic perturbations effect. 13 RFP Workshop, Stockholm 9-11 /10/ 2008

  36. Conclusions and future work Strong reduction of the diffusion coefficients for the main gas in the large helical structure of high current RFX-mod plasmas. Transport simulations are performed in a helical geometry defined by the dominant tearing mode m=1,n=-7 by using mono-energetic test particles. The residual magnetic chaos and collisions are enough to ensure an ambipolar transport in QSH at high current between 400 and 1000 eV (Ns~1.05). In high temperature low magnetic chaos QSH: passing ions well confined, trapped ions mostly contribute to transport. An opposite behavior respect to a MH scenario. Nichel diffusion coefficients in QSH and MH are about the same. Dominance of collision mechanisms on magnetic perturbations effect. Future Work Further investigation to understand the difference on the absolute values found. 13 RFP Workshop, Stockholm 9-11 /10/ 2008

  37. MORE.... RFP Workshop, Stockholm 9-11 /10/ 2008

  38. 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 RFP Workshop, Stockholm 9-11 /10/ 2008

  39. 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 RFP Workshop, Stockholm 9-11 /10/ 2008

  40. particles deposition Almost constant inside the helical structure: 1-5m²/s Dloc (m²/s) (Dr)² (cm²) yM 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 Trapped, passing, uniform pitch particles show different slopes for the relation Dr² versus time t. RFP Workshop, Stockholm 9-11 /10/ 2008

  41. 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) RFP Workshop, Stockholm 9-11 /10/ 2008

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