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

2. RFP Workshop, Stockholm 9-11 /10/ 2008 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. Contents [0] R. B. White and M. S. Chance, Phys. Fluids 27, 2455 1984. 1

3. RFP Workshop, Stockholm 9-11 /10/ 2008 High-current RFX-mod plasmas: main parameters, thermal structures and magnetic topology. Contents

4. RFP Workshop, Stockholm 9-11 /10/ 2008 Large helical structures appear in high current RFX-mod plasmas: 1.5MA QSH b 1,7 b 1,8 b 1,9 I p (MA) b  (mT) F (ms) Helical structure in RFX-mod plasmas I p  1.2  1.5 MA n e  1  4·10 19 m -3 F  - 0.02 N s  1.05 Main parameters range 2 NsNs

5. RFP Workshop, Stockholm 9-11 /10/ 2008 Helical structure in RFX-mod plasmas Large helical structures appear in high current RFX-mod plasmas: 1.5MA QSH b 1,7 b 1,8 b 1,9 I p (MA) b  (mT) F (ms) I p  1.2  1.5 MA n e  1  4·10 19 m -3 F  - 0.02 N s  1.05 Significant electron temperature radial profile in the plasma core: 25-50% of plasma volume 1keV Main parameters range 2 NsNs

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

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

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

9. RFP Workshop, Stockholm 9-11 /10/ 2008 Contents Particle transport by the ORBIT [0] code in the helical geometry of QSH regimes: the method. [0] R. B. White and M. S. Chance, Phys. Fluids 27, 2455 1984.

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

11. RFP Workshop, Stockholm 9-11 /10/ 2008 test particle   background  :  are mono-energetic and energy is conserved during collision mechanisms  particles change their guiding center position randomly by a gyroradius  particles change randomly also their velocity direction with respect to B pitch angle: B vv  vv   B rLrL Interaction of test particles with the plasma background 5

12. RFP Workshop, Stockholm 9-11 /10/ 2008 test particle   background  :  are mono-energetic and energy is conserved during collision mechanisms  particles change their guiding center position randomly by a gyroradius  particles change randomly also their velocity direction with respect to B pitch angle: B vv  vv   B rLrL Interaction of test particles with the plasma background main gas ions electrons impurities CVI OVII  E(eV)  tor RFX-mod >1.2MA e- H+H+ [3] [3] B.A.Trubnikov, Rev. Plasma Phys. 1, (105), 1965 5

13. RFP Workshop, Stockholm 9-11 /10/ 2008 Ion and Electron diffusion coefficients in QSH regimes: discussion on the ambipolar electric field implementation. Contents

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

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

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

17. RFP Workshop, Stockholm 9-11 /10/ 2008 Ion D i in SH and QSH The effect of residual chaos in QSH does not affect dramatically D i A decrease of D i is expected at higher temperatures inside the helical core both in SH and QSH <500eV dominance of drift effects  T >500eV strong collisionality reduction  1/T 3/2 Ion and electron diffusion coefficients in SH and QSH 7

18. RFP Workshop, Stockholm 9-11 /10/ 2008 Ion D i in SH and QSH The effect of residual chaos in QSH does not affect dramatically D i A decrease of D i is expected at higher temperatures inside the helical core both in SH and QSH <500eV dominance of drift effects  T >500eV strong collisionality reduction  1/T 3/2 Electron diffusion coefficient inside the helical core show a very different behavior in SH and QSH regimes: Electron D e in SH and QSH x10 D e,QSH  10·D e,SH Note that in QSH (800eV): D i,QSH  1-1.5 D e,QSH Ion and electron diffusion coefficients in SH and QSH 7

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

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

21. RFP Workshop, Stockholm 9-11 /10/ 2008 Transport simulation performed for different level of secondary modes: n=8-24 x k D e (m²/s) k SH MH Typical RFX-mod QSH Ratio of D i and D e at several level of secondary modes and more temperatures: D e /D i (m²/s) 1keV 0.7keV 0.4keV N s ~1 (pure SH case): 1.03<N s <1.1: Electrons are confined in the magnetic island D e and D i are of the same order (at 700eV) N s >1.1: D e rapidly increase with the level of secondary modes D e <<D i D e ~D i D e >>D i NsNs Ambipolar transport in high temperature QSH plasma 8

22. RFP Workshop, Stockholm 9-11 /10/ 2008 Contents Different trapped and passing particles contribution to the diffusion coefficents in high temperature helical structures.

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

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

25. RFP Workshop, Stockholm 9-11 /10/ 2008 Effect of the particles pitch angle on density distribution TRAPPED almost linear ions distribution for low pitch angle values PASSING  No significant dependence on as approaches to 1, ions are gradually less moved from their initial helical flux location Simulations with selected values of pitch angle range have been recently performed, with the following plasma parameters: T i ~800eVn e ~3·10 19 m -3 ~0.7kHz 10

26. RFP Workshop, Stockholm 9-11 /10/ 2008 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: TRAPPED almost linear ions distribution for low pitch angle values PASSING Note that: T i ~800eVn e ~3·10 19 m -3 ~0.7kHz 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  No significant dependence on as approaches to 1, ions are gradually less moved from their initial helical flux location 10

27. RFP Workshop, Stockholm 9-11 /10/ 2008 Diffusion of impurities in MH and QSH states. Contents

28. RFP Workshop, Stockholm 9-11 /10/ 2008 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] 1D collisional-radiative impurity transport code reproduces the emission pattern. While hydrogen injection by pellet shows an improvement of confinement inside the island, this is not observed for impurities. t(s) with D QSH ~20m²/s very close to the one typical of MH case. experiment simulated r/a D(m²/s) v(m/s) D and v radial profiles to be implemented in the code for a good matching with experimental data: [5] L.Carraro, submitted for IAEA Conf. 2008 11 20 0

29. RFP Workshop, Stockholm 9-11 /10/ 2008 D Ni ~ 0.5-2m²/s D H + ~ 20m²/s MH D Ni ~ 0.5-2m²/s D H + ~ 0.4-1.5m²/s QSH Qualitative agreement between experiment and simulation. Differences on the order of D Ni to be further investigated. Impurities transport : a test particle approach Collisions: 25/toroidal transit Ni: 0.1/toroidal transit H+:H+:H+:H+: T Ni =600eV=T i T e =800eV T OVI =600eV=T CV n OVI =n CVI =1% n e n e =n H+ =3·10 19 m -3 n Ni =0.1% n e D (m²/s) Collisions for toroidal transit RFX-MOD @ 600eV Investigation by ORBIT both in MH and QSH regimes: Fully Collisional Banana regimes Plateau 12

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

31. RFP Workshop, Stockholm 9-11 /10/ 2008 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. Future Work -Full radial profiles of temperature and density to be implemented - Collisionality depending on particle position 13

32. RFP Workshop, Stockholm 9-11 /10/ 2008 Conclusions and future work 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). 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

33. RFP Workshop, Stockholm 9-11 /10/ 2008 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. To higher N S values and for N S =1 the ambipolar field should be implemented. (In the range ~ 400-1000eV) Future Work 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

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

35. RFP Workshop, Stockholm 9-11 /10/ 2008 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. Nichel diffusion coefficients in QSH and MH are about the same. Dominance of collision mechanisms on magnetic perturbations effect. 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

36. RFP Workshop, Stockholm 9-11 /10/ 2008 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. Future Work Further investigation to understand the difference on the absolute values found. Nichel diffusion coefficients in QSH and MH are about the same. Dominance of collision mechanisms on magnetic perturbations effect. 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

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

38. RFP Workshop, Stockholm 9-11 /10/ 2008 dldl A S C Magnetic flux from Poincaré: Helical flux contour on a poloidal section : test particles deposited in the o-point loss surface  M loss    M loss  M o-point = 0 Helical magnetic flux definition

39. RFP Workshop, Stockholm 9-11 /10/ 2008 Banana orbits size increases with their energy Passing ion orbit in a QSH (1,-7) Colors of the trajectories are relative to different helical flux values. Trapped ion orbit Helical banana size: 0.5 - 5cm300 – 1200eV Poloidal banana width: 0.2 cm (800 eV) For a given energy E the banana size of an impurity with atomic mass A is proportional to : Electrons experience very small neoclassical effects : their banana orbits are less than few mm still at 800 eV.  v  (E/A) 1/2

40. RFP Workshop, Stockholm 9-11 /10/ 2008 Local diffusion coefficient evaluation D i is evaluated locally too because: -it may vary inside the helical domain -the approximations due to the non linear density distribution are avoided (  r)² (cm²) t(ms) Trapped, passing, uniform pitch particles show different slopes for the relation  r² versus time t. MM D loc (m²/s) Almost constant inside the helical structure: 1-5m²/s particles deposition

41. RFP Workshop, Stockholm 9-11 /10/ 2008 Correlation of D with experimental magnetic perturbations 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. D i,QSH (m²/s) D i,SH /D i,QSH D i,QSH (m²/s) (mT) Best QSH are very close to the corresponding SH case for ions