1. RFX-mod Workshop, Padova 20-22/01/ 2009 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 RFX-mod Programme Workshop 2009, January 20-22, Padova, Italy Consorzio RFX, Associazione Euratom-Enea sulla Fusione, Padova, Italy

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

3. RFX-mod Workshop, Padova 20-22/01/ 2009 Helical structures in RFX-mod plasmas  =20-30 cm The (1,-7) mode is not anymore just a small perturbation. In high current RFX-mod plasmas, the magnetic topology is not anymore axisymmetric but helically deformed 1. -Thomson scattering (TS) -SXR diagnostics -radiation distribution from bolometry -magnetic signals  topology reconstructions (ORBIT and FLiT codes) : Evidences from: 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)  SXRTS POINCARE’

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

5. RFX-mod Workshop, Padova 20-22/01/ 2009 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 2. secondary modes collisions with plasma background HELICAL EQUILIBRIUM FROM MAGNETIC TOPOLOGY [2]Gobbin et al., Phys. Plasmas 14, (072305), 2007 mode (1,-7) + B 0

6. RFX-mod Workshop, Padova 20-22/01/ 2009 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 2. secondary modes collisions with plasma background HELICAL EQUILIBRIUM FROM MAGNETIC TOPOLOGY [2]Gobbin et al., Phys. Plasmas 14, (072305), 2007 mode (1,-7) + B 0 D i,QSH  1.5-4 m 2 /s D i,QSH  2D i,SH D e,QSH  10·D e,SH D e,QSH  2-3 m²/s  D i,QSH @T i = 500-1000 eV D e in the helical core show a very different behavior in SH and QSH regimes: but: D i in SH and QSH D e in SH and QSH x10IONSELECTRONS

7. RFX-mod Workshop, Padova 20-22/01/ 2009..the level of secondary modes: D e fast increases as N s becomes greater than 1 while D i is nearly constant. We expect from experimental data a dependence of the global D on the secondary modes amplitude. DeDe DiDi NsNs m²/s D e < 0.1m 2 /s D e > 10m 2 /s N s  (SH: N s =1) Diffusion coefficients depend on…

8. RFX-mod Workshop, Padova 20-22/01/ 2009..the level of secondary modes: D e fast increases as N s becomes greater than 1 while D i is nearly constant. We expect from experimental data a dependence of the global D on the secondary modes amplitude. DeDe DiDi NsNs m²/s D e < 0.1m 2 /s D e > 10m 2 /s N s  (SH: N s =1) …the particles pitch angle! Diffusion coefficients depend on… pitch: B  v ~1  ~  PASSING ions well confined in the high T helical structure D pas ~0.02-0.1 m²/s TRAPPED particles diffuse rapidly across the helical structure D trap ~2-6 m²/s

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

10. RFX-mod Workshop, Padova 20-22/01/ 2009 Experimental data: pellet injection in helical structures Injection of pellet in the helical structures can give informations on particles transport for the main gas to be compared with the predictions from ORBIT numerical simulations. ORBIT: 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. D i,QSH ~ 2.5 – 4 m 2 /s D i,MH ~ 20m 2 /s  QSH /  MH ~2-3 - density refuelling in the hot helical structure Fast CCD camera can provide informations on: PELLET: - estimate of the particle confinement time in MH and QSH/SHAx regimes - pellet trajectory and ablation - magnetic field structure

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

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

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

14. RFX-mod Workshop, Padova 20-22/01/ 2009 Energy transport: in progress... - isothermal helical flux surfaces Te=Te(  ); 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); helical flux - low residual magnetic chaos  drift modes of electrostatic nature in helical structure may become important for transport 5 ; [5] Guo S.C., submitted to Phys. Rev. Lett. (2008)

15. RFX-mod Workshop, Padova 20-22/01/ 2009 Energy transport: in progress... - isothermal helical flux surfaces Te=Te(  ); 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); Semi-analytical and numerical approaches; Adaption of stellarator codes (VMEC…) The heat diffusion equation must be solved in a helical geometry in order to evaluate the energy diffusion coefficients. HELICAL EQUILIBRIUM DESCRIPTION Metric tensor g ij , ,    helical flux - low residual magnetic chaos  drift modes of electrostatic nature in helical structure may become important for transport 5 ; [5] Guo S.C., submitted to Phys. Rev. Lett. (2008)

16. RFX-mod Workshop, Padova 20-22/01/ 2009 A more complete description of transport Numerical methods to study the neoclassical transport in 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. MONO-ENERGETIC D i,j D ij integration over energy (Maxwellian distribution) allows to obtain informations on flux-surface-averaged flows: particles flux density energy flux density current density (by Monte-Carlo, full-f or  f schemes, variational approach DKES)

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

18. RFX-mod Workshop, Padova 20-22/01/ 2009 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: D i,QSH  D e,QSH  2.5-4m 2 /s  1/5 D MH (@ T=600eV – 1keV) Strong dependence of D e on N S and a better confinement for passing particles Qualitative agreement with pellet experiments

19. RFX-mod Workshop, Padova 20-22/01/ 2009 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. Nichel diffusion coefficients in QSH and MH are about the same. Dominance of collision mechanisms on magnetic perturbations effect. Particle transport simulations in helical states by ORBIT: D i,QSH  D e,QSH  2.5-4m 2 /s  1/5 D MH (@ T=600eV – 1keV) Strong dependence of D e on N S and a better confinement for passing particles D Ni,QSH  D Ni,MH Qualitative agreement between theory and experiments. More investigation is required to understand the quantitative discrepancy. Qualitative agreement with pellet experiments

20. RFX-mod Workshop, Padova 20-22/01/ 2009 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. Nichel diffusion coefficients in QSH and MH are about the same. Dominance of collision mechanisms on magnetic perturbations effect. Particle transport simulations in helical states by ORBIT: D i,QSH  D e,QSH  2.5-4m 2 /s  1/5 D MH (@ T=600eV – 1keV) Strong dependence of D e on N S and a better confinement for passing particles D Ni,QSH  D Ni,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. Qualitative agreement with pellet experiments

21. RFX-mod Workshop, Padova 20-22/01/ 2009 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. Nichel diffusion coefficients in QSH and MH are about the same. Dominance of collision mechanisms on magnetic perturbations effect. Particle transport simulations in helical states by ORBIT: D i,QSH  D e,QSH  2.5-4m 2 /s  1/5 D MH (@ T=600eV – 1keV) Strong dependence of D e on N S and a better confinement for passing particles D Ni,QSH  D Ni,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. Qualitative agreement with pellet experiments Numerical methods adopted in the stellarator community to study global neoclassical transport could be applied also to helical RFP plasmas.

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

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

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

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

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

28. RFX-mod Workshop, Padova 20-22/01/ 2009 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: (R,Z,   M, ,  Z R mode (1,-7) + B 0 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 )  MM

29. RFX-mod Workshop, Padova 20-22/01/ 2009 The level of secondary modes significantly affects the diffusion of electrons in high temperature QSH. N s  n=8-24 x k Secondary modes spectrum is multiplied by a constant k; this changes the N s parameter: Effect of secondary modes on D e DeDe DiDi NsNs m²/s D e increases rapidily as Ns becomes greater than 1 while D i is nearly constant. We expect from experimental data a dependence of the global D on the secondary modes. (SH: N s =1, k=0) Input to ORBIT D e < 0.1m 2 /s D e > 10m 2 /s

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

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

32. RFX-mod Workshop, Padova 20-22/01/ 2009 ~1  ~  PASSING PASSING ions with  are  well confined in the high T helical structure low collisionality and residual chaos TRAPPED TRAPPED particles diffuse rapidly across the helical structure poloidal and helical trapping banana orbits pitch: B  v 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. D pas ~0.02-0.1 m²/s small thermal drift follow helical field lines 0.5 - 5cm@ (300 – 1200eV) width: D trap ~2-6 m²/s D trap /D pas ~ 100 !!

33. RFX-mod Workshop, Padova 20-22/01/ 2009 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] 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: [3] L.Carraro, submitted to Nucl. Fusion 20 0

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

35. RFX-mod Workshop, Padova 20-22/01/ 2009 The level of secondary modes significantly affects the diffusion of electrons in high temperature QSH: n=8-24 x k Effect of secondary modes on D e The ion diffusion coefficient depends slightly on the level of secondary modes… DeDe DiDi NsNs m²/s global ambipolar D … but experimentally the global ambipolar D will be a function of the N s parameter: D e (m²/s) k SH MH Typical RFX-mod QSH D e ~ 3m 2 /s D e < 0.1m 2 /s D e > 12m 2 /s NsNs

36. RFX-mod Workshop, Padova 20-22/01/ 2009 n  Source helical magnetic flux  M (X,Z  ) associated to each point inside the helix (1,-7) [2] 1.Helical flux used as new radial flux coordinate  M 2.Transport inside the helical structure particles distribution over the helical domain is recorded 3.Evaluation of a diffusion coefficient D Test particle approach in helical RFX-mod plasmas [2]Gobbin et al., Phys. Plasmas 14, (072305), 2007 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. secondary modes collisions with plasma background with:

37. RFX-mod Workshop, Padova 20-22/01/ 2009 Ion D i in SH and QSH The effect of residual chaos in QSH does not affect dramatically D i Electron diffusion coefficients 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 (@Te>800eV): D e,QSH  2-3 m²/s  D i,QSH Ion and electron diffusion coefficients in SH and QSH D i,QSH  2.5-4 m 2 /s D i,QSH  2D i,SH @T i = 500-1000 eV