1. 1 of 22A.V.Chankin & D.P.Coster, 18 th PSI Conference, Toledo, Spain, 29 May 2008 Comparison of 2D Models for the Plasma Edge with Experimental Measurements and Assessment of Deficiencies A.V.Chankin and D.P.Coster Max-Planck-Institut für Plasmaphysik Acknowledgements: L.K.Aho-Mantila, N.Asakura, X.Bonnin, G.D.Conway, G.Corrigan, R.Dux, S.K.Erents, A.Herrmann, Ch.Fuchs, W.Fundamenski, G.Haas, J.Horacek, L.D.Horton, A.Kallenbach, M.Kaufmann, Ch.Konz, V.Kotov, A.S.Kukushkin, T.Kurki-Suonio, B.Kurzan, K.Lackner, C.Maggi, H.W.Müller, J.Neuhauser, R.A.Pitts, R.Pugno, M.Reich, D.Reiter, V.Rohde, W.Schneider, S.K.Sipilä, P.C.Stangeby, M.Wischmeier, E.Wolfrum

2. 2 of 22A.V.Chankin & D.P.Coster, 18 th PSI Conference, Toledo, Spain, 29 May 2008 Outline Introduction: 2D edge fluid codes Measurements and simulations of: - parallel ion flow in SOL - divertor and target parameters - E r in SOL Possible causes of discrepancies between modelling and experiment Summary

3. 3 of 22A.V.Chankin & D.P.Coster, 18 th PSI Conference, Toledo, Spain, 29 May 2008 Computational grid and vessel structures - Plasma description: collisional parallel transport model, with kinetic limiters for transp. coeff.; anomalous perp. coefficients, drifts included - Neutrals description: kinetic Monte-Carlo codes, inside and outside of computational grid Main 2D edge fluid codes for SOL and divertor modelling SOLPS: B2-Eirene (AUG), EDGE2D-Nimbus,Eirene (JET), UEDGE-DEGAS (DIII-D) Physical and chemical sputtering from surfaces Multiple impurity charged states separatrix input power Consensus (prior to 2000): 2D edge fluid codes reproduce existing experiments within a factor of 2

4. 4 of 22A.V.Chankin & D.P.Coster, 18 th PSI Conference, Toledo, Spain, 29 May 2008 reciprocating probe Parallel ion SOL flow in JET – comparison with EDGE2D [S.K.Erents et al., PPCF 2000 & 2004] ballooning Parallel flow: ballooning + drift Bt -independent (Average flow) Bt -dependent

5. 5 of 22A.V.Chankin & D.P.Coster, 18 th PSI Conference, Toledo, Spain, 29 May 2008 recipr. probe Parallel ion SOL flow in JET – comparison with EDGE2D EDGE2D underestimates effect of Bt reversal by factor ~ 3 UEDGE underestimates effect of Bt reversal in JT-60U by factor 2 [N.Asakura et al., 2004]

6. 6 of 22A.V.Chankin & D.P.Coster, 18 th PSI Conference, Toledo, Spain, 29 May 2008 JT-60U: measured ion flow at outer midplane agrees with Pfirsch-Schlüter ion flow formula: Parallel flows in JT- 60U and TCV: effect of B t reversal [N.Asakura, et al., PRL 2000]  Measured flows are consistent with P-S formula, when p i, E r … are taken from experiment Same conclusion for TCV [R.A.Pitts et al., EPS-2007]

7. 7 of 22A.V.Chankin & D.P.Coster, 18 th PSI Conference, Toledo, Spain, 29 May 2008 Parallel flow in SOLPS: simulating AUG Ohmic shots Parallel flow at outer midpl. M || But: simulated flows are below measured in AUG by factor 3 (as in JET)  Simulated flows are consistent with P-S formula (p i, E r … - from code)

8. 8 of 22A.V.Chankin & D.P.Coster, 18 th PSI Conference, Toledo, Spain, 29 May 2008 Simulated vs. measured parallel ion flows Both in the codes and experiments, flows are broadly consistent with Pfirsch-Schlüter formula (at outer midplane position) But absolute values in codes < experimental by factors 2-3

9. 9 of 22A.V.Chankin & D.P.Coster, 18 th PSI Conference, Toledo, Spain, 29 May 2008 SOLPS simulations of AUG divertor conditions Fitting experimental outer midplane profiles by choice of D ,  e,  i 0 1 2 3 4 5 Edge Thomson scattering Lithium beam SOLPS 0 100 200 300 400 500 600 700 800 10 10 0 1 -0.02 0 0.02 SOL core D perp.  e  i  i neoclassical D: #17151 SOLPS: #12096 =  e  i Ion temperature Electron temperature [L.D.Horton et al., 2005] Distance from separatrix [m] H-mode #17151    Ohmic #18737Ohmic #21320

10. 10 of 22A.V.Chankin & D.P.Coster, 18 th PSI Conference, Toledo, Spain, 29 May 2008 SOLPS simulation of AUG divertor conditions - results distance along target (m) H-mode #17151: H a,code > H a,exp Ohmic #18737: T e,code n e,exp Conclusion confirmed by available evidence: - target Langmuir probe data - divertor spectroscopy: Ha, CIII emissions - sub-divertor neutral flux - carbon content at plasma edge At very low plasma n e, SOLPS predicts AUG target profiles reasonably well [M.Wischmeier et al., 2007]  For matching upstream profiles and boundary conditions, in medium to high density plasmas, SOLPS predicts colder and denser plasma in divertor than in experiment

11. 11 of 22A.V.Chankin & D.P.Coster, 18 th PSI Conference, Toledo, Spain, 29 May 2008 SOLPS simulation of AUG divertor conditions - results  SOLPS fails to simulate large asymmetry between the targets, and detachment at inner target [M.Wischmeier, et al., 2007]  Talk by M.Wischmeier, next session, O-25

12. 12 of 22A.V.Chankin & D.P.Coster, 18 th PSI Conference, Toledo, Spain, 29 May 2008 SOL flow and divertor discrepancies parallel ion SOL flows -EDGE2D vs. JET -SOLPS vs. AUG -UEDGE vs. JT-60U target T e (n e, recycling) - SOLPS vs. AUG SOL E r - SOLPS vs. AUG - EDGE2D vs. JET Debye sheath Ion V || compensating E r xB drift  Lower target T e in codes and flatter T e profiles  expect lower E r in codes than in experiment: confirmed – see next Radial electric field: e E r   3  r T e,target  E r underestimate in codes  SOL flow underestimate

13. 13 of 22A.V.Chankin & D.P.Coster, 18 th PSI Conference, Toledo, Spain, 29 May 2008 SOL E r discrepancy – code results Flat SOL V p profiles : eE r < |  T e |  low -eE r /  T e ratio V p (plasma potential) and T e profiles across SOL at outer midplane SOLPS modelling ASDEX Upgrade, EDGE2D modelling JET plasmas [Chankin et al.,NF 2007]

14. 14 of 22A.V.Chankin & D.P.Coster, 18 th PSI Conference, Toledo, Spain, 29 May 2008 Experimental -eE r /  r T e ratios in the SOL significantly exceed code predicted values E r from Langmuir probe measurements Tokamak comments ASDEX Upgrade * 3.1 standard Ohmic shot [H-W.Müller, 2007] JET 1.6 average over Ohmic, L-mode, H-mode shots [K.Erents et al., 2004] JT-60U 2.4 L-mode, middle of density scan range [N.Asakura 2007] TCV 3.3 – 5.0 Ohmic, middle of density scan range [R.A.Pitts, I.Horacek, 2007] Alcator C-Mod 1.7 – 1.8 Ohmic L-mode [B.LaBombard et al., 2004] * Similar values - from Doppler reflectometer measurements, when using probe  T e -eE r /  r T e

15. 15 of 22A.V.Chankin & D.P.Coster, 18 th PSI Conference, Toledo, Spain, 29 May 2008 Potential causes of discrepancies Neutrals Plasma role of fluctuations; problem of time-averaging (a  b  a  b) non-local kinetic effects of parallel transport [ W.Fundamenski 2006, S.I.Krasheninnikov 2007 ] excessive ionisation due to low perp. mobility in codes

16. 16 of 22A.V.Chankin & D.P.Coster, 18 th PSI Conference, Toledo, Spain, 29 May 2008 Non-local kinetic effects in SOL and divertor Present 2D edge fluid codes (SOLPS/B2, EDGE2D, UEDGE) assume classical (Spitzer-Härm/Braginskii) heat flow along field lines for ions and electrons However, real heat conduction starts to deviate from classical collisional formula(s) beginning with L m.p.f. /L  Te > 0.01 (typically ~ 0.1 in SOLs existing experiments, and expected in ITER) The deviation is due to: most of the parallel heat flux being carried by supra-thermal electrons with velocities: Weakly collisional: L m.p.f.  Contributions of electrons with different velocities v to the heat flux q e Standard corrections for kinetic effects in fluid codes, introduction of “kinetic flux limiters” – far insufficient (see later) ( Focus on electrons since  e || >>  i || ) Kinetic effects: - may increase parallel heat flux in divertor, Debye sheath - affect atomic physics rates (ionisation, excitation)

17. 17 of 22A.V.Chankin & D.P.Coster, 18 th PSI Conference, Toledo, Spain, 29 May 2008 Example of existing kinetic codes ALLA [Batishchev et al., 1996-1999]: Fokker-Planck code for ions and electrons, with full Coulomb collision operator, kinetic neutrals, “logical sheath” condition 1D in physical space, adaptive mesh 2D in velocity space (energies E ||, E  ), adaptive mesh

18. 18 of 22A.V.Chankin & D.P.Coster, 18 th PSI Conference, Toledo, Spain, 29 May 2008 Kinetic code results on parallel  e In upstream SOL plasma, depletion of supra-thermal electron population  use of flux limiters for heat fluxes in fluid codes is justified. Their values depend on plasma conditions and geometry of experiment (variation 0.03 – 0.8 reported) In divertor, parallel heat flux may exceeds classical  instead of flux limiters, flux enhancements  e >  e,Braginskii/Spitzer-Härm [K.Lackner, et al., 1984]* [R.Chodura, 1988] [A.S.Kukushkin, A.M.Runov, 1994] [K.Kupfer et al., 1996] [O.V.Batishchev et al., 1997] [W.Fundamenski, 2005] (review) * Used a fit to kinetic results by Luciani et al., 1983

19. 19 of 22A.V.Chankin & D.P.Coster, 18 th PSI Conference, Toledo, Spain, 29 May 2008 Progress in the ITER Physics Basis [Nucl. Fusion 47 (2007) S1-S413] Chapter 4: Power and particle control Section 2: Experimental basis Parallel energy transport is determined by classical conduction and convection, with kinetic corrections to heat diffusivities at low (separatrix) collisionalities Consensus view reflected in: Kinetic code results on parallel  e (cont.) ?

20. 20 of 22A.V.Chankin & D.P.Coster, 18 th PSI Conference, Toledo, Spain, 29 May 2008 Kinetic simulations for SOL of ASDEX Upgrade H-mode ASCOT code, adapted for kinetic electron transport in SOL of AUG H-mode shot #17151 [L.Aho-Mantila et al., 2008] Test electrons are launched at outer midplane with local Maxwellian distribution consistent with T e of the background generated by SOLPS. Electrons collide with the background plasma and traced down to targets. Test electron energy distributions at the targets are recorded and compared with the target T e of the background (SOLPS) plasma. Fraction of total target electron heat flux carried by supra-thermal electrons:  70 % near outer strike point Helsinki University of Technology & IPP Garching

21. 21 of 22A.V.Chankin & D.P.Coster, 18 th PSI Conference, Toledo, Spain, 29 May 2008 ITER H-mode scenario: n e,sep = 4x10 19 m -3 T e,sep = 150 eV q 95 = 3 R=6.3 m AUG standard Ohmic #18737: n e,sep = 1.3x10 19 m -3 T e,sep = 47 eV q 95 = 4 R=1.7 m  ee = 13.8  ee = 11.6 Yes: Ohmic plasmas in AUG at low-medium densities have similar separatrix electron collisionality as that expected in ITER Are kinetic effects in SOL of AUG relevant for ITER ?

22. 22 of 22A.V.Chankin & D.P.Coster, 18 th PSI Conference, Toledo, Spain, 29 May 2008  Discrepancies between 2D fluid edge codes and experiments: - parallel ion SOL flow - divertor parameters, target asymmetries - E r in the SOL  Outer target, E r and ion SOL flow discrepancies are related to each other and caused by the codes tendency to underestimate divertor T e and overestimate n e  Cause of the discrepancies is unknown, presently under investigation: - neutrals treatment by kinetic Monte-Carlo codes - role of fluctuations, present in experiments but missing in codes - non-local kinetic effects of parallel electron transport Summary

23. 23 of 22A.V.Chankin & D.P.Coster, 18 th PSI Conference, Toledo, Spain, 29 May 2008 Spares

24. 24 of 22A.V.Chankin & D.P.Coster, 18 th PSI Conference, Toledo, Spain, 29 May 2008 0 1 2 3 4 5 Edge Thomson scattering Lithium beam SOLPS 0 100 200 300 400 500 600 700 800 10 10 0 1 -0.02 0 0.02 SOL core D perp.  e  i  i neoclassical D: #17151 SOLPS: #12096 =  e  i Ion temperature Electron temperature [L.D.Horton et al., 2005] Distance from separatrix [m] H-mode #17151 SOLPS simulation of AUG divertor conditions (cont.) Satisfy experimental boundary conditions: - Input power into the grid - Particle balance: Gas puff, NBI source, cryo-pump efficiency - Power to target:  determine separatrix position, density Input power Pumping Gas puff, NBI source

25. 25 of 22A.V.Chankin & D.P.Coster, 18 th PSI Conference, Toledo, Spain, 29 May 2008 Some results (Batishchev et al. 1996-1999) Parallel electron heat flux density, for case T e /T e = 10 (upstream to target T e ratio) L m.p.f. /L = 0.1, typical for the SOL of ASDEX Upgrade: At hot end, depletion of energetic electrons At cold end, large surplus of energetic electrons  flux enhancement needed (rather than flux limit)  Solution for IPP: develop kinetic module for SOLPS(B2) for parallel electron heat flux (later – also for ions)  e >  e,Spitzer-Harm