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  1. Max-Planck-Institut für Plasmaphysik Comparison of 2D Models for the Plasma Edge with Experimental Measurements and Assessment of Deficiencies A.V.Chankin and D.P.Coster 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 A.V.Chankin & D.P.Coster, 18th PSI Conference, Toledo, Spain, 29 May 2008

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

  3. separatrix input power Main 2D edge fluid codes for SOL and divertor modelling SOLPS: B2-Eirene (AUG), EDGE2D-Nimbus,Eirene (JET), UEDGE-DEGAS (DIII-D) • Plasmadescription: 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 Computational grid and vessel structures • Physical and chemical sputtering from surfaces • Multiple impurity charged states • Consensus (prior to 2000): 2D edge fluid codes • reproduce existing experiments within a factor of 2 A.V.Chankin & D.P.Coster, 18th PSI Conference, Toledo, Spain, 29 May 2008

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

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

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

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

  8. 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 A.V.Chankin & D.P.Coster, 18th PSI Conference, Toledo, Spain, 29 May 2008

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

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

  11. 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 A.V.Chankin & D.P.Coster, 18th PSI Conference, Toledo, Spain, 29 May 2008

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

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

  14. Experimental -eEr/ srTe ratios in the SOL significantly exceed code predicted values Er from Langmuir probe measurements -eEr/ srTe *Similar values - from Doppler reflectometer measurements, when using probesTe A.V.Chankin & D.P.Coster, 18th PSI Conference, Toledo, Spain, 29 May 2008

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

  16. Contributions of electrons with different velocities v to the heat flux qe Non-local kinetic effects in SOL and divertor (Focus on electrons sincee|| >> i||) • 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 Lm.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: Lm.p.f. • Standard corrections for kinetic effects in fluid • codes, introduction of “kinetic flux limiters” – • far insufficient (see later) • Kinetic effects: • - may increase parallel heat flux in divertor, Debye sheath • - affect atomic physics rates (ionisation, excitation) A.V.Chankin & D.P.Coster, 18th PSI Conference, Toledo, Spain, 29 May 2008

  17. 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 A.V.Chankin & D.P.Coster, 18th PSI Conference, Toledo, Spain, 29 May 2008

  18. 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 [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) e > e,Braginskii/Spitzer-Härm *Used a fit to kinetic results by Luciani et al., 1983 A.V.Chankin & D.P.Coster, 18th PSI Conference, Toledo, Spain, 29 May 2008

  19. Consensus view reflected in: 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 diffusivitiesat low (separatrix) collisionalities ? Kinetic code results on parallel e (cont.) A.V.Chankin & D.P.Coster, 18th PSI Conference, Toledo, Spain, 29 May 2008

  20. Kinetic simulations for SOL of ASDEX Upgrade H-mode Helsinki University of Technology & IPP Garching • 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 Te 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 Te • of the background (SOLPS) plasma. • Fraction of total target electron heat flux carried • by supra-thermal electrons:  70 % near outer • strike point A.V.Chankin & D.P.Coster, 18th PSI Conference, Toledo, Spain, 29 May 2008

  21. AUG standard Ohmic #18737: ne,sep = 1.3x1019m-3 Te,sep = 47 eV q95 = 4 R=1.7 m ITER H-mode scenario: ne,sep = 4x1019m-3 Te,sep = 150 eV q95 = 3 R=6.3 m n*ee=13.8 n*ee=11.6 Are kinetic effects in SOL of AUG relevant for ITER ? • Yes: Ohmic plasmas in AUG at low-medium densities have similar separatrix • electron collisionality as that expected in ITER A.V.Chankin & D.P.Coster, 18th PSI Conference, Toledo, Spain, 29 May 2008

  22. Summary • Discrepancies between 2D fluid edge codes and experiments: - parallel ion SOL flow - divertor parameters, target asymmetries - Er in the SOL • Outer target, Er and ion SOL flow discrepancies are related to each other and caused by the codes tendency to underestimate divertor Te and overestimate ne • 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 A.V.Chankin & D.P.Coster, 18th PSI Conference, Toledo, Spain, 29 May 2008

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

  24. D: #17151 SOLPS: #12096 5 H-mode #17151 Edge Thomson scattering 4 Lithium beam 3 SOLPS 2 1 0 800 700 600 500 Ion temperature 400 300 200 Electron 100 temperature 0 Input power core SOL c c 1 10 = e i Gas puff, NBI source D 0 10 perp. c e c [L.D.Horton et al., 2005] i -1 10 c Pumping neoclassical i 0.02 0 -0.02 Distance from separatrix [m] 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 A.V.Chankin & D.P.Coster, 18th PSI Conference, Toledo, Spain, 29 May 2008

  25. e > e,Spitzer-Harm Some results (Batishchev et al. 1996-1999) Parallel electron heat flux density, for case Te/Te = 10 (upstream to target Te ratio) Lm.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) A.V.Chankin & D.P.Coster, 18th PSI Conference, Toledo, Spain, 29 May 2008