National Institute for Fusion Science,322-6 Oroshi-cho, Toki 509-5292, Japan

1. Model prediction of impurity retention in ergodic layer and comparison with edge carbon emission in LHD (Impurity retention in the ergodic layer of LHD) M. Kobayashi, Y. Fenga, S. Morita, M.B. Chowdhuri, M. Goto, K. Sato, S. Masuzaki, I. Yamada, K. Narihara, H. Funabaa, N. Tamura, Y. Nakamura, T. Morisaki, N. Ohyabu, H. Yamada, A. Komori, O. Motojima and the LHD experimental group National Institute for Fusion Science,322-6 Oroshi-cho, Toki 509-5292, Japan a Max-Planck-Institute fuer Plasmaphysik, Wendelsteinstrasse 1, D-17491 Greifswald, Germany 18th PSI 26-30 May 2008, Toledo, Spain

2. Implication of impurity screening at high density operation Even at very high density operation with more than 1021 m-3 & peaked density profile, no significant impurity accumulation Zeff < 2 Neo classical transport model in core region can not interpret it. Implication of a possible mechanism of impurity retention (screening) in the edge region.

3. dominant terms ion thermal force friction LCFS Ti dTi/ds Recycling target ViII core s SOL Introduction : Condition for impurity retention in 1D model 1D impurity transport model along B field lines In force balance, impurity velocity becomes, Z-independent Condition for impurity retention >1  impurity retention Impurity retention : dense and cold plasma, flow acceleration, suppress //-grad T.

4. Outline of the talk 1. Introduction : IDB plasma with Zeff < 2 2. 3D impurity transport modelling in LHD Geometrical effect on impurity transport 3. Comparison with experiments Density dependence of carbon emission 4. Summary

5. Basic field structure: island overlapping  stochastic radial poloidal Connection length / m Low-order islands m/n radial 10/2 Edge surface Layers* 10/3 10/4 10/5 Stochastic Region* 10/6 10/7 10/8 Confinement Region* poloidal *Terminology: N. Ohyabu et al., Nucl. Fusion, Vol. 34, No.3 (1994)

6. 3D modelling of LHD edge region (EMC3-EIRENE) Computational mesh, configuration and installations Core, CX-neutral transport, particle source SOL, EMC3 simulation domain Vacuum of plasma* C0 wall LCMS PSOL Divertor legs EMC3 SOL Core plasma target H,H2 Example of LHD helical divertor Physics model • Standard fluid equations of mass, momentum, ion and electron energy • Trace impurity fluid model (Carbon) • Kinetic model for neutral gas (Eirene) • Boundary conditions • Bohm condition at divertor plates • Power entering the SOL • Density on LCMS • Sputtering coefficient Cross-field transport coefficients • e=i=3D roughly holds • spatially constant (global transport) • determined experimentally

7. From thermal-force to friction-dominated impurity transport (1018 m-3) 1.0 0.1 0.01 Thermal force dominant inward flow Carbon density distribution Impurity flow nLCMS=2×1019 m-3 Increase ne Plasma ion flow nvII 3×1019 4×1019 Impurity flow friction dominant outward flow

8. Edge surface layers : effective retention Stochastic region : flat profile (suppression of thermal force) Carbon density 2e19 m-3 thermal 3e19 m-3 4e19 m-3 friction edge surface stochastic Stochastic Edge surface

9. Island structure affects plasma transport Te/eV 190 radial Thomson (t=1.24,1.27,1.3) * * EMC3/EIRENE 0 poloidal Te / eV 10/7 10/5 m/n=10/3 R / cm EMC3-EIRENE

10. Reduction of II-conductive heat flux by -transport downstream qII q qII upstream LCMS w/o  Ti w  target core r SOL 1D radial energy transport for ions:  II If Q << 1 (long connection length),-heat conduction makes significant contributions. Condition for significant reduction of parallel ion heat conduction: Q~10-4 (LHD) (Y .Feng, Nucl. Fusion 46 2006)

11. Ionization potential : CIII (C+2) : 48 eV CIV (C+3) : 65 eV CV (C+4) : 392 eV CVI (C+5) : 490 eV big gap Impurity density profiles of different charge states accumulation retention edge surface layer nup=4e19 m-3 nup=2e19 m-3 • Clear separation of profile between C+1~C+3 & C+4~C+6 Impurity retention : C+1,C+2,C+3 C+4,C+5,C+6

12. Density dependence of carbon emission : indication of impurity retention Spectroscopy CIII/ne w/o fric. CIV/ne CIV/ne w/o fric. CIII/ne CV/ne CV/ne w/o fric. CIII: 977Å, 1S22S2-1S22S2P (VUV monochromators) CIV: 1548Å, 1S22S-1S22P (VUV monochromators) CV: 40.27Å, 1S2-1S2P (EUV spectrometer) Absolutely calibrated

13. Other works : Impurity transport analysis of ergodic layer Importance of friction of background plasma to exhaust impurity. M.Z. Tokar, POP 6 (1999) 2808 Viscosity terms related to thermal flux. D.Kh. Morozov et al., POP 2 (1995) 1540. Core carbon content (C6+) reduction with decreasing edge Te in Tore Supra. Y. Corre et al., NF 47 (2007) 119 Prediction of impurity retention @ high density with 3D modelling Y. Feng et al. NF 46 (2006) 807 (W7-AS) M. Kobayashi et al. CPP 48 (2008) 255 (LHD)

14. Summary The impurity transport in the ergodic layer of LHD is analyzed, using the edge transport code (EMC3-EIRENE) in comparison with edge carbon emission. • Magnetic field structure of the ergodic layer in LHD : Edge surface layer : short and long flux tubes coexist. Stochastic region : remnant islands with Lc > ~ 100 m. • Plasma transport, particle and energy, follows the island structure as confirmed by the 3D modelling as well as experiments. • 3D code predicts impurity retention in the ergodic layer : Flow acceleration in edge surface layers Cross-field transport prevents large // T drop  suppress thermal force. • Good agreement in carbon emission btw 3D modelling & exp. :  Indication of impurity retention in ergodic layer by friction force. • The retention model could apply also for high Z impurity : Balance btw friction & thermal force is Z-independent High Z impurity has shorter neutral penetration length than low Z impurity.