19th IAEA Conference on Fusion Energy Lyon, October 19, 2002 Summary of Theory Papers K. Itoh National Institute for Fus

1. 19th IAEA Conference on Fusion Energy Lyon, October 19, 2002 Summary of Theory Papers K. Itoh National Institute for Fusion Science, Japan Summarizing ~100 papers out of ~380, guideline is taken: New progress Impacts for future research Easy to understand, Easy to access (Not necessarily "best" from theoretical point of view.) Please wait the written article for more complete summary..

2. Photo by S. Murakami

3. Acknowledgements: I would like to acknowledge helps and contributions form my colleague in preparing this summary. D. Barnes, A. Bergmann, P. Beyer, C-S Chang, C. Z. Cheng, M.-S. Chu, U. Daybelge, R. Dendy, P. H. Diamond, J. Q. Dong, A. Fujisawa, A. Fukuyama, T. Fulop, M. Furukawa, X. Garbet, P. Ghendrih, R. J. Hastie, A. Hatayama, T. Hayashi, P. Helander, A. Hirose, C. Holland, S. Hudson, K. Ichiguchi, Y. Idomura, Y. Ishii, S.-I. Itoh, N. Kasuya, Y.Kishimoto, E. Kim, Y. Kolesnichenko, S. Krasheninnikov, Z. Lin, V. Lutsenko, D. Mikkeksen, R. Moestam, K. McClements, V. Mirnov, S. Murakami, H. Naitou, H. Ohtani, V. Parail, W. Park, S. Parker, V. P. Pastukhov, F. Porcelli, M. Sato, K. C. Shaing, A. Smolyakov, P. B. Snyder, T. Tamano, P. W. Terry, Y. Todo, L. Villard, M. Vlad, M. Wakatani, R. Waltz, A. Wang, M. Yagi, V. Yavorskij,C. Zhang, F. Zonca (Alphabetical order)

4. Issues 1. Transport and confinement 2. Direct simulation of turbulence 3. MHD: understanding and control 4. Energetic particles 5. Heating and current drive 6. Edge modelling 7. Statistical Approaches View point of this summary Emphasis is made on interactions between dynamics with different length/time scales. Comprehensive understanding, direction of future research Summary and Prospects

5. 1. Theory of transport phenomena 1.1 Transport-code analysis Progress of integrated transport modelling (THP1/7 Hoang, THP1/9Kinsey, THP3/8 Parail) 1.2 Transport-barrier mechanism Core:Multiple kinds of fluctuations (TH1/4 Yagi) Electron and ion barriers(THP1/11 Newman) Edge: Radial electric field bifurcation and nonlinearity is examined.(THP3/5 Kasuya) (THP3/11 Daybelge) Non-uniform neutral particles(THP3/3 Fülöp) Suppression of cross-phase in sheared flow (THP1/16 Terry)

6. 1.3 Anomalous torque, off-diagonal elements, etc. Zonal flow excitation and exp. evidence (THP1/3 Holland) Angular momentum flux (THP1/2 Coppi) Nonlinear diffusion regimes in stochastic B fields (THP1/17 Vlad) Finite/Long Range Transportation; Diffusion model does not always suffice. Fluctuations by subcritical excitations (hysteresis) (THP3/6Moestam) with finite correlation lengths. Superdiffusion (TH2/3 Carreras) 1.4 Self-organized criticality (SOC) Model SOC model captures this feature. Nonlocal transport, plausible structures, tail of PDF (TH2/2 Tangri) (THP3/2 Dendy) Application to ELMs (THP3/9 Sánchez) 1.5 Alternative modeling based on variational principle Minimum canonical enstrophy (THP1/10 Mahajan, ICP/12 Ogawa) (THP1/15 Tamano, THP1/4 Dnestrovskij, THP1/21 Zhang)

7. 1.6 Large orbit neoclassical transport theory (TH2/6 Shaing, THP1/1 Bergmann, THP3/1 Chang, ICP-6 Nuhrenberg, EXC5/3 Murakami) Strongly-inhomogeneous radial electric field TH/P1-1 Bergmann

8. 1.7 Linear instabilities: basics of analysis • Microscopic instabilities shorter than : For understanding of electron transport Dong TH1/6, Smolyakov THP1/14, Hirose THP1/6 Smolyakov THP1/14 • Ballooning modes: Blob and other phenomena at edge low-n and resistivity (Hastie THP2/4), flow(Furukawa THP2/3) • Other effects safety factor (Wang P1/20), drift reversal, helical system (Yokoyama ICP/8)

9. 2. Direct Simulation and turbulent transport Towards combined-comprehensive analysis of turbulence and transport

10. Direct nonlinear simulation and turbulent transport Author Mode Specific subject Note JenkoITG+ETG Multiple-scales, finite-beta YagiITG+short scale modes Three-scales, KishimotoETG /ITG Semi-three-scales, reduced c-i LinITG/TEM Bohm, g-Bohm global VillardITG/TEM Nonlocal transport, helical global GarbetITG/TEM reversed-q and ITB global OttavianiETG/ITG finite- , Bohm vs g-Bohm global WaltzITG Bohm vs g-Bohm global, ParkerITG/TEM finite- , kinetic electronstoroidal tube, Mikkelsen ITG/TEM Comparison with experiments IdomuraITG Maxwellian canonical variable BeyerResis. ball. stochastic magnetic field, global, ergodic div. Krasheninnikov dissipative blob and ejection SoL fluid GhendrihInterchange bumps and PDF SoL fluid NevinsX-point mode3D nonlocal ES divertor Pastukhov Interchange 2D, large scale convection FRC

11. 2.1 Progress of codes and benchmarking Convergence of code analysis, e.g., gyro-kinetic/fluid codes for ITG+zonal 2.2 Multiple scale turbulence Nonlinear interplay, cooperative phenomena, and possible bifurcation (Quoted from abstract) Yagi TH1/4 Jenko TH1/2 Interactions via driven-zonal flows(TH1/5 Kishimoto)

12. 2.3 Global simulation and Bohm vs gyro-Bohm Discussion on-going 2.4 Combined with global profiles micro basis for transport barriers Garbet TH2/1 TH1/1 Lin Cf. THP1/12 Ottaviani and others THP1/19 Waltz

13. 2.5 Mesoscales zonal flow, streamer, blob, bump, etc. (TH2/5 Pastukov, TH4/2Krasheninnikov) Ghendrih THP2/14 2.6 Modellinghelical plasmas W7-X model Villard TH3/1

14. 3. MHD: understanding and control 3.1 Global understanding including plasma shapes e.g., TH 5/1 Park, TH 6/3 Hayashi Nonlinear MHD simulations of spherical tokamak and helical plasmas Nonlinear Simulation Studies of Tokamaks and ST's TH 5/1 Park TH 6/3 Hayashi Flattening is observed in pressure (left) and flow (right)

15. 3.2 Fast Events, Nonlinear instabilities • Nonlinear neoclassical tearing mode: electron inertia, etc. (THP2/5 Kruger), (TH4/7 Porcelli) Coupling with sound wave is favourable in larger devices Growth/decay rates? • Onsets: sawtooth crash and beta collapse Kinetic effects for sawtooth(THP2/9Naitou)Double Tearing Mode (TH 5/2 Ishii)

16. 3.3 Helical systems and others MHD in LHD:more stable than prediction of linear theory Helical systems: Nonlinear MHD mode (TH 6/1 Ichiguchi, THP2/10 Nakamura) (THP2/12 Strauss, THP2/2 García) RFP Nonlinear MHD Analysis (THP2/8 Mirnov) FRC: Equlibrium and Stability Large scale convection (TH2/5Pastsukov), Particle simulation(THP2/11 Ohtani), Stability (TH4/6 Barnes) TH 6/1 Ichiguchi

17. 3.4 Control Resistive Wall Mode in Tokamaks: for beta limit Feedback control, efficient control method clarified (THP3/10 Chu) (THP3/12 Liu) (THP3/13 Mauer) Nyquist diagramsof transfer functions for the RWM (THP3/10 Chu) (TH 6/2 Hudson) Deceleration by RWM (THP1/18 Wakatani);possible nonlinear inst. Three dimensional magnetic surfaces

18. 4. Energetic particles and Alfven Eigenmodes motivation: ignited plasmas 4.1 Role of Geometry Tokamak ITB and new modes (Fukuyama, Breizman, Zonca, ・・・) THP3/14 Fukuyama ST (THP3/17 McClements) Excitation of Alfvenic instabilities in ST, TH/7-1Rb Cheng (compressional Alfven wave eigenmodes) Helical systems (THP3/16 Lutsenko, THP2/12 Strauss)

19. ITER JET TH/7-1Rb Cheng

20. 4.2 Combined analysis of large-scale dynamics of waves and particles (TH4/5 Zonca) Comparison with experiments is successful Shear Reversed Plasmas (TH4/4 Breizman), Low Aspect Ratio Plasma (TH/7-1Ra Gorelenkov), NSTX, JT-60U (TH/7-1Rb Cheng, THP3/14 Fukuyama) Ergodization

21. Quasi-linear method is successfully applied. THP3/18 Todo Simulation study of beam ion loss due to Alfven eigenmode bursts 4.3 Runaway electrons and ions Runaway ions are possible to occur. Electron run-away distribution is affected by pitch-angle scattering TH8/1 Helander

22. 5. Heating and current drive • Analysis of ICRF waves in realistic/complex geometries • Proper treatment of microscopic wave structure for accurate • evaluation of absorption • Toroidal asymmetry in helical systems (THP3/21 Batchelor) • RF-driven and Bootstrap currents(THP3/22 Peysson) • Magnetic braiding and current injection by anomalous • current diffusivity (THP2/1 Cohen),

23. 6. Edge modelling 6.1 Transport A&M analysis(THP2/13 Coster, THP2/15 Hatayama) DOD Degree of detachment is enhanced by W- div. in JT-60U (THP2/15 Hatayama) 6.2 Other important phenomena: Stability, magnetic braiding, etc. Magnetic braiding and current injection (THP2/1 Cohen), MARFE(THP3/4 Herrera) X-point transport(THP3/1 Chan) New boundary concept(ICP/4 Kotschenreuter)

24. 6.3 ELMs and pedestal Analyses based on quasi-linear pictures Impact of shaping TH3/1 Snyder JET 1.5D and 2D transport codes THP3/8 Parail Theory of ELM events must be explored.

25. 7. Statistical Approaches Importance of the tail component is widely recognized. Statistical approach is needed; probability density function (PDF) essential. (1) Longer life-time of larger-amplitude modon Local Reynolds stress is obtained from H-M eq. as (Stretched non-Gaussian exponential tail)(TH2/4 Kim) (2) Stronger nonlinear noise for stronger fluctuations Power-law tails (TH1/4 Yagi)Multiple-Scale Turbulence and Bifurcation

26. PDF of SOC modelling:Substantial tail is obtained PDF of heat flux in Direct Simulations weak shear flow strong shear flow Statistical theory of L-H transition Langevin equation for : PDF and transition rates Average of gradient-flux relationtransition rate (PDP/4 Itoh) THP1/03 Holland Exponential tail for bursty flux in SOL (THP2/14Ghendrih)

27. Prospects for Integrations Integrations Limited applicable boundary Integrations with better perspective

28. Final Remark This conference covers majority of progress that has been made in the area of fusion theory. 2. Comprehensive views have emerged by combined efforts with different methodologies. 3. In the next IAEA Conference, "Theory Overview" session is profitable and necessary. You are encouraged to prepare theory overview papers.