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9 th IAEA TCM on H-mode physics and transport Catamaran Resort Hotel, Sep.24-26,2003

9 th IAEA TCM on H-mode physics and transport Catamaran Resort Hotel, Sep.24-26,2003. Transport within transport barriers : theorist’s view of the feature. Theoretical understandings of transport barrier as a complex system. Y. Kishimoto Naka Fusion Research Establishment

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9 th IAEA TCM on H-mode physics and transport Catamaran Resort Hotel, Sep.24-26,2003

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  1. 9th IAEA TCM on H-mode physics and transport Catamaran Resort Hotel, Sep.24-26,2003 Transport within transport barriers : theorist’s view of the feature Theoretical understandings of transport barrier as a complex system Y. Kishimoto Naka Fusion Research Establishment Japan Atomic Energy Research Institute (JAERI)

  2. Contents Introduction Background and motivation 2. Fluctuation dynamics in wide frequency and wave number space • Key issues of nonlinear fluctuation dynamic essential for transport barrier physics • Possibility of “control” of fluctuation and related transport 3. Summary Discussion • Prof. P. Diamond : Furture direction in transport barrier Physics • Prof. K. Itoh : Prospect of transport physics in science • Dr. X. Q. Xu : Prospect for Edge physics Acknowledgement : T.S. Hahm, K. Itoh, S-I. Itoh, M. Yagi, Z. Lin, P. Diamond, E-J. Kim, C.Holland, A.K. Wong, R. White, D.R. Ernst J.Q. Li, Y. Idomura, N. Miyato, T. Matsumoto

  3. L-mode Current Pressure 1.0 1.0 0.5 0.5 0 0 Inductive current dominant H-mode High bp High bp-H RS-mode BS current dominant High performance is realized by having “structure” [Itoh S.I., et al., J.Nucl.Materials, ’95, Zohm, PPCF, ’96, Burrell, PoP, ’97, Ida, PPCF, ’98 • H-mode : ASTEX (1982) • CNTA-NBI mode • Core H-mode • DaH-mode • Reversed (Negative) Shear mode • Enhanced Reversed Shear mode • High Density H-mode • Helical Electron ITB • High bp mode • High bp-H mode • High li-mode • High Ti mode • I-mode • Improved Ohmic Confinement mode • Lower-Hybrid Heating mode • Pellet mode • Pellet Ehhanced Performance H-mode • Radiation Improved Mode • Super shot • VH-mode • etc ………. High confinement Steady state Understanding the “selection rule” of the distinct states and the control

  4. Complex nonlinear loop system of structural plasma Neoclassical dynamics Fluctuation and self-organization dynamics Global linkage as nonlinear loop system, and “control” Identification of the degree of complexity of the state

  5. 11 Contribution papers Neoclassical dynamics (E8: Yagi, E10: Ernst) 2. Fluctuation and self-organization dynamics E1: Diamond E2: Hahm E3: Kim E4: Holland E5: Wang E6: K-Itoh E7: White Global linkage as a nonlinear loop, and control E8: Yagi E9: S. Itoh E10: Ernst E11: Xu (E1: Diamond) 4. Identification of the degree of complexity of the state (E9 : S. Itoh) (E3: Kim)

  6. electron skin size electron skin size ion MHD ion Fluctuation dynamics in wide wave number space 1. Linear free energy source in complicated magnetic field • Mode structure in reversed/weak magnetic shear cf. Failure of ballooning picture 2. Nonlinear free energy source • Normal/inverse spectrum cascade • Fluctuation due to nonlinear/turbulent dissipation. cf. CDBM • Secondary and higher order nonlinear instabilities with different time and spatial scales cf. Generalized zonal/streamer mode, Zonal mode driven KH mode, etc 3. Interaction and interference among activities with different time and spatial scales, and through spatial dimension • Non-local, non-diffusive “new energy/information transfer channel” using not only spectral-space and “spatial dimension” [Diamond, Hahm, et al. H-WS, ’03]

  7. Linear free energy source reversed shear ETG electron normal shear ETG skin size (※) negative shear ITG ion normal shear ITG • Global linear gyro-kinetic dispersion in reversed shear plasma [Idomura, et al., NF, ’02] • Short wavelength ITG mode (shear-less slab) [Smolyakov, Yagi, et al., PRL, ’02] Slab mode-like structure Gap structure [Idomura, et al., PoP,’02, Kishimoto, et al., PPCF, ’99] • Short wavelength ITG mode in current carrying plasma [Wang, H-WS, ’03] [Voitsekhovitch, Garbet, et al., PoP, ’02]

  8. Flow : Field : Pressure : [Hallatshek-Biskamp PRL, ’01] electron “Pressure anisotropy (Stringer-Winsor term)” “Reynolds stress” skin size “Collisional damping” “Maxwell stress” [Lin, et al., PRL, ’99, Kim, et al., PRL, ’03] ion MHD Nonlinear free energy source Various “Zonal modes” are exited through modulational instability [Holland-Diamond, PoP, ’02, Jenco et al., IAEA, ’02, Miyato, et al., PPCF, ’02] • Small scale pressure corrugations are hardly controllable  SOC dynamics • Large scale component may change the q-profile

  9. Maternal fluctuation q-profile p-profile • GAM : • Stringer-Winsor : Nonlinear free energy source Nonlinear turbulent-convective cell system with complex “activator” and “suppressor” roles Transport Neo-classical mean shear flow streamer Low m/n drive • Kelvin-Helmholtz mode • GKH mode [Kim-Diamond, PoP, ’03] Flow driven tertiary nonlinear instability collisonal damping [K-Itoh, et al., White, et al., Holland-Diamond, Yagi, et al., H-WS, ’03]

  10. Nonlinear fluctuation dynamics • Local inverse/normal cascade electron • Nonlinearly generated “convective cell mode” skin size Mixed turbulent/zonal fluctuation system ion MHD [Idomura, PoP, ’00] Ti Internal kink event [Jenko-Kendel,PoP, ’02] Wendelsteien 7ASsimulation MHD-driven Er-field [Kendel, PoP, ’03] ETG streamers found near threshold are essentially linear structures whose nonlinear interaction is weak. [Dorland, et al., IAEA, ’02] [Matsumoto, Naitoh, PoP, ’03] Zonal-A Zonal-f [Miyato-Kishimoto, JPS, ’03] [Holland-Diamond, et al. H-WS, ’03]

  11. Zonal pressure and b-increase Reduced MHD equation [Ichiguchi, et al., IAEA,’02] [Carreras, et al., PoP,’01] • Resistive interchange modes induce a staircase structure, leading to a linearly unstable high-b profile

  12. linear saturation Quasi-steady state Impact of zonal flow on transport (1) Gyro-kinetic PIC simulation using global profile effect and canonical Maxwellan particle distribution [Idomura, et al., NF, 2002] Zonal fluctuation Turbulent fluctuation : m/n=0/0 GAM fluctuation : m/n=1/0 • Macro-scale “mean flow”, same level as that of the equilibrium, regulated by equilibrium profile [Lin, et al., Science, ’98]

  13. [Smolyakov, et al., PoP, ’00, Malkov, et al., PoP, ’01, Li-Kishimoto, PoP,’02] [White, et al., H-WS, ’03] (b) Modulational instability and zonal flow Parameter to change the ratio of “turbulence” part and “zonal” part • ITG case (adiabatic electron except k||=0) • ETG case (adiabatic ion) Large grow rate for Streamer-like anisotropic pump wave :

  14. (A) S=0.2 (B) S=0.1 Self-organization to flow dominated fluctuations • Weak magnetic shear increases linear instability sources, but nonlinearly transfers energy to zonal components disappearance of anomaly in high pressure state KH-mode like instability Zonal flow energy • Drift-Alfven turbulence in edge plasma [Kishimoto,Li, et al., IAEA ’02] [Kendel, Scott, et al., PoP, ’03]

  15. 1.0 0.8 0.6 0.4 0.2 DW 1.0 0.8 0.6 0.4 ZF 0.2 Characteristics of flow dominated fluctuations Time averaged spectrum w/o zonal flow wavelet analysis ETG GKH ? with zonal flow KH Near marginal and quasi-linear process Condensation to KH-mode [Kim-Diamond, PoP ’02]

  16. No flow case rate strong flow case rate Statistical nature of turbulence-zonal fluctuation system “Fractal dimension” and “PFD” : Probability Distribution Function • Shrinking dimensionality due to coherent structure • Coherency increases with near Gaussian PDF of flux [Matsumoto, et al., Toki-conf, ’03]

  17. Size distribution of heat pulse from GK simulation [Nevince,’00, Holland, et al., IAEA,’02] Statistical nature of turbulence Fractal dimension • TEXTOR: Signal from Langmuir probes [Budaeev, et al., PPCF, ’93] d= 12-16 (attached) d=6-7 (detached) d=30 (from 15) (induced H-mode) • CHS : Electron density fluctuation [Komori, et al., PRL, ’94] d~ 6.1 (RF heating) d~6.2 (NBI heating) d~8.4 (RF+NBI) 2. Probability Distribution PDF of density fluctuation of PISCES-A linear device and SoL of the Tore Supra [Antar,et al.,PRL,’01] “Noise forcing by coherent structure” • Non-Gaussian PDF for the Reynolds stress and hest flux • [Kim, et al., IAEA,’02] • Probabilistic view of L-H transition [S-Itoh, et al.,Kim-Diamond, H-WS, ’03]

  18. electron skin size ion MHD Interference among different scale fluctuations • Interaction through quasi-coherent zonal modes [Hahm-Burrel, PoP, ’02, Hahm, et al., PoP, ’99] [Li-Kishimoto, PRL, ’02, Idomura, et al., NF, ’02] • Time varying Random shearing • Scattering to high-k • Interaction through micro-scale structure, eddy viscosity, noise, etc. [Itoh, et al.,PPCF,’01, Yagi, et al., IAEA, ’02] Open new nonlinear energy transfer channel Trigger problem

  19. L-state H-state low-k high-k ITG transport modulation due to small scale flow GF-ITG simulation with micro-scale ETG driven flows (b) Upper state Probabilistic damping trigger No flow (a) Lower state • Non-local mode coupling and associated energy transfer to high kx damped region • Micro-scale flow intermittently quenches ITG turbulence [courtesy of Miura and JFT-2M group] [Li-Kishimoto, PRL, ’02, PoP, ’03]

  20. Multiple-scale turbulence and bifurcation Langevan approach for 2-scale plasma turbulence system Semi-Micro (cf. ITG) MicroMode (cf. skin/ETG) Semi-micro mode amplitude • For micro-mode dominated solution, semi-micro mode is quenched, and vise-versa. • Mechanism of ITB formation with different ion and electron dynamics [Yagi, et al., IAEA, ’02,Itoh-Itoh, PPCF, ’01] cf. Distinct dynamics between ion and electron [Koide, et al., PPCF, ’98]

  21. electron skin size ion Nonlinear transfer channel of fluctuation In spectral space Energy transfer among different scale fluctuations through local/non-local cascade or inverse cascade process In real position space Radial energy transfer through propagation and/or spread • Inverse cascade of “radial” shorter wavelength modes • Radial “diffusion” and/or “convection” • from linearly unstable region to stable zone [Diamond-Hahm-Lin, et al. H-WS, ’03] [White, et al., H-WS, ’03] Modulational approach with spatial dimension • Successive excitation of secondary and tertiary instabilities using spatial dimension

  22. JT-60U E29728 t=6.0 3 g P Full code (w/rotation) 2 kqPi=0.53 g(105sec-1) 1 0 10 x(m2/s) 1 xi xe 0.1 0 0.5 1 r/a Nonlinear transfer channel of fluctuation Garbet, et al., NF, ’94 [Rewoldt-Shirai, et al., NF, ’02] A turbulent zone spreading radially in such a way that its level is no longer directly related to local plasma parameter • Toroidal linear coupling “convection” • Nonlinear mode coupling “conduction” Mattor-Diamond, Rep. UCRL, ’93 • Coupling through equilibrium profile Newmann, Diamond, et al. ITB dynamics based on turbulent-transport equation system cf. Transport phenomena hardly explained from linear analysis

  23. ETG KH KH ETG-ZF KH-ZF Spatial convection of instability q(r) q-min surface rdius • Increase of linear instability source for reversed shear plasma 0 -2cm +2cm ① t=2ms • Turbulent energy is “nonlinearly” converted to flow component through “spatial dimension”. ② t=2ms ③ t=6ms ④ t=8ms ① Origin of “structure” is anomalous transport!! ② ③ ④ [Idomura, et al., PoP, ’00] Strong turbulence Transport suppression

  24. ITG GK simulation linear phase saturation phase [Sydora, et al., PPCF, ’96] Turbulent spreading and diffusion Some evidence from numerical simulation Garbet, et al., NF, ’94, Sydora, et al., PPCF, ’96,Parker et al., PoP, ’96, Lin, et al., IAEA, ’02, also PRL, ’02 ETG GF simulation no rational surface (no damping) linear phase steady state phase [courtesy of J-Li]

  25. Linear damping region I r r0 r0+D Turbulent spreading and size scaling Discussion about transport size scaling (B or GB) • No device size dependence of radial eddy length : Dx~7ri : Scale size is “microscopic” • Radial spreading of fluctuation into stable zone Nonlinear model of turbulent propagation Front like solution PDF of particle diffusion : close to “Gaussian” with no significant tail, suggesting “diffusive transport” [Lin, et al., IAEA, ’02] [Hahm, et al., H-mode WS, ’03]

  26. Non-local transport where local diffusivity depend on finite radial length : Size scaling of transport • GB scaling well above the instability threshold • Break of the GB scaling to Bohm scaling (worse) near threshold Stabilization effect due to shearing in the ballooning phase velocities due to global profile variation [Waltz-Candy, et al., PoP, ’02, also IAEA, ’02]

  27. Summary : prospect for future direction • The physics of key elements dominating the transport barrier, specifically nonlinear process, is extensively studied, and the understandings have been developed. • Interaction and/or interference among different time and scale fluctuations, not only in wide frequency/wave number space, but also real space dynamics, becoming crucially important. • Statistical approaches to identify the degree of complexity of the state and transition dynamics are becoming necessary. • Numerical approach to handle wider dynamical range is becoming tough, for example, micro-scale electron dynamics, but continuous efforts are crucial. • Methodology to control the nonlinear loop system is becoming necessary. cf. integration of key element. • Close interplay and interference among theory, simulation and experiment is desirable.

  28. Role of H-mode and ITB physics in science ? [Koshyk-Hamilton, JAS, 01] [courtesy of Earth simulator center]

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