FPT Discussions on Current Research Topics Z. Lin University of California, Irvine, California 92697, USA

Electron transport Momentum transport GAM Finite-  effects Coupling between turbulence and energetic particles Outline

Case studies of electron heat transport mechanism in tokamak  Comparative studies of CTEM, ITG, & ETG GTC simulations: while saturation can be understood in context of fluid processes, kinetic processes related to instability drive often responsible for transport Transport: eddy mixing or wave-particle decorrelation? InstabilityElectron temperature gradient (ETG) Ion temperature gradient (ITG) Collisionless trapped electron mode (CTEM) Electron driveParallel resonanceNon-resonancePrecessional resonance SaturationNonlinear toroidal coupling Zonal flows Electron heat Transport Wave-particle decorrelation Nonlinear mode scattering off trapped electron? Processional resonance de-tuning? Avalanche?

Transport driven by local fluctuation intensity Effective wave-particle decorrelation time  wp =4  e /3  v r 2 ~ 4.2L T / v e  wp << 1/  ~ 33: linear time scale not important to transport Wave-particle correlation length  v r  wp << streamer length Electron radial excursion diffusive: streamer length does not determine transport directly From linear to nonlinear,  e /  v r 2 decreases by a factor of ~5  Nonlinear loss of wave-particle correlation r/er/e ee e/vr2e/vr2 time (L T /v e )

Kinetic & fluid time scales in ETG turbulence  auto >> 1/  >>  wp ~ 1/  k || v e Wave-particle decorrelation of parallel resonance  (  -k || v || ) dominates Quasilinear calculation of  e agrees well with simulation Saturation: wave-wave coupling determines fluctuation intensity Transport: wave-particle decorrelation determines transport level

ITG mode dominates when  i =3.1 Trapped electrons typically interact non-resonantly with ITG mode Trapped electrons increase ITG growth rate High k  modes are CTEM Effects of kinetic electrons on ITG mode k   i  ( v i / L n )  r ( v i / L n ) k   i kinetic electron kinetic electron adiabatic electron adiabatic electron

Convergence using 10 and 40 particles per cell No coherent ITG-electron interaction in linear phase Ion transport: resonant; proportional to intensity [ Lin & Hahm, PoP2004 ] Electron transport: non-resonant  ITG mode scattering off trapped electrons? Relation to energetic particle transport by microturbulence? ITG turbulence drive small electron heat transport heat flux electron ion   ion electron

CTEM mode dominates when  i =1 Driven by electron precessional resonance Modestly ballooning CTEM linear dispersion

Nonlinear convergence using particle per cell Short wavelength modes k   i >0.4 dominate at initial saturation Initial saturation caused by small scale zonal flows k r  i ~1 The 2 nd burst not deterministic; driven by k   i <0.4 Nonlinear saturation time (1/  )

Nonlinear loss of CTEM-electron correlation  Zonal flow the agent? Burst caused by nonlinear growth Electron heat transport mechanism: precessional resonance de-tuning?  n-spectral width; Radial diffusion Nonlinear burst suggestive of avalanche? Nonlinear bursting

Burst originates at r=0.5a, outward propagation faster than inward Inward spreading ballistic with a speed close to drift velocity Relation to EPM avalanche [Zonca, Briguglio, Vlad, etal, PPCF2006]? Nonlinear bursting time (1/  ) ii ee r/  i Ion transport Electron transport

Nonlocality in TransportSecondary modes and structures Strong wave-particle interaction Particle Transport enhanced particle transport by avalanches and spreading shearing and zonal flow effects and particle pinch CTEM induced particle transport EPM induced transport Electron Thermal Transport resonant electron, CTEM induced avalanches Zonal flow and GAM effects on CTEM CTEM induced heat transport electron heat avalanches precession resonance coherence ITB Formation avalanche-barrier interaction spreading vs. barrier competition. Interplay of GAM and shear flows Intrinsic rotation in ITB shear layers CTEM resonance detuning in electron ITB shearing effects on CTEM Transport scalings Gyro-Bohm breaking  spreading and avalanches probabilistic heat flux scaling interplay collisionless GAM, ZF saturation  stiffness quantification CTEM dynamics precession resonance coherence  radial front propagation Momentum Transport wave momentum flux and spreading enhancement driven intrinsic rotation. symmetry breaking energetic ions  Alfven wave momentum flux CTEM, KBM driven momentum flux

GAM linear physics: short wavelength, collisionless & collisional damping Nonlinear excitation: turbulence & zonal flows Effects on turbulence: active or passive? Role of quasimodes? Acoustic eigenmode? Higher frequency harmonics? EM: roles of low-order rational surfaces in driving ZF & GAM? Geodesic Acoustic Modes & Zonal Flow

GTC electromagnetic simulation   e (v e  e 2 /L T ) time (L T /v e ) Demonstrate finite-  stabilization of ITG and excitation of KBM/AITG Demonstrate Alfven wave propagation in tokamak, continuum damping, and existence of toroidal frequency gap  Truly global geometry allowing all n -modes  Recover MHD dispersion relation of Alfven wave in tokamak; Allow E || [ Nishimura, Lin, and Wang, PoP2007 ]

Coupling of TT & EP in ITER: turbulence in the presence of energetic particles; Many interacting EP modes lead to EP turbulence Kinetic effects of thermal ions: damping of TAE; coupling between Alfvenic and acoustic branches, e.g., GBAAE Cross-gap coupling between Alfvenic and acoustic modes Cross-scale coupling between TT & EP, e.g., coherent structures (zonal flows/fields), structure corrugation & dynamic modulation Turbulent transport & energetic particle physics

Fundamental constituents Fundamental constituents Derived Observables Primacy hierarchy Linear SAW wave Nonlinear saturation TransportScaling Trend Statistics ObservablesPolarization, structure, frequency, threshold Spectral intensity, bispectra, zonal flows/fields EP PDF & transport Similarity experiment ITPA database Agent/ mechanism EP spatial gradient, velocity anisotropy Wave-wave, wave-particle interaction Cross- phase, relaxation Dimensionle ss scaling Inter- machine