1. Turbulent transport in collisionless plasmas: eddy mixing or wave-particle decorrelation? Z. Lin Y. Nishimura, I. Holod, W. L. Zhang, Y. Xiao, L. Chen University of California, Irvine, California 92697, USA P. H. Diamond University of California, San Diego, California 92093, USA T. S. Hahm, S. Ethier, G. Rewoldt PPPL, Princeton University, Princeton, New Jersey 08543, USA F. Zonca Associazione EURATOM-ENEA sulla Fusione, Frascati, Italy S. Klasky Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA Supported by US DOE SciDAC GPS Center

2. ITG: isotropic eddies ETG: radial streamers Fluid picture: eddy mixing Kinetic process: wave-particle decorelation Turbulence Structure & Transport in Tokamak

3. To understand physical mechanism of electron heat transport in tokamak driven by driftwave turbulence  Eddy mixing or wave-particle decorrelation?  Resonant vs. non-resonant transport?  Accuracy of mixing length estimate?  Choice of time scales in transport models?  Relation between instability drive, nonlinear saturation and turbulent transport? Gyrokinetic particle simulation of microturbulence  Systematic measurement of nonlinear spatial & temporal scales  Quantitative test of quasilinear theory in tokamak geometry Motivation: electron heat transport in tokamak

4. 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?

5. GTC global gyrokinetic particle simulation GTC [ Lin et al, Science1998 ] global field-aligned mesh: reduces computation by a/  ~100  Twisted across flux surfaces by magnetic shear  # of spatial grids N~(a/  ) 2  Respect physical periodicity  Radial variations of equilibrium quantities Gyrokinetic particle-in-cell approach  Efficient sampling of 5D phase space Massively parallel computing  Resources made available by US SciDAC  GTC selected for early applications of 250TF ORNL computer Object-oriented GTC for collaborative code development and for integrating kinetic electron, electromagnetic, multiple ion species, and MHD equilibrium

6. GTC nonlinear convergence in ETG simulation Convergence from 400 to 2000 particles per cell  Weak Cyclone parameters: R/L T =5.3, s=0.78, q=1.4, a/  e =500,  /  r ~1/4  ORNL Cray XT3, 6400 PE, 4x10 10 particles Noise driven flux is 4000 times smaller than ETG driven flux  Noise spectrum in ETG simulation measured. Noise driven flux calculated & measured [Holod and Lin, PoP2007] Initial saturation: nonlinear toroidal coupling [Lin, Chen, Zonca, PoP2005; PPCF2005]   e (v e  e 2 /L T ) time (L T /v e )

7. Initial expansion of fluctuation envelop Eddies flow along streamers in steady state? Breaking and reconnection of streamers Scale separation important  Enabled by ORNL XT3 Advanced visualization and statistical analysis needed! Turbulence Evolution

8. ETG radial streamers; Length scales Streamers generated via nonlinear toroidal coupling  Streamer generation growth rate > linear growth rate Mixing length arguments: long streamer drive large transport? Electrons excursion distance < streamer length [Lin, Chen, Zonca, PoP2005], [Joiner, Applegate, Cowley, Dorland, Roach, PPCF2006] Streamer length > 10 2 distance of mode rational surfaces  Phase space island overlap due to parallel motion; diffusive processes Time= 400 L T /v e Time= 1400 L T /v e

9. 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 )

10. Effective wave-particle decorrelation time Parallel decorrelation time (Electron streaming across wave fields; independence of amplitude) Radial turbulence scattering time (Diffusion across radial width of m-harmonics) Resonant broadening time (Diffusion across radial streamer length) Eddy turnover time (Streamer rotation) Auto-correlation time (Fluid terminology) Linear growth time Relevant time scales in ETG turbulence

11. Parallel decorrelation time due to parallel spectral width ~ 5.3 Radial turbulence scattering time due to radial width of m-harmonics, together with radial diffusion and parallel motion ~ 8.0 Parallel wave-particle decorrelation time ~  wp time (L T /v e )

12. Calculate radial-toroidal two-point correlation function Calculate radial correlation function along the ridge Streamer correlation length L r ~54  e >> electron excursion distance Eddy turnover time ~ 42 Resonance broadening ~ 437 Eddy trapping not important Fluid eddy turnover time >>  wp Radial separation (  e ) 

13. Streamer auto-correlation time  auto >>  wp Calculate two-time, two-point (t-  ) correlation function Streamers move with a toroidal velocity ~ linear phase velocity Calculate Lagrangian time correlation function in wave frame Auto-correlation time  auto ~ 346 >>  wp Kinetic time scales shorter than fluid time scales Time separation (L T /v e ) 

14. 4.25.38.04243734633 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

15. Collaboration: TREND in large scale simulation US SciDAC: Scientific Discovery through Advanced Computing Turbulence: GPS & PMP CEMM RF Energetic particle US FSP: Fusion Simulation Project CPES: edge +MHD + atomic+… SWIM: MHD + RF FACETS: core + edge + wall EU ITM Japan BPSI “Preaching to the choir”