Turbulent transport in collisionless plasmas: eddy mixing or wave-particle decorrelation?

Z. LinY. Nishimura, I. Holod, W. L. Zhang, Y. Xiao, L. ChenUniversity of California, Irvine, California 92697, USA

P. H. DiamondUniversity of California, San Diego, California 92093, USA

T. S. Hahm, S. Ethier, G. RewoldtPPPL, Princeton University, Princeton, New Jersey 08543, USA

F. ZoncaAssociazione EURATOM-ENEA sulla Fusione, Frascati, Italy

S. KlaskyOak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA

Supported by US DOE SciDAC GPS Center

• ITG: isotropic eddies

• ETG: radial streamers

• Fluid picture: eddy mixing

• Kinetic process: wave-particle decorelation

Turbulence Structure & Transport in Tokamak

• 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

• 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?

Instability Electron temperature gradient (ETG)

Ion temperature gradient (ITG)

Collisionless trapped electron mode (CTEM)

Electron drive Parallel resonance Non-resonance Precessional resonance

Saturation Nonlinear toroidal coupling

Zonal flows Zonal flows

Electron heat Transport

Wave-particle decorrelation

Nonlinear mode scattering off trapped electron?

Processional resonance de-tuning? Avalanche?

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

GTC nonlinear convergence in ETG simulation• Convergence from 400 to 2000 particles per cell

Weak Cyclone parameters: R/LT=5.3, s=0.78, q=1.4, a/e=500, /r~1/4

ORNL Cray XT3, 6400 PE, 4x1010 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]

time (LT/ve)

• 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

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 > 102 distance of mode rational surfaces Phase space island overlap due to parallel motion; diffusive processes

Time=400 LT/ve

Time=1400 LT/ve

Transport driven by local fluctuation intensity• Effective wave-particle decorrelation time wp=4e/3vr

2 ~ 4.2LT/ve

• wp << 1/~ 33: linear time scale not important to transport

• Wave-particle correlation length vrwp << streamer length

• Electron radial excursion diffusive: streamer length does not determine transport directly

• From linear to nonlinear, e/vr2 decreases by a factor of ~5

Nonlinear loss of wave-particle correlation

r/e

2rve

e/vr2

time (LT/ve)

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

2

4

3e

wprv

||||

1

ek v

2 2 2

3

4 es k

reddy

r

L

v

24

3r

rbe

L

auto

1

• 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

2 2 2

3

4 es k

2 2 2

3

4 es k

k R

ek

ek

time (LT/ve)

||||

1

ek v

• Calculate radial-toroidal two-point correlation function

• Calculate radial correlation function along the ridge

• Streamer correlation length Lr ~54 e>> electron excursion distance

• Eddy turnover time

~ 42

• Resonance broadening

~ 437

• Eddy trapping not important

Fluid eddy turnover time >> wp

reddy

r

L

v

24

3r

rbe

L

Radial separation (e)

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 (LT/ve)

4.2 5.3 8.0 42 437 346 33

Kinetic & fluid time scales in ETG turbulence

2

4

3e

wprv

||||

1

ek v

2 2 2

3

4 es k

reddy

r

L

v

24

3r

rbe

L

auto 1

• auto >> 1/ >>wp ~ 1/k||ve

• 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

• 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”