23 rd IAEA Fusion Energy Conference, Daejeon, Republic of Korea, October 2010Y. Sarazin 1 / 14...

23rd IAEA Fusion Energy Conference, Daejeon, Republic of Korea, October 2010 Y. Sarazin 1 / 14

Global Gyrokinetic SimulationsGlobal Gyrokinetic Simulationsof

Heat Transport Heat Transport & Plasma Plasma Rotation Rotation Y Sarazin1, V Grandgirard1, J Abiteboul1, S Allfrey1, X

Garbet1, Ph Ghendrih1, G Latu1, A Strugarek1, G Dif-Pradalier2,

P H Diamond2,3, B F McMillan4, T M Tran4, L Villard4, S Ku5,C S Chang5, S Jolliet6, A Bottino7, P Angelino8

1. CEA, IRFM Cadarache, Saint Paul-lez-Durance cedex, France.2. Center for Astrophys. & Space Sciences, UCSD, La Jolla, California, USA.3. National Fusion Research Institute, Daejeon, Republic of Korea.4. CRPP, Assoc. Euratom-Confédération Suisse, EPFL, Lausanne, Switzerland. 5. Courant Institute of Math. Sciences, New York Univ., New York, USA.6. Japan Atomic Energy Agency, Higashi-Ueno 6-9-3, Tokyo, Japan.7. Max-Planck IPP, Association Euratom, Garching, Germany.8. Labo. of Computational Systems Biotech., EPFL, Lausanne, Switzerland.

GYSELA


IntroductiIntroductiononOpen questions for ITER regarding turbulent transport:

Impact of large scale transport on scaling laws

cE=F(*,*,,…)? meso-scale avalanches / ZF interaction => gyro-Bohm scaling

Generation & magnitude of poloidal / toroidal rotation?Critical for turbulence saturation & MHD stability Turbulence-generated poloidal & toroidal corrugations

How to trigger & maintain transport barriers?New generation of gyrokinetic codes able to address these issues

… thanks to the large increase of HPC resources (PetaFlop scale)

GYSELA [Grandgirard JCP '06], ORB5 [Jolliet CPC '07], XGC1 [Chang PoP '08], ELMFIRE [Heikkinen JCP '08],

GT5D [Idomura NF '09], global-GENE [Görler '09, Lapillonne '10], multi scale TRINITY [Barnes '10], FEFI [Scott

CPP '10]

[Strugarek '10]


Main characteristics of 3 gyrokinetic Main characteristics of 3 gyrokinetic codescodes

All three codes are (for simulations used)

Full-f (no scale separation fluctuations/equilibrium) Flux driven Electrostatic, adiabatic electrons, collisional Global

geometry

[Grandgirard JCP '06, PPCF '08]

GYSELASemi-Lagrangian

ORB5PIC, optimized loading

XGC1PIC, X-point

[Jolliet CPC '07] [Chang & Ku PoP '08, '09]

[Brizard & Hahm RMP '07]

;

Consistent formulation of Gyrokinetic theory


Resilience of temperature Resilience of temperature profileprofile Modest increase of temperature when Source magnitude

S0~Padd

Caveat: requires long simulation runs (~E with cE *3)

[Sarazin NF '10]

Consequence: stored energy less than Padd

experimental degradation of E with Padd is recovered

GYSELA


=r/a

Inward & outward Inward & outward avalanchesavalanches Transport dominated by large scale avalanches (length corr)

Intermittent (1/f Fourier frequency spectrum)

Propagation velocity * cs (103 m.s1 in ITER)

Outward/inward fronts - sometimes related to positive/negative Er

time

(1

04

c1) GYSELA

(*=1/512)

ORB5

(*=1/280)

Heat flux[gBohm units]

=r/a

18

16

14

12

10

8

6

4

2

0

16

14

12

10

8

6

4

20 0.5 1.0 0.3 0.5 0.7

[Idomura NF '09][McMillan PoP '09]

Exp. Evidences:

[Politzer PRL '00,

Tamura IAEA '10, Endler JNM '99, Rudakov

PPCF '01, Boedo PoP

'01, Grulke PoP '06, Antar

PoP '07, Müller PoP '07,

Zweben PPCF '07,

Fedorczak JNM '09,

Pedrosa EPS '10, etc…]

[Sarazin NF '10]


Common understanding: Local transport assumption Edge = core boundary

condition

Simulation with prescribed H-mode pedestal (XGC1):Edge ITG turbulence observed to propagate inwards destabilization of the core

Edge turbulence does propagate Edge turbulence does propagate inwardsinwards

[Ku NF '09]

time

[R

/vT]

=r/a

Turbulence intensity [Ku NF '09]

XGC1

(*=1/180)

XGC1

(*=1/180)

Reminiscent of inward propagation of temperature front after ELM event on JET[Sarazin PPCF '02]

Iso-contours of Te(JET #49637)

D

Tim

e [

s]


Gyro-Bohm scaling despite Gyro-Bohm scaling despite avalanchesavalanches

Usual framework:Small scale vortices (corri) local transport gyroBohm scalingThen:If avalanches feel the system size breaking of gyroBohm scaling?

Answer is NO:still gyroBohm at small *

(see [Jolliet & Idomura IAEA '10] at intermediate *)

adapted from [McMillan PRL '10]


Gyro-Bohm scaling despite Gyro-Bohm scaling despite avalanchesavalanches

Usual framework:Small scale vortices (corri) local transport gyroBohm scalingThen:If avalanches feel the system size breaking of gyroBohm scaling?

Answer is NO:still gyroBohm at small *

(see [Jolliet & Idomura IAEA '10] at intermediate *) Possible reasons:

corri

GYSELAPoloidal cross section of (non axi-symmetric component)

Smaller *

Avalanches are meso-scale


ct

4.105

2.105

GYSELA(*=1/256,*=0.05)

80 100 120 140 160 =r/a

Gra

die

nt

R/L

T 8

6

4

2

0

ExB shearing rate

Wave-like structure of ZF controls Wave-like structure of ZF controls avalanche sizeavalanche size Zonal Flows radially localized

Limit extension of avalanches

"Staircase" structure Framework for non-local

formulation of transport

[Dif-Pradalier PRE '10]

THC/P4-06

Radial profile:

wave-like pattern

predicted by theory

scales like i

[Diamond, Itoh, Itoh, Hahm PPCF '05]

GYSELA


Poloidal flow neoclassical – shear Poloidal flow neoclassical – shear is NOTis NOT

[Dif-Pradalier PRL '09]

In turbulent regime (no transport barrier): v still mainly neoclassical:

Difference (vvneo) well captured by Reynolds'stress

Reynolds'stress component when collisionality

Compare Er from 2 expressions:Turbulent regime

EGYSELA ~ lin E

neo

turbulence drives mean shear


exact momentum (waves + part.) conservation law

Local toroidal momentum balance well fulfilled:radial current (=0 due to charge

conservation)

Reynolds' stress polarization term

Local balance of parallel momentum is Local balance of parallel momentum is satisfiedsatisfied

[Abiteboul EPS '10]

[Diamond-Kim PF '91, Peeters PRL '07 PoP '09,

Hahm PoP '08, Gürcan PoP '08 '09,

Camenen PRL '09, Mc Devitt PRL '10]

GYSELA

[Brizard '10, Scott '10,

Abiteboul & Garbet '10]

Large contribution from neo. & turb. components of RS tensor


UU from supra-thermal & barely passing from supra-thermal & barely passing particlesparticles Co-current toroidal spin-up

carried out by

particles

supra-thermalbarely passing cf. [Fenzi '10

this conf. EX/3-4]

Thermal boundary

[Hahm PoP '08, Peeters PoP '09,Garbet "Festival de Théorie" '09]

Theoretical QL prediction for U//

Consistent with QL theoretical prediction


Avalanches transport both heat Avalanches transport both heat & U& U Dipolar structure (conservation) of U|| associated to 1st

relaxation

GYSELA

In saturated non-linear regime: Avalanches of heat also transport // momentum

-> OK with exp./theo. ; suggests similar eff (Prandtl number

~1)

-> reminiscent to exp. observations on JETCross-correlation (Qturb, U||)

GYSELA

[Hidalgo PRL '03]

[Diamond PoP '08]


ConclusiConclusionsons New generation of global full-f GK codes (GYSELA, ORB5, XGC1,

…)

Turbulent transport: excellent qualitative agreement

Transport dominated by meso-scale transport events: inward & outward avalanches -> non local / non diffusive new paradigm for core-edge interactions & transients

Gyro-Bohm effective diffusivity at sufficiently small *

(<1/250) critical role of zonal flow radial profile

Poloidal rotation mainly neoclassical – shear is NOT

(turbulence)

Many players / rich physics in toroidal momentum balanceSupra-thermal particles drive co-current spin-up

Transport of U|| correlated to heat transport

23 rd IAEA Fusion Energy Conference, Daejeon, Republic of Korea, October 2010Y. Sarazin 1 / 14...

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