(1)Max-Planck-Institut für Plasmaphysik, Garching, Germany(2)Department of Physics&Astronomy, University of California, Los Angeles, CA 90095, USA

(3)Massachusetts Institute of Technology, Plasma Science and Fusion Center, USA(4)Center for Energy Research, University of California, San Diego, CA 92093, USA

1st IAEA Technical Meeting onFusion Data Processing, Validation and Analysis

1st of June - 3rd of June 2015Nice, France

Recent progress in comparing gyrokinetic GENE simula-

tions with experimental measurements

T. Görler(1)

F. Jenko(2,1), D. Told(2,1), A. White(3), C. Holland(4), T.L. Rhodes(2)

Thanks to:A. Banon Navarro, J. Citrin, J. Garcia, T. Happel, H. Doerk,

C. Lechte, E. Fable, F. Casson

Outline

● Brief overview: validation of gyrokinetic turbulence simulations – theory, successful projects, crucial questions

● A subject of interest: the DIII-D L-mode 'shortfall' Detailed study with the nonlinear gyrokinetic code GENE

● Comparison of gyrokinetic turbulence simulations with the experiment: ASDEX-Upgrade L- and H-modes, JET hybrid discharges, Doppler reflectometry

• Summary

3

The gyrokinetic modelGyrokinetic Vlasov equation

with gyrocenter position

parallel velocity

and magnetic moment

Poisson equation

Ampère’s law

Nonlinear 5D partial integro-differential system of equations remains to be solved!

Idea: removal of irrelevant space-time scales (gyrophase information)

Details may be found in [Brizard & Hahm, Rev. Mod. Phys. 79, 421 (2007)]

4

• Nonlinear gyrokinetic theory derived in 1980s (Frieman, Chen, Dubin, Hahm, Brizard)

• Very first PIC-based implementation in mid-80s, grid-based Vlasov and semi-Lagrange codes in (late) 90s [Review by Garbet et al., NF 2010]

● Mostly simulations with reduced physics (simplified electron response, collisionless, circular geometries, etc.) → comparison with experiment limited to qualitative findings

● Major improvement in the last decade:→ first heat flux-matched simulations in mid-2000 [Candy, PRL'03]→ more sophisticated comparisons based on synthetic diagnostics, e.g.

[Bravenec, Rev. Sci. Instrum. 2006; Leerink, 2010], see also next session→ ready for direct and qualitative validation, mainly in plasma core→ many examples in this session, also pushing towards edge

Evolution of GK application and validation

5

[T. Rh

od

es , N

F 5

1 (2

011)]

Validity of Gyrokinetics in core plasmas?

• Applicability of gyrokinetics demonstrated for various physical scenarios – e.g. in H-mode [C. Holland et al., PoP 18 (2011)] QH-mode [C. Holland et al., NF 52 (2012)]

• However, modeling of outer-core low-Te DIII-D L-mode discharges failed in several situations with various codes → shortfall(GYRO, TGLF, GEM)

[C. Holland et al., PoP 16 (2009)]

[T. Rhodes et al., NF 51 (2011)]

[J. Chowdhury et al., PoP 21 (2014)]

[J.E. Kinsey et al., PoP 22 (2015)]

6

Validity of GK in outer-core L-modes?• Questions:

– Can Gyrokinetic Theory describe outer-core L-modes (in general)?

– Extension of TGLF physics base required?

– Core-edge coupling? Highly nonlinear regimes [B. Scott, PPCF 49 (2007)]?Implications for quasi-linear modeling?

• 'Pro' arguments (shortfall absent): Shortfall less pronounced or absent for high Te discharges both in GYRO&TGLF

Recent TGLF study found no shortfall for a low NBI DIII-D discharge[J.E. Kinsey et al., PoP 22, 012507 (2015)]

CMOD L-mode (both low- and high Te) GYRO simulations matching the ion heat flux [N.T. Howard et al., PoP 20, 032510 (2013)]

ASDEX-Upgrade L-modes study with GENE, GKW → no shortfall[D. Told et al., PoP 20, 122312 (2013)]

No shortfall found with GENE for original DIII-D discharge:good agreement with experiment in various observables[T. Görler et al., PoP 21, 122307 (2014)]

7

Running GENE (genecode.org) with

• fully gyrokinetic ions & electrons

• electromagnetic (A||) fluctuations (at low β)

• collisions – modeled via linearized

Landau-Boltzmann coll. operator• geometry metric by field line tracing of EFIT or Miller equilibria• external ExB shear flows and parallel flow shear• minimum direct space grid for nonlinear runs

256x48x16x32x8 in the radial, binormal, parallel, v|| and μ directions

with perpendicular box size of at least 128x128 ρs

• time averaging over at least 200-500 a/cs in the saturated phase

(t>200 a/cs)

• Mostly local (fluxtube) simulations in perp. Fourier space (*~1/533)

Numerical simulations in this talk

Investigating the DIII-D 'shortfall' discharge

9

DIII-D #128913 (L-mode, 2.5 MW NBI) – linear analysis

real frequency

ETG

ITGmicrotearing

Heat transport driven on various scales:

Correct Qe prediction might require triple-scale simulations (expensive!)

However, Qi most likely mainly determined by 0.05 ≤ kyρs ≤ 2 (10 ≤ n ≤ 100) ;

restrict the following discussion to this transport channel

10

transport 'shortfall' at ρ = 0.75 for nominal parameters only factor of 2contrary to a factor of ~7 reported in Ref. [1] = [C. Holland et al., PoP 16 (2009)]

ion temperature gradient (α/LTi) variations within exp. error bars yield correct heat

transfer rates at multiple radial positions

electron heat flux not matched possibly due to unresolved sub-ion-scale turbulence as discussed above (ETG-ai predicts about 0.45 MW at ρ=0.75)

neoclassical transport negligible in radial range under consideration

(b) electron heat transfer rate

DIII-D #128913 – nonlinear results

(a) ion heat transfer rate in MW

Ref. [1], nominal

Ref. [1], -20%ExB

,

+10%a/LTi

-2%α/LTiGENE, nominal

GENE, -10%α/LTi

Ref. [1], +20%ExB

+22%

α/L Ti

GENE-neoclassic

DIII-D #128913L-mode (t~1.5s)

Ref. [1], nominal

Ref. [1], -20%ExB,

+10%a/LTi

-2%α/LTi

GENE, nominal

GENE, -10%α/LTi

Ref. [1], +20%ExB

ONETWO

GENE-neoclassic+2

2%α/

L Ti

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Ti / keV

(a) time trace at =0.74 (b) flux-matching procedure

(c) reconstructed Ti profile ExB shear flow activated after initial saturation;

turbulence reduced by about 40-50%

stiffness demonstrated by ion temperature gradient (α/L

Ti) variations at various radial positions

consistency check: ion temperature profile reconstructed from flux-matched gradients within error bars

ExB shear flow activated

Nonlinear results - details

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Validation/synthetic diagnostics

density fluct. on (R,Z) grid in lab(!)frame

interpolated to relevant area

BES array filter

PSF

raw data as seen at BES pos.

synth. data with PSF filter

Here: BES, CECE modeling similar to [C. Holland, PoP16, 052301]

spectral shape validated with both codes → mature synthetic modeling

underprediction consistent with heat transport → general fluctuation level not sufficient at nominal parameters

Ref. [1], nom.

10-6δne

2 / kHz spectra (BES)

Ref. [1], nom.

10-6δTe

2 / kHz spectra (CECE)

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Synthetic CECE – brief discussionHere: CECE modeling following [C. Holland, PoP16, 052301] but modified!

less uncertainty in PSFs

important: here, strong anisotropy of temperature fluctuations → CECE susceptible to T

┴

→ agreement much better than with total temperature fluctuations

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Synthetic BES – brief discussionHere: BES modeling similar to [C. Holland, PoP16, 052301]

BES not matched as good as CECE→ PSFs poorly estimated?

However, impact of point spread function (PSF) shape seems to be negligible here

further reasons:

● tilted PSFs important?

● impact of temperature fluctuations on BES signal?

● sensitivity scan in density gradient required?

10-6δne

2 / kHz spectra (BES)

PSF I PSF II

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• fluctuation levels: correct trend with GENE

•Fluctuation amplitudes and cross phases determine transport magnitude

Comparison: fluctuation amplitudes and cross phases

•Cross phase (n,T) comparison: for similar discharge #138040 and #138038 (ECH)

• remarkable agreement for both cases at ρ=0.65,0.75in relevant k

y range

•no transport underprediction!

GENE-synth +22%a/LTi

GENE-synth,-10%a/L

Ti

GENE-synthRef. [1], synth

BES CECEGENE-synth +22%a/L

Ti

GENE-synth

Ref. [1], synth(total T)

density fluctuations electron temperature fluctuations

exp. values [A. White et al., PoP ’10]

Me

an

(α)

16

-r (cm)

Z (cm

)

1/e1/e

2/e

Overpredicted eddy-tilting linked to shortfall?•Shafer et al., PoP 2012:shear implemented in simulation larger than in experiment? → may be responsible for underpredicted transport

• however, similar 2D corr. functions and wave number spectra found in GENE and GYRO despite different transport levels (here: nom. parameters)

• extensive scan: sign of shear, co-moving frame effects → can get close to BES but transport only varies within 30%

Shafer et al., PoP'12

Shafer et al., PoP'12

GYRO-synthGENE-synth

-kr(cm-1)

kz (cm

-1)

Synthetic GENE

2/e1/e

17

Finite-size effects important?

Ti ne

ρ* quite small!

Simulation domain in (R,Z) and n, T

fluctuations

good agreement with local code (in line with small ρ*) → no strong core/outer-core coupling found

deviation at ρtor

=0.85 due to global

simulation domain

overprediction in inner-core due to missing fast ion effects [→ Holland, NF'12, J. Citrin PRL'13]? Experimental error bars of temperature, density gradients or ExB shear?

preliminary global GENE result

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Code comparison at =0.5 (verification)

● electrostatic, no shear flow, carbon impurities(!)

● excellent agreement linearly

● nonlinear results agree well within the statistical error bars

Similar investigations at ρ=0.75 on-going

GYRO/GS2: [R. Bravenec et al., PoP 18, 122505 (2011)]

GY

RO

/GS

2 /GE

M:

[R. V

. Br ave ne c et a l.,

Po P

2 0, 10 45 06 (20 13 )]

linear

nonlinear

Further validation studieswith GENE

20

Successful flux matching for AUG L-mode – no shortfall

Flux matching within experimental uncertainties (2 discharges, 2 radial positions)

GENE and GKW in good agreement,TGLF observes shortfall (nonlinearly)

[E. F

able et al ., PP

CF

2 013]

Linear GK:growth rate spectra

NL gyrokinetics:transport spectra

[Told, Jenko, Görler et al., PoP 2013]

21

ASDEX Upgrade H-mode [Happel, Bañón Navarro, Görler et al., PoP 2015]

•Both transport channels matched within the error bars

•Radial density fluctuation profile from Doppler reflectometry largely reproduced

•Future comparison shall involve density spectra (spectral indices as shown on the right) and cross phases

[Bañón Navarro, Happel, Görler et al., PoP 2015]

22

Synthetic Doppler Reflectometry project

•Couple turbulence code GENE and full wave code IPF-FD3D for comparison with expt. Signal

•Seems to provide missing link, e.g., to recover rollover ('knee') position of the Doppler spectra!

k-3.8

AUG-Doppler-Reflectometry[C. Tröster, PhD thesis, 2008]

k-3.7

GENE simulation resultkr~0, outboard midplane

knee position determined by turb. physics (drive)

→ see talk by C. Lechte this afternoon (O-24)

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JET hybrid scenarios

low-δ JET hybrid discharge (#75225) at =0.33

high-δ JET hybrid discharge (#77923) at =0.33

high-δ JET hybrid discharge (#77923) at =0.64

[Garcia et al., NF 55, 05307 (2015)] [Citrin et al., PPCF 57, 014032 (2015)]

•Extensive transport-based validation studies:ion heat flux can successfully be matched in various JET hybrid scenarios

•Electromagnetic effects AND fast ions can be crucial ingredients(similar finding to Holland, NF'12, and Citrin, PRL'13)

ConclusionsGyrokinetics already validated for many scenarios

Here: extension to outer-core L-mode - ion heat transport shortfall in gyrokinetic ab-initio simulations not universal; counter-examples shown for DIII-D, AUG

electron heat transport underpredictions may very well be related to unresolved scales (ETGs) – not to missing physics in the gyrokinetic theory (see also [Görler et al., PRL/PoP'08; Howard et al., PoP'14+talk])

realism of simulations supported by good agreement between synthetic and actual diagnostics measurements

here: outer-core scenarios not in highly nonlinear regime (not shown); finite-size effects not important in addressed radial domain

investigation of the code discrepancies for DIII-D on-going; AUG results confirmed by several codes

further examples for validation studies shown here: Doppler reflectometry, AUG H-mode and JET hybrid discharges