Saturation rules for ETG transport in quasilinear transport models

Saturation rules for ETG transport in quasilinear transport models J. Citrin 1, C. Bourdelle 2, N. Bonanomi 3, T. Goerler 4, P. Mantica 3 1 FOM Institute DIFFER, PO Box 6336, 5600 HH, Eindhoven, The Netherlands 2 CEA, IRFM, F-13108 Saint Paul Lez Durance, France 3 Istituto di Fisica del Plasma CNR, 20125 Milano, Italy 4 Max Planck Institute for Plasma Physics, Boltzmannstr. 2, 85748 Garching, Germany DIFFER huisstijl presentatie 30 september 2016 DIFFER is part of and

Motivation Significant ETG fluxes reported at experimental conditions in recent multi-scale simulations (T Görler et al, PRL 2008, N. Howard et al, PoP 2014, NF 2016) Complex multi-scale physics, with strong dependence on ion turbulence level and zonal flows, and electromagnetic effects (Maeyema PRL 2015) We desire accurate ETG saturation levels in quasilinear transport models, for full profile and discharge evolution prediction Tuning a quasilinear ETG saturation rule from multi-scale nonlinear simulations is not everyone s cup of tea What can single-scale simulations teach us nonetheless? Can we find a cheaper way to tune the quasilinear models? Madrid Gyrokinetic Theory Workshop, 2016 Jonathan Citrin 2

Outline Phenomology of single scale ETG simulations Phenomology of multi-scale simulations ETG saturation rules in quasilinear models Madrid Gyrokinetic Theory Workshop, 2016 Jonathan Citrin 3

Case study of agreement of single-scale ETG simulation with experimental fluxes Single scale (adiabatic ions) ETG nonlinear simulation of JET 78834, with strong electron heating L x /n kx /min kk yy ρρ ee /n ky /n z /n w / n v = 200/256/0.05/24/48/48/12 Electron heat flux: nonlinear GENE single scale ETG ETG saturation reached using γγ EE to break up radial streamers Ion scales (TEM/ITG) alone cannot explain the exp. q e flux and the exp. q e stiffness ~50% of the electron flux from electron scale Mantica, Bonanomi, Citrin, Goerler et al, IAEA 2016 Madrid Gyrokinetic Theory Workshop, 2016 Jonathan Citrin 4

Case study of agreement of single-scale ETG simulation with experimental fluxes Ion scale simulations: Miller, electromagnetic, collisions, kinetic electrons, carbon imp, fast ions, Z eff ~1.9. L x /n kx /ky ρρ ii min/n ky /n z /n w /n v = 100/128/0.05/24/32/48/8 Ion heat flux (same discharge) q i,gb in good agreement with experimental power balance Slight sensitivity of ion heat flux on RR/LL TTTT (trapped electron drive) However, within range of RR/LL TTTT studied in electron scale simulations, ion heat flux always agrees Madrid Gyrokinetic Theory Workshop, 2016 Jonathan Citrin 5

Ingredients needed for reasonable flux in single scale electron scale simulations Avoid electron scale zonal flows Avoid crazy radial streamers Madrid Gyrokinetic Theory Workshop, 2016 Jonathan Citrin 6

Radial streamers can be controlled by rotation shear. Proxy for ion scale eddies? LL xx LL yy (box sizes), no destabilization of electron scale ZF From γγ EE 2 times exp value, stabilizes ETG to experimentally relevant levels. ETG flux level remains roughly constant for higher γγ EE (encouraging) What does this mean? A proxy for ion scale eddies? γ ExB =0: Not saturated unrealistic level ~ x50 exp q e Φ(x,y) γexb =0.001 cc ee /RR Φ(x,y) γ ExB =0.007 cc ee /RR ( 4 exp level) Saturated comparable to exp Saturation mechanism? Drift-wave, drift-wave coupling? Φ(x,y) Madrid Gyrokinetic Theory Workshop, 2016 Jonathan Citrin 7

No convergence with box size: electron scale zonal flows enters the picture Increasing the radial box size destabilizes electron scale zonal flows TT γγ EE = 0, ττ ZZ ee eeeeee = 2.2, TT ii L x ~ 366, L y ~ 84 RR LL TTTT = 6.5 (just above linear threshold). Linearly unstable, but then saturates strongly due to zonal flows. ETG Dimits shift regime Φ contour plot Strong ZF Madrid Gyrokinetic Theory Workshop, 2016 Jonathan Citrin 8

No convergence with box size: electron scale zonal flows enters the picture γγ EE = 0, ττ = 2.2, Test sensitivity of ZF saturation to RR/LL TTTT RR = 7.0. L LL x ~ 366, L y ~ 84 TTTT Increasing RR/LL TTTT by just 0.5 leads to huge streamers that aren t stabilized by ZF. Out of Dimits shift zone. This effectively means very high stiffness Open question: are these electron scale zonal flows ever experimentally relevant? Do ion scale eddies short them out? Perhaps relevant only when ion scales fully suppressed From lots of dedicated tests, hard to find convergence of Dimits shift threshold Strong regime sensitivity between i) ZF dominance, ii) streamer dominance, iii) reasonable finite flux on: LL xx /LL yy, n x, kinetic or adiabatic ions (low kk xx ρρ ee is on ion scales), ββ, γγ EE, collisionality. See also Colyer et al., 2016 Madrid Gyrokinetic Theory Workshop, 2016 Jonathan Citrin 9

Outline Phenomology of single scale ETG simulations Phenomology of multi-scale simulations ETG saturation rules in quasilinear models Madrid Gyrokinetic Theory Workshop, 2016 Jonathan Citrin 10

Multi-scale simulations show multiple regimes of multi-scale interaction N Howard NF 2016 High aa/ll TTTT, interaction with ion-scale ZF leads to weak ETG Low aa/ll TTTT, weak ion-scale ZF, significant strengthening of ETG Indications that at lower (stable) aa/ll TTTT, ETG significantly reduces again due to emergence of electron scale ZF (i.e. back to regime as in Colyer et al) Madrid Gyrokinetic Theory Workshop, 2016 Jonathan Citrin 11

Multi-scale simulation of our JET electron heated discharge Mantica, Bonanomi, Citrin, Goerler et al, IAEA 2016 (PhD thesis, Nicola Bonanomi) Multiscale GENE, local, δδδδ ETG linearly unstable At nominal parameters, ionscale eddies kill ETG Stretching RR/LL TTTT and RR/LL TTTT to edges of error bars seem to recover ETG heat flux as in single-scale case Madrid Gyrokinetic Theory Workshop, 2016 Jonathan Citrin 12

Tentative conclusions from nonlinear simulation phenomology Electron scale zonal flows only matter when ion-scale turbulence is completely stabilized (e.g. spherical tokamak with high rotation) Therefore, if in regime where ion-scale unstable, OK for single-scale simulations where electron scale zonal flows are not included? What then matters is whether ion-scale eddies saturate the electron scale, or are weak enough to allow electron scale to sature by DW- DW saturation. If we know when this occurs, can we then use single-scale simulations to tune and validate quasilinear ETG saturation rules? Of course, this is all with electrostatic simulations. Further complications observed to occur in EM (Maeyama PRL 2015) Madrid Gyrokinetic Theory Workshop, 2016 Jonathan Citrin 13

Outline Phenomology of single scale ETG simulations Phenomology of multi-scale simulations ETG saturation rules in quasilinear models Madrid Gyrokinetic Theory Workshop, 2016 Jonathan Citrin 14

First multi-scale ETG quasilinear transport model saturation rule now in TGLF-SAT1 TGLF: a gyrofluid quasilinear turbulence transport model (Staebler PoP 2007). Now with multi-scale saturation rule (Staebler PoP 2016) 2 terms in quadratic nonlinearity that claim to lead to saturation Zonal flow mixing term. Can couple high kk yy ETG with ion scale ZF kk xx γγ DDDDDD : Drift wave mixing term Madrid Gyrokinetic Theory Workshop, 2016 Jonathan Citrin 15

φφ(kk xx, kk yy ) γγ mmmmmmmmmm kk yy 2 First multi-scale ETG quasilinear transport model saturation rule now in TGLF-SAT1 Main idea of the model: the γγ used in the ETG mixing length rule should be small when ZF mixing dominates, and equal to γγ DDDDDD (saturation mechanism) when ZF is weak Same parameters as GYRO multi-scale case: high aa/ll TTTT (Staebler PoP 2016) Carry out Lorentzian broadening for final γγ mmmmmmmmmm Model for VV ZZZZ based on ion scale linear spectrum, and tuned to GYRO simulations Same parameters as GYRO multi-scale case: low aa/ll TTTT Can recover GYRO multi-scale electron heat fluxes (see Staebler PoP 2016) Madrid Gyrokinetic Theory Workshop, 2016 Jonathan Citrin 16

ETG saturation rule in QuaLiKiz gyrokinetic quasilinear tranport model QuaLiKiz: a gyrokinetic quasilinear turbulent transport model (Bourdelle PoP 2007, PPCF 2016, Citrin PoP 2012) ff ss + vv rf s + e s EE vv ff ss = 0 Electrostatic Vlasov (collisionless here for simplicity) δδff ss ωω, kk = FF MM TT ss 1 ωω kk nnnn ss ωω kk kk vv nnωω ssss ee ss φφ kk Linearized Vlasov with harmonic perturbations ss dd 3 vvdd 3 xx δδff ss ee ss φφ kk = 0 Weak form for quasineutrality to close dispersion relation Madrid Gyrokinetic Theory Workshop, 2016 Jonathan Citrin 17

Sketch of QuaLiKiz model construction Dispersion relation: kk vv for passing ions and electrons bounce average for trapped ions and electrons (kk vv = 0) collisions only for trapped electrons DD ωω = dddddddddddddddd nn 2 ssee ss ss kk = kk θθ TT ss ss qqqq xx 1 ωω kk nnnn ss ωω kk kk vv, 0 + iiii nnωω ssdd JJ 0 2 k ρρ ss, δδ ss δδδδ(rr, θθ) 2 = 0 From eikonal: δδδδ, δδδδ e in(φ q r θθ) x distance from q surface φφ eigenfunction solved from high ωω expansion of D(ωω) and Gaussian ansatz ωω ωω rr + iiii is the only unknown in the above equation. Root finding in upper complex plane (instabilities only) Madrid Gyrokinetic Theory Workshop, 2016 Jonathan Citrin 18

Setting quasilinear fluxes with a nonlinear saturation rule Transport fluxes for species j: carried by ExB radial drifts Γ jj, QQ jj, Π jj kk δδnn jj, δδtt jj, δδvv SS kk δδφφ kk Use moments of linearized δδff ss evaluated at the instabilities, i.e. from solutions of DD ωω kk Spectral form factor SS kk and saturated amplitude of δδδδ 2 are unknowns. Their model, validated by nonlinear simulations, is the saturation rule SS kk kk 3 ffffff kk > kk mmmmmm kk ffffff kk < kk mmmmmm kk mmmmmm iiii kk aaaa max γγ kk kk 2 Casati NF 09, PRL 09 δδφφ kk 2 = CCCC kk max + finite kk xx corrections at low-s from nonlinear physics (JC, PoP 2012) Madrid Gyrokinetic Theory Workshop, 2016 Jonathan Citrin 19 γγ kk kk 2 C is scalar factor set by matching heat fluxes in single NL simulation (for ion and electron scales separately)

QuaLiKiz reproduces nonlinear fluxes Scans for GA-standard case parameters (numerous other scans and comparisons have also been successfully carried out) GA-standard s-scan 25 20 15 χ i χ e D p GA-standard R/L Ti scan vs GYRO GB-flux χ eff / χ GB 10 5 0-5 -10 4 6 8 10 12 14 R/L T Validation against experimental fluxes: e.g. Tore Supra (Casati PhD 2009, Villegas PRL 2010), JET (Baiocchi NF 2015, J. Citrin Varenna 2016, S.Breton, C. Bourdelle) Continuous comparison of QLK to both nonlinear and experiment part of our culture For transport studies, trivial parallelization of code over wavenumbers and radii Madrid Gyrokinetic Theory Workshop, 2016 Jonathan Citrin

From Bonanomi et al. EPS 2015 ICRH heated JET discharge 78834 GENE simulations ETG contribution in QuaLiKiz fluxes based on recent work on JET QuaLiKiz GA-STD s-scan with new ETG contribution GENE single-scale NL simulation with γγ EE to break apart streamers and avoid box effects. ~50% of electron power balance in agreement with observation. Used to tune scalar prefactor in QuaLiKiz ETG nonlinear saturation rule. Corresponds to regime with drift-wave drift-wave coupling saturation mechanism? Impact shown on GASTD case magnetic shear scan. Up to 50% of qq ee in some cases Madrid Gyrokinetic Theory Workshop, 2016 Jonathan Citrin 21

Extensive coupling work to JETTO-SANCO JETTO flux driven transport solver with sources and equilibrium [1,2] SANCO impurity density and charge state evolution, radiation Includes Pereverzev and G. Corrigan numerical treatment for stiff transport Neoclassical transport from NCLASS or NEO 1s of JET plasma takes ~20h walltime with QuaLiKiz on 16 CPUs (2.33GHz) (Note: this is with rotation. Without rotation, around 4 quicker due to symmetry in 2D integration) Extensive testing done on well diagnosed and studied hybrid scenario 75225 and baseline scenario 87412 First QuaLiKiz integrated modelling simulations with impact of rotation on turbulence, multiple ions, and momentum transport [1] G. Cenacchi, A. Taroni, JETTO: A free-boundary plasma transport code, JET-IR (1988) [2] M. Romanelli et al., 2003, 23rd International Toki Conference Madrid Gyrokinetic Theory Workshop, 2016 Jonathan Citrin 22

Main result: JETTO-SANCO integrated modelling Agreement excellent in ALL channels for ρ>0.5 First ever 4-channel flux driven QuaLiKiz simulation. ~100 CPUh JET 75225 (C-wall hybrid scenario) Time window from 6-7s C impurity in SANCO D and C modelled separately Boundary condition at ρρ = 0.8 Includes rotation (ρρ > 0.5) and momentum transport! Pr ~0.5 Agreement excellent in all channels for ρρ > 0.5 For ρρ < 0.5, Ti underprediction due to lack of EM effects in QLK 23

Sensitivity to ETG model in JET hybrid scenario integrated modelling Comparison with and without ETG model Original fit and boundary conditions Fit with reduced TT ee, TT ii boundary conditions at ρρ = 0.8 by ~20% ETG scales can be important for agreement, but sensitive to e.g. boundary conditions Madrid Gyrokinetic Theory Workshop, 2016 Jonathan Citrin 24

JETTO-QLK also validated by comparison to a JET-ILW baseline scenario Comparison with and without ETG-scales Time window averaged between 10-10.5s ILW baseline scenario JET 87412 (3.5MA/3.35T) Good agreement in All channels apart from V tor Boundary condition at ρρ = 0.85 Stable for ρρ < 0.2. No sawtooth model Assuming core measurements T i =T e due to poor core CX NTV torque due to NTMs flatten profile? Quality of core CX for VV tttttt? Interesting interplay between momentum transport and profiles obtained without ETG. Under investigation Madrid Gyrokinetic Theory Workshop, 2016 Jonathan Citrin 25

Summary Electrostatic multi-scale nonlinear simulations seem to show 3 regimes of ETG transport: i) Ion-scales stable extensive ETG Dimits shift regime ii) Ion-scales weak, significant ETG flux (saturated by DW-DW coupling?) iii) Ion-scales strong, ETG scales are suppressed Can thus avoid electron-scale ZF in single-scale ETG when ion-scale is active? TGLF saturation rule has model to transition between regimes (ii) and (iii), based on model of ion-scale ZF advection of ETG modes. Recovers GYRO multi-scale runs QuaLiKiz saturation rule seems only to recover regime (ii), no multi-scale apart from implicit ignoring of ETG zonal flow. Nevertheless, seems to improve agreement in limited validation set. Future work: simple model for determining regime change between (ii) and (iii). Then can validate saturate rule for (ii) cases on single-scale ETG? Madrid Gyrokinetic Theory Workshop, 2016 Jonathan Citrin 26