Towards Multiscale Gyrokinetic Simulations of ITER-like Plasmas

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1 Frank Jenko Max-Planck-Institut für Plasmaphysik, Garching Universität Ulm Towards Multiscale Gyrokinetic Simulations of ITER-like Plasmas 23 rd IAEA Fusion Energy Conference October 2010, Daejeon, Republic of Korea Thanks to: S. Brunner, T. Dannert, H. Doerk, T. Görler, S. Günter, D. Hatch, T. Hauff, X. Lapillonne, P. Marcus, B. McMillan, F. Merz, M. Pueschel, O. Sauter, P.W. Terry, D. Told, L.Villard

2 Gyrokinetics is going multi-scale Source: Y. Kishimoto The new frontier is multiscale gyrokinetics (integration!) as is demonstrated at this meeting This talk will address several issues of relevance to ITER: nonlocal and finite-size effects turbulence at high plasma beta role of sub-ion-gyroradius scales, core and edge transport barriers

3 The global gyrokinetic code GENE GENE is a physically comprehensive Vlasov code: supports local and global (full-torus), gradient/flux-driven simulations allows for kinetic electrons & electromagnetic fluctuations, collisions is coupled to various MHD codes and the transport code TRINITY It is well benchmarked and hyperscalable Barnes, THC/P4-01 gene.rzg.mpg.de Strong scaling on BG/P

4 Nonlocal and finite-size effects: ρ* scaling

5 Finite system size: Local limit recovered Simulations of gradient-driven ITG turbulence (adiabatic electrons) with ORB5 and GENE show that the local limit is recovered, provided the geometry is treated consistently, settling a long-standing debate. Local (flux-tube) limit McMillan et al., PRL 105, (2010)

6 Finite system size: Profile shape matters Local (flux-tube) limit PRL 105, (2010) Both codes also show that it is the parameter which really matters this should be kept in mind when dealing, e.g. with Internal Transport Barriers.

7 Nonlocal and finite-size effects: Heat flux avalanches

8 time Can avalanches break gyro-bohm? Global flux-driven simulations of ITG-ae turbulence with GENE (for ρ*=1/140) flux-surface averaged radial heat flux associated ExB shearing rate (radial shear layers) radius radius avalanches are mesoscale ; radial extent ~20-40 ρ i their propagation speed is found to be ~ρ*v ti propagation direction is correlated with sign(ω E ) importance of low-frequency zonal flows & mean flows Same phenomenology as, e.g., McMillan (PoP 2009) and Sarazin THC/3-5

9 Heat flux avalanches are quasi-local Global ITG-ae turbulence simulations with GENE: Radial extent and propagation speed do not depend much on ρ* ρ*=1/140 ρ*=1/280 ρ*=1/560 ρ*=1/1000 ITER-like

10 Interesting insights from local simulations ITG turbulence (adiabatic electrons) ITG turbulence (kinetic electrons) Avalanches are not inherently nonlocal ETG turbulence (adiabatic ions) Avalanches are less pronounced in more complete model TEM turbulence Avalanches are not to be identified with streamers Avalanches tend to be absent

11 Turbulence at high β: Field line stochasticity and magnetic transport

12 Some background on microtearing modes Stochastic field lines due to microtearing modes (gyrokinetic analogues of MHD tearing modes, driven mainly by T e ) [Drake Chen Callen; PRL 1977] Linear gyrokinetics: Microtearing modes exist not only in STs, but also in standard tokamaks, including ITER [Vermare 2008; Told 2008, Schneller 2009] Intrinsic multiscale nature

13 GENE simulations of microtearing turbulence Magnetic electron heat diffusivity and magnetic fluctuation level: à la Rechster-Rosenbluth Balancing linear growth with nonlinear damping like Drake et al., PRL 1980, but for different reasons (high-k dissipation) Nonlinear gyrokinetics confirms that microtearing turbulence is able to produce experimentally relevant transport levels

14 Electromagnetic ITG/TEM turbulence at high β ITG turbulence Turbulent fluxes versus β Q i es linear stabilization KBMs TEM turbulence Turbulent fluxes versus β Q e es KBMs Pueschel et al., PoP 2010 Gyrokinetic simulations up to onset of kinetic ballooning modes (moderate downshift with respect to critical β for ideal MHD ballooning modes) Significant deviations from quasilinear expectations ( modelling?) Weakly damped microtearing modes are nonlinearly excited (leads to field line stochasticity: δb x /B 0 ~β/β crit ) Terry, THC/P4-27

15 Turbulent energetic particle transport Magnetic transport of beam ions (GENE) Analytic theory Hauff et al., PRL 2009 Beam ions: Electrostatic transport falls off only as (E/T) -1, and magnetic transport is independent of energy Link with anomalies of current profile evolution in AUG and DIII-D?

16 Role of sub-iongyroradius scales: ETG turbulence and E/ITBs

17 High-k turbulence and transport High-k ETG turbulence can induce significant electron heat transport: is possible a,b,c (at positive shear) a Jenko et al., PoP 2000; b Nevins et al., PoP 2006; c Görler et al. PRL 2008 For comparison: (Cyclone base case, exceeding experimental values) About 10 (<1) such electron gyro-bohms are sufficient to explain χ e in the outer half (internal transport barrier) of various tokamak discharges b TGLF transport simulations of 32 DIII-D hybrid discharges: ion transport close to neoclassical, electron transport dominated by high-k ETG modes d For certain MAST and NSTX discharges, gyrokinetic ETG simulations yield χ e s which are consistent with experimental values e d Kinsey et al., APS 2009; e Roach et al., PPCF 2009

18 GENE runs for AUG H-mode edge plasmas Experimental temperature & density profiles are used #20431 Metric coefficients extracted from MHD equilibrium via field-line tracing with the GIST code a a Xanthopoulos et al., PoP 2009

19 Local (high-k) gyrokinetics for edge barriers Significant ETG activity at k ρ i» 1 Φ contours at outboard side ρ i AUG #20431 High-wavenumber ETG turbulence is able to explain the residual electron heat transport in H-mode edge plasmas Edge turbulence codes should be able to retain high-wavenumber activity

20 Global gyrokinetics for internal barriers TCV #29866 Global GENE simulations with quite comprehensive physics (and R/L Te =25 12) for TCV e-itbs reveal χ e dominance, high-k activity

21 Global GENE simulation: eitbs in TCV D. Told

22 Conclusions

23 Some key conclusions The transition from nonlocal to local turbulence (ρ* 0) has been revisited cooperatively, settling a long-standing debate Heat flux avalanches seem to be mesoscale (ρ i -related) phenomena and are found not to break the gyro-bohm scaling Turbulence at high plasma beta requires further considerations, e.g., concerning transport models and the role of microtearing modes Turbulent transport of energetic ions offers a possible explanation for observed anomalies of current profile evolution (AUG, DIII-D) Transport at high wavenumbers can be important, in particular in core/edge transport barriers and for high-performance scenarios

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