Validating Simulations of Multi-Scale Plasma Turbulence in ITER-Relevant, Alcator C-Mod Plasmas

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1 Validating Simulations of Multi-Scale Plasma Turbulence in ITER-Relevant, Alcator C-Mod Plasmas Nathan Howard 1 with C. Holland 2, A.E. White 1, M. Greenwald 1, J. Candy 3, P. Rodriguez- Fernandez 1, and A. Creely 1 1 MIT Plasma Science and Fusion Center Cambridge, MA University of California San Diego La Jolla, CA General Atomics San Diego, CA IAEA Technical Meeting on Fusion Data Processing, Validation, and Analysis May 30 th June 2 nd,

2 Interactions Between Short and Long Wavelength Turbulence Can Play an Important Role in Core Transport Anomalous ion and electron heat transport is often attributed to long wavelength, ion-scale turbulence. - ITG/TEM assumed dominant at ion-scales (k q r s < 1.0) - ETG at electron-scales (k q r s > 1.0) is often ignored However, there is both theoretical and experimental evidence for an important role of ETG is some plasma conditions - Theory/simulation predicts formation of ETG streamers - High-k scattering reports fluctuations at electron-scales Simulations which capture both ion and electron scale turbulence and their coupling are extremely computational expensive. Cross-scale coupling plays an important role in reproducing L-mode exp. Only ~2 quantitative comparisons between multi-scale simulation and experiment have made to date [N.T. Howard NF 2016, C. Holland NF 2017] 2

3 Interactions Between Short and Long Wavelength Turbulence Can Play an Important Role in Core Transport Anomalous ion and electron heat transport is often attributed to long wavelength, ion-scale turbulence. - ITG/TEM assumed dominant at ion-scales (k q r s < 1.0) - ETG at electron-scales (k q r s > 1.0) is often ignored However, there is both theoretical and experimental evidence for an important role of ETG is some plasma conditions - Theory/simulation predicts formation of ETG streamers - High-k scattering reports fluctuations at electron-scales Simulations Gyrokinetic which capture simulations both ion capturing and electrons all scale relevant turbulence turbulence and their scales coupling are extremely computational expensive. must be validated against experiment to better understand the Cross-scale required coupling physics plays an important for prediction role in reproducing of ITER and L-mode beyond exp. Only ~2 quantitative comparisons between multi-scale simulation and experiment have made to date [N.T. Howard NF 2016, C. Holland NF 2017] 3

4 Understanding Coupling of Ion and Electron-Scale Turbulence Requires Multi-Scale Simulation Multi-Scale Gyrokinetic Simulation - Captures both long and shortwavelengths (ITG/TEM/ETG) - k q r s up to ~60.0 = k q r e ~ Extremely expensive - Must resolve electron spatiotemporal scales and ion-scales : A handful ever - Almost all previous work used reduced electron-mass. - Should not be compared with experiment Electron mass ratio: m = (m D /m e ).5 = 60.0 For a deuterium plasma - Reduced-mass approximation insufficient in some conditions - [N.T. Howard PPCF 2015] 4 4

5 Previous Work Demonstrated the Role of Cross-Scale Coupling Using Multi-Scale Simulation of Alcator C-Mod L-mode Discharges Key features of cross-scale interactions were identified: 1.) Ion-scale turbulence (& ion heat flux) is enhanced by the presence of electron-scale turbulence. - Due to modification of zonal flow shear and energy transfer in conditions with marginal ionscale turbulence 2.) ETG streamers were observed to coexist with ITG turbulence and drive up to 70% exp. Q e in near marginal conditions Standard ion-scale simulation ~20k CPU hours Multi-scale simulation ~20M CPU hours 3.) Strongly driven ( >> marginal) ion-scale turbulence was found to destroy electron-scale ETG streamers 5

6 Previous Work Demonstrated the Role of Cross-Scale Coupling Using Multi-Scale Simulation of Alcator C-Mod L-mode Discharges Key features of cross-scale interactions were identified: 1.) Ion-scale turbulence (& ion heat flux) is enhanced by the presence of electron-scale turbulence. - Due to modification of zonal flows and energy transfer in conditions with marginal ion-scale turbulence 2.) ETG streamers were observed to coexist with ITG turbulence and drive up to 70% exp. Q e in near marginal conditions Standard ion-scale simulation ~20k CPU hours Multi-scale simulation ~20M CPU hours 3.) Strongly driven ( >> marginal) ion-scale turbulence was found to destroy electron-scale ETG streamers Cross-scale coupling played a dominant role in reproducing exp. L-mode results. In this work we attempt to extend multi-scale simulation to high performance plasma regimes which may have more reactor relevance. 6

7 An Alcator C-Mod ELM-y H-mode Condition Has Been Studied Using Multi-Scale Gyrokinetic Simulation Similar to operational scenarios for ITER: - Approx. ITER density - ITER B-field (5.4T) - Intrinsically rotating - Predominately electron heated (ICRF+Ohmic) - Well coupled ions and electrons: T e ~ T i Linear stability analysis indicates: - ITG is dominant at ion-scales (k q r s <1.0) - High-k TEM/ETG is present at electron-scales (k q r s > 1.0) Open questions are: 1.) Does cross-scale coupling play an important role in ITER-like H-mode conditions? 2.) Do the mechanisms of cross-scale coupling look similar to L-mode? 3.) What are the implications of cross-scale coupling for prediction of H-mode plasmas? 7

8 Using GYRO, Realistic Mass, Ion and Multi-Scale Simulations Have Been Performed on a C-Mod ELM-y H-mode Discharge Simulations were performed at r/a = 0.6 using the GYRO code - High physics fidelity : - All experimental inputs - 3 gyrokinetic species (deuterium, electrons, impurities) - Electro-magnetic turbulence (f & A ) - Rotation effects (ExB shear, etc.) - Electron-ion and ion-ion collisions - Realistic electron mass: µ = (m i /m e ).5 = Simulation box size of 71 x 55r s radial grid points (for multi-scale simulation) toroidal modes (for multi-scale simulation) - Ion-scale simulations capture ITG/TEM up to k q r s up to ~1.1 - Multi-scale simulations capture (ITG/TEM/ETG) up to k q r s up to ~42.0 = k q r e ~ Utilized ~22k cores. Approximately 20-25M CPU hours per multi-scale simulation. - Results from 3 multi-scale simulations are presented here. 8

9 Ion-Scale Sims Reveal that Low-k Transport is Extremely Stiff With Experiment Just Above the ITG Critical Gradient Tiny a/l Ti changes (2%), dramatically increase driven heat flux are. - Implies extremely stiff heat transport (~10x a corresponding L-mode) - Note that Q i, exp ~ Q e,exp & Q/Q GB ~ 1.85 implying very marginal conditions Experimentally relevant levels of ion heat flux are obtained just 2% above the ITG critical gradient. 9

10 Within Uncertainties in the Simulation (~10%) and Experiment, Ion-Scale Simulation Can Reproduce Experimental Heat Fluxes When uncertainties are considered, agreement is found between ionscale simulation and experiment For the condition with a/l Ti increased 10% above experiment, ion-scale simulation reproduces experimental Q i and Q e within uncertainties Does this imply the ion-scale model is that multi-scale turbulence is unimportant? 10

11 The Multi-Scale Simulation Base Case is Able to Reproduce Experimental Q i & Q e Within Uncertainties Both ion & multi-scale simulation can reproduce experimental heat fluxes within simulation and experimental uncertainties. Agreement occurs at a lower value of a/l Ti (+8% for multi versus +10% for ion) For these conditions, experimental heat fluxes are insufficient to distinguish between the ion & multi-scale sim. Additional quantities are needed to discriminate between models 11

12 Signatures of Cross-Scale Coupling are Observed in Multi- Scale Simulation That Are Similar to the L-mode Results Small (~10%) of multi-scale Q e from high-k turbulence. However, clear signatures of crossscale coupling are observed with same a/l Ti input. There is a clear enhancement of the low-k turbulence as result of the coupling. This leads to 80% increases in the low-k driven heat transport. 12

13 Incremental Diffusivities Can Be Used to Discriminate Between Ion and Multi-Scale Results Similar comparisons were made in L-mode conditions [N.T Howard NF 2016] Partial sawtooth heat pulses used to determine the incremental electron diffusivity [A. Creely NF 16] - Obtained via simulation by measuring slope of Q e versus Using 3 ECE channels around of r/a = 0.6 we can measure the % change in a/l Te - Up to a 20% increase in the local value of a/l Te occurs during a partial sawtooth. Measured value of incremental diffusivity is: c inc = 1.8 +/- 0.3 m 2 /s 13

14 Partial Sawteeth in the ELM-y H-Mode Can Produce a 20% Increase in the Local Value of a/l Te Similar comparisons were made in L-mode conditions [N.T Howard NF 2016] Partial sawtooth heat pulses used to determine the incremental electron diffusivity [A. Creely NF 16] - Obtained via simulation by measuring slope of Q e versus Using 3 ECE channels around of r/a = 0.6 we can measure the % change in a/l Te - Up to a 20% increase in the local value of a/l Te occurs during a partial sawtooth. Measured value of incremental diffusivity is: c inc = 1.8 +/- 0.3 m 2 /s 14

15 To Evaluate the Incremental c, an Additional Multi-Scale Simulation was Performed with a +20% Increase in a/l Te Multi-scale simulation predicts significantly higher values of c inc 2.5x increase is found from ion to multi-scale simulation Both ion and multi-scale under-predict the c inc outside of error bars Different from previous L-mode work, where multi-scale simulation could reproduce Q i, Q e, and c inc What physics is missing from the multi-scale simulation that could explain the experiment? 15

16 To Evaluate the Incremental c, an Additional Multi-Scale Simulation was Performed with a +20% Increase in a/l Te Multi-scale simulation predicts significantly higher values of c inc 2.5x increase is found from ion to multi-scale simulation Both ion and multi-scale under-predict the c inc outside of error bars Different from previous L-mode work, where multi-scale simulation could reproduce Q i, Q e, and c inc What physics is missing from the multi-scale simulation that could explain the experiment? 16

17 To Evaluate the Incremental c, an Additional Multi-Scale Simulation was Performed with a +20% Increase in a/l Te Multi-scale simulation predicts significantly higher values of c inc 2.5x increase is found from ion to multi-scale simulation Both ion and multi-scale under-predict the c inc outside of error bars Different from previous L-mode work, where multi-scale simulation could reproduce Q i, Q e, and c inc What physics is missing from the multi-scale simulation that could explain the experiment? 17

18 Extreme Stiffness of Ion-Scale Turbulence + Cross-Scale Coupling, May Explain Large c inc Values Recall that these conditions are extremely close to marginal and exhibit extremely stiff low-k transport driven by ITG (+2% a/l Ti drives 50% more Q e ) Ion-scale simulations ITG drives both ion and electron heat transport. The propagation of a heat pulse in the electron temperature (from which c inc is measured) is dictated by the local electron heat flux. Exp. Increases in both & will drive significant electron heat transport Two processes can generate changes in a/l Ti during a heat pulse: 1.) Electron-ion equilibration - Can account for a 1% change in a/l Ti 2.) Ion heat pulse generated by sawtooth a few % change in a/l Ti (modeled via TRANSP) 18

19 Preliminary: A Multi-Scale Simulation with a 2% Increase in a/l Ti & 20% Increase in a/l Te Reproduces the Exp. c inc To test this theory, we have begun a multi-scale simulation which attempts to better reproduce the conditions under which the heat pulse propagates. Includes +20% a/l Te and +2% a/l Ti above base multi-scale simulation. Simulation is still in progress, but current values from the simulation indicate c inc =1.6 m 2 /s, in quantitative agreement with the measured value. 19

20 Prediction of ITER-like Conditions Will Likely Require the Physics of Cross-Scale Coupling ; Multi-Scale Simulation Posses A Real Challenge for Model Validation Cross-scale coupling was found to enhance long-wavelength turbulence significantly in ELM-y H-mode conditions. To discriminate between the models, comparisons with c inc measurements were made. - Cross-scale coupling plays an important role in enhancing c inc but does not alone explain the measured incremental diffusivities. The extreme stiffness, characteristic of high performance discharges, appears to demonstrate that experimentally relevant perturbations to a/l Ti and a/l Te can explain measured values of c inc Because of the extreme computational requirements (75M CPU hours), this study was only able to probe very limited simulation sensitivities and uncertainties in inputs. - Validation of multi-scale simulation needs more intelligent approaches for validation. It may be the development of reduced models (TGLF, Qualikiz) based on multi-scale results is the best way to probe uncertainties in simulation and experiment 20