1. Gyrokinetic Calculations of Microturbulence and Transport for NSTX and Alcator C-MOD H-modes Martha Redi Princeton Plasma Physics Laboratory NSTX Physics Meeting March 17, 2003 Princeton Plasma Physics Laboratory Acknowledgement: R. Bell, D. Gates, K. Hill, S. Kaye, B. LeBlanc, J. Menard, D. R. Mikkelsen, G. Rewoldt (PPPL), C. Fiore, P. Bonoli, D. Ernst, J. Rice, S. Wukitch (MIT) W. Dorland (U. Maryland) J. Candy, R. Waltz (General Atomics) C. Bourdelle (Association Euratom-CEA, France)

2. Motivation - Investigate microinstabilities in NSTX and CMOD H-mode plasmas exhibiting unusual plasma transport - High  e, low  i, resilient T e profiles on NSTX; ITB formation on CMOD - Identify underlying key plasma parameters for control of plasma performance METHOD - GS2 and GYRO flux tube simulations - Complete electron dynamics. 3 radii, 4 species. - Linear electromagnetic; nonlinear, electrostatic calculations (CMOD) RESULTS : - Gyrokinetics connection with transport: Questions remaining on NSTX Consistent with transport  analysis on CMOD

3. GS2 criterion H-mode plasmas: GS2: Linear, fully electromagnetic, 4 species Criteria:  /L<<1 for GS2, but profile effects can mix different wavelengths =>  * stabilization (GYRO) NSTX zone, rho-star, # ion gyroradii across plasma 0.25r/a  *=0.0185/0.6= 0.031 32 0.65r/a 0.014 71 0.80r/a 0.0064 157 CMOD 0.25r/a0.008 122 0.45r/a0.008 122 0.65r/a0.006 167

4. NSTX: NBI in MHD Quiescent Discharge: T i > T e, Resilient Te Profiles LeBlanc-APS-02 I p = 0.8 MA B T = 0.5 T P NBI = 4 MW E NBI = 90 keV  T = 16% W = 0.23 MJ 108730

5. Two Distinct Plasma Conditions: Resilient T e Profiles during Flattop Period Overlay of 8 consecutive time points: 0.38 - 0. 49 s. Overlay of 11 consecutive time points: 0.53 - 0.69 s. Shoulders at 65 and 125 cm disappear during the later phase LeBlanc-APS-02

6. NSTX H-mode: Electron Temperature Profile Resiliency During H-mode Te(r) remains resilient electron density increases ion temperature decreases Examine microinstability Growth rates at 3 zones What clamps Electron temperature profile?

7. Gyrokinetic Model Equations Kotschenreuther, et al Comp. Phys. Comm. 88, 128 (1995) Perturbed electrostatic potential: Linearized gyrokinetic equation in the ballooning representation, Using the “s-  ” model MHD equilibrium: Where

8. GS2 Evolution of Linear Growth Rates for k   I = 0.1 to 0.8 Some stable, some unstable

9. NSTX r/a=0.8: ITG Range of Frequencies

10. NSTX r/a=0.8: ETG Range of Frequencies

11. NSTX r/a=0.65: ITG Range of Frequencies

12. NSTX Core: ITG Range of Frequencies

13. NSTX: Examine Microinstability Growth Rates at 3 Zones

14. Experimental  Ti < ITG Critical Gradient r/a=0.25 R  Ti/Ti < R  c Ti/Ti r/a=0.65 R  Ti/Ti ~ R  c Ti/Ti r/a=0.80 R  Ti/Ti < R  c Ti/Ti  Stable ITG drift modes are consistent with the Kotschenreuther Criterion

15. NSTX: Critical Gradient Below or At Marginal Stability for ITG

16. NSTX:Above Critical Gradient for ETG Modes

17. Summary: Comparison of NSTX H-mode Transport Coefficients to Gyrokinetic Stability Why is  e so large and  i so small? Does ETG maintain resilient T e profiles? Need nonlinear and global calculations; MSE and fluctuation diagnostics 0.25 r/a 0.80 0.65 ii ee ITGETG <   neo stable Likely ExB stabilized stable <   neo ExB stabilizedLikely ExB stabilized ExB stabilizedstable <   neo ExB stabilizedunstable Likely ExB stabilized unstable >>  i t=0.4s t=0.6s t=0.4s t=0.6s t=0.4s t=0.6s >>  i

18. Trigger: CMOD Internal Transport Barrier Examine Microinstability Growth Rates at 3 Zones Ne Te Ni(deut)Ti

19. CMOD -Microturbulent Eigenfunctions: Ballooning Structure along field line Real and imaginary Parts of electrostatic Eigenfunction outside ITB region k   i = 0.1 to 0.8 Highest growth rates at 0.4-0.5 “Classic” Ion Temperature Gradient Drift Mode

20. ITB Trigger Time: Linear, Electromagnetic Gyrokinetic Calculations with GS2: Drift wave Microturbulence at k   i = 0.1 to 80. Low k   I : ITG =>  I anomalous outside ITB TEM and ITG: already stabilized at and within ITB High k   i : ETG driven by strong  T e =>  e anomalous at and outside ITB Electron drift direction Ion drift direction

21. NONLINEAR GS2 Simulations confirm linear results ITB TRIGGER: Before n e peaks, region of reduced transport and stable ITG microturbulence is established without ExB shear Quiescent, microturbulence in ITB region Moderate microturbulence in plasma core High microturbulence level outside half-radius Just inside ITB Outside ITB In plasma core  dV 2 -Strongest driving force: grad Te/Te

22. Heat Pulse Propagation (Wukitch, Phys. Plas 9 (2002) 2149) Sawtooth heat pulse propagation measurements of similar experiments: Effective  heatpulse reduced (by factor~10) in a narrow radial region of ~1 cm, located near the foot of the particle barrier, not necessarily within the barrier GS2 =>  drops to neoclassical in core and by 1/2 at the barrier

23. TRANSP analysis indicates barrier in  eff (r,t) persists after density rise is arrested (1.25 - 1.45 sec) ITB phase has been “controlled”  eff = (n e  T e  e + n i  T i  i )  (n e  T e + n i  T i ) Bonoli, APS 2001

24. CMOD H-mode GS2 Results ITB TRIGGER: Before n e peaks, region of reduced transport and stable microturbulence is established without ExB shear ITG, toroidal ion temperature gradient mode =>  I anomalous, unstable outside ITB stabilized at & within the ITB,  e drops within ITB At ITB, stabilized by steep density profile and moderate  Te ETG at higher values of k   I =>  e anomalous outside and at ITB Primary contribution to    D: from small values of k   I, long Expect neoclassical  e,  i in core, as found with TRANSP Nonlinear simulations confirm quiescent microturbulence at ITB Sensitivity studies => ITB observed with off-axis but not on-axis RF is due to weaker (  T e )/T e at the barrier, low q(r), 3% Boron ITB also occurs spontaneously in ohmic H-mode, Full story will require detailed comparative study of experiments. Need: Ti(r) and reflectometry fluctuation measurements at ITB

25. SUMMARY : GS2 linear calculations of drift wave instabilities in the ion temperature gradient and electron temperature gradient range of frequencies, and ExB shear rate: Roughly consistent with improved ion confinement in NSTX and improved confinement within and at ITB in CMOD H-mode plasmas Remarkably good ion transport in NSTX H-mode (Gates, PoP 2002) would be expected from stable ITG throughout plasma Profile effects (GYRO) via  * stabilization may stabilize ITG everywhere. Electron transport => q monotonic so unstable ETG at all r…need MSE Resilient temperature profiles on NSTX may be maintained through ETG instabilities, Nonlinear calculations needed. Tearing parity microturbulence found - in contrast to tokamaks - effects on transport to be determined. Internal transport Barrier on CMOD appears after off-axis RF heating, where microstabilities are quiescent. Nonlinear calculations in ~ agreement with linear. Sawtooth propagation measurements confirm low transport in the region at the trigger time (Wukitch, PoP, 2002).