Studies of Turbulence and Transport in Alcator C- Mod H-Mode Plasmas with Phase Contrast Imaging and Comparisons with GYRO*

Transcription

1 Studies of Turbulence and Transport in C- Mod H-Mode Plasmas with Phase Contrast Imaging and Comparisons with GYRO* M. Porkolab 1, L. Lin 1, E.M. Edlund 1, J.C. Rost 1, C.L. Fiore 1, M. Greenwald 1, Y. Lin 1, D.R. Mikkelsen 2, N. Tsujii 1, and S.J. Wukitch 1 1 Plasma Science and Fusion Center, MIT, Cambridge, MA Princeton Plasma Physics Laboratory, Princeton, New Jersey 8543 Acknowledgments: The authors want to thank Jeff Candy and Ron Waltz (General Atomics) for providing the GYRO code and help with the GYRO simulations. 5th APS-DPP, Dallas, TX, Nov 19, 28 *Work supported by U. S. DOE under DE-FG2-94-ER54235 and DE-FC2-99-ER54512.

2 Outline Phase Contrast Imaging (PCI) Diagnostic Plasma Overview Fluctuation Measurements Gyrokinetic Simulation of Turbulent Transport Comparisons between Fluctuation Measurements and GYRO Predictions Summary

3 Phase Contrast Imaging x z laser beam plasma n ~ parabolic mirror F = 8 inch Unscattered Scattered Scattered d s front view of phase plate phase plate lens detector EM Wave passing through plasma acquires spatially dependent phase shift Δφ : Δ φ( x) = - λ r n ( x) dz 13 1, r = cm and λ = 1.6 um e e Before phase plate: iφ Ee E + iδφ E, I E 2 E 2 ( 1 + ( Δφ ) 2 ) After phase plate: 2 2 i E + iδφ E, I E E 1+ 2Δ PCI Each detector channel maps to a x j. Each signal is s = n ( x ) dz j e j e λ /8 ( φ )

4 PCI System.6 PCI B PCI measures density fluctuations along 32 vertical chords. z [m] e- i R [m] k< k> Wavenumber Range:.5cm -1 < k R < 55 cm -1 Frequency Range: 2kHz~5MHz The localization upgrade allows PCI to resolve the direction of propagation of the longer wavelength turbulence in ITG and TEM range. The improved calibration also allows for the intensity of the observed fluctuations to be determined absolutely.

5 Localization can be obtained by taking advantage of the variation of magnetic pitch angle along vertical chords. R The magnetic pitch angle β=tan -1 (B R /B Φ ) changes along a vertical chord passing through. z [m].4.2 B B R B ktop R Fluctuations also rotate from the bottom to the top as the field pitch angle rotates, since. k B β[ o ] 5 1 B B R B R k bottom This rotation is imaged onto the phase plate, and by partially masking the plate, we can select a vertical region of interest.

6 Masked phase plate allows for some localized measurements. (a) Conventional phase plate Unscattered wave: λ /8 thick gold coating Scattered wave : l k z 1 z 2 s β 1 β 2 from plasma bottom (z<): from plasma top (z>): ZnSe substrate wp (b) Combination of phase plate and mask Aluminum mask rotable on a rotatory stage d

7 Localizing performance improves for short wavelength fluctuations. l k z 1 z 2 s β 1 β 2 For short wavelength turbulence (large k), S>w p, two scattered beams are completely separated. Thus, by adding a mask on the top of the phase plate, we can view one beam but filter the other one completely and obtain localized turbulence measurement. wp 2 πλf S k β1 β2 kδβ 9 where β = β degree 1/2 1/2 λ F = ( z ) [ ] [ ] cm [ ] = 23 cm For longer wavelength turbulence (smaller k), S w p,, PCI can be set to preferentially view the turbulence from the top or the bottom, thus allowing it to resolve the direction of propagation.

8 Absolute calibration is obtained by measuring the calibrated sound waves with PCI 4 15 khz tweeter Fluctuation Intensity [1 32 m -4 ] : PCI measurements : Spherical Wave Modeling : Calibrated Microphone Distance to the loudspeaker: d [m] PCI Measurement [1-4 Volt 2 ] ndl :.22 1 m PCI Signal: 4. 1 V in this example. e The uncertainties of this absolute calibration is ~5 %, which will be reduced in future PCI measurements with multiple gauged pressure fluctuations.

9 Use GYRO to predict fluctuations and associated transport GYRO is an initial value Eulerian (continuum) 5D gyrokinetic code calculates evolution of (small) deviation from equilibrium distribution functions using kinetic equations averaged over fast gyromotion in a 5D (x,y,z,ε,μ) phase space. GYRO is believed to contain all the necessary ingredients for quantitatively accurate transport predictions takes measured experimental profiles as inputs realistic geometry (Miller formulation) trapped and passing electrons finite beta (magnetic fluctuations) e-i pitch angle collisions Equilibrium sheared ExB and toroidal rotation profiles

10 Use a synthetic PCI diagnostic for quantitative codeexperiment comparisons. PCI beam path ~ n/n.4 z [m] In order to do direct comparisons of simulation and experiment, we need to not only model the turbulence, but also how a given a diagnostic sees turbulence. A synthetic PCI diagnostic has been developed to post-analyze GYRO output and emulate the PCI measurements.[1] R [m] [1] J.C. Rost, M. Porkolab, J.R. Dorris et al, Bull. Am. Phys. Soc. 52 (16), 334 (27).

11 ITB plasmas in are marked by peaked density profiles H-Mode starts Stored Energy [kj] Neutron Rate [1 12 sec -1 ] Line-integrated density [1 2 m -2 ] ICRF Power [MW] D α [a.u.] Off-axis ITB forms Central RF added On-axis Shot: Time [sec] (a) (b) (c) (d) (e) Electron Temperature [kev] Electron Density [1 2 m -3 ] (a) shot: :.85 sec : 1.15 sec : 1.35 sec R maj [m] (b) :.85 sec : 1.15 sec : 1.35 sec shot: R [m]

12 PCI Measurements 5 4 H-Mode starts ITB forms Central RF added Shot: Channel: [a.u.] Frequency [khz] ICRF Power [MW] off-axis ICRF On-axis ICRF Time [sec]

13 Frequency/Wavenumber Spectra before the ITB onset (a) (b) B B [1 32 m -4 /cm -1 /Hz] [1 32 m -4 /cm -1 /Hz] PCI QC ITG Positive k Negative k PCI QC ITG Positive k Negative k Frequency [khz] Frequency [khz] (a) Bottom Localized Nyquist Wavenumber [.85,.95] sec 2πf/k ~ 4 km/sec Wavenumber [cm -1 ] 2πf/k ~ 4 km/sec Nyquist Wavenumber (b) Top Localized Nyquist Wavenumber [.8,.9] sec Wavenumber [cm -1 ] Nyquist Wavenumber ITG QC ITG QC PCI has also measured that the broadband turbulence above 2 khz propagates in the ion diamagnetic direction and its phase velocity is ~4 km/sec. Being able to resolve the direction of the propagation also indicates that these fluctuations are from r/a<.85 where the magnetic pitch angle is larger. PCI has measured that the edge localized QC modes propagate in the electron diamagnetic direction.

14 In non-itb plasmas, the fluctuation above 3 khz observed by PCI agrees with ITG in GYRO simulation. 1. Freq: [3, 5] khz PCI Measurement: (b) Frequency [khz] Synthetic PCI (a) shot: trange: [.85,.95] sec 2πf/k ~ 4 km/sec Wavenumber [cm -1 ] [1 32 m -4 /cm -1 /Hz] Autopower [1 32 m -4 /cm -1 ] Autopower [1 32 m -4 /cm -1 ] GYRO Simulation: Nn: 28; n: 5 Nn: 16; n:1 Freq: [3, 5] khz Wavenumber [cm -1 ] Freq: [2, 3] khz PCI Measurement: GYRO Simulation: Nn: 28; n: 5 Nn: 16; n:1 Freq: [2, 3] khz Wavenumber [cm -1 ]

15 Frequency/Wavenumber Spectra during the ITB (a) (b) B B [1 32 m -4 /cm -1 /Hz] PCI ITG Positive k Negative k [1 32 m -4 /cm -1 /Hz] PCI QC QC ITG Frequency [khz] Positive k Negative k Frequency [khz] (a) Bottom Localized Nyquist Wavenumber [1.5, 1.15] sec Wavenumber [cm -1 ] 2πf/k ~ 2 km/sec Nyquist Wavenumber (b) Top Localized Nyquist Wavenumber 2πf/k ~ 2 km/sec [1.1, 1.2] sec Wavenumber [cm -1 ] Nyquist Wavenumber QC QC Since the broadband turbulence is mixed together with the edge localized QC modes, PCI cannot well resolve its propagating direction. Phase velocity of the broadband turbulence is ~2 km/sec.

16 GYRO simulation in the core shows that ITG dominates in ITBs but its intensity is lower than the overall experimental measurements which also include contributions from the plasma edge. Frequency [khz] Synthetic PCI shot: trange: [1.5,1.15] sec 2πf/k ~ 2 km/sec [1 32 m -4 /cm -1 /Hz] Autopower [1 32 m -4 /cm -1 ] PCI Measurement: GYRO Simulation: Freq: [2, 3] khz Wavenumber [cm -1 ] Wavenumber [cm -1 ]

17 Comparison with Hirex shows that the high-frequency broadband turbulence comes from the plasma core. E E E E inferred r inferred r infer rd e r inferred r 2π fbφ = k 18 kv/m ; before ITB formation PCI 9 kv/m ; during ITB 9 kv/m ; after on-axis ICR F Er [kv/m] Stable ITG TEM ETG Hirex Er (t=1.15)-er (t=.85) : :Er (t=1.35)-er (t=.85) R maj [m] Δ inferred E r 9 kv/m Δ 1± 3 kv/m measured E r Change of radial electric field after ITB formation inferred from the highfrequency broadband turbulence agrees with Hirex measurements.

18 Linear stability analysis shows that ITG is always the most unstable instability. Frequency [khz] ITG frequency is linearly proportional to k θ ρ s. ITG growth rate spectrum peaks at k θ ρ s ~.4. ITG remains to the most unstable mode before and during ITB. Growth Rate [1 3 sec -1 ] k θ ρ s k θ ρ s Maximum Growth Rate γmax [1 3 sec -1 ] :.85 sec : 1.15 sec : 1.35 sec r/a

19 TEM remains linearly stable even after reducing the ion temperature gradient until ITG is stabilized. 4 Growth Rate.5 a/ln 3 2 TEM dominates ITG r/ a=.6 a/ L =.16 before ITB n a/ L =.8 during ITB n 1 Stable a/l T during ITB before ITB linear runs covering a/ L n 4. a/ L T 4.

20 Nonlinearly simulated transport agrees with experiments before ITB, while it is larger than experiments during ITB. non-itb χeff [m 2 /sec] Exp. : Local sim.: Global sim.: Nn: 28; n: 5 Nn: 16; n:1 (a) The uncertainty of analyzing χ e and χ i separately is huge when Ti is close to Te; hence, we only discuss χ eff. χeff [m 2 /sec] r/a Exp. : Local sim.: Global sim.: ITB (48ρ s ) (32ρ s ) (b) Global GYRO simulations match well with local simulations. Global GYRO simulations with different domain size also agree well with each other r/a Simulations cover.8. k θ ρ s

21 Discrepancy between experimental and simulated diffusivities can be attributed to the uncertainty of Ti or ExB shear. χeff [m 2 r/a= : Sim. (a) : Exp. Base -1% -2% -1% Base -2% a L = dt i / Ti Ti dr a/l Ti a χeff [m 2 r/a=.6 1. : Sim..8.6 Exp..4.2 Cs/a = s ExB Shear Rate [Cs/a] Experimental uncertainty of Ti is above 2%. E B shear rates are not well determined for the considered plasmas.

22 For the measured temperature and density profiles, significant transport contribution from the TEM is not likely. χeff [m 2 r/a= x.6 base x1.4 Exp. ITG dominates x1.8 x2.2 x2.6 ITG/TEM x3. : Sim. x3.4 x3.8 TEM dominates a/l n The impact of varying n on turbulent transport is very weak. Significant TEM turbulence is found only after doubling the experimental n. Simulated turbulent transport can only be reduced to the experimental level after tripling the experimental n.

23 Summary Agreement is obtained in transport between code simulations and experiments after reducing the measured ion temperature gradient by ~15% and/or adding the E B shear suppression, all within the experimental uncertainty. Simulated fluctuations with GYRO also agree with experimental measurements. - Before the ITB formation, the fluctuations above 3 khz are measured to be core-localized (r/a<.85) and agree with the ITG spectrum in nonlinear GYRO simulations, including the direction of propagation, wavenumber spectrum, and the absolute intensity, all within an experimental uncertainty. - After the ITB formation, the core and edge turbulence spectrum overlaps on the PCI due to the reduced E B Doppler shift. Consequently, GYRO simulation in the core shows weaker fluctuation intensity than experiments which also include contributions from the plasma edge, which may well dominate at sufficiently low frequencies.

24 Sign-up