Plasma Science and Fusion Center

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1 Plasma Science and Fusion Center Turbulence and transport studies in ALCATOR C Mod using Phase Contrast Imaging (PCI) Diagnos@cs and Comparison with TRANSP and Nonlinear Global GYRO Miklos Porkolab (in collabora/on with Liang Lin, E. Edlund, J. Dorris, C. Rost and the Alcator team) MIT Plasma Science and Fusion Center (PSFC) with special thanks to Ron Waltz and Jeff Candy, General Atomics References: L. Lin, M. Porkolab,E. M. Edlund, et al, Phys. Plasmas 16, (2009); also, in Plasma Phys. Contr. Fusion 51, (2009) Presented at EFTSOMP2010, June 29, 2010, Dublin, Ireland

2 Well known experimental results from Alcator C (Greenwald, Parker, 1984), as well as other tokamaks up to the indicate that Ohmic confinement follows a linear scaling with density, followed by a saturated confinement regime in L mode; Why? Gyrokine@cs? The results imply that in the linear confinement (neo Alcator) regime the electron thermal diffusivity should decrease as the density increases.

3 Turbulence measurements in Alcator C Mod plasmas as a func@on of density show good agreement with the GYRO in ohmic plasmas at frequencies above 80 KHz with phase veloci@es dominantly in the ion diamagne@c direc@on

4 Turbulence measured with Phase Contrast Imaging (PCI) at high frequencies in H mode plasmas (high densi@es) shows good agreement with GYRO nonlinear simula@ons with phase veloci@es in the ion diamagne@c direc@on

5 ( Experimental results using TRANSP analysis)

6 Measured transport coefficients at low significantly deviate form the GYRO code and cannot be resolved even with of density and temperature profiles

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10 As density increases the dri` speed decreases to c s and confinement improves Do current driven dri- waves play a role? Theorists say no!

11 Summary of Turbulence and Transport Study

12 SUMMARY PHASE CONTRAST IMAGING IS A POWERFUL DIAGNOSTIC TOOL TO MEASURE WAVES, INSTABILITIES AND TURBULENCE IN TOKAMAK PLASMAS THE COST IS VERY REASONABLE ( K$) THE SHORTCOMING OF THE DIAGNOSTIC IS LACK OF GOOD LOCALIZATION ALONG THE LASER BEAM

13 Phase Contrast Imaging (PCI) in Alcator C Mod

14 Edge Turbulence on Alcator C-Mod I. Cziegler J.L. Terry, B. LaBombard, J.W. Hughes MIT - Plasma Science and Fusion Center rd 3 EFTSOMP Dublin, Ireland, June 2010

15 Background and motivations: Edge-SOL transport schematic Open field line region, Scrape-Off-Layer limiter Closed flux surfaces, plasma edge Material surfaces

16 Background and motivations: Edge-SOL transport schematic limiter In the SOL the turbulence is manifested as filaments (blobs) Blobs propagate rapidly radially, carrying plasma to the main walls Dominate transport 0 LCFS Z (cm) cm APD spot size s major radius (cm)

17 Background and motivations: Edge-SOL transport schematic limiter In the SOL the turbulence is manifested as filaments (blobs) Blobs propagate rapidly radially, carrying plasma to the main walls Dominate transport through SOL Source of SOL plasma Wavelike edge fluct. Why is SOL transport the way it is? 0 LCFS Z (cm) cm APD spot size s major radius (cm)

18 How does cross-field particle transport work? Observations in Ohmic L-modes 1) As central density is raised, density profiles flatten in the SOL 2) Fluxes across the LCFS increase exponentially with density m -2 s Cross-Field Particle Flux 1mm outside LCFS Line-Averaged Density (10 20 m -3 ) factor of ~ m L-mode profiles Near SOL Far SOL (mm) Distance into SOL n e /n G [1] Search for the underlying cause of this increase of transport as n grows. e

19 Observations: Enhanced D-Alpha H-mode QC mode leads to cross-field transport Frequency (khz)250 EDA H-mode spectrogram QC mode (m 2 /sec) D eff Time (s) In EDA H-mode QCM provides edge relaxation instead of large ELM s The Quasi-Coherent Mode is an EM edge oscillation Frequency range ~ khz Propagates in the EDD in lab 0 QC mode D = Ã/ n eff Ä e [2] 16 /m 2 ) D not meant to imply diffusive transport: eff

20 Experimental setup Gas-Puff-Imaging diagnostics Side View Top View? gas puff injects? neutral D2, sensitive to ne, Te limiter Toroidal view of Outboard Edge? small toroidal extent (~5cm) allows localization? 90 channels cover ~ 5cm x 5cm nozzle? views coupled to APD arrays, 2MHz? limiter gas puff

21 The edge of Ohmic L-mode plasmas is dominated by EDD while the SOL is dominated by IDD propagating features Frequency (khz) poloidal arrays + time history: S(k è í)=s(k è,í)/s(í) Shows dispersion and dominant frequencies Dispersions are found to be 100 very nearly linear: 50 k è(í)> v ph=2ð í/ k è ñ = -1.1cm ñ = 0.1cm ñ = 1.2cm EDGE IDD : EDD IDD : EDD IDD : EDD v ph Frequency (khz) SEPARATRIX REGION Frequency (khz) S(k,í) è Frequency (khz) k pol (cm -1 ) SOL S(í)=S (í)+s (í) k<0 k>0 Shows power spectra Characteristic scales can be seen shot EDGE SOL k pol (cm -1 ) k pol (cm -1 ) k pol (cm -1 )

22 EDD velocity in edge is close to ù /k pol * far SOL IDD velocity matches ExB (expected for blobs) Measured pol. velocity (km/s) Distance into SOL (cm) EDD propagation in the edge is close to the electron diamagnetic flow velocity estimated from TS profile Poloidal velocity in the far SOL where blobs are seen matches ExB velocity estimated from probe measurements B =6.8T t I =1.0MA p Overlap region between the two features [3] IDD : EDD Normalized total power Normalized total power Distance into SOL (cm) e. prop. feature I. prop. feature n e /n G Distance into SOL (cm)

23 Wavenumber filtered spectra on underlying dynamics S k>0 (í) can yield information Relative fluctuation power EDD propagating part k è ñ s shot t= s

24 Wavenumber filtered spectra on underlying dynamics S k>0 (í) can yield information Relative fluctuation power EDD propagating part ã k è ñ s shot t= s Spectra are often clear power laws Spectral indices contain information about the spectral transfer dynamics similar to Kolmogorov cascades

25 Wavenumber filtered spectra on underlying dynamics S k>0 (í) can yield information Relative fluctuation power EDD propagating part ã = -1.3± ã = -4.6± ã 1 k è ñ s ã 2 shot t= s Spectra are often clear power laws Spectral indices contain information about the spectral transfer dynamics similar to Kolmogorov cascades c Break-in-slope í may indicate: - dissipation scale - scale of energy input In the latter case: - ã 1 indicates inverse cascade - indicates forward cascade ã 2

26 The total spectral power and the distribution in L-mode show a strong dependence on n e /n G n e/n G = 0.15 n e/n G = 0.16 n e /n G = n e /n G = Total relative fluctuation power clear peak at high freq part k ñ ã = -4.6± low intensity broad plateau med intensity pl. diminishing forward transfer (features breaking up) is reproducible - Wakatani-Hasegawa (collisional drift)[4]: ã = -3 (Kolmogorov-Kraichnan 2D) - Hasegawa-Mima (theory)[5], Fyfe (sim)[6], Xia (exp)[7]: ã = -6 - Chen, Fowler (dimensional)[8]: ã = -5 - Chen (exp): ã = -4.6 break-in-slope spectral position develops a peak hindered inverse dynamics? increased dissipation? k ñ s ã 2 ã 2 ã 2 ã high intensity no plateau è s k è ñ s k è ñ s k è ñ s c k ñ s~ n e /n G B t = 4.6T 5.4T 6.8T

27 Bispectral analysis: estimation of three-wave interactions and spectral transfer Bicoherence spectra? strength of phase coupling? no information on energy flow, coupling coefficients Spectral transfer function can be estimated from two separate times:

28 Bispectral analysis results: energy input at the same scale for H-mode and L-mode stronger transfer towards large scales in L-mode From S(k í) we can move to spatial separation rather than time using è k (í)> v =2ðí/k, and the appropriate Galilean transformation for the velocities. è ph è viewing chans large errors } Äz } S(k í) è Frequency (khz) EDD propagating part large errors time average instead of ensemble average k ñ =0.11 s shot t= s Frequency (khz)

29 Total fluctuation power increases with Greenwald fraction Total relative fluctuation power n e/n G = n e/n G = 0.16 n e /n G = n e /n G = n e/n G total power

30 Evidence that the EDD propagating edge turbulence is a major factor in edge particle transport and may be related to the robust tokamak (Greenwald) density limit EDGE REGION SOL densities Total relative fluctuation power (x10-5 ) EDD propagating part m L-mode profiles Near SOL Far SOL Distance into SOL(mm) m -2 s Cross-Field Particle Flux 1mm outside LCFS n e /n G factor of ~ n /n e G Line-Averaged Density (10 20 m -3 )

31 The physical variable â p seems to parametrize the turbulence more sensitively than the Greenwald fraction Total relative fluctuation power (x10-5 ) EDGE REGION EDD propagating part I. Cziegler et al, PoP (2010) n /n e G âp- normalized pressure better to the free energy source p and perhaps an interchangeballooning type drive? â p

32 Significant reduction in EDD turb. power at L-H transition and suggested connection to the QC mode n e n e (10 m ) n e EDD, edge Frequency (khz) L-mode ELMfree EDA Frequency (khz) Frequency (khz) shot n e n e L-mode ELM free IDD, SOL EDA H-mode Time (s) k (cm -1 ) pol EDD propagating part k ñ =0.11 s shot t= s Frequency (khz) k (cm -1 ) pol k (cm -1 ) pol Edge turbulence drops at L-H transition No change in norm. SOL fluct. level Further evidence to transport-relevance of EDD edge turbulence critical wavenumber is at the same physical scale as QCM

33 Fluctuations in the far SOL show no change in character or relative amplitude n e n e (10 m ) n e EDD, edge Frequency (khz) L-mode ELMfree EDA Frequency (khz) Frequency (khz) shot n e n e L-mode ELM free IDD, SOL EDA H-mode Time (s) k (cm -1 ) pol EDD propagating part k ñ =0.11 s shot t= s Frequency (khz) k (cm -1 ) pol k (cm -1 ) pol IDD propagating part SOL Frequency (khz)

34 Summary Drift-wave-like edge turbulence overlaps with IDD features at the SOL boundary Short wavelength spectra ã = -4.6 quite reproducible but not explained 2 Found evidence that the edge turbulence may be responsible for cross field particle transport, ie creating blobs The energy input scale is k ñ s~0.1 and shows likely connection to QCM (resistive ballooning drive) through spectral transfer Sensitive dependence on n /n (or e G â p - indication of grad-p source?) What theory predicts the right spectra and what consequences does the right model have for transport?

35 References [1] B. LaBombard et al., Nucl. Fusion 40 (2000) 2041 [2] J. L. Terry et al., Nucl. Fusion 45 (2005) 1321 [3] I. Cziegler et al, Phys. Plasmas (2010) [4] A. Hasegawa, M. Wakatani, Phys. Rev. Lett. 50, 9 (1983) 682 [5] A. Hasegawa et al., Phys. Fluids 22 (1979) 11 [6] D. Fyfe, D. Montgomery, Phys. Fluids 22 (1978) 2 [7] H. Xia, M.G. Shats, Phys. Rev. Lett. 91(15) (2003) [8] F. Chen, Phys. Rev. Lett (1965)