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Presented at PPPL, Princeton, NJ May 20, 2008

Measurements of Core Electron Temperature Fluctuations. A. E. White University of California-Los Angeles, Los Angeles, California, USA L. Schmitz, a) W.A. Peebles, a) T.A. Carter, a) G.R. McKee, b) C. Holland, c M.E. Austin, d) K.H. Burrell, e) J. Candy, e)

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Presented at PPPL, Princeton, NJ May 20, 2008

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  1. Measurements of Core Electron Temperature Fluctuations A. E. White University of California-Los Angeles, Los Angeles, California, USA L. Schmitz,a) W.A. Peebles,a) T.A. Carter,a) G.R. McKee,b) C. Holland,c M.E. Austin,d) K.H. Burrell,e) J. Candy,e) J.C. DeBoo,e) E.J. Doyle,a) M.A. Makowski,f) R. Prater,e) T.L. Rhodes,a) M.W. Shafer,b) G.M. Staebler,e) G.R. Tynan,c) R.E. Waltz,e)G. Wanga) and the DIII-D Team,e) a)University of California-Los Angeles, Los Angeles, California, USA b)University of Wisconsin-Madison
, Madison, Wisconsin, USA c)University of California-San Diego, La Jolla, California, USA d)University of Texas, Austin, Texas, USA e)General Atomics, P.O. Box 85608, San Diego, California, USA f)Lawrence Livermore National Laboratory, Livermore, California, USA ~ Presented at PPPL, Princeton, NJ May 20, 2008 1

  2. Both Electron Temperature and Density Fluctuations Provide Information about Physics of Turbulence and Transport • Several types of instabilities may contribute to electron heat and particle transport in the tokamak– Ion temperature gradient (ITG) mode ( < 1), – Trapped electron mode (TEM) ( < 2 ) – Electron temperature gradient (ETG) mode ( > 2 ) • Core electron temperature and density fluctuations both contribute to energy transport flux(Liewer 1985, Wootton 1990, Ross 1992) • Measurements of Te probe physics of non-Boltzmann electron response, in particular, trapped electrons • Turbulence models: electron heat and particle transport result from non Boltzmann (non-adiabatic) electrons • Trapped electrons destabilize ITG mode, drive TEM unstable ~ 2

  3. Summary of Results • Time history of Te/Te during single discharge reveals changes in amplitude in L-mode, H-mode and Ohmic plasmas • Electron temperature fluctuations, Te/Te, and density fluctuations, ñ/n, have similar spectra, amplitudes and increase with radius • GYRO predicts Te/Te ~ ñe/ne, consistent with observations. GYRO/synthetic diagnostics do not fully reproduce increase in fluctuation level with radius. • Electron Cyclotron Heating (ECH) during beam heated L-mode plasmas results in increased Te/Te, but not ñ/n ~ ~ ~ ~ 3

  4. Correlation Electron Cyclotron Emission (CECE) Diagnostic Measures Local, Low-k Electron Temperature Fluctuations SSB receiver with two channel filter bank ∆f1 ∆f2 250 MHz • Emission in non-overlapping frequency bands • Separated by less than turbulence correlation length • Cross-correlate signals to measure RMS amplitude and spectrum ∆f2 ∆f1 110 MHz 4

  5. The Thermal Noise is Uncorrelated When Intermediate Frequency Filter Bandwidths Do Not Overlap • The thermal noise feature is broadband in frequency • The temperature fluctuation feature can be measured (~ 100 ms average) in cases of moderate filter overlap when Bsig< Bvid • MHD modes (Bsig<< Bvid ) often observed in a single radiometer channel

  6. Beam Emission Spectroscopy (BES) Diagnostic Measures Local Density Fluctuations at Same Radius as CECE • Measurement locations separated toroidally and vertically • CECE and BES measure turbulence on Ion Temperature Gradient (ITG) and Trapped Electron mode (TEM) scales ~ CECE Te/Te ~ n/n BES 1.2 cm 0.9 cm 6

  7. Outline • Temporal evolution of electron temperature fluctuations • Comparison between electron temperature and density fluctuations in beam heated L-mode plasmas • Comparison with nonlinear simulations • Comparison of electron temperature and density fluctuations in ECH experiment 7

  8. Temperature Fluctuations Are Measured in L-mode, H-mode and Ohmic Plasmas in a Single Discharge • Shot parameters • Ip = 1 MA • BT = 2.1 T, • 2.5 -10 MW beam power • upper single null • Measure Te/Te at r/a = 0.75 • Early L-mode 700-900 ms • Stationary L-mode 1400-1600 ms • ELM-free H-mode 1895-1930 ms • Ohmic 3700-3900 ms ~ r/a = 0.74 8

  9. Spectra Evolve in Time, with Large Reduction in Te/Te After L-H Transition ~ • Typical cross-power spectra of Te/Te at r/a = 0.75 • Spectrum broadens and narrows in response to Doppler shifts due to changing ExB rotation • Normalized fluctuation levels in Ohmic (1%) are lower than L-mode (1.5%) at same radius • H-mode temperature • fluctuations are below • sensitivity limit (0.5%, 35 ms) H-mode results are consistent with • QH-mode experiments, a • factor 5 reduction has been • observed at same radius (Schmitz, PRL 100, 035002,(2008)) ~ VExB = 4.1 km/sec VExB = 7.1 km/sec VExB = 6.5 km/sec VExB = 2.4 km/sec 9

  10. Outline • Temporal evolution of temperature fluctuations • Comparison between temperature and density fluctuations in beam heated L-mode plasmas • Comparison with linear and nonlinear simulations • Comparison of temperature and density fluctuations in ECH experiment 10

  11. The Profile of Temperature Fluctuations in L-mode Is Compared to the Profile of Density Fluctuations Use series of repeat discharges to measure profiles of Te/Te and n/n Stationary, sawtooth-free L-mode. ne ~ 2.5 x 10 19 m-3 Te ~ 450 eV Ti ~ 500 eV ~ ~ 1300-1700 ms used in analysis 11

  12. Plasma Profiles, Plasma Frequencies, and Optical Depth in L-mode Plasma of Interest • 2nd Harmonic ECE is far from being cut-off by RH wave • Plasma is optically thick ( )in region of interest • Density fluctuations will not contribute to temperature fluctuation signal CECE and BES diagnostics scanned between 0.3 < r/a < 0.9 12

  13. Temperature and Density Fluctuations Have Similar Spectra and Normalized Fluctuation Amplitude Profiles • Shot 128915 • r/a = 0.74 • Data averaged 1300-1700 ms • Spectra Integrated 40-400 kHz ~ ~ • Te/Te and n/n measured between 0.3< r/a < 0.9 13

  14. Outline • Temporal evolution of temperature fluctuations • Comparison between temperature and density fluctuations in beam heated L-mode plasmas • Comparison with nonlinear simulations • Comparison of temperature and density fluctuations in ECH experiment 14

  15. ~ Compare Measured Te/Te and ñ/n With Results From Local, Nonlinear GYRO Simulations • Comparisons between profiles of two fluctuating fields and nonlinear gyrokinetic simulations provide unique and challenging tests of the turbulence models • GYRO is an initial value, Eulerian (Continuum) 5-D gyrokinetic transport code • Local simulations include real geometry, drift-kinetic electrons, e-i pitch-angle collisions, realistic mass ratio and equilibrium ExB flow, electromagnetic effects • Take experimental profiles (Te, Ti, ne, Er) as input 15

  16. Synthetic Diagnostics That Model the BES and CECE Sample Volumes are Used to Spatially Filter the Raw GYRO Data CECE PSF CECE Sample volumes BES PSF BES sample volumes CECE sample volume: Antenna pattern and natural linewidth BES sample volume:Collection optics, neutral beam/sight-line geometry, neutral beam cross-section intensity and the finite atomic transition time of the collisionally excited beam atoms [Shafer RSI 2006) 16

  17. Shapes of BES and CECE Sample Volumes Result In Different Filtering of the High Frequencies • In measurements, Doppler shift due • to ExB plasma rotation dominates • Observed spectrum of fluctuations r/a =0.5 (McKee, PRL 2000) • BES sample volume extended radially • (∆r ~ 2 cm, ∆z ~ 1.5 cm) - Radial extent causes symmetric attenuation of all wavenumbers r/a =0.5 • CECE sample volume extended vertically • (∆r ~ 1 cm, ∆z ~ 3.5 cm) - Poloidal extent causes more attenuation of higher wavenumbers (Bravenec, RSI 1995) 17

  18. At r/a = 0.75 GYRO Underestimates the Experimental Fluctuation Levels ~ ~ ~ ~ • Density Fluctuations Density Fluctuations GYRO (40-400 kHz) ne/ne = 0.33+-0.007 Experiment (40-400 kHz) n/n = 1.1+-0.2% ~ (ne/ne)2/kHz • Temperature Fluctuations GYRO (40-400 kHz) Te/Te = 0.5+-0.02 Experiment (40-400 kHz) Te/Te = 1.5+-0.2% ~ (Te/Te)2/kHz Temperature Fluctuations 18 18

  19. At r/a = 0.5 GYRO Shows Reasonable Agreement With Experimental Fluctuation Levels • Density Fluctuations GYRO (40-400 kHz) ne/ne = 0.56+0.008 % Experiment (40-400 kHz) n/n = 0.55+-0.12% ~ (ne/ne)2/kHz ~ ~ • Temperature Fluctuations ~ (Te/Te)2/kHz GYRO (40-400 kHz) Te/Te = 0.66+-0.2 % Experiment (40-400 kHz) Te/Te = 0.4+-0.2% ~ ~ ~ 19

  20. ~ ~ GYRO Predicts Te/Te and ne/ne are Similar in Amplitude but Radial Profile Trend is not Reproduced • Te/Te ~ ne/ne, consistent with experiment • At r/a = 0.5, reasonable quantitative agreement • Trend that fluctuation levels increase with radius not reproduced ~ ~ • At r/a = 0.5, • At r/a = 0.75, • Common result: 2 (RMS level) 20

  21. GYRO Predicts Temperature Fluctuation Contribution to Energy Flux at r/a = 0.5 • GYRO flux-tube simulation at r/a = 0.5 has good quantitative agreement with experiment • fluctuation levels • energy fluxes • GYRO predictsTe drives 80%of energy transport ne drives 20% of energy transport ~ ~ 21

  22. Outline • Temporal evolution of temperature fluctuations • Comparison between temperature and density fluctuations in beam heated L-mode plasmas • Comparison with nonlinear simulations • Comparison of temperature and density fluctuations in ECH experiment 22

  23. Experiment Using Local ECH to Change Local Te Gradient and Turbulence Drives • Baseline discharge with beam heating only • Ip = 1 MA, • BT = 2.0 T, • 2.5 MW of co-injected beam power • Inner wall limited • Compare to discharge with additional EC heating at r/a ~ 0.17 • Density is held constant • Heat fluxes and heat diffusivities increase • TGLF indicates increase in TEM growth rate Times used in analysis 1500-1700 ms 23

  24. Increases in Heat Flux and TEM Growth Rate Correlate With Increase in Te/Te, but ñ/n Does Not Change ~ ~ CECE : Te/Te increases by 50% NB only 1.0+-0.2% NB + ECH 1.5+-0.2% ~ BES : n/n stays the same NB only 1.2+-0.2% NB + ECH 1.2+-0.2% • Change in spectral shape due to dominant Doppler shift • Reduction in Er with ECH causes spectra to shift to lower frequencies • The correlation reflectometer shows no change in correlation length of electron density fluctuations 24

  25. Summary of Results • Time history of Te/Te during single discharge reveals changes in amplitude in L-mode, H-mode and Ohmic plasmas • Electron temperature fluctuations, Te/Te, and density fluctuations, ñ/n, have similar spectra, amplitudes and increase with radius • GYRO predicts Te/Te ~ ñe/ne, consistent with observations. GYRO/synthetic diagnostics do not fully reproduce increase in fluctuation level with radius. • Electron Cyclotron Heating (ECH) during beam heated L-mode plasmas results in increased Te/Te, but not ñ/n ~ ~ ~ ~ 25

  26. Future Work • GYRO predicts phase between Te and ne, measure phase between Te and ñe using CECE and reflectometry (Haese 1997) • Dimensionless parameter scans and comparison of Te/Te and n/n • Simulations of results where Te/Te and ñ/n respond differently to ECH • Flux-matched profiles, TGLF transport model (J. E. Kinsey POP May, 2008 ) ~ ~ ~ ~ ~ ~ Simultaneous measurements of multiple fluctuating fields improve understanding of turbulence and transport, provide the opportunity for challenging comparisons with nonlinear gyrokinetic simulations 26

  27. BACK-UP SLIDES 27

  28. Generic PSF Convolution Integral and CECE PSF model as Asymmetric Gaussian

  29. BES PSF

  30. ITG is dominant Instability at Long Wavelengths, r/a = 0.5 GYRO Transport Fluxes Linear Growth Rate ci ce

  31. ITG is dominant instability at Low-k, TEM dominant at Higher-k, at r/a = 0.75 Linear Growth Rate GYRO Transport Fluxes ci ITG TEM nei ce gExB kqrs kqrs

  32. Local GYRO Simulations Match the Experimental Heat Diffusivities Well at r/a = 0.5, not at r/a = 0.75 Electron heat diffusivity Ion heat diffusivity Experiment Experiment GYRO GYRO

  33. Use TGLF to Calculate Flux-Matched Profiles Disagreements with experimental fluctuation levels motivate future workwith simulations and experiments

  34. Growth Rate of Most Unstable Mode Increases With Radius, Consistent With Measured Fluctuations • TGLF (Trapped gyro-Landau-fluid) code used for linear stability analysis • ITG mode (fREAL < 0) is fastest growing mode for long wavelengths in CECE range • Te associated with ITG mode • Linear growth rate of fastest growing mode (TEM) peaks at ~ 0.7 • Transport fluxes peak at longer wavelengths, • ~ 0.2 at r/a = 0.75 ~ 34

  35. ~ Core Te/Te Reduction in Quiescent H-mode Experiments Suggests Contribution to Qturb • Flow shear stabilization is not expected to suppress the dominant ITG mode in L-mode • In QH-mode, TEM mode are dominant • EXB shearing rate is found to exceed the calculated linear growth rate 35

  36. Correlation Radiometry Needed for Measurements of Turbulent Temperature Fluctuations from ECE • The magnetized plasma radiates as a black body from an optically thick emission layer with the ECE intensity proportional to the electron temperature • Emission at harmonics of the cyclotron frequency, , originates at a particular frequency determined by B-field strength • Single ECE radiometer channel sensitivity limited by the thermal noise level given by • Standard cross-correlation techniques are used to improve sensitivity to turbulent fluctuations ~ Bif ~ 110 MHz , Bvid ~ 2.5 MHz : sensitivity Te/Te > 15% Sensitivity improves Te/Te > 0.2% ~ • Past Work: TEXT (Cima 1995, Deng 1998 ), W7-AS (Sattler 1994, Hartfuss 1996, Watts 2004), RTP (Deng 2001), DIII-D (Rettig 1997, Schmitz 2008) 36

  37. CECE Gaussian Optics Provide Small Spot-Size Needed for Turbulence Measurements Laboratory tests: 94 GHz incident beam focused using parabolic mirror The beam agrees well with a Gaussian spatial profile. 1/e2 power diameter CECE is sensitive to long wavelength fluctuations of electron temperature Small spot-size makes turbulence measurements possible 37

  38. Radial Extent of CECE Sample Volume is Determined by the Natural Linewidth, with Small Corrections From Filter Width • Natural linewidth of the emission layer is given by the emissivity (ECESIM – DIII-D IDL-based code) • Linewidth (∆ r ~ 0.8 cm) is determined by the relativistic broadening and re-absorption in the plasma amplitude • Radial sample size (∆r ~ 1 cm) for a single IF filter is slightly wider than the natural linewidth • Separation of sample volumes determines radial wavenumber resolution, kr < 4 cm-1 amplitude 38

  39. ~ The CECE radiometer is calibrated to measure Te and Te , No calibration needed for Te/Te measurements ~ Calibrated fixed filter CECE signals give Te ~ Calibrated tunable YIG CECE signals give Te from correlation function Calibrated YIG CECE signals normalized to local Te give Te/Te from the correlation function ~ ~ ~ ~ Te and Te/Te can also be calculated by integrating the cross-power spectrum, Pxy, over frequency range, [f1 , fN] of interest ~ Relatively calibrated signals give Te/Te From the correlation coefficient function

  40. Thermal noise fluctuations decorrelate when ∆f ~ Bif independent of radiation source, or sample volume in plasma (a) 2-18 GHz noise source (input to first amplifier in radiometer) (b) W-band noise source (input at antenna) (c) L-mode and H-mode plasmas (c)

  41. Contribution from Density Fluctuations to Signal Due to Low Optical Depth are Negligible [Rempel RSI 1994] In optically grey plasma the density fluctuations can contribute to signal, leading to apparent temperature fluctuations

  42. Ray-tracing code GENRAY is used to estimate the effects of refraction on the CECE sample volume size and location Ray-tracing (disk-to-disk) 25.4 cm diameter (at mirror) to 3.8 cm diameter (in plasma) Low-density plasmas n0~3.5x1019 m-3 Refractive effects: Sample volume location Vertical up-shift < 0.5 cm Sample volume diameter Spot size changes < 0.2 cm* *Comparable to measurement uncertainty of spot-size in lab

  43. Refractive effects are negligible for plasmas under consideration: ne < 0.8 necut-off • Modulations of the index of refraction along the line of sight will not cause apparent Te if ECE is far from cut-off ~ (a) Case with density, ne = 4.3x10-19 m-3 only 80 % of cut-off density for 2fc 93 GHz. ne, cut-off (93 GHz) ~5.35 x10-19 m-3. (b) Case with density > 100 % of cut-off density. Substantial refractive effects obvious for 15 degree mirror, no signal is seen for 7 degree mirror.

  44. Profile Comparison from ECH Experiment 44

  45. CERFIT Analysis Indicates Slight Reduction In Er for ECH Case - Expect Narrowing of Turbulent Spectra 45

  46. Temperature Fluctuations Increase Across Radius with ECH 46

  47. TGLF Results from ECH Experiment: TEM Linear Growth Rate Increases with ECH Gamma/(Cs/a) Gamma/(Cs/a) 47

  48. Beam Emission Spectroscopy (BES) measures spatially localized, long-wavelength density fluctuations

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