Upper limit on turbulent electron temperature fluctuations on Alcator C-Mod APS DPP Meeting Albuquerque 2003

Transcription

1 Upper limit on turbulent electron temperature fluctuations on Alcator C-Mod APS DPP Meeting Albuquerque 2003 Christopher Watts, Y. In (U. Idaho), A.E. Hubbard (MIT PSFC) R. Gandy (U. Southern Mississippi), J. Heard (Clarion U.), P. Phillips (UT-FRC) Dept. of Physics New Mexico Tech Socorro, NM

2 Abstract Correlation radiometry has been used successfully in the past to measure turbulent electron temperature fluctuations in the core of both stellarators and tokamaks. Using the disjoint frequency technique on Alcator C-mod we obtain an upper bound on the average Te fluctuation amplitude. This limit of about 1% is significantly lower than the fluctuation amplitude observed on either TEXT-U or W7-AS. Although a high-resolution microwave system is used, the system spot size may not be sufficient to resolve very high k fluctuations. Fluctuation detection may also suffer from the system's location off the midplane

3 Motivation Electrostatic turbulence is suspected to be the culprit behind anomalous transport in large toroidal confinement devices. Particle and heat transport are given by quasi-linear theory to be: Particle flux: Γ e = n e v e = n e E θ B Heat flux: Q e = 3 2 p ev e = 3 2 n e T e E θ B T e Γ e Core electron temperature fluctuations, properly phased with potential fluctuations lead to anomalous heat flux. Cannot yet measure T e and E θ simultaneously. But, can compare expectations of heat flux scaling with results of T e measurement in various parameter regimes.

4 Problem in Measuring T e Previous attempts to measure temperature fluctuations using an ECE heterodyne system suffered from the problem of wave noise. Radiative wave noise obscures the underlying temperature fluctuations. Thermal noise level: ~6% T e / T e : ~2% Power spectrum of ECE signal is flat to Nyquist frequency, typical of thermal noise dominated signal. normalized power frequency (khz)

5 Correlation Radiometry Two standard techniques: 1) Dual line of sight radiometer Pair of channels along 2 different sightlines overlap in space Advantages: less data required for analysis, better radial resolution, good for poloidal coherence length 2) Single line of sight radiometer: Pair of channels, disjoint in frequency but spatially overlapping Advantages: simple to implement, good for radial coherence length

6 Cross-correlation eliminates uncorrelated thermal noise (by averaging many sample bins), and extracts the time averaged fluctuation signal T e,rms (ω ) T e 2 = R[s 1(ω)s 2 * (ω)] S 1 S 2 The sensitivity is given by: T 2 T 1 4 N 2B V B IF In a typical case of video (signal) bandwidth B v ~ 300 khz, IF (diagnostic) bandwidth B IF ~ 500 MHz, and number of samples N ~ 10 6 a sensitivity of 0.1% is achieved

7 C-Mod Heterodyne-ECE System The optical design includes a single elliptical cylindrical collection mirror imaging onto two parabolic collimating mirrors that couple to two overmoded waveguides. See Heard, et al., Rev Sci. Inst. 70, 1011 for details

8 Fluctuation Data (or lack of) Concentrate on discharges with B t =5.4 places the sample volumes near the edge previous work reported the largest fluctuation amplitude here (TEXT, W7-AS) Discharges in: both L and H-mode with and without RF heating densities from 5x10 19 m -3 to 2x10 20 m -3

9 Typical T e Spectrum cross power 10-9 statistical limit Spectrum is flat frequency (khz) peak at low frequency corresponding to MHD activity dashed line represents the statistical confidence level for random noise. No turbulent electron temperature fluctuations are detectable.

10 Similar spectrum at the edge of TEXT-U tokamak Broadband fluctuations typical of turbulent fluctuations are apparent 10-7 r/a= 0.94 r/a= 0.64 r/a= cross power statistical limit frequency (khz)

11 Integrated Spectrum: T e,rms /T e RF heating No RF heating % Temperature Fluctuation r/a= midplane (cm) Integrated from 50 to 500 khz Lower filter limit eliminates the contribution from low frequency MHD oscillations. Fluctuation amplitude does not rise above 1% for any of the discharges examined. Essentially represents the integrated statistical noise limit

12 Core Sawteeth Is the diagnostic is in fact working correctly? We can establish that the CRECE system is sensitive to fluctuations by looking at the C-mod core during large sawtooth oscillations. Spectrum in the core B t = 4.7 T,, R = 74 cm cross power statistical limit frequency (khz) Broadband fluctuations extending from khz. During periods of smaller sawtooth oscillations these fluctuations are absent.

13 Cross phase shows inward convection Steady increase in phase with frequency indicates an inward velocity that decreases with decreasing minor radius. Based on the sample volume separation of 4.5 cm yields inward velocities of 15x10 6 cm/s and 3.7x10 6 cm/s 4 3 r mid = 75.4 cm r mid = cm r mid = 74.0 cm 3.7x10 6 cm/s cross phase (radians) x10 7 cm/s frequency (khz) Consistent with two of the sample volumes being located just inside the mixing radius

14 Diagnostic Limitations The measured fluctuation amplitude is puzzling. Either: turbulent electron temperature fluctuations a very lo level in Alcator C-mod there is a diagnostic inadequacy Radiometer measurements of ECE fluctuations lose sensitivity to modes with wave number k = 2π /λ 2π /w w is the characteristic dimension of the emission volume It results in several significant modifications to the measured spectrum: (1) reduced fluctuation amplitude, (2) reduced frequency of the peak of the spectrum, ω 0 (3) longer correlation lengths (4) a larger apparent phase speed

15 Turbulence Model Gaussian shapes are assumed for the turbulence spectrum centered at a peak frequency ω 0 wave numbers k r,0 and k θ,0 for both the radial and poloidal directions. The Gaussians have correlation lengths finite widths in wave number and frequency space, θ, r and ω. True power spectrum is modeled by: S(k,ω)~e [(k r k r,0 ) r /2π ]2 e [(k θ k θ,0 ) θ /2π ]2 e [(ω ω 0 )/ ω]2 This spectrum is multiplied by a factor representing the effect of the finite sample volume size in attenuating higher wave numbers: e (k r w r /π )2 e (k θ w θ /π )2 wr,θ are the sample volume 1/e half-widths

16 C-Mod parameters The measured diagnostic 1/e widths are wθ is measured to be ~6.2 mm, sensitivity to wavenumbers k θ < 5.1 cm GHz bandwidth corresponds to w r ~4.0 mm +~ 2mm for the emission layer thickness. Sensitivity of k x < 5.2 cm -1 The spreading of the waist along the beam is described by a hyperbola w = w 0 1+ s s 0 r θ s 2 w ± s 1 2 z s 0 x 0

17 Model spectrum with optics effect Model is a two-component spectrum long wavelength component centered at zero frequency short poloidal wavelength component centered at 90 khz due to ExB rotation 10-7 original spectrum optics effect 10-8 cross power frequency (khz) The spectrum is significantly attenuated over the high frequency turbulence region low frequency region is unaffected.

18 Assume relative fluctuations similar to other machines: amplitude is ~4% correlation lengths θ, r are similar, ~2 cm. k r,0 = 0 cm -1 kθ,0 must be of order 15 cm -1 for the diagnostic not to observe the fluctuations This represents a factor of 3-5 increase in poloidal wavenumber over that measured in TEXT-U and W7-AS

19 Summary Analysis of the data show no evidence of the turbulent temperature fluctuations reported on other devices. The lack of observed fluctuations may be due to the spatial resolution of the diagnostic Based on the measured resolution of the optics the average poloidal wavenumber of the turbulence spectrum is greater than about 10 cm -1 (if fluctuations are present) Upper limit on fluctuation amplitude contributing to anomalous heat transport of T e,rms /T e <1%