Turbulence Measurements with the Upgraded Phase Contrast Imaging Diagnostic in L. Lin, M. Porkolab, E. M. Edlund, Y. Lin, S. J. Wukitch Plasma Science and Fusion Center, MIT, Cambridge, MA, 02139 48 th Annual Meeting of the Division of Plasma Physics October 30-November 3, 2006 Philadelphia, Pennsylvania *Work supported by U. S. DOE under DE-FG02-94-ER54235 and DE-FC02-99-ER54512.
Outline Phase Contrast Imaging Diagnostic (PCI) in Principle of Phase Contrast Imaging PCI System in Recent Results from PCI System in Localized Measurements along Vertical Chords New Features of QC Modes Observed with the Low-k Setup Possibly Coupled Coherence Turbulence Detected with the Medium-k Setup PCI High k Detecting Capability Test
Principle of Phase Contrast Imaging OBJECT: Plasma density fluctuations introduce phase variations to the laser beam. ( ) n = n + ncos k x 0 p Δ 2 iδ E= E 1 + E cos( k x 0 0 p ) 2 2 iδ + E cos k x 0 p 2 Δ= -λ rln 1 I E E E I 0 e * 2 = = 0 0 PLASMA X ( ) IMAGE: Laser phase variations are converted to intensity variations by the phase plate. /2 delay Δ 2 iδ E= ie 1 + E cos k x 0 0 p 2 2 iδ + E exp( k x 0 p ) 2 * I = E E I [1 + 2Δcos(k x)] 0 p IMAGE ( ) Z
PCI Geometry
PCI System in PCI measures electron density fluctuations along 32 vertical chords. Wave number Range: Localization 0.5cm -1 < k R < 55 cm -1 60cm<R<79cm Frequency Range Laser 2kHz~5MHz 60 Watt CO 2 CW tunable 50 or 80 MHz λ=10.6μm (Heterodyned) TEM 00 A masking phase plate system has been installed to localize short wavelength fluctuations along the laser beam. Optional optics configurations are available for optimizing turbulence measurements in different wavenumber ranges.
(I) Localized Measurement along Vertical Chords The vertical localization capability has been demonstrated. An ITG-like turbulence has been measured.
Principle of Vertical Localization Cross Section along the Beam R Φ The magnetic pitch angle β=arctan(b R /B Φ ) changes along a vertical chord passing through the plasma. Since the fluctuation wavenumbers are mainly perpendicular to the field lines, they also rotate from the bottom to the top of the plasma as the field pitch angle rotates.
This rotation is imaged onto the phase plate used in the PCI system, and by partially masking that phase plate, we can select a vertical region of interest (a) The front view of the conventional phase plate λ 0 /8 thick metal coating -β : Unscattered wave : Scattered wave ZnSe Substrate s k Conventional phase plate, which provides a π/2 phase delay on the unscattered wave. (b) The front view of phase plate and mask Metal Mask θ The combination of the phase plate and mask will select a scattered beam which is parallel to the direction of fluctuation.
Spatial Resolution Estimate on Magnetic Pitch Angle β = tan -1 (BR /B Φ) [degree] Vertical Axis z [m]
Partially Localized Turbulence Measurement The Bottom Plasma View θ = 15 o
The Top Plasma View θ= -15 o The vertical localization capability has been demonstrated The top/bottom Quasi-Coherent (QC) modes have been differentiated by the masked PCI system An ITG-like turbulence has been measured
Localization Estimate for Short Wavelength ETG Turbulence Shot: 1050803004; θ: 9 deg Shot: 1050803004; θ: 4.5 deg B T e ρ k k e θ θ = 3.5 T = T = 1 kev ρ i ~0.002 cm e ~ 0.1 (ETG) ~50 cm -1 k θ ~30 cm ; k ~50 cm -1-1 θ The localizing system will be used together with the high-k setup to search for the short wavelength ETG turbulence in the next campaign.
(II) New Features of the Quasi-Coherent (QC) Modes Observed with the Low-k Setup PCI As we increase distance of X-point from the PCI chords, we observe the following: 1. The normalized intensity of the QC modes is reduced toward the X-point. 2. The spatial location of this intensity reduction moves with the X-point. 3. A new turbulence spectrum localized toward the X-point.
PCI Measurements with Different X-point Locations R x-point = 55.9 cm PCI QC Modes New Turbulence Δ ~6cm
R x-point = 53.9 cm PCI Increasing Distance of X-Point from PCI Chords QC Modes New Turbulence Δ ~8cm
PCI Measurements Increasing Distance at R of x-point = X-Point 52.1 cm from PCI Chords R x-point = 52.1 cm PCI QC Modes Δ ~10cm
PCI Spectrograms with Different X-point Locations P i ( f ) Max P ( f ) i 295 khz 55 khz R x-point = 55.9 cm R x-point = 53.9 cm R x-point = 52.1 cm Δ ~6cm Δ ~8cm Δ ~10cm Increasing Distance of X-Point from PCI Chords The QC modes appear on more PCI chords.
The normalized intensity of the QC modes is reduced toward the X-point. Furthermore, the spatial location of this reduction moves with the X-point. Normalized QC Intensity f f 1 2 P ( f ) df ( f f ) ( f1) + ( f2) [, ] 1 2 2 1 P P 2 f f f QC R 0
The expanded beam enables the PCI system to investigate the spatial k R structure of the low-k turbulence. k R of the QC modes increases toward HFS. R 0
Summary (II) The normalized intensity of the QC modes is reduced toward HFS. The spatial location of this intensity reduction along the major radius moves with the X-point. k R of the QC modes increases toward HFS. A new turbulence spectrum localized toward the X-point has been observed. - It moves with the X-point; its k R could not be determined yet.
(III) Coupled Modes Detected with the Medium-k (12 cm -1 ) Setup PCI Three coupled (f 3 ~f 2 +f 1 and k R3 ~k R2 +k R1 ) semi-coherent modes Second harmonic of the Quasi-Coherent (QC) modes
Plasma Overview WkJ [ ] 20-2 ndl e [10 m ] D α [a.u.] P RF[MW] Time [sec]
PCI Measurements Frequency vs. Time Mode 3 f 3 ~ 610 khz Mode 2 (TAE-like) f 2 ~ 535 khz Mode 4 (2 nd harmonic of QC) f 4 ~ 150 khz Mode 1 (QC) f 1 ~ 75 khz
Wavenumber vs. Frequency Shot: 1060407013, Time: 0.920 sec 2 3 Coupled Modes: f ~ f + f 3 1 2 k ~ k + k R3 R1 R2 4 1 2nd harmonic: k f ~ 2 4 1 ~ 2 f k R4 R1
Wavenumber Spectra Mode 1 f [ 70, 90 ] khz Mode 2 f [ ] 525,545 khz Mode 3 f [ ] 605,625 khz Mode 4 [ ] f 145,165 khz
P( k) = P + Aexp Mode 1 Mode 2 Mode 3 GuassAmp Fit: ( k k ) 2 c f [khz] [ 70, 90] [525,545] [605,625] 0 2 2k w P 0 [a. u.] 1.4 10-2 1.6 10-3 0.5 10-3 k c [cm -1 ] 4.1 1.0 6.4 k w [cm -1 ] 1.0 0.4 1.0 A [a. u.] 7.7 10-2 5.0 10-3 2.8 10-3 Three Coupled Modes: f3 ~ f1 + f2 k ~ k + k R3 R1 R2 Mode 1 Mode 4 f [khz] [ 70, 90] [145,165] P 0 [a. u.] 1.4 10-2 1.6 10-2 k c [cm -1 ] 4.1 9.1 k w [cm -1 ] 1.0 2.2 A [a. u.] 7.7 10-2 3.1 10-2 2nd harmonic: k f ~ 2 4 1 ~ 2 f k R4 R1
(IV) PCI high k detecting capability has been tested recently with sound waves in air. The PCI wavenumber detection capability has been tested up to 55 cm -1. A system composed of four transducers at frequencies of 30, 75, 125 and 200 khz has been built, absolute calibration is under way. The high-k setup will be tried with plasmas in the next campaign.
PCI System Test with 75 KHz Sound Wave The strong peaks corresponds to the sound wave at k = 14 cm -1, f =75 khz and its harmonics.
Wavenumber Spectrum P(k) Normalized Wavenumber Spectrum P(k)/ P(k)dk 1 st 1 st 2 nd 3 rd 2 nd 4 th 3 rd 4 th
PCI System Test with 200 KHz Sound Wave The strong peak corresponds to the sound wave at k = 37 cm -1 f =200 khz.
References 1. L. Lin et al., Rev. Sci. Instrum. 77, 10E918 (2006). 2. M. Porkolab et al., IEEE Trans. Plasma Sci., 34, 229 (2006). 3. S. Kado et al., Jpn. J. Appl. Phys. 34, 6492 (1995). 4. P. Devynck et al., Plasma Phys. Control. Fusion, 35, 63, (1993). 5. E. Nelson-Melby et al., Phys. Rev. Letts. 90, 155004 (2003). 6. N. Basse et al., Phys. Plasmas 12, 052512 (2005). 7. S. Coda, PhD Dissertation, MIT, Dept. of Physics, 1997. 8. A. Mazurenko, PhD Dissertation, MIT, Dept. of Physics, 2001. 9. E. Nelson-Melby, PhD Dissertation, MIT, Dept. of Physics, 2001.
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