Imaging EBW emission on MAST to diagnose the plasma edge

Transcription

1 Imaging EBW emission on MAST to diagnose the plasma edge Roddy Vann 1, Simon Freethy 1,2, Billy Huang 2,3, Vladimir Shevchenko 2 and the MAST team Roddy.Vann@york.ac.uk 1 York Plasma Institute, Department of Physics, University of York, York YO10 5DD 2 Culham Centre for Fusion Energy, Oxfordshire OX14 3DB 3 Centre for Advanced Instrumentation, Durham University, Durham DH1 3LE

2 Synthetic Aperture Microwave Imaging (SAMI) SAMI is 3-D: 2 viewing angles + 1 frequency SAMI operates in 2 modes simultaneously Mode: Physics delivered: SAMI PASSIVE IMAGING of thermal emission from plasma in 2D+1F ACTIVE PROBING with 2D+1F imaging of back-scattered signal Mode conversion (MC) physics Edge current density profile Edge density fluctuations Pedestal physics 2D+1F velocity map of turbulence 2D+1F MHD spectra

3 1. Motivation and background 2. Results from spinning mirror 3. Synthetic Aperture Microwave Imaging 4. Results from passive emission 5. Results from active probing

4 ELM cycle is an interplay between pressure gradient and current density in the edge Edge pressure gradient and current density linked via the bootstrap current Pressure gradient measurements trustworthy from Thomson scattering Current density is much more difficult to measure (MSE helpful but limited resolution): we want to test neoclassical current calculations Edge current density Peeling/kink modes (current-driven) Stable region Ballooning modes (pressure-driven) Edge pressure gradient

5 MAST H-mode plasmas are overdense so there is no ECE Relevant MAST parameters: n core ~ 4.5 x m -3 B(R=1m) ~ 0.5 T Electron cyclotron frequency (and harmonics) in BLUE Plasma frequency in RED Frequency [GHz] shot 380ms at midplane Major radius [m]

6 But what about emission of electron Bernstein waves? Relevant MAST parameters: n core ~ 4.5 x m -3 B(R=1m) ~ 0.5 T Electron cyclotron frequency (and harmonics) in BLUE Plasma frequency in RED Frequency [GHz] shot 380ms at midplane Major radius [m] Electron Bernstein waves (EBWs): are electrostatic & longitudinal generated at harmonics of the local electron cyclotron frequency power spectrum depends on T e at birth location

7 B-X-O mode conversion: directional emission allows observation of field-line pitch Ordinary mode extraordinary Mode electron Bernstein wave 2 2 uh ce pe ce 4 sin ce pe high 2 Bernstein waves converted to X- mode at UH layer and reflected Reflection at high density cut-off if ω high ω pe If ω high ω pe then X-mode converted to O-mode which exits plasma

8 B-X-O mode conversion: directional emission allows observation of field-line pitch Ordinary mode extraordinary Mode electron Bernstein wave 2 2 uh ce pe ce 4 sin ce pe high 2 Bernstein waves converted to X- mode at UH layer and reflected Reflection at high density cut-off if ω high ω pe If ω high ω pe then X-mode converted Emission is co-planar with density gradient to O-mode which exits plasma and magnetic field at mode conversion surface.

9 1. Motivation and background 2. Results from spinning mirror 3. Synthetic Aperture Microwave Imaging 4. Results from passive emission 5. Results from active probing

10 Spinning mirror radiometer scans density cut-off surface As the mirror spins, the path of the detected ray traces an elliptical path over the density cut-off surface. Plasma Dual polarisation horn antenna Deduce location and shape of emission pattern (assuming bi-gaussian) from amplitude measured as mirror rotates. 30 Spinning mirror Antenna elevation, degrees Volpe, Rev. Sci. Inst D905 (2010) 20 >90% >80% >70% >60% >50% >40% Viewing trajectory B-X-O MC window Antenna azimuth, degrees

11 Spinning mirror radiometer scans density cut-off surface As the mirror spins, the path of the detected ray traces an elliptical path over the density cut-off surface. Plasma Dual polarisation horn antenna Deduce location and shape of emission pattern (assuming bi-gaussian) from amplitude measured as mirror rotates. 30 Spinning mirror Antenna elevation, degrees Volpe, Rev. Sci. Inst D905 (2010) 20 >90% >80% >70% >60% >50% >40% Viewing trajectory B-X-O MC window Antenna azimuth, degrees

12 Spinning mirror radiometer scans density cut-off surface As the mirror spins, the path of the detected ray traces an elliptical path over the density cut-off surface. Plasma Dual polarisation horn antenna Deduce location and shape of emission pattern (assuming bi-gaussian) from amplitude measured as mirror rotates. 30 Spinning mirror Antenna elevation, degrees Volpe, Rev. Sci. Inst D905 (2010) 20 >90% >80% >70% >60% >50% >40% Viewing trajectory B-X-O MC window Antenna azimuth, degrees

13 EBW emission signal, V Observed change in pitch angle implies a double current sheet in steep gradient region Optimal tilt X X X X X X X 18 GHz 17 GHz 16 GHz 15 GHz 14 GHz 13 GHz 11.5 GHz Pitch Angle, deg d(pitch angle) d(major radius) b) ~ current density LCFS MAST shot ms MSE data WKB results Full wave Major radius, m Time, s Shevchenko, De Bock, Freethy, Saveliev & Vann, Fusion Science and Technology (2011)

14 Change in pitch angle implies a double current sheet Pitch angle (degrees) J=+3.2MA/m 2 J=-2.8MA/m 2 Plasma edge MAST shot ms Major radius (m) Results are consistent with MSE at measurement boundaries. Bootstrap current ~ 1MA/m 2 much smaller and further inside LCFS. Temporal resolution limited by rotation period of mirror (~10ms). Measurements can only be taken on a 1-D path (roughly an ellipse) Shevchenko, De Bock, Freethy, Saveliev & Vann, Fusion Science and Technology (2011)

15 1. Motivation and background 2. Results from spinning mirror 3. Synthetic Aperture Microwave Imaging 4. Results from passive emission 5. Results from active probing

16 (Far-field) aperture synthesis is widely used in radio astronomy Very Large Array radio telescope Array diameter ~ 20km Image: NRAO

17 Aperture synthesis uses phase differences between antennas to reconstruct emission pattern Phase difference between antenna pairs steers beam Cross-correlation between pairs of antennas gives spatial Fourier transform of emission pattern. Number of pixels ~ N 2 (where N = number of antennas) Cross-correlation is Fourier transform of emission pattern a * 1 2 ta()d t t 2 2 ixu A e We can therefore inverse Fourier transform the cross-correlations to recover emission pattern. θ Far-away point source θ u sin 2 xu Baselines must be chosen carefully to provide good coverage of Fourier space. x λ Antenna 1 Antenna 2

18 Cross-correlations are calculated in software post-shot for flexibility We choose to do cross-correlations in software because N fast ADCs are more flexible (and cheaper!) than N 2 mixers (where N = no. of antennas) Digitisation rate determined by required bandwidth for good S/N ratio.

19 Frequency down-conversion at 16 LO frequencies and sideband separation I & Q components allow to separate Upper (USB) and Lower (LSB) sidebands and analyse them independently 90 o I ADC Local oscillator switches between 16 programmable frequencies within GHz range (switching time ~300ns) Q ADC IF LSB USB 100MHz 100MHz f LO 10-35GHz f

20 Vivaldi antennas provide great performance at small size: we digitise from 8 antennas = 28 baselines Vivaldi antennas are etched onto PCBs (dielectric consistency important) Small size (20x60mm) Excellent polarisation separation Bonus: low cost Mounted in 150mm diameter array; 37 locations; digitise 8 simultaneously Antipodal Notched

21 Digitisation requirements are extremely demanding 16 channels (8 antennas; cost of RF electronics) 14 bit sample depth (dynamic range of the plasma during ELMs) 250Msamples/s (sampling time & S/N ratio) 0.5s total acquisition time (length of MAST shot) <350ps cross-channel skew (error in cross-correlation) 8 Gbytes/s data rate 4 Gbytes of data per shot and then we have to get the data out of the area FPGA board ADC card

22 FPGA-based solution provides high performance and flexibility Field-programmable gate arrays (FPGAs) are arrays of (thousands of) programmable logic blocks Wire-speed signal processing with flexibility of software Cost transferred from hardware to firmware But beware: Programming effort is significant! Can run Linux on a soft processor : ideal for instrument control Currently acquisition only; later we ll do cross-correlations on-board Only solid state storage in area; data transfer via high-speed UDP Xilinx s ML605 FPGA board 4DSP s FMC108 ADC card

23 SAMI installation on MAST Antennas situated outside vessel Window size = 150mm RF electronics mounted on adjoining bracket Digitisation & services rack ~ 4m away from vessel Reliable phase information requires care with connections 23/28

24 Calibration: off-vessel & through-vessel Off-vessel calibration performed at every frequency to obtain complex coefficients for each baseline for both upper and lower sidebands. Through-vessel calibration used to confirm robustness of off-vessel calibration all available ports were tested it was found that vacuum windows and flanges have very little effect on the image coordinates and shape deviations of reconstructed images were within ±2 for frequencies in 10-18GHz range

25 1. Motivation and background 2. Results from spinning mirror 3. Synthetic Aperture Microwave Imaging 4. Results from passive emission 5. Results from active probing

26 EBW emission in MAST shot #27004 First ever image of EBW emission from tokamak plasma 2-D space + 1-D frequency This movie: LO frequency = 10 GHz 10μs integration time, but smoothed over 3 frames 160μs between frames There are 15 other movies like this one (at the other frequencies). Emission windows in expected configuration We observe large fluctuations (despite good signal-to-noise ratio)

27 Image straight after ELM shows change in pitch angle at ~12.5 GHz Shot #26815, DND H-mode, shortly after ELM: ms Time-averaged over 10ms to eliminate fluctuations Current sheet at ~ 12.5 GHz? (NB further validation required) 10 GHz 11 GHz 12 GHz 13 GHz 14 GHz 15 GHz 16 GHz 17 GHz

28 Modelling explains some peculiarities of EBE shapes ELM-free period in H-mode Shape of EBE brightness at UHR is certainly important! (and in this case leads to an apparent splitting of upper emission pattern) Disturbance of the MC layer by MHD and fluctuations (not accounted here) is also important! #27004, 360ms, 16 GHz X-O MC windows EBE brightness at UHR X = Predicted emission pattern

29 1. Motivation and background 2. Results from spinning mirror 3. Synthetic Aperture Microwave Imaging 4. Results from passive emission 5. Results from active probing

30 Diagnostic also actively probes density fluctuations and turbulence We configure one of the antennas as transmitter at 12 MHz from local oscillator frequency. Remainder of antennas act as detectors. Diagnostic simultaneously images both emission and back-scattering. Plasma Receiving antennas Transmitting antenna Edge fluctuations in H-mode (reverse of emission measurements) Probe of high-k core turbulence in L-mode Doppler shift tells us about flows (actually motion of blobs)

31 Calibration using rotating corner reflector Rotating multiple corner reflector Imaging phased array of antennas Probing signal Back-reflected signal Rotating corner reflector was used in calibration 35cm

32 Calibration: successful across frequency range 13 GHz, max Doppler shift ±1kHz 17 GHz, max Doppler shift ±1.3kHz

33 Preliminary 2-D velocity maps: MAST shot 50ms (L-mode) & 220ms (H-mode) -0.4km/s 0km/s -0.7km/s Vertical angle, deg L-mode Vertical angle, deg H-mode 0km/s 0.4km/s 0.7km/s Horizontal angle, deg Horizontal angle, deg Velocity maps of fluctuations estimated from Doppler shifts of back-scattered signal at 10 GHz mixed with 12 MHz transmitted signal Remember: these maps available for all 16 frequencies Note difference in flow directions during L-mode and H-mode phases

34 Coherent structures in inter-elm periods I p Z axis n e D α BS spectra are plotted against time to illustrate dynamics during and in between ELMs Central un-shifted IF frequency is 12 MHz Broadening is caused by Doppler shifts of BS signals from density fluctuations Structures symmetrical around 12MHz are caused by coherent MHD events or modes in the plasma like GAM These structures may develop and stay until ELM or may collapse themselves before ELM Coherent structure destroyed by ELM Coherent structure collapsed by itself

35 Plasma rotation at the beginning of shot depends strongly on radial location Low density L-mode: 2 identical shots 2 different frequencies inner layer reaches 0.24km/s and saturates outer layer increases velocity 3 times slower 0.23km/s 0.24km/s 13 GHz 16 GHz

36 Summary: first images of Bernstein wave emission & edge flows Original motivation: measure the tokamak edge current density to better understand edge-localised modes (ELMs). Measurements with a spinning mirror (with ~10ms time resolution) indicated a double current layer. We have designed and built a microwave imaging system with ~10μs time resolution which uses phase correlations instead of focusing optics. We have obtained first ever 3-D (2-D spatial + 1-D frequency) images of Bernstein wave emission from a tokamak plasma There is good agreement with a 1-D full-wave hot plasma code. We have obtained preliminary images of edge rotation profiles.

37 Current & future work: preliminary results are very encouraging but much remains to be done! Detailed verification of observations Refine image inversion algorithm (pursue SVD-based techniques); perform sideband separation and cross-correlations in real time on the FPGA board(s). Explain high fluctuation levels: candidates include: o core fluctuations in temperature o turbulent generation of non-maxwellian distributions in core o magnetic field variations (refraction effects) o edge density gradient perturbations o changing upper hybrid position/conditions) Proceed to calculations of current density profiles. A 3-D full-wave hot plasma FDTD simulation code is being written (estimated completion end of 2012) necessary for any simulation of back-scattering system and may be necessary for detailed analysis of passive imaging. Diagnostic upgrade: go to 16 antennas and sample at 1 GSPS for better resolution and continuous radial coverage; cover both polarisations with fast array switching Add more active probing channels for stereo imaging. Explore possibilities for deploying the diagnostic on other machine(s) during shutdown for MAST Upgrade. Long-term: investigate phased-array steering of EBW heating & current drive

38 BACKUP SLIDES FOLLOW

39 SAMI off-vessel calibration

40 Example of off-vessel calibration at 15 GHz Black crosses indicate positions of the point source. Colour map represents reconstructed images. Typical errors are within +/- 2 degrees. 40/28

41 How do we resolve under-specified image inversion problem? Inverse Fourier transform: sum over point samples corresponding to antenna baselines: 2 ix 2 ju j du 2 2 x ju ( j) e j x A u e A u x But we don t know anything about the cross-correlations that would be measured at any other baselines! Solution: employ a singular value decomposition (SVD) technique Pixellate emission surface with surface elements, each of which emits a signal y k. Calculate the cross-correlation at each baseline j due to each y k i.e. calculate the matrix M such that My Γ. (Note that there are more surface elements than baselines i.e. y is much longer than Γ.) 1 Perform a singular decomposition of M, calculate its pseudo-inverse M and identify a basis y m for its kernel (i.e. emission patterns that produce zero crosscorrelations at all antennas); let Y be the matrix whose columns are these kernel basis vectors. 1 Then y M Γ YΛ for some vector Λ. We then choose Λ to minimise y 1 and y 2 constrained by yk 0 k.