1. John Howard A Diallo, M Creese, (ANU) S Allen, R Ellis, M Fenstermacher, W Meyer, G Porter (LLNL, GA) J Chung, (NFRI) O Ford, J Svennson, R Konig, R Wolf (IPP) Imaging spectro-polarimetry of plasmas 1

2. Outline “Coherence imaging” interferometric systems –Principles –Spatial heterodyne Doppler coherence imaging systems –Doppler tomography in the DIII-D divertor Motional Stark Effect imaging on KSTAR –Measurement principles –Optical system and calibration –KSTAR measurements –Modeling results (using full QM treatment)

3. “Coherence imaging”: An alternative approach to spectroscopy 3 Interferogram S = I(1+  cos  ) Polarizer Waveplate (delay  LB  ) Input Spectral Lines Fourier transform To recover the fringe properties, measurements are required at multiple interferometric delays A simple polarization interferometer gives contrast and phase at a single optical delay Incident Fast Slow

4. Spatial heterodyne interferometer Savart plate introduces lateral displacement that gives an angular phase shear  generates straight parallel fringes imprinted on image. Demodulate for brightness, fringe contrast, fringe phase  plasma properties DIII-D Divertor raw image

5. Why do “coherence imaging”? When spectral information content is small (e.g. shift, width), it suffices to image the optical coherence (interferogram fringe contrast and phase) of the light emission at a small number of optical delays. The spatial heterodyne coherence imaging system is a “snapshot” imaging polarization interferometer that allows local estimates of interferometric phase and contrast at one or more optical delays (with multiple independent carriers). Why measure optical coherence? –Interferometers have throughput advantage (for R>100) –Robust alignment, birefringent optics, simple instrument function –Can be deployed for synchronous fluctuation studies (Doppler, MSE) –2D imaging with simple interpretation

6. Interferometric quantities are invertible For a single spectral line, the interferometer signal is DC level gives line-integrated emissivity: I(r) is the local emissivity Fringe contrast gives emissivity-weighted “temperature”: T i (r) is the local ion temperature T C is a constant “temperature” characterizing the instrument resolution (like a slit width) Phase gives emissivity-weighted flow component in direction of view: v D (r) is the local flow velocity  0 is the dc phase delay offset. It also includes a superimposed spatial carrier.  D is the Doppler shift phase Assume inhomogeneous, drifting Maxwellian distribution

7. Scrape-off-layer and divertor Doppler spectroscopy on the DIII-D tokamak - CIII 465nm and CII 514nm LCFS DIII-D Poloidal cross section Divertor raw image SOL brightness projection SOL flow projection With A Diallo, M. Creese, S Allen, R Ellis, W. Meyer, G Porter, M Fenstermacher

8. Demodulated DIII-D divertor brightness and phase images during detachment 8 Foruier demodulated brightness (top) and phase (bottom) projections at representative times during the divertor evolution for DIII-D discharge #141170: (a) 500 ms, (b) 2000 ms and (c) 4000 ms.

9. Typical DIII-D raw image data Camera frame rate typically 10-20 frames per second, 688x520 pixels, 12 bits Exposure time typically 10-100 ms LabVIEW control software + demodulation

10. Tomographic reconstruction algorithm details  Iterative linear reconstruction technique (ASIRT) on 1cm x 1cm grid (no apriori constraints on the reconstruction domain)  Assume toroidal symmetry  Use reconstructed emissivity and computed B.dl/|B| as integral weights in parallel flow speed tomography Right: Line of sight trajectories in R-Z plane for one projection-image column (above) (Colour coding indicates integral weight)

11. Tomographically inverted DIII-D divertor brightness and flow images 11 Fourier demodulated brightness (top) and phase (bottom) projections at representative times during the divertor detachment for DIII-D discharge #141170: (a) 500 ms, (b) 2000 ms and (c) 4000 ms. With Diallo, Allen, Ellis, Porter, Meyer, Fenstermacher, Brooks, Boivin Corresponding tomographic inversions of brightness (top) and phase (bottom) The flow is seen only in regions where the brightness is significant

12. Comparison with UEDGE modeling 12 Some similarities between UEDGE modeling and tomographically inverted brightness and parallel flow speed. But observed are ~2x as high as modeling predicts.

13. Outline “Coherence imaging” interferometric systems –Principles –Spatial heterodyne Doppler coherence imaging systems –Doppler tomography in the DIII-D divertor Motional Stark Effect imaging on KSTAR –Measurement principles –Optical system and calibration –KSTAR measurements –Modeling results (using full QM treatment)

14. A typical Doppler shifted Stark effect spectrum EdgeCentre Modelled interferometric image of beam Courtesy, Oliver Ford, IPP Motional Stark effect polarimetry senses the internal magnetic field 14 Top view KSTAR MSE viewing geometry Motional Stark effect (MSE) polarimetry measures the polarization orientation of Stark-split D  656 nm emission from an injected neutral heating beam. The splitting and polarization is produced by the induced E-field (E = v x B ) in the reference frame of the injected neutral atom. MSE can deliver information about the internal magnetic field inside a current-carrying plasma Angle-varying Doppler shift  every observation position requires its own colour filter. Interferometric approach – periodic filter allows 2-D spatial imaging  B z (r,z) Beam View range Edge Centre

15. Oliver Ford, IPP

16. Imaging spectro-polarimetry for MSE 16 Recall simple polarization interferometer: Output signal S = I(1+  cos  ) Polarizers Waveplate (delay  ) Input If input is polarized already (angle  ), remove the first polarizer Resulting interferogram fringe contrast depends on polarization orientation: S = I(1+  cos2  cos  ) Add a quarter wave plate. Fringe phase depends on polarization orientation: S = I[1+  cos(  2  The  and  components interfere constructively (no need to isolate or separate) Quarter waveplate

17. How do we image the multiplet?  For one of the multiplet components (e.g.  ), the interferometer output is: S  = I  [1+   cos(    2  )]  For the orthogonal component (    ) the sign is reversed S  = I  [1-   cos(    2  )]  For MSE triplet, after adding the interferograms, the effective signal contrast depends on the component contrast difference   –  . Choose interferometer optical delay  to maximize the contrast difference   –  

18. Model of KSTAR isolated full energy Stark multiplet and associated nett contrast 18 Good contrast (~80%) across full field of view (i.e. Stark splitting doesn’t change significantly). But significant phase variation due to large Doppler shift Optical delay 1000 waves  a-BBO plate thickness ~5 mm 2nm bandpass filter tilted to track Doppler shift across FOV KSTAR parameters: Bt = 2.0T on axis, Ip = 600 kA D beam, 85keV/amu, 1.0 degrees divergence Centre Edge 

19. Imaging MSE instrument S = I 0 [1 +  cos(k x x  cos(k y y  Instrument produces orthogonal phase modulated spatial carriers Demodulate fringe pattern to obtain Doppler shift  and polarization  Insert shearing (Savart) plates to provide carrier fringes:

20. Optical system layout From plasma Telescope Cell Camera Filter Mirror

21. Power spectrum of interference pattern    All information is encoded on distinct spatial heterodyne carriers: Polarimetric angles:  (orientation and ellipticity) Interferometer contrast and phase:  (splitting and Doppler shift) Calibration image using Neon lamp at 660nm

22. Typical calibration data (a)Central horizontal slices across a sequence of demodulated polarization angle images . The Doppler phase image  is insensitive to the calibration polarizer angle. (Turning mirror removed). (b)Deviation from linearity of the measured polarization angle at the centre of the calibration image versus polarizer angle. Cell size for averaging is ~1.5-2 carrier wavelengths (10-14 pixels). There is a small systematic variation. Random noise ~0.1 degrees (calibration image).

23. Typical MSE double heterodyne image Conclusion: Need new camera Solution: CID camera + remote + shield Pixelfly 1300x1000 100ms exp Frame rate 10Hz This is our calibration image! Day 2 Day 3 Day 1 Beam direction Radiation noise Plasma Boundary/ port opening Orthogonal spatial carriers Internal reflection and sparks (not an issue for imaging MSE)

24. Measured and modelled Doppler phase images are in good agreement Line-of sight integration effects may account for the small discrepancies. Viewing from above mid-plane accounts for tilt of phase contours System tolerant of large beam energy changes (70-90 keV) MeasurementModel Centre Edge

25. QM modeling of system polarization response Apply QM model developed by Yuh, Scott, Hutchinson, Isler etal to estimate importance of Zeeman effect on MSE nett polarization (all components E, v and B) No line of sight integration effects Statistical populations Uniform brightness beam (no CRM modeling) KSTAR viewing geometry Simple circular flux surfaces with Shafranov shift Spectro-polarimeter – sum over 36 cpts 25

26. E,v and B components 26 E (  ) B 5% of intensity V (  ) IntensityOrientationEllipticity Centre Edge

27. Comparison with ideal Stark effect model 27 Stark-Zeeman Geometric model (no Zeeman) Difference orientation angle variation across MSE image less than ~0.1 o  Standard geometric models for interpretation are OK Difference orientation angle

28. Measured and model “nett polarization” images Simple circular plasma model - 2.0T, 600kA A typical measured nett polarization image - 2.0T, 600kA Note: A fixed constant shift of 16 degrees has been subtracted – thermal drift? Low brightness regions Reflection artifact Nett polarization angle = plasma MSE angle - Gas MSE reference angle

29. Typical KSTAR midplane radial profile evolution during RMP ELM suppression xpts Edge Axis System should be self calibrating – edge polarization angle is determined by toroidal current and PF coils – other angles are referred to the edge. (alleviates issues with thermal drifts, window Faraday rotation, in situ calibration problems etc.) Edge Axis Common mode noise structures from beam-into-gas calibration have been removed Ramp up

30. The imaging spectro-polarimeter encodes both ellipticity and orientation 30 Image of 660nm lamp transmission through a polarizer Image of 660nm lamp transmission through a polarizer followed by a wave plate

31. Plasma images show strong ellipticity 31 Typical raw image of beam emission Beam direction Orthogonal carriers Ellipticity

32. Ellipticity images Beam emission images show larger than expected ellipticity Beam into gas Beam into plasma 80 keV 85 keVEllipticity unlike QM model. Window linear birefringence? Dependence on beam energy indicates other than some B-dependent optical effect. Beam into gas

33. Attributes of MSE imaging approach 33  Analyse full multiplet so no need for narrowband filters  Simple inexpensive instrument - No filter tuning issues or incidence angle sensitivities  Tolerant of beam energy changes (10-20%)  Higher light efficiency ?  Multiple heterodyne options, single channel or imaging  2D toroidal current imaging (in principle) - Possibility of synchronous imaging of sawteeth, MHD, ELMs, E r etc.  Insensitive to “broadband” polarized background contamination  Insensitive to non-statistical populations  Full Stokes polarimetry  Possibility of self calibration based on unpolarized plasma radiation (Voslamber 1995) mirror/window degradation  Fringe phase shift gives 4  where  is the polarization tilt angle.  Can be applied to spectrally complex elliptically polarized multiplets (Zeeman effect)

34. Conclusion 34  Doppler Coherence Imaging systems can be used to extract 2d images of plasma flows and temperature  Imaging spectro-polarimeters utilizing spatial heterodyne encoding can encode both Doppler and polarimetric information  Modeling indicates that imaging MSE should be a reliable tool for obtaining 2d maps of the internal magnetic field in tokamaks.  IMSE significantly increases the information available to infer the current profile.