1. John Howard J Chung, O Ford, R Wolf, J Svennson, R Konig 2D MSE imaging on the KSTAR tokamak and future prospects 1

2. Outline Measurement principles –Doppler imaging on DIII-D Optical system and calibration KSTAR measurements Modeling results (using full QM treatment)

3. An alternative approach to spectroscopy 3 Simple polarization interferometer: Interferogram S = I(1+  cos  ) Polarizers Waveplate at 45 degrees (delay  LB  ) Input Spectral Lines Fourier transform Interferogram 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

4. Spatial heterodyne interferometer Savart plate introduces angular phase shear  generates straight parallel fringes imprinted on image. Demodulate for local fringe brightness, contrast and phase. Phase shift tracks Doppler colour changes  flow fields DIII-D Divertor raw image

5. Tomographically inverted DIII-D divertor brightness and flow images 5 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) Reasonable agreement with UEDGE modeling

6. Motional Stark effect polarimetry senses the internal magnetic field 6 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 A typical Doppler shifted Stark effect spectrum EdgeCentre Modelled interferometric image of beam Courtesy, Oliver Ford, IPP

7. Imaging spectro-polarimetry for MSE 7 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 spectrally isolate) Quarter waveplate

8. 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 (  slightly different wavelength), it is S  = I  [1-   cos(    2  )]  For MSE triplet, after adding the interferograms, the effective signal contrast depends on the component contrast difference   –  . Choose optical delay  to maximize the contrast difference   –  

9. Model of KSTAR isolated full energy Stark multiplet and associated nett contrast 9 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  Centre Edge

10. Final 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  A first quarter wave plate and shearing Savart plates results in a phase encoded double spatial-heterodyne system for  and amplitude encoding for 

11. 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

12. 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)

13. 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. (a)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).

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

15. Typical MSE double heterodyne image Pixelfly 1300x1000 100ms exp Frame rate 10Hz Day 1 Beam direction Radiation noise Plasma Boundary/ port opening Orthogonal spatial carriers Internal reflection and sparks (not an issue for imaging MSE)

16. Typical MSE double heterodyne image Pixelfly 1300x1000 100ms exp Frame rate 10Hz Day 2

17. Typical MSE double heterodyne image Pixelfly 1300x1000 100ms exp Frame rate 10Hz Day 3

18. Typical MSE double heterodyne image Conclusion: Need new camera Solution: CID camera + remote + shield Pixelfly 1300x1000 100ms exp Frame rate 10Hz This is our beam-into-gas calibration image

19. 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

20. 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 Window Faraday effect? thermal drift? misalignment? Low brightness regions Reflection artifact Nett polarization angle = plasma MSE angle - Gas MSE reference angle

21. 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 partly removed Ramp up

22. Tolerant of polarized background reflections 22 Reflections from internal structures have little effect on inferred polarization angle. True for broadband emission, polarized or unpolarized

23. 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 (three directions with corresponding polarized 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 Stark-Zeeman component lines 23

24. Modeled E,v and B components 24 E (  ) B (5% of intensity) V (  ) Polarization orientation Ellipticity CentreEdge Nett ellipticity angles are comparable in magnitude to polarization tilt

25. Comparison with ideal Stark effect model 25 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

26. Plasma images show strong ellipticity 26 Typical raw image of beam emission Beam direction Orthogonal carriers (mostly linear) Elliptically polarized light

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

28. Attributes of MSE imaging approach 28  Analyse full multiplet so no need for multiple discrete narrowband filters  Simple inexpensive instrument  ~10 3 more channels at <10% total cost  No filter tuning issues or incidence angle sensitivities  Tolerant of beam energy changes (10-20%), other beam energy components, overlapping beams.  Multiple heterodyne options (spatial/temporal), single channel or imaging  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  Can be applied to spectrally complex elliptically polarized multiplets (Zeeman effect)  New opportunities. For example: 2D toroidal current imaging (in principle) and possibility of synchronous imaging of sawteeth, MHD, ELMs, E r etc.

29. Future directions/possibilities Replace crystal quartz window to eliminate Faraday rotation and anomalous ellipticity and install radiation hard camera for next KSTAR campaign. Fast system for real-time equilibrium Time-multiplex system for high spatial resolution imaging (RMP effects) Use gated intensified camera to synchronously study magnetic reconnection for comparison with ECE imaging. MSE/Zeeman imaging at ASDEX and DIII-D (for pedestal and ELM suppression studies)

30. Conclusion 30  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.