Imaging spectropolarimetry of plasmas John Howard A Diallo

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Imaging spectro-polarimetry of plasmas John Howard A Diallo, M Creese, (ANU) S Allen, R

Imaging spectro-polarimetry of plasmas 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) 1

Outline • “Coherence imaging” interferometric systems – Principles – Spatial heterodyne Doppler coherence imaging

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)

“Coherence imaging”: An alternative approach to spectroscopy A simple polarization interferometer gives contrast and

“Coherence imaging”: An alternative approach to spectroscopy A simple polarization interferometer gives contrast and phase at a single optical delay Waveplate (delay f=2 p. LB/l) Incident Input Slow Interferogram S = I(1+z cosf) Fast Polarizer Spectral To recover the fringe properties, measurements are required at Lines multiple interferometric delays Fourier transform 3

Spatial heterodyne interferometer Savart plate introduces lateral displacement that gives an angular phase shear

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

Why do “coherence imaging”? • When spectral information content is small (e. g. shift,

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) 2 D imaging with simple interpretation

Interferometric quantities are invertible Assume inhomogeneous, drifting Maxwellian distribution For a single spectral line,

Interferometric quantities are invertible Assume inhomogeneous, drifting Maxwellian distribution For a single spectral line, the interferometer signal is f 0 is the dc phase delay offset. It also includes a superimposed spatial carrier. DC level gives line-integrated emissivity: f. D is the Doppler shift phase I(r) is the local emissivity Fringe contrast gives emissivity-weighted “temperature”: Ti(r) is the local ion temperature TC 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

Scrape-off-layer and divertor Doppler spectroscopy on the DIII-D tokamak - CIII 465 nm and

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

Demodulated DIII-D divertor brightness and phase images during detachment Foruier demodulated brightness (top) and

Demodulated DIII-D divertor brightness and phase images during detachment 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. 8

Typical DIII-D raw image data Camera frame rate typically 10 -20 frames per second,

Typical DIII-D raw image data Camera frame rate typically 10 -20 frames per second, 688 x 520 pixels, 12 bits Exposure time typically 10 -100 ms Lab. VIEW control software + demodulation

Tomographic reconstruction algorithm details Ø Iterative linear reconstruction technique (ASIRT) on 1 cm x

Tomographic reconstruction algorithm details Ø Iterative linear reconstruction technique (ASIRT) on 1 cm x 1 cm grid (no apriori constraints on the reconstruction domain) Ø Assume toroidal symmetry Ø 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)

Tomographically inverted DIII-D divertor brightness and flow images Fourier demodulated brightness (top) and phase

Tomographically inverted DIII-D divertor brightness and flow images 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. Corresponding tomographic inversions of brightness (top) and phase (bottom) The flow is seen only in regions where the brightness is significant With Diallo, Allen, Ellis, Porter, Meyer, Fenstermacher, Brooks, Boivin 11

Comparison with UEDGE modeling Some similarities between UEDGE modeling and tomographically inverted brightness and

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

Outline • “Coherence imaging” interferometric systems – Principles – Spatial heterodyne Doppler coherence imaging

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)

Motional Stark effect polarimetry senses the internal magnetic field Top view KSTAR MSE viewing

Motional Stark effect polarimetry senses the internal magnetic field Top view KSTAR MSE viewing geometry Beam A typical Doppler shifted Stark effect spectrum Edge Centre View range Edge Modelled interferometric image of beam Centre Courtesy, Oliver Ford, IPP Motional Stark effect (MSE) polarimetry measures the polarization orientation of Stark-split Da 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 Bz(r, z) 14

Oliver Ford, IPP

Oliver Ford, IPP

Imaging spectro-polarimetry for MSE Recall simple polarization interferometer: Quarter waveplate Input Waveplate (delay f)

Imaging spectro-polarimetry for MSE Recall simple polarization interferometer: Quarter waveplate Input Waveplate (delay f) Output signal S = I(1+z cosf) Polarizers If input is polarized already (angle y), remove the first polarizer Resulting interferogram fringe contrast depends on polarization orientation: S = I(1+z cos 2 y cosf) Add a quarter wave plate. Fringe phase depends on polarization orientation: S = I[1+z cos(f + 2 y)] The p and s components interfere constructively (no need to isolate or separate) 16

How do we image the multiplet? v. For one of the multiplet components (e.

How do we image the multiplet? v. For one of the multiplet components (e. g. p), the interferometer output is: Sp = Ip [1+zp cos(fp+2 y)] v. For the orthogonal component (y y+p/2) the sign is reversed Ss = Is [1 -zs cos(fs+2 y)] v. For MSE triplet, after adding the interferograms, the effective signal contrast depends on the component contrast difference zp – zs. Choose interferometer optical delay t to maximize the contrast difference zp – zs

Model of KSTAR isolated full energy Stark multiplet and associated nett contrast Edge s

Model of KSTAR isolated full energy Stark multiplet and associated nett contrast Edge s p Centre 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 2 nm bandpass filter tilted to track Doppler shift across FOV KSTAR parameters: Bt = 2. 0 T on axis, Ip = 600 k. A D beam, 85 ke. V/amu, 1. 0 degrees divergence 18

Imaging MSE instrument Insert shearing (Savart) plates to provide carrier fringes: S = I

Imaging MSE instrument Insert shearing (Savart) plates to provide carrier fringes: S = I 0 [1 + z cos(kxx + f+2 y) + z cos(kyy - f+2 y) ] Instrument produces orthogonal phase modulated spatial carriers Demodulate fringe pattern to obtain Doppler shift f and polarization y

Optical system layout Mirror Telescope Camera Cell Filter From plasma

Optical system layout Mirror Telescope Camera Cell Filter From plasma

Power spectrum of interference pattern Calibration image using Neon lamp at 660 nm -f+2

Power spectrum of interference pattern Calibration image using Neon lamp at 660 nm -f+2 y 2 e All information is encoded on distinct spatial heterodyne carriers: Polarimetric angles: (y, e) (orientation and ellipticity) Interferometer contrast and phase: (z, f) (splitting and Doppler shift)

Typical calibration data (a) Central horizontal slices across a sequence of demodulated polarization angle

Typical calibration data (a) Central horizontal slices across a sequence of demodulated polarization angle images y. The Doppler phase image f 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).

Typical MSE double heterodyne image Pixelfly 1300 x 1000 Plasma Boundary/ port opening Radiation

Typical MSE double heterodyne image Pixelfly 1300 x 1000 Plasma Boundary/ port opening Radiation noise Orthogonal spatial carriers 100 ms exp Frame rate 10 Hz Internal reflection and sparks (not an issue for imaging MSE) This is our calibration image! Day 2 Day 1 3 Day Beam direction Conclusion: Need new camera Solution: CID camera + remote + shield

Measured and modelled Doppler phase images are in good agreement Measurement Centre Model Edge

Measured and modelled Doppler phase images are in good agreement Measurement Centre Model Edge 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 ke. V)

QM modeling of system polarization response • Apply QM model developed by Yuh, Scott,

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

E, v and B components Intensity Centre Orientation Ellipticity Edge E (p) V (s)

E, v and B components Intensity Centre Orientation Ellipticity Edge E (p) V (s) B 5% of intensity

Comparison with ideal Stark effect model Stark-Zeeman Difference orientation angle Geometric model (no Zeeman)

Comparison with ideal Stark effect model Stark-Zeeman Difference orientation angle Geometric model (no Zeeman) Difference orientation angle variation across MSE image less than ~0. 1 o Standard geometric models for interpretation are OK

Measured and model “nett polarization” images Low brightness regions Simple circular plasma model 2.

Measured and model “nett polarization” images Low brightness regions Simple circular plasma model 2. 0 T, 600 k. A Reflection artifact A typical measured nett polarization image - 2. 0 T, 600 k. A Note: A fixed constant shift of 16 degrees has been subtracted – thermal drift? Nett polarization angle = plasma MSE angle - Gas MSE reference angle

Typical KSTAR midplane radial profile evolution during RMP ELM suppression xpts System should be

Typical KSTAR midplane radial profile evolution during RMP ELM suppression xpts 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. ) Ramp up Edge Axis Edge Common mode noise structures from beam-into-gas calibration have been removed

The imaging spectro-polarimeter encodes both ellipticity and orientation Image of 660 nm lamp transmission

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

Plasma images show strong ellipticity Orthogonal carriers Ellipticity Beam direction Typical raw image of

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

Ellipticity images Beam emission images show larger than expected ellipticity Beam into gas Beam

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

Attributes of MSE imaging approach q Analyse full multiplet so no need for narrowband

Attributes of MSE imaging approach q 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 q 2 D toroidal current imaging (in principle) - Possibility of synchronous imaging of sawteeth, MHD, ELMs, Er etc. q Insensitive to “broadband” polarized background contamination q Insensitive to non-statistical populations q Full Stokes polarimetry Possibility of self calibration based on unpolarized plasma radiation (Voslamber 1995) mirror/window degradation q Fringe phase shift gives 4 y where y is the polarization tilt angle. q Can be applied to spectrally complex elliptically polarized multiplets (Zeeman effect) 33

Conclusion v Doppler Coherence Imaging systems can be used to extract 2 d images

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