A Phase Contrast Imaging–Interferometer system for detection of multiscale electron density fluctuations on DIII-D E. M. Davis, J. C. Rost, M. Porkolab, A. Marinoni MIT Plasma Science & Fusion Center, Cambridge, MA 56 th APS Division of Plasma Physics New Orleans, LA, October 29, 2014 This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Fusion Energy Sciences under Award Numbers DE-FG02-94ER54235, DE-FC02-04ER54698, and DE-FC02-99ER54512 and the U.S. Department of Energy, National Nuclear Security Administration under Award Number DE-NA0002135.
Outline Motivation Phase Contrast Imaging (PCI) Fundamentals Implementation on DIII-D Response characteristics Interferometry Fundamentals Synthetic diagnostic study of low- k capabilities Low- n MHD capabilities Implementation of a combined PCI–Interferometer on DIII-D Planned layout Hardware Potential upgrades Conclusions and future work 2 / 20
Port space and vessel windows will be limited on all future devices – combining diagnostics will be necessary Phase contrast imaging (PCI) and interferometry are compatible and complementary: Parameter PCI Interferometer probe single CO 2 beam single CO 2 beam beam frequency 10 kHz < f < 2 MHz 10 kHz < f < 2 MHz bandwidth spatial 1 . 5 cm − 1 < k < 30 cm − 1 0 < k < 5 cm − 1 bandwidth ∗ All parameters for DIII-D’s currently existing PCI and under-construction interferometer 3 / 20
A combined PCI-Interferometer will allow novel turbulence and MHD investigations on DIII-D Turbulence and Transport : combined system will “fill-out” measured k -space; important for model validation 30 0 1.5 5 Core MHD : n ≤ 8 detected through cross correlation with DIII-D’s existing interferometer (∆ φ = 45 ◦ ), allowing studies of toroidal structure and influence on fast particles Proof of principle : ITER and next-step devices will certainly have an interferometer Minimal system additions may also allow PCI measurements 4 / 20
Electron density fluctuations modulate the phase of electromagnetic waves propagating through a plasma For a CO 2 laser beam ( λ 0 = 10 . 6 µ m) in a tokamak plasma, the index of refraction N is � 2 N ≈ 1 − 1 � ω pe 2 ω 0 Thus, a CO 2 beam propagating through a tokamak plasma will acquire a phase shift φ relative to vacuum φ = ω � � ( N − 1) dl = − r e λ 0 n e dl c n e , there will be a corresponding φ = ¯ φ + ˜ Further, if n e = ¯ n e + ˜ φ � ˜ φ = − r e λ 0 ˜ (1) n e dl 5 / 20
Phase Contrast Imaging (PCI) transforms “invisible” phase modulations into measurable intensity variations Plasma fluctuations scatter a portion of the incident radiation E = E 0 e i ˜ φ but do not alter the resulting intensity 2 � φ � � E 0 e i ˜ = E 2 I ∝ 0 = const � � � Delaying unscattered beam by π/ 2 with a phase plate yields intensity modulations: E ≈ E 0 (1 + i ˜ φ ) ⇒ E PCI ≈ E 0 ( i + i ˜ φ ) I PCI ∝ | E 0 | 2 (1 + 2˜ φ ) (2) 6 / 20
DIII-D’s PCI operates in any tokamak plasma and has high bandwidth, making it a model burning plasma diagnostic R+2 CO 2 laser is a compromise between high signal and low refraction Large bandwidth: R+1 Bandwidth 10 kHz < f < 2 MHz 1 . 5 cm − 1 < k R < 30 cm − 1 R − 1 Resolves k R (∆ k R ≈ 2 cm − 1 ) R − 2 Localization of high- k R measurements DIII-D PCI beampath 7 / 20
The k R of vertically line-integrated measurements is related to k θ via a spatially varying geometric factor PCI beam R+2 R+1 R − 1 R − 2 density fluctuation Only fluctuations perpendicular to beam are detected PCI’s vertical beam and imaging configuration on DIII-D measure k R k R = k θ csc [ α ( R , z )] (3) where α is angle between beam and local flux surface 8 / 20
PCI’s phase plate allows fluctuation detection for k > k min If the scattered beam falls within the phase groove (∆ < d / 2), the signal is cutoff , giving k min = k 0 d 2 f On DIII-D, an f = 80 . 7” mir- ror focuses the CO 2 beam onto a 1 mm phase groove, providing The scattered and unscat- tered beams are separated ( k R ) min = 1 . 5 cm − 1 (4) by a distance ∆ Typical parameters ( B ∼ 2 T, ∆ = kf T e ∼ 1 keV, α ∼ π/ 4) give k 0 k θ ρ s � 0 . 25 9 / 20
Low- k cutoff readily seen in experimental data from PCI L-mode H-mode [AU] [AU] 1 1 500 500 150000 150000 t = 2.00s t = 2.60s low- k cutoff low- k cutoff 400 400 300 300 10 -2 10 -2 200 200 100 100 10 -4 10 -4 0 0 -10 -5 0 5 10 -10 -5 0 5 10 10 / 20
Interferometry measures low- k fluctuations invisible to PCI The plasma leg undergoes a phase shift φ = φ ( r , t ), and the resulting electric field at the detector is E det = E R + E P e i φ with corresponding intensity Interferometer with magnifica- tion M measures fluctuations I det = E 2 R + E 2 P +2 E R E P cos φ 0 ≤ k ≤ 2 π M s With s = 1 mm and M = 0 . 08 0 ≤ k R ≤ 5 . 0 cm − 1 (5) complementing PCI’s k -range 11 / 20
Synthetic diagnostics and GYRO simulations used to model PCI and interferometer response Equilibrium Profiles cross section Gyro-predicted fluctuations PCI beam saturated period for analysis 12 / 20
Synthetic diagnostics confirm that interferometry’s low- k detection complements PCI’s high- k capabilities Synthetic S(f) Synthetic PCI S(f, k) 10 25 synthetic interferometer synthetic PCI 10 24 10 23 13 / 20
Toroidally spaced interferometers allow novel low- n mode studies; applications to fast particle transport DIII-D plan view DIII-D cross section 360° PCI beam PCI beam r e t e m o s m r e a f e r e b t n a l I c r t i e r m e t v e a m e o b r e l a f r t n e t o n z i I r o h V2 interferometer 180° beam Cross-correlating signals from toroidally spaced interferometers (∆ φ = 45 ◦ ) allows low- n toroidal mode identification n = min(8 | f τ + j | ) , j ∈ Z (6) where f is the mode frequency and τ is the time delay 14 / 20
Interferometry and PCI can be simultaneously implemented with minimal optical table changes and no port changes to vessel expansion optics phase position galvanometers plate feedback for feedback from vessel P ~ 2 W interferometer detector P ~ 0.25 W AOM electronics box interferometer legend 14 W CO2 laser plasma beam reference beam Frequency shifting reference beam with acousto-optic modulator (AOM) allows heterodyne detection Two-color detection is not required to measure fluctuations 15 / 20
Maximizing signal from imaged fluctuations requires “matching” beam radii and phase front curvatures Magnification and imaging requirements set plasma beam parameters, but reference beam can be varied to maximize signal: � � P = � S � ω 0 · d A ∼ ( w R 0 / w R ) cos( δκ ∗ ) dA A A where � 1 δκ ∗ = k 0 r 2 � − 1 2 R P R R Matching results in the following profiles near the detector 3.5 -0.10 0.20 3.0 -0.15 0.15 Plasma Reference 2.5 -0.20 0.10 -1.0 -0.5 0.0 -1.0 -0.5 0.0 -1.0 -0.5 0.0 16 / 20
Thermoelectrically-cooled detector signal-to-noise ratio ∼ 100 times larger than room temperature detectors VIGO PVM-2TE-10.6 selected as interferometer detector 2-stage thermoelectric cooling D ∗ ≥ 10 8 cm Hz 1 / 2 / W Estimated detector signal-to-noise ratio: � ˜ � 2 φ meas ∼ 10 4 SNR ≡ (7) ˜ φ noise Note : PCI’s LN 2 -cooled detector ( D ∗ = 2 × 10 10 cm Hz 1 / 2 / W) needed to detect high- f , high- k low amplitude signals 17 / 20
Analog I/Q demodulation initially planned to recover phase from heterodyne measurement bandpass filter -1.5 dB detector signal demodulator ~13 dBm noise figure ≤ 10 dB -0.6 dB fiber optic I/Q link -5.3 dB to digitizer LO signal unknown dBm RF amp +10 dB inside electronics box Demodulator noise figure ≤ 10 dB results in total system (detector-to-digitizer) signal-to-noise ratio SNR � 10 3 (8) 18 / 20
Potential upgrades identified to improve interferometer response and explore additional physics Matching reference and plasma arm optical path lengths Historically, matching increases SNR by ∼ 10 However, our laser’s large coherence length ( L c ∼ 1 km) may make matching unnecessary for our ∼ 10 m beam path k -resolved measurements via interferometer detector array Electron density gradient fluctuation measurements via differential interferometry Equilibrium and fluctuation measurements via: Two-color (e.g. CO 2 -HeNe) interferometry, or Dispersion interferometry Radially viewing PCI–interferometer for pure k θ detection 19 / 20
Conclusions PCI and interferometry are compatible and complementary reactor-relevant diagnostics that already inform compelling physics investigations on today’s devices A combined PCI–interferometer on DIII-D will allow: n e measurements (0 ≤ k R ≤ 20 cm − 1 ) Multiscale ˜ Low- n MHD studies Diagnostic proof-of-principle The combined PCI–interferometer has been designed and is currently being constructed at DIII-D Minimal changes to the existing PCI optical table allow interferometric measurements First data expected during DIII-D’s 2014 “winter” campaign Opportunities to improve system response and investigate additional physics have been identified 20 / 20
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