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A Phase Contrast ImagingInterferometer 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

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SLIDE 1

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

56th 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.

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SLIDE 2

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

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SLIDE 3

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 beam single CO2 beam single CO2 beam frequency bandwidth 10 kHz < f < 2 MHz 10 kHz < f < 2 MHz spatial bandwidth 1.5 cm−1 < k < 30 cm−1 0 < k < 5 cm−1

∗All parameters for DIII-D’s currently existing PCI and

under-construction interferometer

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SLIDE 4

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

1.5 5 30

Core MHD: n ≤ 8 detected through cross correlation with DIII-D’s existing interferometer (∆φ = 45◦), allowing studies

  • f 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

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SLIDE 5

Electron density fluctuations modulate the phase of electromagnetic waves propagating through a plasma

For a CO2 laser beam (λ0 = 10.6 µm) in a tokamak plasma, the index of refraction N is N ≈ 1 − 1 2 ωpe ω0 2 Thus, a CO2 beam propagating through a tokamak plasma will acquire a phase shift φ relative to vacuum φ = ω c

  • (N − 1)dl = −reλ0
  • nedl

Further, if ne = ¯ ne + ˜ ne, there will be a corresponding φ = ¯ φ + ˜ φ ˜ φ = −reλ0

  • ˜

nedl (1)

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SLIDE 6

Phase Contrast Imaging (PCI) transforms “invisible” phase modulations into measurable intensity variations

Plasma fluctuations scatter a portion of the incident radiation E = E0ei ˜

φ

but do not alter the resulting intensity I ∝

  • E0ei ˜

φ

  • 2

= E 2

0 = const

Delaying unscattered beam by π/2 with a phase plate yields intensity modulations: E ≈ E0(1 + i ˜ φ) ⇒ EPCI ≈ E0(i + i ˜ φ) IPCI ∝ |E0|2(1 + 2˜ φ) (2)

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SLIDE 7

DIII-D’s PCI operates in any tokamak plasma and has high bandwidth, making it a model burning plasma diagnostic

R+2 R−2 R+1 R−1

DIII-D PCI beampath

CO2 laser is a compromise between high signal and low refraction Large bandwidth: Bandwidth 10 kHz < f < 2 MHz 1.5 cm−1 < kR < 30 cm−1 Resolves kR (∆kR ≈ 2 cm−1) Localization of high-kR measurements

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SLIDE 8

The kR of vertically line-integrated measurements is related to kθ via a spatially varying geometric factor

PCI beam density fluctuation

R+2 R− 2 R+1 R− 1

Only fluctuations perpendicular to beam are detected PCI’s vertical beam and imaging configuration on DIII-D measure kR kR = kθ csc [α(R, z)] (3) where α is angle between beam and local flux surface

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PCI’s phase plate allows fluctuation detection for k > kmin

The scattered and unscat- tered beams are separated by a distance ∆ ∆ = kf k0 If the scattered beam falls within the phase groove (∆ < d/2), the signal is cutoff, giving kmin = k0d 2f On DIII-D, an f = 80.7” mir- ror focuses the CO2 beam onto a 1 mm phase groove, providing (kR)min = 1.5 cm−1 (4) Typical parameters (B ∼ 2 T, Te ∼ 1 keV, α ∼ π/4) give kθρs 0.25

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Low-k cutoff readily seen in experimental data from PCI

  • 10
  • 5

5 10 100 200 300 400 500

L-mode

low-k cutoff

150000 t = 2.00s

10-2 1 10-4

[AU]

10-2 1 10-4

[AU]

  • 10
  • 5

5 10 100 200 300 400 500

H-mode

low-k cutoff

150000 t = 2.60s

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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 Edet = ER + EPeiφ with corresponding intensity Idet = E 2

R +E 2 P +2EREP cos φ

Interferometer with magnifica- tion M measures fluctuations 0 ≤ k ≤ 2πM s With s = 1 mm and M = 0.08 0 ≤ kR ≤ 5.0 cm−1 (5) complementing PCI’s k-range

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SLIDE 12

Synthetic diagnostics and GYRO simulations used to model PCI and interferometer response

Equilibrium Profiles

Gyro-predicted fluctuations

saturated period for analysis

cross section

PCI beam

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SLIDE 13

Synthetic diagnostics confirm that interferometry’s low-k detection complements PCI’s high-k capabilities

synthetic interferometer synthetic PCI

Synthetic S(f) Synthetic PCI S(f, k)

1023 1024 1025

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Toroidally spaced interferometers allow novel low-n mode studies; applications to fast particle transport

DIII-D plan view 360° 180°

I n t e r f e r

  • m

e t e r v e r t i c a l b e a m s I n t e r f e r

  • m

e t e r h

  • r

i z

  • n

t a l b e a m PCI beam

DIII-D cross section

PCI beam V2 interferometer 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

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Interferometry and PCI can be simultaneously implemented with minimal optical table changes and no port changes

14 W CO2 laser to vessel electronics box from vessel P ~ 2 W

AOM

expansion optics phase plate interferometer detector P ~ 0.25 W galvanometers for feedback position feedback plasma beam reference beam interferometer legend

Frequency shifting reference beam with acousto-optic modulator (AOM) allows heterodyne detection Two-color detection is not required to measure fluctuations

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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 =

  • A

Sω0 · dA ∼

  • A

(wR0/wR) cos(δκ∗) dA where δκ∗ = k0r2 2 1 RP − 1 RR

  • Matching results in the following profiles near the detector

Plasma Reference

3.5 3.0 2.5 0.0

  • 0.5
  • 1.0

0.0

  • 0.5
  • 1.0
  • 0.10
  • 0.15
  • 0.20

0.0

  • 0.5
  • 1.0

0.20 0.15 0.10

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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∗ ≥ 108 cm Hz1/2 / W Estimated detector signal-to-noise ratio: SNR ≡ ˜ φmeas ˜ φnoise 2 ∼ 104 (7) Note: PCI’s LN2-cooled detector (D∗ = 2 × 1010 cm Hz1/2 / W) needed to detect high-f , high-k low amplitude signals

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SLIDE 18

Analog I/Q demodulation initially planned to recover phase from heterodyne measurement

detector signal ~13 dBm LO signal unknown dBm RF amp +10 dB bandpass filter

  • 1.5 dB

I/Q

  • 5.3 dB
  • 0.6 dB

inside electronics box fiber

  • ptic

link to digitizer demodulator noise figure ≤ 10 dB

Demodulator noise figure ≤ 10 dB results in total system (detector-to-digitizer) signal-to-noise ratio SNR 103 (8)

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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 (Lc ∼ 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. CO2-HeNe) interferometry, or Dispersion interferometry

Radially viewing PCI–interferometer for pure kθ detection

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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:

Multiscale ˜ ne measurements (0 ≤ kR ≤ 20 cm−1) 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

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