A combined PCI–interferometer system for …16 Davis/APS/Nov. 2016 A low-noise, thermoelectrically-cooled detector measures the 27 MHz heterodyne interferometer signal TE-cooled

A combined PCI–interferometer system formeasurement of multiscale fluctuations on DIII-D

byE. M. Davis 1, J. C. Rost 1,M. Porkolab 1, A. Marinoni 1,and M. A. Van Zeeland 2

1MIT PSFC, Cambridge, MA2General Atomics, San Diego, CA

Presented at the58th annual meeting of the

APS Division of Plasma PhysicsSan Jose, CA1 Nov. 2016

R+2

R−2

R+1

R−1

1 Davis/APS/Nov. 2016

Upgraded system is now operational and provides PCI andinterferometry measurements with single probe beam!

R+2

R−2

R+1

R−1

A single beam makesboth measurements!

Interferometer sees turbulence

10-8 10-710-9

[rad2/kHz]

80

120

40

f [k

Hz]

24

1.0 1.40.6

t [s]

13

density [1019 m-3]

ECH [MW]

Dα

[AU

]

interferometer Gϕϕ(f,t)

L-H transition

166880

. . . and MHD!BT [T]

-1.9

-1.8

Ip [MA]

1.6

1.4

1.2

neL [1020 m-2]0.5

0.7

0.9

Dα [AU]

1.2 1.6 2.0

t [s]

123

Pinj [MW]4

8

-5 -4 -3 -2 -1 0 1 2 3 4 5

n

f [k

Hz]

150

100

50

01.2 1.6 2.0

t [s]1.2 1.6 2.0

t [s]

shot 167341


OUTLINE

• Motivation: transport due to turbulence and MHD willcritically influence the viability of future fusion reactors

• Interferometric Methods− Heterodyne interferometry− Phase contrast imaging (PCI)

• DIII-D’s new combined PCI-interferometer− Implementation− Sound-wave calibration

• Plasma data− Low-k turbulence− Reversed-shear Alfven eigenmodes (RSAEs)− Core-localized MHD− Inter-ELM fluctuations

• Conclusions and future work


MOTIVATION


DIII-D’s combined PCI-Interferometer will allownovel turbulence and MHD investigations

• Turbulence and Transport: combined system will “fill-out”measured k-space; important for model validation

PCIInterferometer

|k| [cm-1]

0 1.5 5 20

• Core MHD: |n| ≤ 4 characterized through cross correlationwith DIII-D’s V2 interferometer (∆ζ = 45◦), allowing studies oftoroidal structure and influence on fast particles

• Proof of principle: minimal additions to interferometersystems on next-step devices may allow PCI measurements


Port space and vessel windows will be limited on all futuredevices – combining diagnostics will be necessary

DIII-D’s phase contrast imaging (PCI) system and its recentlyconstructed interferometer are compatible & complementary:

Parameter Interferometer PCI

probebeam single CO2 beam single CO2 beam

frequencybandwidth 10 kHz < f < 5 MHz 10 kHz < f < 5 MHz

spatialbandwidth 0 ≤ k < 5 cm−1 1.5 cm−1 < k ≤ 20 cm−1

measuredsensitivity 1× 1015 m-2/

√kHz 1× 1014 m-2/

√kHz


INTERFEROMETRIC METHODS


Electron density fluctuations modulate the phase ofelectromagnetic waves propagating through a plasma

For a CO2 laser beam (λ0 = 10.6 µm) in a tokamak plasma, theindex of refraction N is

N ≈ 1− 12

(ωpe

ω0

)2

Thus, a CO2 beam propagating through a tokamak plasma willacquire 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)


Interferometric methods convert “invisible” phase delaysinto measurable intensity variations

While the plasma imparts phase delay φ to incident radiation

E = E0eiφ

it does not alter the beam’s resulting intensity

I ∝∣∣∣E0eiφ

∣∣∣2 = E20 = const

Interfering exiting radiation with reference radiation EReiφR

Etot = EReiφR + E0eiφ

we obtain measurable intensity modulations

I ∝ E2R + E2

0 + 2ERE0 cos (φ− φR) (2)


Heterodyne interferometry uses a frequency-shiftedexternal reference beam to measure absolute phase

source frequencyshifter

ω0 ω0

ω0 + ωLO

plasmane(r, t)

combiner

ω0

ω0 + ωLO

and

detector

V(t) ∝ cos(ωLOt - ϕ)

Demodulation against ωLO yields the in-phase (I) andquadrature (Q) signals

I = V0 cos(φ) Q = V0 sin(φ)

allowing determination of absolute phase via

φ = tan−1(

QI

)(3)


An imaging system’s magnification determinesits maximum detectable wavenumber

Imaging a beam on asquare detector of sidelength s gives an amplituderesponse

R(k) ∝ sinc(

kkmax

)where

kmax =2πM

s= 5 cm−1 (4)

and M = 0.08 is the interfer-ometer’s magnification.


Phase Contrast Imaging (PCI) uses a spatially-filteredinternal reference beam to measure phase fluctuations

Upon exiting the plasma, the probing radiation can bedecomposed into scattered and unscattered components

E = E0eiφ = E0ei(φ+φ) ≈ E0eiφ(1 + iφ)

Delaying unscattered beamby π/2 with a phase plateand imaging on detector arrayyields intensity modulations

EPCI ≈ E0eiφ(i + iφ)

IPCI ∝ |E0|2(1 + 2φ) (5)


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

The scattered andunscattered beams areseparated by distance ∆

∆ =kFk0

after focusing via opticwith focal length F

If the scattered beam falls withinthe phase groove (∆ < d/2), thesignal is cutoff, giving

kmin =k0d2F

= 1.5 cm−1 (6)

0.5 1.0 1.5 2.0 2.5 3.00.0

0.2

0.4

0.6

0.8

1.0

Resp

onse

, ℛ

(k)

k / kmin


IMPLEMENTATION and CALIBRATION of acombined PCI-Interferometer on DIII-D


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

R+2

R−2

R+1

R−1

DIII-D PCI beampath

• CO2 laser provides high signaland low refraction

• Large bandwidth:

Bandwidth

10 kHz < f < 5 MHz

1.5 cm−1 < kR < 20 cm−1

• 32-element, LN2-cooled HgCdTedetector array resolves kR

• Localization of high-kRmeasurements


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

to vessel(~10 W)

electronics box

from vessel(~2 W)

14 W CO2 laser

AOM

phaseplate

steeringmirrors

λ/2

interferometerdetector (~500 mW)

interferometer reference arm interferometer plasma arm

PCIshared probe beam feedback beam

expansionlens

para

bolic

mir

rors

PCI detector(~200 mW)

Key:

Two-color detection is not required to measure fluctuations


A low-noise, thermoelectrically-cooled detector measuresthe 27 MHz heterodyne interferometer signal

TE-cooled detectorand preamp

• Single 1 mm× 1 mm photovoltaicHgCdTe detector element

• 2-stage thermoelectric cooling• D∗ ≈ 5× 107 Jones• 50 MHz bandwidth• Estimated detector SNR:

SNR ≡

(φmeas

φnoise

)2

∼ 500 (7)

Note: The PCI signal’s homodyne signal (. 1 MHz) allows use of aslower, lower-noise LN2-cooled detector (D∗ = 2× 1010 Jones)


Analog I/Q demodulation recovers phase φ(t) fromheterodyne measurement

to digitizer

Q(t) ∝ sin[ϕ(t)]

I(t) ∝ cos[ϕ(t)]

I&Q demodulatornoise figure ≤ 10 dB

automatic gaincontrol amplifier

+10 dBm

-4 dBm

coax to annex

bandpassfilter

low-passfilter

localoscillator

detector

+30 dB

isolationtransformer

• Phase computed as

φ(t) = tan−1 [Q(t)/I(t)] (8)

• Demodulator noise figure results in total-system(detector-to-digitizer) signal-to-noise ratio SNR ≥ 50


The local oscillator (LO) frequency is coupled to the laservia a Germanium AOM on sound-speed timescales

Piezo-actuator

Gecs

ωLO

LO to annex(coax)

ω0

ω0

ω0+ωLO

d

• Sound waves propagate from the driving piezo to theinteraction region in time

τ =dcs

(9)

• In Germanium, cs = 5500 m/s� c


LO-frequency drift can produce phase noise and was foundto be the dominant source of noise in our system

For LO-coupling delay τ

VLO(t) = V0 cos {[ωLO(t)] t}Vdet(t) = V0 cos {[ωLO(t − τ)] t − φ(t)}

Demodulating the detected heterodyne signal against the LOsignal then introduces phase noise into the measured phase

φmeas(t) = φ(t) +

(dωLO

dt

)τ

The phase noise can be minimized by:• Delaying LO signal by time τ (e.g. longer cable run)• Improving LO stability• Generating LO signal optically


Delaying the LO signal compensates for frequency drift anddramatically reduces phase noise• Fast measurements suggest:

− τ ≈ 2.5 µs− LO stability > 10× worse than spec’d

• Sending the LO signal through an additional ∼ 500 m of coaximparts 2.5 µs delay relative to Vdet

nois

e f

loor

[rad

2 /

Hz]

f [Hz]104 105 106

10-11

10-10

10-9

LO not delayedLO delayed by 500 m of coax

interferometer S(f) with no plasma


The system response can be empirically characterizedby shooting sound waves through the beam path

• Using sound wave dispersion relation cs = 2πf/k ≈ 343 m/s,we can determine k from an imposed frequency f

• Sound wave amplitude and spatial structure measured witha calibrated microphone


Tests with a broadband ultrasonic speaker confirm thatinterferometer cutoff is in agreement with expectations

30

20

10

f [k

Hz]

1062t [s]

10-810-9

[rad2 / kHz]

5 cm-1

• Ultrasonic speaker has fmin = 10 kHz• Interferometer detects soundwaves at

f = 25 kHz⇔ kmax = 4.6 cm−1 (10)


The interferometer’s measured response is inquantitative agreement with expectations

measured responsemeasured noiseexpected response

1 2 3k [cm-1]

10-10

10-8

10-6

Resp

onse

[ra

d2]

• This particular loudspeaker has fmax ∼ 18 kHz (3.25 cm−1)

• Increased noise floor below 1 cm−1 is attributable tolow-frequency (f < 5 kHz) vibrations in machine hall


EXAMPLE CAPABILITIES


Interferometer sees turbulence suppressionacross L-H transition

10-8 10-710-9

[rad2/kHz]

80

120

40

f [k

Hz]

24

1.0 1.40.6

t [s]

13

density [1019 m-3]

ECH [MW]

Dα

[AU

]

interferometer Gϕϕ(f,t)

L-H transition

166880


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

DIII-D plan view 360°

180°

Interfero

meter

vertica

l beams

Interfe

romet

er

horiz

ontal b

eam

PCI beam

Δζ = 45°

DIII-D cross section

PCI beam

V2 interferometerbeam

Cross-correlating signals from toroidally spaced interferometers(∆ζ = 45◦) allows |n| ≤ 4 toroidal mode identification


Toroidally correlated interferometers displayexcellent agreement with magnetic measurements

BT [T]-1.9

-1.8

Ip [MA]

1.6

1.4

1.2

neL [1020 m-2]0.5

0.7

0.9

Dα [AU]

1.2 1.6 2.0

t [s]

123

Pinj [MW]4

8

-5 -4 -3 -2 -1 0 1 2 3 4 5

n

f [k

Hz]

150

100

50

01.2 1.6 2.0

t [s]1.2 1.6 2.0

t [s]

shot 167341


The correlated interferometers measure mode numbersof reversed-shear Alfven eigenmodes (RSAEs)

3 2 1 0 1 2 3 4

n10-14 10-13 10-12 10-11 10-10

|Gxy(f )|

150

100

50

f [k

Hz]

0.4 0.6 0.8

t [s]

0.4 0.6 0.8

t [s]

magnitude mode number

0.4 0.6 0.8t [s]

q0

2

4

Pinj [MW]

13

neL [1020 m-2]

0.1

0.2

Ip [MA]0.5

1.0

BT [T]-1.9

-2.1

shot 167550


Correlated interferometers measure core-localizedfluctuations that are invisible to magnetics

200

100f [k

Hz]

10-2

10-6

Gxx(f)

fast magnetics

10

8

6

4

2

0

n

1.2 1.6 2.0

t [s]

1.51.3

Ip [MA]

0.8

0.4

neL [1020 m-2]

Pinj [MW]8

4

1.0q00.7

Dα [AU]

1

3

1.8

1.4

βN

1.2 1.6 2.0

t [s]

-1.8

-1.9BT [T] shot 167342

100

50

f [k

Hz]

200

100f [k

Hz]

• Polarimeter corroborates fluctuations are core-localized• Core-localized fluctuations triggered when q0 < 1


Correlated interferometers shed light on torodial structureand dynamics of high-bandwidth inter-ELM fluctuations

4

2

Dα [

AU

]

2.55 2.65

t [s]

400

500

f [k

Hz]

10-8

10-6

Gxx(f)

fast magnetics (b1)

400

500

f [k

Hz]

-3

-2

-1

0

1

2

3

4

n


CONCLUSIONS and FUTURE WORK

• PCI and interferometry are compatible and complementaryreactor-relevant diagnostics that already yield compellingphysics results on today’s devices

• A combined PCI–interferometer has been built at DIII-D− Small changes to the pre-existing PCI optical table have

allowed heterodyne interferometric measurements− Cross-calibration sound wave measurements have confirmed

the system’s multiscale capabilities• DIII-D’s combined PCI–interferometer provides:

− Multiscale ne measurements (0 ≤ kR ≤ 20 cm−1)− Low-n, core MHD measurements; not possible via magnetics− Diagnostic proof-of-principle

• The new measurement capabilities will be thoroughlyexploited in coming campaign


ACKNOWLEDGMENTS

This material is based upon work supported by the U.S.Department of Energy, Office of Science, Office of Fusion EnergySciences under Award Numbers:• DE-FG02-94ER54235• DE-FC02-04ER54698• DE-FC02-99ER54512

The authors would also like to thank:• Dr. David Pace for allowing use of his 200 MS/s digitizer• Dr. Daniel Finkenthal for sharing his RF expertise• General Atomics and the DIII-D team for their support


Documents

A combined PCI–interferometer system for …16 Davis/APS/Nov. 2016 A low-noise, thermoelectrically-cooled detector measures the 27 MHz heterodyne interferometer signal TE-cooled