High Temporal Resolution Polarimetry onthe MST Reversed Field Pinch

W.X. Ding, S.D. Terry, D.L. BrowerElectrical Engineering Department

University of California, Los Angeles

J.K. Anderson, C.B. Forest, J.S. SarffPhysics Department

University of Wisconsin-Madison

The 11 channel far-infrared polarimeter on MST is beingmodified to reduce the time response from 100 to 10 µsec inorder to permit high time resolution measurement of thepoloidal magnetic field and toroidal current density profiles.Changes in the Faraday rotation profile associated with fastevents like the sawtooth crash can then be temporallyresolved. Initial polarimetry measurements indicate abroadening of the current density profile and increase in qo

after the sawtooth crash. In addition, direct measurement ofmagnetic fluctuations associated with global tearing modes[5-30 kHz] will also be possible. The effect of these modes onthe plasma density is already clearly resolved and providesinsight into the dynamics of these structures. Improved timeresponse is achieved by replacing the mechanical spindlebearing[1 kHz] which rotates the laser polarization with anadded laser beam. High speed polarization rotation isrealized by combining two circularly-polarized, orthogonalfar-infrared laser beams with intermediate frequency of 250kHz. This change will improve the system signal levels,reduce phase noise [on the interferometer and polarimeter],as well as increase time response. The phase between theprobing beams is recovered by use of a digital complexphase demodulation algorithm. System calibration and firstexperimental results will be presented.

*Supported by USDOE under grant DE-FG03-86ER-53225,Task III.

Abstract

Introduction

• MST is a toroidal reversed-field pinch [R=1.5 m,a=0.52m, Ip=200-600 kA].

• Improvement of MST energy confinement is achieved bythe current density profile control to suppress globaltearing modes.

• Measurement of current density profile by polarimetrywill play an important role in further improving MSTplasma confinement through understanding stabilityand transport.

Polarimeter Upgrade

• Replace mechanical λ/2-plate rotator with 3- λ laser

• Requires adding a 3rd FIR laser cavity• Detection scheme remains unchanged• Benefits

- polarimeter and interferometer phase noise reduced- polarimeter time response reduced from 1000 to 10 µsec, can measure

* tearing modes [5-30 kHz]* current profile changes during dynamo

- increased signal levels due to removal of ‘lossy’ mechanical rotator

3-λ Laser Technique

• 3 FIR lasers with fixed frequency offsets• Mixing products

- probe 1 with LO beam- probe 2 with LO beam- probe 1 and probe 2

• Phase difference between probe 1 and 2 is directlyproportional to the Faraday rotation angle

• Faraday rotation can also be determined from thedifference between the probe-LO mixing products

• Interferometer phase is the average of the two probe-LO mixing products

Reference Mixer

Plasma Mixer

Plasma

Combiner

Beam Splitter

L.O.Beam

Probe Beams

ω2

λ/4 Plate

λ/2 Plate

FIR LASER

ω2ω1

ω1

ω3

Lens

Lens

Polarimetry Calibration

• Beamsplitter polarization sensitive reflection andtransmission properties requires calibration

• Polarimetry calibration is done by placing a rotating halfwave plate in the probe beam path.

• Phase difference between probing beam and referencebeam is calculated by digital phase comparator (DPC)

• Calibration factors result from fitting experimental curvesfor different channels.

Polarimeter Calibration

-200

-100

0

100

200

Mea

sure

d P

hase

(de

g.)

16012080400 Quartz Rotation (deg.)

Calibration 0.51

-200

-100

0

100

200

Mea

sure

d P

hase

(de

g.)

16012080400 Quartz Rotation (deg.)

Calibration 0.16R-Ro = -32 cm

R-Ro = -2 cm

Calibration Factors

0

0.2

0.4

0.6

0.8

1

-40 -20 0 20 40

c f - 2000C

alib

rati

on

F

acto

rs

R - Ro [cm]

Mirror

Beamsplitter f=639.4 GHz (λ=0.4325mm)

Dependence of transmissivity vs. Angle of polarization.

Scheme of measurement

The instruction of the beamsplitter (BS) appliance:In order to get 50% transmittance it is necessary to install the BS-plane in the opticalpath with the angle 45° relatively the incidence beam. The 45° rotation of the BS mustbe done around the rotation axe marked out on the two opposite sides of the BS ringby two marked spots.

0 15 30 45 60 75 9045

46

47

48

49

50

51

52

53

54

55

Beamsplitter M155X165T10

vertical polarization - 900 - horizontal polarization

Tra

nsm

. %

Angle of polarization

Ev e r t

Eh o r i z 45

k

Beamsplitter DetectorSource Polarizer

Angle ofpolarization

Rotation Axe

marked spot

marked spot

Polarimetry Phase Noise

• Fast polarimetry phase noise (rms noise )depends on system signal-noise ratio (S/N)and bandwidth.

• For bandwidth 2 kHz, phase noise is lessthan 0.050 compared to 0.18 0 for slowpolarimetry

0.5

0.4

0.3

0.2

0.1

0.0

rms

nois

e (d

eg.)

20015010050 bandwidth(kHz)

n17 S/N=6.1*103

n02 S/N=5.3*103

p13 S/N=5.4*10 3

shot 39,2-sep-2000

0.5

0.4

0.3

0.2

0.1

0.0

rms

nois

e (d

eg.)

20015010050 bandwidth (kHz)

n09 S/N=6.0*103

p06 S/N=4.5*103

p21 S/N=1.7*103

shot39,2-sep-2000

Change with Dynamo: Fast Polarimeter

400300200100

0

Ip(k

A)

6040200Time(ms)

150100500

-50Vtg (V)

6

4

2

0

-2

-4

Fara

day

Rot

atio

n(de

gree

)

6040200Time (ms)

500

400

300

200

100

0

N17 N09 N02 P06 P13 P21 Vloop

Shot 63,2-sep-2000

Fluctuation of Faraday rotation is well correlated to sawteeth activity

MHD Activity Observed by Fast Polarimeter

6

4

2

0

-2

-4

Far

aday

Ro

tati

on

[d

eg.]

26.025.525.024.524.0

Time (ms)

m=1 activity before sawtooth crash

-17 cm -9 -2 6 13 21

Polarimeter Correlation with Magnetics

1.2

1.0

0.8

0.6

0.4

0.2

Coh

eren

ce

806040200Frequency [kHz]

coherence statistic noise

coherence between Faraday rotation and magnetic signal(10 ms average)

12kHz, m=1

Equilibrium ALPHA Model

• The equilibrium ∇× B=λ(r)B+(β/2B2 )B×∇ p is calculatedapproximately by choosing λ=λ0(1-rα) and adjusting theparameters to agree with the measured toroidal plasmacurrent, flux and field at the plasma surface.

• Central current density J0=λ0/µ0B0 can be deduced fromthis model (also called α-Model) .

Current Change during Dynamo fromALPHA Model and [Slow] Polarimeter

J(0) = (2/µoacp) [1/ne(0)] dΨ/dx

where cp is a constant

Ip = 430 kA Before Crash After Crash[9.3 msec] [10.3 msec]

ne(0) 1.4 (1013 cm-3) 1.2 (1013 cm-3)

dΨ/dx 0.31 (deg/cm) 0.21 (deg/cm)

J(0) : meas. 2.5 (MA/m2) 1.9 (MA/m2)

J(0) : model 2.6 (MA/m2) 1.85 (MA/m2)

When comparing before/after the sawtooth crash:

Measurement and ALPHA Model are in agreement

Faraday Rotation Change with Dynamo

-8

-6

-4

-2

0

2

4

6

8

-60 -40 -20 0 20 40 60

Signal-9.3Signal-10.3

Fara

day

Rot

atio

n [

deg.

]

R-Ro [cm]

Sawtooth Crash @ 9.7 msec

Current Profile Broadens

Comparison of Alpha Model with(Slow) Polarimeter Measurments5

4

3

2

1

0

J0 (M

A/M

^2)

1210864 Time (ms)

Data from alpha Model Experimental data

shot 100, Jan-21-1999

Fast Polarimetry

0.30

0.25

0.20

0.15

0.10

0.05

0.00

dΨ

/dx

(cm

-1)

50403020100time (ms)

4

3

2

1

0

J0 (M

A/m

^2)

slope of Faraday rotation (vs current density ) results from α model

Profile Change with Sawtooth

6

4

2

0

-2

-4Far

aday

Rot

atio

n (d

egre

e)

40200-20R-R0( cm)

t=24.4 ms before ST crash t=25.3 ms after ST crash

Decreased slope after crash implies broader current density profile anddecreased J(0)

Summary

• A high temporal resolution polarimetry system isavailable on MST. Time response of 10 µs has beendemonstrated

• Phase noise of Faraday rotation measurement is lessthan 0.1 degree with bandwidth 50 kHz.

• The dominant magnetic tearing modes in MST havebeen observed. Polarimeter correlation withmagnetics shows coherence up to 100 kHz.

• Axial current density J0 measurement is consistentwith MST α model calculation.

Future Work

• Expand present 6 channel polarimeter system to 11channels.

• Install third laser beam as a LO beam so that electrondensity can be measured simultaneously.0

• Measurement of dynamics of current density profileJ(r,t) in MST .