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1 Abstract Internal magnetic field fluctuations and equilibrium poloidal magnetic field have been measured in the MST reversal field pinch by a 11 chord far-infrared polarimeterinterferometer system with frequency response up to 1 MHz. Fast time resolution and low phase noise of the polarimeter enable us to resolve m=1 resistive tearing modes as a precursor to the sawtooth crash. Turbulent magnetic field fluctuations up to 1 khz have also been observed. The chord-averaged radial magnetic field fluctuation level is about 33 G or 1%. A broad power spectrum peaks at 1- khz and is dominated by m=1 magnetic field fluctuations. By computing the coherence between two toroidally-displaced chords, one can determine the toroidal mode number and rotation speed. The phase of radial magnetic field fluctuations lags poloidal magnetic field fluctuations by 9 degrees which is in agreement with MHD computation for MST. Magnetic field fluctuations are reduced by a factor of four during a high confinement PPCD discharges, consistent with energy confinement improvement.

2 Polarimetry Technique Two counter-rotating circularly polarized FIR beams are launched into plasma. The phase difference between two beams is proportional to Faraday rotation angle. 3 λ e 13 Ψ= ψ = nb = 6 1 λ 3 e // dz. nb e // dz 8π c ε m e Faraday rotation angle is proportional to the product of electron density and magnetic field along the beam direction. Interferometer gives electron density by measuring the average phase of two probe-lo mixing products.

3 3-Wave Laser Polarimetry λ/ Plate Reference Mixer Lens ω Probe Beams Plasma Mixer ω 1 ω Combiner ω 1 λ/4 Plate Plasma Lens ω 3 L.O.Beam Beam Splitter FIR LASER

4 Faraday Rotation Fluctuation m=1 activity, fluctuating amplitude.1-. degree in phase between x=- and 13 Faraday (deg.) - - cm time(ms) out of phase between central chord and edge chords in phase between two edge chords (x=-4,36) 6 Faraday (deg.) 4 - ~ Brms o = 33 G [. 1 ] -4 cm time(ms)

5 Fast Polarimeter Correlation with Magnetic Coil 1. Faraday rotation -Magnetic fluctuation at wall coherence.8 Coherence.6.4 1kHz, m=1 coherence statistical noise Frequency [khz]

6 Central Chord Density Fluctuations P6 interferometer chord.x1-3 density fluctuation amplitude average over 1-ms for density s PPCD s STND no m=1 peak. 4 6 frequency (khz) 8 1

7 Magnetic Fluctuation Signal Analysis Faraday Rotation Ψ(,) xt = c nrtb (,) (, rxtdz,) F linearize the equation using z Z B θ B r Ψ(x,t) = Ψ ( x) + Ψ 1 ( x, t ) nrt (,) = n() r + n (,) rt 1 r θ B(, rxt,) = B (, rxt,) + B (, rxt,) Ψ Ψ z z z1 = c n B dz, F z [ ] = c n B dz+ B n dz 1 F 1 z z1 X x B = B θ = B x π B = µ J πr r, z θ cos θ, r θ ( ), c n B dz = 5. c µ J( ) x ndz. F 1 zo F 1 ( 6 17 J( ) =. 1 A/ m, ndz 1 = 1 m ) o at x = 7 cm For m = 1 mode, ndz. For central chords, cosθ,sinθ 1, we have 1 ( ) = Ψ c[ B ndz] = c B sin θ + B cos θ ndz c B (,) rtn () rdz 1 F z1 F r θ F r

8 For these edge chords, B B x µ Id x z = θ = r π r µ I c n B dz n x d r dz µ I 9 d x n r dz F 1 z = 1 9 min( ξ) =. π π 17 3 ( I = 4kA, n = 1 m, 9 ξ 9) d min at x = 43 cm o The measured fluctuation amplitude for edge chords are about.. It means that density fluctuation contributes the most of Faraday rotation fluctuation signals in edge chords. o Fast polarimetry measures magnetic fluctuation in central chords. A line averaged magnetic fluctuation amplitude can be obtained. Fast polarimetry measures density fluctuation in edge chords with better phase resolution; Toroidal mode number can be determined by the correlation between two toroidally displaced two chords;

9 Fluctuation Signals Analysis Radial Magnetic fluctuations dominate Faraday rotation fluctuations in central chords (x=-,6,13 cm) because density fluctuations are small and probing beam is nearly perpendicular to equilibrium field. Density fluctuations dominate Faraday rotation fluctuations for edge chords (x=-3,-4,36,43 cm) where density fluctuations are large due to advection.

10 J() measurement Cylindrical- Slope Model z o r θ x B θ Ψ() x = c n () r B ()cos r θdz, F e x = rcos θ = R R, z = rsin θ, θ Ψ dψ x, r, Bθ π r = µ J( r) πr, = x dx () Ψ c n B r θ = F e xdz = 5. cfµ J( ) x ne( r) f ( r) dz r where Jr ( ) = J f( r) and assuming f( r) = ( 1 ( r/ a) ) I = J() r ds = J() πr f(, r β) dris total discharge current.. d β J( ) = dψ 1 µ c dx n () r f(, r β) dz F e

11 Comparison of J() Estimate with α Model J (MA/m^) j From Faraday Rotation measurement j ( α model ) ( β=7%) j ( α model ) ( β=1%) Time (ms) J( ) = dψ 1 µ c dx n () r f(, r β) dz F e

12 Current Density Fluctuations 5 4 J = 5% J J (MA/m ) 3 ~ J J 5% Time (ms) s j_sdev=.1568 (1-15 ms) J_avg= J_sdev/J_avg=5% 16 18

13 Time Evolution of Faraday Rotation Angle F =-., I p = 4 ka, 11 channel data, Faraday Rotation (deg.) s cm Time (ms) Faraday Rotation (deg.) cm Time (ms)

14 Time Evolution of Electron Density F =-., I p = 387 ka, 11 channel data, (1 13 cm - ) ne1 ne ne3 ne4 ne5 ne6 nedl Time (ms) (1 13 cm - ) ne7 ne8 ne9 ne1 ne11 nedl Time (ms) 5 6 7

15 Magnetic Fluctuation B r Amplitude and Comparison with MHD code Measured Faraday rotation fluctuation o =.1, 19 3 n = m, L = 1. 4m, c = ( m / T) Line average B r = 33G F Ψ 1 Density (1^19/m^3) Density before ST (t=-.75ms) r/a 1. Br(m=1,n=6)/B x br_m=1,n=6 from DEBS code c F n e B r dz=. degree Faraday fluctuation.1-. degree.4 r/a

16 Spatial Correlation of Magnetic Fluctuation B r 4 Phase between x= 6 cm and 13 cm 8 Phase(degree) - m= m=1 4 6 f(khz) phase n n coherence.6.4. coherence between x=6 and 13 cm 11333(STD) -3ms coherence noise. 4 6 f(khz) 8 1 Coherence coherence between x=-4 and 36 cm m= m=1 coherence phase 1 phase( π). 4 6 f(khz) 8 1-1

17 B r Wavenumber Spectrum <Br> (G/Hz 1/ ) Frequency Spectrum 4 6 Frequency(kHz) 8 1 <Br> (G) Wavenumber Spectrum m=1 (shot 11333, F=-.) - B r ~ n Toroidal Mode Number 6 8

18 Magnetic Fluctuation change during Sawtooth Cycle B r (arb) ~ B r rms ~ r B B 1% time (ms) Amplitude approximately 1% before crash Fluctuations increase at crash by x3

19 Current Density and Magnetic Fluctuations fluctuation amplitude (arb.) 4x J() and B r fluctuation spectrum (FFT) s (F<) J ~ ~ B r 4 6 frequency (khz) 8 J B r 1

20 Quasi Single Helicity in PPCD frequency (khz) QSH Spectrum STND X = 6 cm frequency (khz) time (ms) S137_CH6 (6 cm) PPCD X = 36 cm time (ms) S137_CH1 (36 cm)

21 Fast Polarimetry during PPCD I p =4kA, 11 channel data Faraday Rotation (deg.) cm Time (ms) Faraday Rotation (deg.) cm Time (ms)

22 Sawteeth Ensembled Density Dataset n e dl [x1 15 cm - ] n e dl [x1 15 cm - ] cm Time [msec] -4 cm Time [msec]

23 Ensembled Faraday Dataset Faraday Rot. (deg.) ms + 1m -4-4 R-R (cm) Faraday Rot. (deg.) cm -3 cm - cm 13 cm 43 cm 8 cm time (ms) Faraday Rot. (deg.) cm -9 cm 6cm 36 cm 1 cm Time (ms)

24 Magnetic Fluctuation B r Phase B r lags B θ 9 degree 1 pn, = 6 1 pn, = 6 Ψ Ψ = B B.5 Faraday Rot. (deg.) f(khz) phase (degree) Phase between Br and Bp(n=6) at wall, Phase(Br)-Phase(Bp)=phase-1.6=-9 degree f=khz 4 f(kh) 6 8 1

25 Faraday Rotation (rms_deg. ) Density_fluc (rms ) Magnetic Fluctuation Reduction during PPCD Magnetic field fluctuation (x=6 cm) Standard (113336) PPCD (113511) 4 6 Frequency (khz) Density fluctuation (x=6 cm) 8 Standard ( ) PPCD (113844) Frequency( khz)

26 Br fluctuations vs time Faraday Rotation( deg_rms) Standard 4kA (113336) PPCD 4kA ( ) std_noise ppcd_noise time(ms) 5

27 Magnetic Fluctuation B r Spectrum 14x F< shot (113336) PPCD shot ( ) F< shot ( w/o sawtooth,16-3ms) Average over 1ms --ms s Power Frequency (khz) 8 1 Frequency (khz) standard PPCD Time (ms)

28 Faraday Rotation (rms_deg. ) Density_fluc (rms ) Magnetic Fluctuation Reduction during PPCD Magnetic field fluctuation (x=6 cm) Standard (113336) PPCD (113511) 4 6 Frequency (khz) Density fluctuation (x=6 cm) 8 Standard ( ) PPCD (113844) Frequency( khz)

29 Magnetic Fluctuation Spectra Frequency(kHz) Frequency(kHz) Standard 4kA 1 15 time(ms) PPCD 4kA S36 WL_6 51_CH6_x 1 15 time (ms) amplitude

30 Summary Fast-polarimeter has 4 µs time response and.5 o phase resolution. Internal radial magnetic field fluctuations are measured. ~ Br ~ = 1% Br = 33 G, rms B Internal magnetic field fluctuations are significantly reduced during a high confinement PPCD plasmas. ~ B r 75%

31 Future Work Measurement of dynamics of current density profile J(r,t) in MST with Sawteeth, PPCD, OFCD, pellets, etc. MHD stability studies: B ~ Jrt (, ) B Extract information from all chords Core transport nb, r J Br Core dynamo studies: ~ ~ ~ θ r v B ~ ~ φ r v B toroidal electric field poloidal electric field

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