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.
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-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
Faraday Rotation Fluctuation m=1 activity, fluctuating amplitude.1-. degree in phase between x=- and 13 Faraday (deg.) - - cm 6 13 14. 14.5 15. time(ms) 15.5 16. 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 6 36 14. 14.5 15. time(ms) 15.5 16.
Fast Polarimeter Correlation with Magnetic Coil 1. Faraday rotation -Magnetic fluctuation at wall coherence.8 Coherence.6.4 1kHz, m=1 coherence statistical noise.. 4 6 8 1 Frequency [khz]
Central Chord Density Fluctuations P6 interferometer chord.x1-3 density fluctuation amplitude 1.5 1..5 average over 1-ms for density s113844 - PPCD s1133115 - STND no m=1 peak. 4 6 frequency (khz) 8 1
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
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;
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.
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
Comparison of J() Estimate with α Model J (MA/m^) 3..5. 1.5 1..5. j From Faraday Rotation measurement j ( α model ) ( β=7%) j ( α model ) ( β=1%) - -1 1 Time (ms) J( ) = dψ 1 µ c dx n () r f(, r β) dz F e
Current Density Fluctuations 5 4 J = 5% J J (MA/m ) 3 ~ J J 5% 1 6 8 1 1 14 Time (ms) s113336 j_sdev=.1568 (1-15 ms) J_avg=.93147 J_sdev/J_avg=5% 16 18
Time Evolution of Faraday Rotation Angle F =-., I p = 4 ka, 11 channel data, 113336 Faraday Rotation (deg.) 4-4 4 s113336 6-3 cm -17-13 8 43 8 Time (ms) Faraday Rotation (deg.) 4-4 4 6-4 cm -9 6 1 36 8 Time (ms)
Time Evolution of Electron Density F =-., I p = 387 ka, 11 channel data,1133115 (1 13 cm - ) 1.6 1. ne1 ne ne3 ne4 ne5 ne6 nedl.8.4. 1 3 4 Time (ms) 5 6 7 (1 13 cm - ) 1.6 1. ne7 ne8 ne9 ne1 ne11 nedl.8.4. 1 3 4 Time (ms) 5 6 7
Magnetic Fluctuation B r Amplitude and Comparison with MHD code Measured Faraday rotation fluctuation o =.1, 19 3 n = 1. 1 1 m, L = 1. 4m, c = 4. 88 1 ( m / T) Line average B r = 33G F Ψ 1 Density (1^19/m^3) 1..8.4. Density before ST (t=-.75ms)..4.6.8 r/a 1. Br(m=1,n=6)/B x1-3 15 1 5.. br_m=1,n=6 from DEBS code c F n e B r dz=. degree Faraday fluctuation.1-. degree.4 r/a.6.8 1.
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 8 1 4-4 n coherence.6.4. coherence between x=6 and 13 cm 11333(STD) -3ms coherence noise. 4 6 f(khz) 8 1 Coherence 1..8.6.4. coherence between x=-4 and 36 cm m= m=1 coherence phase 1 phase( π). 4 6 f(khz) 8 1-1
B r Wavenumber Spectrum <Br> (G/Hz 1/ ) 1 8 4 Frequency Spectrum 4 6 Frequency(kHz) 8 1 <Br> (G) 1 1 6 4 Wavenumber Spectrum m=1 (shot 11333, F=-.) - B r ~ n -.86 4 Toroidal Mode Number 6 8
Magnetic Fluctuation change during Sawtooth Cycle B r (arb).8.6.4. ~ B r rms ~ r B B 1%. - -1 1 time (ms) Amplitude approximately 1% before crash Fluctuations increase at crash by x3
Current Density and Magnetic Fluctuations fluctuation amplitude (arb.) 4x1-3 3 1 J() and B r fluctuation spectrum (FFT) s113336 (F<) J ~ ~ B r 4 6 frequency (khz) 8 J B r 1
Quasi Single Helicity in PPCD frequency (khz) 1 8 6 4 QSH Spectrum STND X = 6 cm frequency (khz) 1 8 6 4 1 15 18 1 4 time (ms)..4.6.8 1. S137_CH6 (6 cm) PPCD X = 36 cm 1 15 18 1 4 time (ms)..4.6.8 1. S137_CH1 (36 cm)
Fast Polarimetry during PPCD I p =4kA, 11 channel data Faraday Rotation (deg.) 4-4 1 3 4 5 6-3 cm -17-13 8 43 7 Time (ms) Faraday Rotation (deg.) 4-4 1 3 1136159 4 5 6-4 cm -19 6 1 36 7 Time (ms)
Sawteeth Ensembled Density Dataset n e dl [x1 15 cm - ] n e dl [x1 15 cm - ] 1..8.6.4.. 1..8.6.4.. -3 cm -17-13 8 43 - -1 1 Time [msec] -4 cm -9 6 1 36 - -1 1 Time [msec]
Ensembled Faraday Dataset Faraday Rot. (deg.) 4 - -4-1 ms + 1m -4-4 R-R (cm) Faraday Rot. (deg.) 4-4 -17 cm -3 cm - cm 13 cm 43 cm 8 cm -3 - -1 1 3 time (ms) Faraday Rot. (deg.) 4-4 -4 cm -9 cm 6cm 36 cm 1 cm -3 - -1 1 3 Time (ms)
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.).4.3..1. 4 f(khz) 6 8 1 phase (degree) 4 3 1 11113336 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
Faraday Rotation (rms_deg. ) Density_fluc (rms ).5.4.3..1..1.1.8.6.4. 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 (1133115) PPCD (113844) 1. 4 6 8 1 Frequency( khz)
Br fluctuations vs time Faraday Rotation( deg_rms).6.5.4.3..1 Standard 4kA (113336) PPCD 4kA (1136159) std_noise ppcd_noise 5 1 15 time(ms) 5
Magnetic Fluctuation B r Spectrum 14x1-3 1 1 F< shot (113336) PPCD shot (1136159) F< shot (113336 w/o sawtooth,16-3ms) Average over 1ms --ms s1136159 Power 8 6 4 4 6 Frequency (khz) 8 1 Frequency (khz) 1 75 5 5 standard PPCD 1 15 5 Time (ms)
Faraday Rotation (rms_deg. ) Density_fluc (rms ).5.4.3..1..1.1.8.6.4. 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 (1133115) PPCD (113844) 1. 4 6 8 1 Frequency( khz)
Magnetic Fluctuation Spectra Frequency(kHz) Frequency(kHz) 1 75 5 5 1 75 5 5 Standard 4kA 1 15 time(ms) PPCD 4kA 1.. 3. S36 WL_6 51_CH6_x 1 15 time (ms) 1.. 3. 4. amplitude
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%
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