Faraday Effect Measurement of Internal Magnetic Field and Fluctuations in C-MOD William F. Bergerson 1 Coauthors: P. Xu 2, J. H. Irby 2, D. L. Brower 1, W. X. Ding 1, E. S. Marmar 2 1 University of California Los Angeles, Los Angeles, CA, USA 2 Massachusetts Institute of Technology, Cambridge, MA, USA HTPD Monterey, May 2012
Motivation Magnetically confined fusion devices require detailed time-resolved measurement of J(r) and B(r): J B = P Measurements of δβ and δj associated with instabilities (MHD, fast-particle modes, turbulence, disruptions) are critical to understanding transport Goal for C-Mod: pursue polarimeter development for both magnetic equilibrium and fluctuation measurements ITER q(r) diagnostic - C-Mod has ITER-like (B, n e ), polarimetry geometry (doublepass) and wavelength (118 µm) 2
Outline (1) Measurement principle - Faraday effect ( ) - Cotton-Mouton effect ( ) (2) Key factors for Faraday rotation measurements on high field tokamak - Polarization distortion by optical components - Phase noise (vibrations, stray db/dt, feedback, electronic) - Misalignment to toroidal field (3) Faraday effect measurements - Equilibrium - Fluctuations (4) Future Plans B k B k B k 3
Faraday Rotation Polarization rotation due to parallel magnetic field ( B k ) Linearly Polarized EM wave E k E ψ F n e Plasma B z ψ F = 2.62 10 13 λ 2 n e B z dz amplitude measurement Faraday phase shifts are in the 0-30 degree range in C-Mod (118 µm) 4
Faraday Rotation Polarization rotation due to parallel magnetic field ( B k ) Linearly Polarized EM wave E L-wave k ψ F E Plasma n e B z R-wave Linearly polarized light can be thought of as the sum of R- and L- waves 5
Faraday Rotation (Effect) R- and L- waves are offset in frequency ψ F E Linearly Polarized EM wave E L-wave k Plasma n e B z R-wave ψ F = 2.62 10 13 λ 2 n e B z dz ω c ( n R n L ) 2 dz phase measurement 6
Cotton-Mouton Effect Polarization elliptized due to perpendicular magnetic field E Linearly Polarized EM wave E k Plasma n e B ψ CM = 2.45 10 11 λ 3 n e B 2 dz ω c (n X n O )dz 1) C-M phase shifts up to 20 o possible in C-Mod (118 µm) 2) For tokamaks, B has components parallel and perpendicular to the direction of the electromagnetic probe wave 7
Faraday Effect Detection Technique λ/2 Plate Reference Mixer Double pass layout, λ~ 118 µm: similar to ITER polarimeter ω 2 ω 1 ω 2 Plasma Retro-reflector mounted in inner wall ω 1 FIR LASERS - (2.54 THz) Frequency offset ~ 4 MHz λ/4 Plate Signal Mixer B p B T Phase Measurement: effect of perpendicular B T on R- and L- waves is identical and cancels, no error due to Cotton-Mouton effect Dodel and Kunz, Infrared Physics 18,773-776(1978). 8
FIR Optical Layout Two CW far infrared lasers (Coherent Inc.: λ=117.73 µm, ~150 mw/cavity). Frequency offset 4 MHz (<1 µs time response) ~14 m pathlength Not shown: Air-tight enclosures for humidity control 1.2 cm thick magnetic shield for laser stability C-Mod: B T = 3-8T Ip =.4-2.1MA n e = 0.3-5.0x10 20 m -3 R = 0.68 m a = 0.22 m 9
Upper Table Layout chord 1 2 Main components on upper table: 3 - ¼ wave plate ¼λ - TPX lens -> focus beam on corner cube reflector - low-noise planar diode mixers lens - impact parameter: x1=10, x2=16, and x3= 20 cm corner cube retroreflectors 1 2 mirror 3 2 3 detector 1 focusing mirror Magnetic axis 10
Mesh Beam Splitters May Alter Beam Polarization For an incident angle of 45 0, linearly polarized light may become elliptically polarized AFTER reflection / transmission through beam splitter Effect depends on: 1) Orientation of wire grid with respect to incident beam polarization (drawn) 2) wire grid density (not drawn) -> Both errors minimized in optical layout beam splitter mesh rotated in lower case linearly polarized elliptically polarized 11
Polarimeter Calibration Layout Collinear R- and L- polarized beams ω 1 ω 2 Retro-reflector Rotating λ/2 plate causes phase change Rotating λ/2 plate Measured phase difference is linear if polarization of R- and L- waves are not modified by optics (mesh) Signal Mixer 12
Measured Phase Response Measured phase (deg) Measured phase (deg) Calibration curves can correct for systematic errors Quartz angle (deg) Linear response: beam is comprised of R- and L- circularly polarized waves Quartz angle (deg) Non-linear response: phase change from optical components 13
Measurement Phase Noise deg deg deg 1 0 1 1 0 1 1 0 1 Channel 1 Channel 2 Noise floor Channel 3 Acoustically vibrations in lasers: 0.25 0 rms (500 khz bandwidth) Magnetic field ramp time (s) vibrations and stray B (db/dt): 1-2 o Error at plasma flattop: 0.5 0-1 Hz - Laser relocation addresses both noise sources - Optical feedback to lasers below noise level 14
Toroidal Field Effects: (1) Alignment and (2) Cotton-Mouton effect 1) Misalignment to toroidal field, B T ψ F n e B z dz = n e B P cosα dl + n e B T sinαdl 2) Cotton-Mouton effect ψ CM n e B T 2 dl B P α z C-Mod toroidal magnetic field 4 8T B T Dedicated tests required to determine effect on measured phase shift 15
Negligible B T Effect on Faraday Measurement deg ψ F x 1 = 10 cm B t = 7.5 T B t = 5.4 T n e l 10 20 m 2 Ip (MA) B t (T) time (s) C M effect cancels when using R, L wave approach n e and I p same: change only B T No change in measured phase > No C M effect > No B t effect 16
Equilibrium Faraday Effect deg ψ F x 1 = 10 cm measurement EFIT 1 EFIT 2 ψ F deg ψ F x 2 = 16 cm - Experiment and EFIT agree deg x 3 = 20 cm Bme (s) n e l 10 20 m 2 I p (MA) ψ F Measurements can be used to constrain magnetic equilibrium reconstruction n e B d l 17
Plasma Dynamics Captured during Lower Hybrid Current Drive x 1 = 10 cm ψ F n e B d l deg ψ F Faraday signal evolves with LHCD deg ψ F x 2 = 16 cm Indication for J(r) change Lower hybrid power (kw) Further analysis, modeling, and verification ongoing n e l 10 20 m 2 Time (sec) 18
Cotton-Mouton Measurement λ/2 Plate ω 2 Reference Mixer Probe plasma with linear orthogonal light Plasma CCR: Retro-reflector ω 1 FIR LASERS Signal Mixer ψ CM = 2.45 10 11 λ 3 n e B 2 dz ω c (n X n O )dz Fuchs and Hartfuss, PRL 81,1626-1629(1998) Akiyama, et al., RSI 77, 10F118 (2006) 19
Cotton-Mouton Effect Measured deg ψ CM x 1 =10 cm measurement EFIT ψ CM ω c 2 n e B T dz (n X n O )dz deg ψ F x 2 =16 cm measurement EFIT ψ F ω 2c n e B z dz (n R n L )dz n e l 10 20 m 2 I p (MA) time (s) 1) Cotton-Mouton and Faraday effect measurements consistent with EFIT 2) C-M effect can be used to measure density as B T is known 20
Faraday Fluctuation Measurement ψ n e B d l ψ =ψ 0 + δψ n = n 0 + δn B = B 0 + δb δψ = δn e B d l + n e δb d l Term δn e B d l n e δb d l δn e δb Other fluctuation diagnostics aid in differentiating terms in PCI, reflectometer, scattering, interferometer(3 rd laser) external magnetic coils 21
Discrete and Broadband Fluctuations in Faraday Signal Coherent feature at 80-100 khz ~0.2 0 amplitude Broadband feature at 400-800 khz ~ 0.1 0 amplitude time (s) C-Mod polarimeter has time and phase resolution required for fluctuation measurements
400 300 200 PCI Energetic Particle driven mode during ICRF 200-400 khz Freq (khz) T(0) kev 400 300 200 400 300 200 Polarimeter Magnetics - Low density shot with 3+ MW ICRF - Spike in activity seen in δn and δb diagnostics - Evidence for Alfvenic activity 23
Plans (Three Year Timescale) Locate lasers remotely from tokamak cell [temperature controlled] Lower stray B and acoustic noise (vibration) Use dielectric waveguide to transport beams Increase number of chords from 3 to 10 (depending on access) Horizontal view with one chord below midplane Expand port for radial axis (more chords, δb r ) Add Density measurement capability Exploit Cotton-Mouton effect Add 3rd laser (order on HOLD) magnetic and density fluctuations simultaneously resolved Leverage technique (fluctuation and equilibrium) from C-Mod to address long-pulse AT operations in EAST (preparation for ITER) 24
Summary Three chords operational in 12 campaign -> Measurements and EFIT reconstructions consistent Faraday measurement checked against Cotton-Mouton and B t effects -> No contamination found Fluctuations related to MHD, fast-particles instabilities and turbulence observed Future plans to improve laser stability, increase chords Results increase confidence in Faraday effect measurement for ITER 25
Table 1: Combined Polarimeter Interferometer Diagnos=c Plasma Parameters Mul5field quan55es Physics Issues Interferometry n o (r,t) n k,ω ( ) Differen0al Interferometry n o (r,t) n k,ω ( ) Polarimetry Faraday Effect 1 J φ (r,t), B θ (r,t) b r ( k,ω), b θ ( k,ω), j φ Collec0ve Sca<ering n ( k,ω) ( k,ω) ElectromagneBc Torque 2 electrons: (Hall Dynamo) ions: j b j b // // en e Charge Flux (Maxwell stress) 3 Γ q = Γ i Γ e = < j // b r > eb ParBcle Flux (divergence) 4 Γ e = j //,e b r eb = V //,e B n b r Momentum Flux (KineBc stress) 5 Γ ion = p //, ionb r B T //, i B n b r Nonlinear 3 Wave Coupling 6 < n e v e,r n e > < n e b r n e > Equilibrium Dynamics Ohm s Law 7 3D effects 8 Momentum Transport Maxwell stress Electric Field GeneraBon Zonal flows ParBcle Transport Momentum Transport Intrinsic flow KineBc stress driving/damping mechanisms for density fluctuabons
End of Talk 27
Sawtooth Precursors in Faraday Signal T(0) Sawtooth cycle seen x = 16 cm kev deg ψ f sawteeth X = 16cm deg ψ f X = 10cm x = 10 cm chord largely to B p : measures (Wb) δb n e δbdl time (s) 28
Impurity Driven Snake and Quasi- Coherent Mode (QCM) Observed arb deg SXR X = 10cm ψ f Snake is long lived core helical perturbation ~ 20 khz, 0.5 0 deg arb time (s) X = 10cm ψ f PCI δn e QCM is a common component in ICRF heated plasmas ~ 70 khz, 0.4 0 29
Chords Through or Near the Magnetic Axis Measure δb r Through the magnetic axis, n e B P cosαdl = 0 The residual fluctuation measurement is largely n e δb d l, with δ B δb r because the chord is along the magnetic axis ( term peaks off axis) δn e B d l Topic being considered as a future polarimeter upgrade chord 30
Deconstructing Faraday Phase Change Y R + L wave electric field Plasma X Phase difference between R- and L-waves can be measured parallel and perpendicular with respect to toroidal field direction X direction (parallel to toroidal field) is typically selected, but component perpendicular to toroidal field (Y) can also 31 be measured
Components of Faraday Rotation degrees degrees degrees X component (toroidal) Y component ( X Y to toroidal) Toroidal component (X) perpendicular component (Y) at 5T and 8T suggests no contaminabon by CM effect L R wave Faraday probe technique is insensibve to CM effect 32 C MOD provides good test due to high field and density
Planar-Diode 2.8 THz Mixers Planar Schottky diode technology No fragile whisker contacts Operate interference frequency at 4MHz Bandpass sensitivity up to 1MHz, limited by filters 100-200 V/W High-Sensitivity and low noise allows access to fluctuation data Diode Mixer Housing 1.5 X 0.75 Horn 33 0.27mm X 0.27mm
Key Optical Components Custom mounts -> not easily tunable -> low vibration Thin TPX lens focus beam onto retro reflectors -> 3/16 thick 4 OD -> 85% transmission -> allows for significantly shorter beam path 34
Angle of Mesh Grid Can Alter Beam Polarization same line per inch Proper mesh LPI and orientation W.R.T incident beam polarization required to properly split beam for multiple 35 chords without altering polarization
Impurity Driven Snake phenomenon Observed Snake is long lived helical perturbation in plasma core Mo +32 presence allows for identification through SXR Snake apparent in chord #1 Faraday data as a 0.5 0 oscillation in raw data deg 36