Core Magnetic Fluctuation Measurements In a High-Temperature Plasma - PowerPoint PPT Presentation

Core Magnetic Fluctuation Measurements In a High-Temperature Plasma by Faraday Rotation B.H. Deng, W.X. Ding, D.L. Brower University of California, Los Angeles J.K. Anderson, D. Craig, G. Fiksel, C.B. Forest, D. Holly, V. Mirnov, S.C. Prager, J.S. Sarff, V. Svidzinski, and the MST Group University of Wisconsin-Madison Annual APS Meeting, Division of Plasma Physics Albuquerque, NM October 26-31, 2003 This work is supported by the U.S. DoE.

Highlights 1. High-speed, far-infrared laser polarimetry for Faraday rotation measurements on MST – ∆ t ~ 1 µ s, ∆φ ~ 1 mrad 2. Current achievements on MST – Equilibrium magnetic field and plasma current profile – Comprehensive study of magnetic field and current density fluctuations associated with tearing mode Characteristics: Amplitude, Frequency and Wave-number Spectrum, Spatial Distribution Dynamics: B ⇒ J ( r ) ˜ ( ) ⇒ ˜ θ ( r , t ) ⇒ J φ ( r , t ) B ω , k ˜ B and J B ⇒ τ E , τ p ˜ – Magnetic fluctuation driven charge transport in MST – Fluctuation reduction in confinement-improved PPCD plasmas – Broadband magnetic and density fluctuations 3. Upgrading diagnostic system to three-wave polarimeter- interferometer for simultaneous measurements of n e and B.

Faraday Rotation Measurement Method R-wave ω 1 Plasmas E R = E R cos( ω 1 t − k R z ) E L = E L cos( ω 2 t − k L z ) Diode L-wave ω 2 mixer j ~ ( E R + E L ) 2 ~ E R E L cos[( ω 1 −ω 2 ) t − ( k R − k L ) z ] + ... k L − k R = ω c ( N L − N R ) = ω 2 pe ω ce ~ n e B z c ω 2 Faraday rotation is obtained by phase measurement

3-Wave Polarimeter λ/2 Plate ∫ Ψ= Reference Mixer c n B dz F e z ∫ Φ= Lens c ndz ω 2 n e Probe Beams ω 2 Polarizer ω 1 Signal Mixer ω 1 Lens λ/4 Plate Plasma L.O. ω 3 Beam Beam Splitter FIR Lasers Dodel and Kunz, Infrared Physics 18,773-776 (1978). Rommers and Howard, Plasma Phys. Control. Fusion 38,1805-1816(1996).

3-Wave Polarimeter-Interferometer System MST R 0 = 1.50 m a = 0.52 m I p = 400 kA n e ~ 10 19 m -3 B 0 ~ 4 kG

FIR Polarimeter-Interferometer System I. System resolution spatial: 11 discrete (vertical) chords ~1 µ s time response temporal: interferometer 50 mrad (8 x 10 11 cm -2 ) phase: polarimeter 1 mrad (10 G) II. Measurement capabilities ∫ φ ~ n dl Interferometer: e ∫ Polarimeter: Ψ ~ n B dl || e B θ ( r , t ) ⇒ J φ ( r , t ) n e ( r , t ) and Determine both equilibrium: and fluctuating quantities: ( ) ( ) n k , ω B k , ω ˜ ˜ ˜ J φ III. At present, polarimeter and interferometer operated independently. The system is currently being upgraded to include a third FIR laser, forming a triple laser system, to provide high-speed simultaneous measurements of plasma density and Faraday rotation.

Magnetic Fluctuation and Current Profile Play a Central Role in Self-Organized Magnetic Confinement Magnetic reconnection r r Particle transport ∇ J // (r) δ , δ E T B J Momentum transport Energy transport < E > // =η J // + dynamo Current Profile Dynamo Control Magnetic Fluctuation Induced Electromotive Force

Polarimeter-Interferometer Time History I p = 400 kA, 11 channel data, shot 101033036 Density: shot 1010330115 Faraday Rotation 1.6 ne1 ne2 -32 cm ne3 4 ne4 -17 1.2 ne5 Faraday Rotation (deg.) ne6 -2 nedl 13 0.8 0 28 43 0.4 -4 s1010330036 0.0 0 10 20 30 40 50 60 70 0 20 40 60 80 Time (ms) Time (ms) 1.6 ne7 ne8 ne9 ne10 1.2 -24 cm ne11 4 Faraday Rotation (deg.) -9 nedl 0.8 6 0 21 0.4 36 -4 0.0 0 10 20 30 40 50 60 70 0 20 40 60 80 Time (ms) Time (ms) Lanier et al., Phys. Rev. Lett. 85 ,2120(2000); Phys.Plasmas 8 ,3402(2001)

Faraday Rotation and Current Density Profiles 4 4 Ψ (degrees) Functional Fit 2 2 J φ = J(0)[1-(r/a) 2 ] γ , 0 0 Ψ = n e ∫ -2 -2 B z dz before after -4 -4 1.0 1.5 2.0 1.0 1.5 2.0 R (m) R (m) Equilibrium reconstruction: MSTFIT code MSTFIT Functional Fit 2.0 2.0 1.5 2 ) 1.5 J φ (MA/m before before after 1.0 1.0 after J(0) decreases at sawtooth crash 0.5 0.5 0.0 0.0 0.0 0.2 0.4 0.0 0.2 0.4 Brower, Ding, et al., PRL 88,185005-1(2002) r (m) r (m)

J // Flattens at Sawteeth Crash Equilibrium reconstruction code - solves Grad-Shafranov equation, fitting all experimental data (external magnetics, MSE, Faraday Rotation, pressure) At crash, plasma relaxes toward the Taylor minimum energy state

q-Profile 0.20 1/6 0.15 1/71/8 1/9 0.10 1/10 q 0.05 0.00 -.25 ms .25 ms -0.05 0.1 0.2 0.3 0.4 R-R o (m)

Core Magnetic Fluctuation Measurements 1.0 coherence statistical noise 0.8 12 kHz, m=1 Coherence 0.6 0.4 0.2 crash 0.0 0 20 40 60 80 (m=1,n=6) Frequency [kHz] Ψ = ˜ ∫ B 0 dl + ∫ ˜ ˜ n n 0 B dl ( ) B ≈ 33 G ˜ ~ 1% ∫ B 0 dl < ⇒ Ψ ≈ ˜ ∫ ˜ ˜ rms noise , n n 0 B dl

Magnetic Fluctuations Increase at Sawtooth Crash and Current Profile Flattens -2 -1 0 1 2 → Fluctuations 2.5 400 approximately 1% J(0) (MA/m 2 ) before crash 2.0 300 B r (G) 1.5 → Amplitude increases 200 at crash 1.0 ~ B r ≈ 1% 100 → J(0) decreases 0.5 B 0 0.0 0 -2 -1 0 1 2 Time (ms) magnetic fluctuations act to redistribute current density

Frequency and Mode Number Spectra 100 Dispersion Relation 80 |B r | 2 [G 2 /Hz] 60 400 80 40 toroidal mode number: n 300 60 20 Phase (deg.) 200 40 0 20 40 60 80 100 100 20 Frequency [KHz] 100 0 0 8 7 6 -100 -20 5 4 |B r | 2 [G 2 ] 0 20 40 60 80 3 frequency (kHz) 2 2 ~ n -5/ 3 B r k φ = ∆φ d = n 10 8 7 R 6 5 -20 0 20 40 60 Toroidal mode number

Current Fluctuation r r ∫ δ B • d l = µ 0 δ I Ampere's Law : L Faraday Rotation Fluctuation : r r r r ∫ ∫ δΨ = c F δ B • d l ≈ c F n δ B • d n 0 l 0 Plasma r r [ ] [ ] ∫ ∫ ∫ δ B • d l ≈ δ B z x 1 − δ B z dz dz x 2 L ≈ µ 0 δ I φ = δΨ 1 −δΨ 2 X 1 X 2 c F n 0 Loop between polarimeter chords is equivalent to a Rogowski coil measurement r z Ding,et al. PRL (2003) x

Current Density Fluctuation Measurement δ I 5 δ I 4 δ I 3 δ I 2 δ I 1 15 10 δ j ϕ [ A/cm 2 ] 5 0 δ j 5 δ j 4 δ j 3 δ j 2 δ j 1 -5 -10 -15 -40 -20 0 20 40 r [cm] δ j ϕ ~ 6% J 0 δ j ϕ ( r , t ) r profile can be experimentally determined

Determining Magnetic Fluctuation Profile In principle ∇×δ B =µ 0 δ J , ∇•δ J = 0 0.20 Faraday Fluct. Fitting 0 r exp( − ( r − r δ j φ = ˜ 2 )cos θ 0.15 s w ) j δΨ [deg.] 0.10 ∫ ψ x = c F n 0 ˜ B dl z r r m =ψ x exp − c F ˜ 0.05 ∫ ψ x 0 • d n B l 1 0.00 ( ψ i −ψ i 2 = m ) 2 -20 0 20 40 ∑ χ σ i X [cm] 2 i = 1,11

Magnetic Fluctuation Spatial Structure 80 100 (1,6 ) mode b r 60 b θ b 80 2 ] Magnetic Field [Gauss] z 40 Current Density [kA/m w = 8 cm 20 r s = 17 cm 60 0 40 -20 Global Local -40 20 -60 -80 0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 r /a r/a ˜ B ˜ ≈ 1% j r ≈ 4.5% J 0 = 2 MA / m 2 1 B J 0 0

Current Density Fluctuation over a Sawtooth 120 100 (1,6) mode current fluctutaion 80 60 40 20 -2 -1 0 1 2 Time [ms] 2.5 Mean Current drops 20% 2.0 1.5 -2 -1 0 1 2 Time [ms]

Fluctuation Induced Electromotive Force The generalized Ohm’s law: r r r r r r ∂ B + ∇ P E + r B − 1 − m e J ∂ t + v × J × n e e = η e J e 2 n e n e e r r r r r r , r v = r 0 + δ r J = 0 + δ B = 0 +δ Mean field dynamics , v J J B B v r r r < E > // +<δ r v ×δ > // −<δ J ×δ > // / n e e + ... =η // < J > // B B Hall MHD dynamo dynamo

Parallel Components of Hall Dynamo ∇•δ B = 0, ∇ ×δ B = µ 0 δ J θ ( r s ) ~ 0 b from measurement     2 < δ J × δ B > // ∂ = 1 B P ( r s ) < (1 B ( r s ) 1 + B T   ∂ r rb θ ) b r >       n e e n e e B P r     ≈ 1 B P B 1 + ( B T < δ j φ b r > ) 2     n e e B P δ j is correlated with magnetic probe array data to determine phase difference of a specific mode (e.g.m/n=1/6).

Hall Dynamo and Inductive Electric Field 60 E // η J 0 ≈ 0.5 V / m < δ Jx δ B> // /ne 40 Hall dynamo 20 1.7 V/m effect is 0.50 V/m important 0 near resonant -2 -1 0 1 2 surface! Time [ms] 0.3 < δ Jx δ B> // /n e e 30 0.2 20 0.1 10 0.0 -0.1 0 -2 -1 0 1 2 0.2 0.4 0.6 0.8 Time [ms] r/a

Magnetic Dynamics During Sawtooth Crash 2.5 J [MA/m 2 ] Mean Current 2.0 Current dynamics 100 Current Fluctutaion δ j ϕ [kA/m 2 ] Magnetic Fluctuation 50 0 60 Hall Dynamo 40 V/m Hall Electromotive Force 20 0 (anti-current ) 60 Electric Field 40 Induced Electric Field V/m 20 0 800 <B T > [Gs] Toroidal Flux Generation of 700 Magnetic Field -2 -1 0 1 2 Time [ms]

Fast-Polarimetry During PPCD: Dynamo Suppressed 6 -24 cm Dynamo (sawteeth) Suppressed -9 4 6 Faraday Rotation (deg.) 21 36 2 0 -2 -4 1010326159 -6 0 5 10 15 20 25 30 Time (ms) 6 -32 cm -17 -2 4 Faraday Rotation (deg.) 13 28 43 2 0 -2 -4 PPCD OFF PPCD ON -6 0 5 10 15 20 25 30 Time (ms)