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,
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.
1. High-speed, far-infrared laser polarimetry for Faraday rotation measurements on MST – ∆t ~ 1 µs, ∆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:
– 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 ne and B.
˜ B ⇒ J(r) ˜ B ⇒ τ E ,τ p B
θ (r,t ) ⇒ Jφ (r,t )
and ˜ B ω,k
J
peωce
j ~ (ER + E L)2 ~ ER EL cos[(ω1 −ω2)t − (kR − kL)z]+ ...
Plasmas
Diode mixer
Reference Mixer Plasma L.O. Beam
ω2
λ/4 Plate λ/2 Plate FIR Lasers
ω2 ω1 ω1 ω3
Polarizer Probe Beams Lens Signal Mixer Lens Beam Splitter
F e z n e
Dodel and Kunz, Infrared Physics 18,773-776 (1978). Rommers and Howard, Plasma Phys. Control. Fusion 38,1805-1816(1996).
MST R0 = 1.50 m a = 0.52 m Ip = 400 kA ne ~ 1019 m-3 B0 ~ 4 kG
I. System resolution
spatial: 11 discrete (vertical) chords temporal: ~1 µs time response phase: interferometer 50 mrad (8 x 1011 cm-2) polarimeter 1 mrad (10 G)
II. Measurement capabilities
Interferometer: Polarimeter: Determine both equilibrium: and fluctuating quantities:
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.
dl B n dl n
e e ||
~ ~
Ψ φ ne (r,t) and Bθ (r,t) ⇒ Jφ (r,t) ˜ n k,ω
˜ B k,ω
˜ J
φ
Magnetic reconnection Particle transport Momentum transport Energy transport
Current Profile Control
Magnetic Fluctuation Induced Electromotive Force
Ip = 400 kA, 11 channel data, shot 101033036 Faraday Rotation
4
Faraday Rotation (deg.)
80 60 40 20
Time (ms)
13 28 43
s1010330036
4
Faraday Rotation (deg.)
80 60 40 20
Time (ms)
6 21 36
1.6 1.2 0.8 0.4 0.0
nedl
70 60 50 40 30 20 10
Time (ms)
ne7 ne8 ne9 ne10 ne11
1.6 1.2 0.8 0.4 0.0
nedl
70 60 50 40 30 20 10
Time (ms)
ne1 ne2 ne3 ne4 ne5 ne6
Density: shot 1010330115
Lanier et al., Phys. Rev. Lett. 85,2120(2000); Phys.Plasmas 8,3402(2001)
2.0 1.5 1.0 0.5 0.0 Jφ (MA/m
2)
0.4 0.2 0.0 r (m) before after Functional Fit 2.0 1.5 1.0 0.5 0.0 0.4 0.2 0.0 r (m) before after MSTFIT 4 2
Ψ (degrees) 2.0 1.5 1.0 R (m) before 4 2
2.0 1.5 1.0 R (m) after
Functional Fit
Equilibrium reconstruction: MSTFIT code
Brower, Ding, et al., PRL 88,185005-1(2002)
J(0) decreases at sawtooth 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
0.20 0.15 0.10 0.05 0.00
q 0.4 0.3 0.2 0.1 R-Ro (m)
.25 ms
1/6 1/71/8 1/9 1/10
1.0 0.8 0.6 0.4 0.2 0.0 Coherence 80 60 40 20 Frequency [kHz] coherence statistical noise 12 kHz, m=1
crash (m=1,n=6)
˜ Ψ = ˜ n ∫ B0dl + n0 ∫ ˜ B dl ˜ n ∫ B0dl < rms noise, ⇒ ˜ Ψ ≈ n0 ∫ ˜ B dl
˜ B ≈ 33 G ~ 1%
→ Fluctuations approximately 1% before crash → Amplitude increases at crash → J(0) decreases
B
~ r
B0 ≈ 1%
magnetic fluctuations act to redistribute current density
100 80 60 40 20 |Br|2 [G2/Hz] 100 80 60 40 20 Frequency [KHz]
5 6 7 8
10
2 3 4 5 6 7 8
100 |Br|2 [G2]
60 40 20
Toroidal mode number
B r
2
~ n-5/ 3
400 300 200 100
Phase (deg.) 80 60 40 20 frequency (kHz) 80 60 40 20
toroidal mode number: n
Ampere's Law : δ r B • d r l = µ0
L
δI Faraday Rotation Fluctuation : δΨ = cF n0
δ r B • d r l ≈ cFn δ r B • d r l
L
x1 −
x2
1 −δΨ 2
X1 X2
Ding,et al. PRL (2003)
δI5 δI4 δI3 δI2 δI
1
δj5 δj4 δj3 δj2 δj
1
δjϕ J0 ~ 6%
ψ x = cF n0 ˜ B
z
dl ψ x
m =ψ x exp − cF ˜
n
1
r B
0 • d
r l
0rexp(−(r − r s
2)cosθ
χ
2 =
(ψi −ψi
m)2
σi
2 i=1,11
0.20 0.15 0.10 0.05 0.00 δΨ [deg.] 40 20
X [cm]
Faraday Fluct. Fitting
˜ j
1
J0 ≈ 4.5% J0 = 2 MA / m
2
r
20 40 60 80 Magnetic Field [Gauss] 1.0 0.8 0.6 0.4 0.2 0.0 r /a br bθ b
z
(1,6 ) mode
100 80 60 40 20 Current Density [kA/m
2]
1.0 0.8 0.6 0.4 0.2 0.0 r/a
w = 8 cm
rs = 17 cm
Global Local
2.5 2.0 1.5
1 2 Time [ms] Mean Current drops 20% 120 100 80 60 40 20
1 2 Time [ms] (1,6) mode current fluctutaion
e
// <J>//
0 + δ
0 +δ
0 + δr
2
δj is correlated with magnetic probe array data to determine phase difference of a specific mode (e.g.m/n=1/6).
θ (r s) ~ 0
from measurement
ηJ0 ≈ 0.5V /m
60 40 20
1 2 Time [ms] E //
<δJx δB> // /ne
1.7 V/m 0.50 V/m
30 20 10 0.8 0.6 0.4 0.2 r/a
< δJxδB>// /nee
0.3 0.2 0.1 0.0
1 2 Time [ms]
Hall dynamo effect is important near resonant surface!
Current dynamics Magnetic Fluctuation Hall Electromotive Force (anti-current) Induced Electric Field Generation of Magnetic Field
100 50 δjϕ [kA/m2]
Current Fluctutaion
2.5 2.0 J [MA/m2]
Mean Current
60 40 20 V/m
Hall Dynamo
60 40 20 V/m
Electric Field
800 700 <BT> [Gs]
1 2 Time [ms]
Toroidal Flux
2 4 6 Faraday Rotation (deg.) 30 25 20 15 10 5 Time (ms)
6 21 36
1010326159
2 4 6 Faraday Rotation (deg.) 30 25 20 15 10 5 Time (ms) PPCD ON PPCD OFF
13 28 43
Dynamo (sawteeth) Suppressed
7x10
6
6 5 4 3 2 1 λ= J// / B 0.8 0.6 0.4 0.2 r/a
No PPCD t=13 ms t=18 ms λ =constant
Brower,et al.PRL (2002)
80 60 40 20 P(f) [Gs2/kHz] 80 60 40 20 f [kHz] standard 400ka ppcd 400ka magnetic turbulence
Tearing Modes
Broadband magnetic fluctuations above noise level are observed up to 250 kHz Noise can be further reduced using correlation techniques Better signal to noise ratio can be achieved with higher laser power Increased bandwidth allows us to study magnetic turbulence in high temperature plasma core
2 3 4 5 6 7 8 9
10
2 3
Faraday Rotation Power Spectrum (Deg.
2/Hz)
250 200 150 100 50 Frequency (kHz) Noise Level x = 6 cm
Standard Plasmas Ip = 340 kA ne = 1x10
13 cm
Broadband density fluctuations significantly above noise level are
Power falling off as ~f –α, α = 2.9 +/- 0.1
10
10-12 10
10
10
10
Density Power Spectrum
5 6 7 8
10
2 3 4 5 6 7 8
100
2 3 4 5
Frequency (kHz)
Chan.1 Chan.2 Chan.3 Chan.4 Chan.5 Chan.6 Noise1 Noise2 Noise3 Noise4 Noise5 Noise6
~ f
10
10
10
10
10
10
Density Power Spectrum
5 6 7 8
10
2 3 4 5 6 7 8
100
2 3 4 5
Frequency (kHz)
Chan.6 Chan.7 Chan.8 Chan.9 Chan.10 Chan.11 Noise6 Noise7 Noise8 Noise9 Noise10 Noise11
~ f
A third FIR laser will be added to achieve a three-wave polari- interferometer configuration for simultaneous Faraday rotation and density measurements A new high-power CO2 pump laser has been added (120 W CW) Precision bore Pyrex tubes will replace the metallic corrugated wave- guides of the FIR lasers for better performance at the desired wavelength (432.5 µm) The lasers will be housed in a laser safety room, which will also provide extra noise shielding as well as better IF frequency control
Diagnostic Technique directly applicable to Tokamaks! A high-speed far-infrared (FIR) laser polarimeter for Faraday rotation measurements in MST has achieved a time response of ~ 1 µsec, and a sensitivity of ~1 mrad. Equilibrium and fluctuating magnetic field and associated plasma current profile and fluctuations have been measured in the MST plasma core. Both low and high frequency fluctuations have been measured. Comprehensive study of the dynamics of plasma current density and magnetic field profiles and fluctuations in the core of MST plasmas (both standard and enhanced confinement discharges) has yield much new understanding on the behaviors of RFP plasmas: tearing mode instabilities, dynamo effects, and charge transport Plasma density profiles and fluctuations have also been independently studied in MST with the interferometer configuration. To enhance the power of the diagnostic, the system is being upgraded to a three-wave polari-interferometer for simultaneous high-speed magnetic field and density measurements.