DIII D. by M. Okabayashi. Presented at 20th IAEA Fusion Energy Conference Vilamoura, Portugal November 1st  6th, 2004.


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1 Control of the Resistive Wall Mode with Internal Coils in the Tokamak (EX/31Ra) Active Measurement of Resistive Wall Mode Stability in Rotating High Beta Plasmas (EX/31Rb) by M. Okabayashi Presented at th IAEA Fusion Energy Conference Vilamoura, Portugal November 1st  6th, /MRW//rs
2 EX/31Ra CONTROL OF THE RESISTIVE WALL MODE WITH INTERNAL COILS IN THE TOKAMAK M. Okabayashi, J. Bialek, A. Bondeson, M.S. Chance, M.S. Chu, D.H. Edgell, A.M. Garofalo, R. Hatcher, 1Y. In, 4 G.L. Jackson, 3R.J. Jayakumar, 5 T.H. Jensen, + O. KatsuroHopkins, R.J. La Haye, Y.Q. Liu, G.A. Navratil, H. Reimerdes, J.T. Scoville, E.J. Strait, 3 1 H. Takahashi, M. Takechi, 7, A.D. Turnbull, 3 I.N. Bogatu, 4 P. Gohil, 3 J.S. Kim, 4 M.A. Makowski, 5 J. Manickam, 1 and J. Menard Princeton Plasma Physics Laboratory, Princeton, New Jersey, ,USA Columbia University, New York, New York, USA. 3 General Atomics, P.O. Box 8568, San Diego, California , USA. 4 FarTech, Inc., San Diego, California 911, USA. 5 Lawrence Livermore National Laboratory, Livermore, California, USA. 6 Chalmers University of Technology, Goteborg, Sweden. 7 Japan Atomic Energy Research Institute, Ibaraki, Japan +deceased th IAEA Fusion Energy Conference, Vilamoura, Portugal 4
3 EX/31Rb ACTIVE MEASUREMENT OF RESISTIVE WALL MODE STABILITY IN ROTATING HIGH BETA PLASMAS H. Reimerdes,1 J. Bialek,1 M.S. Chance, M.S. Chu,3 A.M. Garofalo,1 P. Gohil,3 G.L. Jackson,3 R.J. Jayakumar,4 T.H. Jensen, + R.J. La Haye,3 Y.Q. Liu,5 J.E. Menard, G.A. Navratil,1 M. Okabayashi, J.T. Scoville,3 E.J. Strait,3 and H. Takahashi, 1 Columbia University, New York, New York, USA Princeton Plasma Physics Laboratory, Princeton, New Jersey, USA 3 General Atomics, San Diego, California, USA 4 Lawrence Livermore National Laboratory, Livermore, California, USA 5 Chalmers University of Technology, Göteborg, Sweden + deceased th IAEA Fusion Energy Conference, Vilamoura, Portugal 4
4 EXTERNAL KINK CONTROL WITH RESISTIVE WALL l Steady state advanced tokamak scenarios need wall stabilization of external kink modes for operation at high beta with a high fraction of bootstrap current l Finiteconductivity wall Does not completely stabilize ideal kink mode, Converts it to a slowlygrowing Resistive Wall Mode (RWM) l Two approaches to RWM stabilization Passive: fast plasma rotation (EX/31Rb) Active: magnetic feedback control (EX/31a) l New Internal coils installed just after the last IAEA conference: Very productive for RWM physics studies and active control of RWMs Active MHD spectroscopy with applied rotating field: RWM stability physics Plasma rotation sustained by feedbackcontrolled error field correction: Long duration high b plasmas Direct feedback control : RWM stability at higher beta below critical rotation
5 NEW INTERNAL CONTROL COILS ARE AN EFFECTIVE TOOL FOR PURSUING STABILIZATION OF THE RWM Inside vacuum vessel: Faster time response for feedback control Closer to plasma, flexible magnetic field pattern: more efficient coupling 1 "pictureframe" coils Singleturn, watercooled 7 ka max. rated current Protected by graphite tiles 1 gauss/ka on plasma surface B P Sensors Internal Coils
6 NEW INTERNAL CONTROL COILS ARE AN EFFECTIVE TOOL FOR PURSUING STABILIZATION OF THE RWM Inside vacuum vessel: Faster time response for feedback control Closer to plasma, flexible magnetic field pattern: more efficient coupling 1 "pictureframe" coils Singleturn, watercooled 7 ka max. rated current Protected by graphite tiles 1 gauss/ka on plasma surface Vacuum Vessel (Cutaway View) External Coils (Ccoils)
7 FEEDBACK WITH ICOILS INCREASES STABLE PLASMA PRESSURE TO NEAR IDEALWALL LIMIT l VALEN code prediction Normalized Growth Rate gt w No Feedback Ideal kink l VALEN code:  DCON MHD stability  3D geometry of vacuum vessel and coil geometry Resistive Wall Mode: Open loop growth rate l t w is the vacuum vessel flux diffusion time (5 ms is used in VALEN code). NoWall Limit C b =.4 b C b.6.8 b  b no.wall ideal.wall  b no.wall 1. IdealWall Limit
8 FEEDBACK WITH ICOILS INCREASES STABLE PLASMA PRESSURE TO NEAR IDEALWALL LIMIT l Ccoil stabilizes Slowly growing RWMs Normalized Growth Rate gt w NoWall Limit No Feedback External Ccoils Accessible with External Ccoils C b =.4 b C b.6 Ideal kink.8 b  b no.wall ideal.wall  b no.wall 1. IdealWall Limit l VALEN code:  DCON MHD stability  3D geometry of vacuum vessel and coil geometry l t w is the vacuum vessel flux diffusion time constant (5 ms is used in VALEN code)
9 FEEDBACK WITH ICOILS INCREASES STABLE PLASMA PRESSURE TO NEAR IDEALWALL LIMIT l Icoil stabilizes RWMs with growth rate 1 times faster than Ccoils Normalized Growth Rate gt w NoWall Limit No Feedback External Ccoils Internal Icoils Accessible with External Ccoils C b =.4 b C b.6 Accessible with Internal Icoils Ideal kink.8 b  b no.wall ideal.wall  b no.wall 1. IdealWall Limit l VALEN code:  DCON MHD stability  3D geometry of vacuum vessel and coil geometry l t w is the vacuum vessel flux diffusion time (5 ms is used in VALEN code)
10 γτ w 3 OBSERVED OPEN LOOP GROWTH RATES AGREE WITH VALEN PREDICTION VALEN prediction No Feedback 1 C 1. Nowall β Idealwall limit limit
11 TWO DISTINCT STABILIZATION APPROACHES HAVE BEEN PROPOSED Plasma Rotation Required: A few % of Alfven velocity 8. Ω = Magnetic Feedback Required: Practical power level System stability limits gain 8. Ω = γτ w . NoWall Limit STABLE β Exp/31Rb Increase Rotation IdealWall Limit γτ w . NoWall Limit Gain = β Exp/31Ra Higher Gain STABLE IdealWall Limit
12 WALL STABILIZATION WITH ROTATION ALLOWS HIGH BETA OPERATION l Stable at b N ª 6 l i and b T reaching to 6% l Beta exceeds estimated nowall limit for >1s ( > t w ) b N 4li ~ Estimated NoWall Limit 1154 l Broad current profiles can greatly benefit from wall stabilization t= ms q J b (A/cm ) T (%) q Normalized r ~.6 (q=) 1 Rotation W rot / W A (%) r Time (ms)
13 HOW MUCH PLASMA ROTATION IS REQUIRED TO STABILIZE THE n=1 RWM? 3 β N ~Estimated nowall limit 1 15 Ω rot/(π) at ρ=.6 (khz) Ω crit /(π) BESL n=1 amplitude (Gauss) Time (ms) Insufficient error field correction causes slowdown Onset of RWM marks critical rotation Ω crit Measured rotation threshold Ω crit /Ω A (%) (q = ) no wall limit C β.5 1. ideal wall limit
14 HOW MUCH PLASMA ROTATION IS REQUIRED TO STABILIZE THE n=1 RWM? 3 β N ~Estimated nowall limit 1 15 Ω rot/(π) at ρ=.6 (khz) Ω crit /(π) BESL n=1 amplitude (Gauss) Time (ms) Insufficient error field correction causes slowdown Onset of RWM marks critical rotation Ω crit Comparison with MARS calculation with experimental rotation profile .5 Ω crit /Ω A (%) (q = ) Soundwave damping overestimates the critical rotation kinetic sound wave (κ =.5).5 1 C β no wall limit ideal wall limit Kinetic damping underestimates the critical rotation MARS includes rotation and viscous dissipation
15 β N Upper I coil (φ=3deg) (ka) (1 Hz) Midplane Br (φ=139deg) (Gauss) (1 Hz) Magnitude of n=1 plasma response (Gauss/kA) Tor. phase of n=1 plasma response (Deg.) MHD SPECTROSCOPY PROBES THE RWM STABILITY WHILE THE PLASMA REMAINS STABLE nowall limit  Hz C β ~.5 Estimated nowall limit Hz  Hz +4 Hz Direction +1 Hz of plasma rotation +4 Hz 1 Time (ms) Plasma Response Amplitude and phase Amplitude Experiment / fit / t=15ms / t=18ms C β ~.4 Phase shift (Deg.) C β ~.54 Frequency of applied field (Hz)
16 SPECTRUM REVEALS GROWTH RATE AND MODE ROTATION FREQUENCY OF THE STABLE RWM. Amplitude C β ~.5 Spectrum Analysis with a Single Mode Model γ =γ RWM + i ω RWM Growth rate γ RWM τ W experiment C β ~.4 phase shift (Deg.) Amplification Factor = M (1+γ τ w ) (iω ext τ w  γ τ w ) Coupling between external field and RWM Mode rotation frequency ω RWM τ W 4 Experiment / fit / t=15ms / t=18ms  4 Frequency of applied field (Hz) C β
17 SPECTRUM REVEALS GROWTH RATE AND MODE ROTATION FREQUENCY OF THE STABLE RWM. Amplitude C β ~.5 Spectrum Analysis with a Single Mode Model γ =γ RWM + i ω RWM Growth rate γ RWM τ W experiment Experiment / fit / t=15ms / t=18ms  4 Frequency of applied field (Hz) C β ~.4 phase shift (Deg.) Amplification Factor = M (1+γ τ w ) (iω ext τ w  γ τ w ) MARS Comparison Growth rate Coupling between external field and RWM  sound wave / kinetic overestimates stabilizing effect Mode rotation frequency  kinetic : agreement  sound wave damping underestimate coupling kinetic sound wave (κ =.5) Mode rotation frequency ω RWM τ W C β
18 TWO DISTINCT STABILIZATION APPROACHES HAVE BEEN PROPOSED Plasma Rotation Required: A few % of Alfven velocity 8. Magnetic Feedback Required: Practical power level System stability limits gain 8. Ω = γτ w . NoWall Limit STABLE β Increase Rotation IdealWall Limit γτ w . NoWall Limit Gain = β Higher Gain STABLE IdealWall Limit Ω rot > Ω crit Ω rot < Ω crit Rational surface damping mechanism > Ω at q= as a measure of rotations
19 DIRECT MAGNETIC FEEDBACK SUSTAINS BETA ABOVE NOWALL LIMIT EVEN WHEN Ω rot < Ω crit βn.4l i Estimated nowall limit 3. Ωrot (%) ΩA Feedback (at q=) on 1% Feedback Current 5. (ka) 5. δbp n=1 4 Amplitude Stable (gauss) 1 13 Time (ms) Feedback off Growth time 4ms
20 FEEDBACK SUSTAINS A DISCHARGE WITH NEARZERO ROTATION AT ALL n=1 RATIONAL SURFACES Comparison case without feedback is unstable even with lower beta and faster rotation 3 Rotation IdealWall Frequency (khz) β /l Feedback Limit N i 3 1 NoFeedback NoWall Limit (approx.) ms ms δb p (Gauss) 1 frot (khz) at ρ = Time (ms) Feedback Stabilized with Low Rotation q(ρ) ρ 1.
21 FEEDBACK WITH ICOILS HAS ACHIEVED HIGH b n AT ROTATION BELOW CRITICAL PREDICTED BY MARS C b = b b  b no.wall ideal.wall ideal wall limit  b no.wall C b 1. Unstable (without feedback) MARS prediction Stable (without feedback) CCOIL time no wall limit NO FEEDBACK Rotation (km/s)
22 FEEDBACK WITH ICOILS HAS ACHIEVED HIGH b n AT ROTATION BELOW CRITICAL PREDICTED BY MARS l With near zero Rotation, C b is near the maximum set by control system characteristics C b = b b  b no.wall ideal.wall ideal wall limit  b no.wall C b 1. Unstable (without feedback) MARS prediction Stable (without feedback) MARS /VALEN prediction for zero rotation, with measured feedback system time response ICOIL ªZERO ROTATION CCOIL time no wall limit NO FEEDBACK 5 1 Rotation (km/s) 15
23 FEEDBACK WITH ICOILS HAS ACHIEVED HIGH b n AT ROTATION BELOW CRITICAL PREDICTED BY MARS l With near zero Rotation, C b is near the maximum set by control system characteristics l Feedback with Icoils attained C b higher than with Ccoils C b = b b  b no.wall ideal.wall ideal wall limit  b no.wall C b 1. ICOIL Unstable (without feedback) MARS prediction Stable (without feedback) MARS /VALEN prediction for zero rotation, with measured feedback system time response ICOIL ªZERO ROTATION CCOIL time no wall limit NO FEEDBACK 5 1 Rotation (km/s) 15
24 RWM FEEDBACK ASSISTS IN EXTENDING β n 4 ADVANCED TOKAMAK DISCHARGE MORE THAN 1 SECOND 4. βn Feedback current (ka) Plasma Rotation (km/s) 3 n=1 δb p Mode Amplitude (gauss) Estimated nowall limit F.B on Feedback coil current amplitude No Feedback No Feedback With Feedback With Feedback / Time (ms) 1 The rotation is similar for both cases <j // > (A/cm ) p(ρ) (xe3 Pa) t = ms q(ρ) 5. q(ρ) ρ 1.
25 MARS ANALYSIS PREDICTS THAT STABLE FEEDBACK GAIN RANGE IS NARROW l With experimental profiles and present hardware l Stable mode becomes unstable with higher gain due to finite feedback time response Unstable mode RWM growth rate Stable mode gt w Present hardware Stable window.1. Gain (unnormalized) t w is.5 ms in MARSF
26 MARS ANALYSIS PREDICTS THAT STABLE FEEDBACK GAIN RANGE IS NARROW l Highbandwidth audio amplifiers are being installed to increase the range of stable operation Unstable mode. 1. Present hardware Expected with audio amp. RWM growth rate 1. gt w . audio amplifiers Stable mode Stable window Gain (unnormalized) t w is.5 ms in MARSF
27 OVERALL SUMMARY l Active MHD Spectroscopy has been developed to investigate RWM stability (EX/31Rb) Detailed comparison of experiments with damping models is now possible Sound wave and kinetic damping model results are comparable to experimental values Further improvement of models is needed for a quantitative comparison l Direct magnetic feedback with Icoils has been demonstrated as an essential tool for achieving high b plasmas (EX/31Ra) Internal Coils are more effective and efficient than External Coils High b n close to the idealwall limit has been achieved with W rot < W crit Feedback has assisted in sustaining advanced tokamak discharges with b n ª 4 for over 1 second l Future work Highbandwidth Audioamplifiers to increase the range of stable operation Counter Neutral Beam Injection for greater control of plasma rotation assessing the rotational stabilization
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