Control of the Resistive Wall Mode with Internal Coils in the Tokamak (EX/3-1Ra) Active Measurement of Resistive Wall Mode Stability in Rotating High Beta Plasmas (EX/3-1Rb) by M. Okabayashi Presented at th IAEA Fusion Energy Conference Vilamoura, Portugal November 1st - 6th, 4 48-4/MRW//rs
EX/3-1Ra CONTROL OF THE RESISTIVE WALL MODE WITH INTERNAL COILS IN THE TOKAMAK 1 + 1 3 4 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. Katsuro-Hopkins, 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. Menard1 3 6 3 1 Princeton Plasma Physics Laboratory, Princeton, New Jersey, 8543-451,USA Columbia University, New York, New York, USA. 3 General Atomics, P.O. Box 8568, San Diego, California 9186-568, USA. 4 Far-Tech, 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
EX/3-1Rb 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
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 Finite-conductivity wall Does not completely stabilize ideal kink mode, Converts it to a slowly-growing Resistive Wall Mode (RWM) l Two approaches to RWM stabilization Passive: fast plasma rotation (EX/3-1Rb) Active: magnetic feedback control (EX/3-1a) 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 feedback-controlled error field correction: Long duration high b plasmas Direct feedback control : RWM stability at higher beta below critical rotation
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 "picture-frame" coils Single-turn, water-cooled 7 ka max. rated current Protected by graphite tiles 1 gauss/ka on plasma surface B P Sensors Internal Coils
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 "picture-frame" coils Single-turn, water-cooled 7 ka max. rated current Protected by graphite tiles 1 gauss/ka on plasma surface Vacuum Vessel (Cutaway View) External Coils (C-coils)
FEEDBACK WITH I-COILS INCREASES STABLE PLASMA PRESSURE TO NEAR IDEAL-WALL LIMIT l VALEN code prediction Normalized Growth Rate gt w 1 1 1 No Feedback Ideal kink l VALEN code: - DCON MHD stability - 3D geometry of vacuum vessel and coil geometry -1 1-1 Resistive Wall Mode: Open loop growth rate l t w is the vacuum vessel flux diffusion time (5 ms is used in VALEN code). No-Wall Limit C b =.4 b C b.6.8 b - b no.wall ideal.wall - b no.wall 1. Ideal-Wall Limit
FEEDBACK WITH I-COILS INCREASES STABLE PLASMA PRESSURE TO NEAR IDEAL-WALL LIMIT l C-coil stabilizes Slowly growing RWMs Normalized Growth Rate gt w 1 1 1-1 1-1. No-Wall Limit No Feedback External C-coils Accessible with External C-coils C b =.4 b C b.6 Ideal kink.8 b - b no.wall ideal.wall - b no.wall 1. Ideal-Wall 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)
FEEDBACK WITH I-COILS INCREASES STABLE PLASMA PRESSURE TO NEAR IDEAL-WALL LIMIT l I-coil stabilizes RWMs with growth rate 1 times faster than C-coils Normalized Growth Rate gt w 1 1 1-1 1-1. No-Wall Limit No Feedback External C-coils Internal I-coils Accessible with External C-coils C b =.4 b C b.6 Accessible with Internal I-coils Ideal kink.8 b - b no.wall ideal.wall - b no.wall 1. Ideal-Wall 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)
γτ w 3 OBSERVED OPEN LOOP GROWTH RATES AGREE WITH VALEN PREDICTION VALEN prediction No Feedback 1 C 1. No-wall β Ideal-wall limit limit
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 -. No-Wall Limit STABLE β Exp/3-1Rb Increase Rotation Ideal-Wall Limit γτ w -. No-Wall Limit Gain = β Exp/3-1Ra Higher Gain STABLE Ideal-Wall Limit
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 no-wall limit for >1s ( > t w ) 4 3 1 6 b N 4li ~ Estimated No-Wall Limit 1154 l Broad current profiles can greatly benefit from wall stabilization 1154 @ t= ms 5 1 4 4 q 95 8 3 J b (A/cm ) T (%) q Normalized 6. 4 4. r ~.6 (q=) 1 Rotation W rot / W A...4.6.8 1. (%) r 1 15 5 Time (ms)
HOW MUCH PLASMA ROTATION IS REQUIRED TO STABILIZE THE n=1 RWM? 3 β N ~Estimated no-wall limit 1 15 Ω rot/(π) at ρ=.6 (khz) Ω crit /(π) 1 5 8 6 BESL n=1 amplitude (Gauss) 4 1 13 14 15 Time (ms) 16 17 Insufficient error field correction causes slow-down 19174 Onset of RWM marks critical rotation Ω crit 3.. 1. -.5 Measured rotation threshold Ω crit /Ω A (%) (q = ) no wall limit C β.5 1. ideal wall limit
HOW MUCH PLASMA ROTATION IS REQUIRED TO STABILIZE THE n=1 RWM? 3 β N 19174 ~Estimated no-wall limit 1 15 Ω rot/(π) at ρ=.6 (khz) Ω crit /(π) 1 5 8 6 BESL n=1 amplitude (Gauss) 4 1 13 14 15 Time (ms) 16 17 Insufficient error field correction causes slow-down Onset of RWM marks critical rotation Ω crit 3.. 1. 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
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 3 1. -. 1-1 - 1 1 5-5 no-wall limit - Hz C β ~.5 Estimated no-wall limit 119418 119419 1194 +1 Hz - Hz +4 Hz Direction +1 Hz of plasma rotation +4 Hz 1 Time (ms). 1. 8 4-4 Plasma Response Amplitude and phase Amplitude Experiment / fit / t=15ms / t=18ms C β ~.4 Phase shift (Deg.) C β ~.5-4 Frequency of applied field (Hz)
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 1. 8 4 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 - -4. Mode rotation frequency ω RWM τ W -4 Experiment / fit / t=15ms / t=18ms - 4 Frequency of applied field (Hz) 1...4.6.8 1. C β
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 1. 8 4-4 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 - -4. 1. kinetic sound wave (κ =.5) Mode rotation frequency ω RWM τ W..4.6.8 1. C β
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 -. No-Wall Limit STABLE β Increase Rotation Ideal-Wall Limit γτ w -. No-Wall Limit Gain = β Higher Gain STABLE Ideal-Wall Limit Ω rot > Ω crit Ω rot < Ω crit Rational surface damping mechanism > Ω at q= as a measure of rotations
DIRECT MAGNETIC FEEDBACK SUSTAINS BETA ABOVE NO-WALL LIMIT EVEN WHEN Ω rot < Ω crit 11439 3. βn.4l i Estimated no-wall 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) 14 15 Feedback off Growth time 4ms
FEEDBACK SUSTAINS A DISCHARGE WITH NEAR-ZERO ROTATION AT ALL n=1 RATIONAL SURFACES Comparison case without feedback is unstable even with lower beta and faster rotation 3 Rotation 4 11434 114336 Ideal-Wall Frequency (khz) β /l Feedback Limit N i 3 1 No-Feedback No-Wall Limit (approx.) 1 11434 15 ms 114336 139 ms 9 3 15 δb p (Gauss) 1 frot (khz) at ρ =.6 1 14 16 Time (ms) Feedback Stabilized with Low Rotation 5 4 3 1 q(ρ) ρ 1.
FEEDBACK WITH I-COILS 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) C-COIL time no wall limit NO FEEDBACK 1 15 5 Rotation (km/s)
FEEDBACK WITH I-COILS 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 I-COIL ªZERO ROTATION C-COIL time no wall limit NO FEEDBACK 5 1 Rotation (km/s) 15
FEEDBACK WITH I-COILS 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 I-coils attained C b higher than with C-coils C b = b b - b no.wall ideal.wall ideal wall limit - b no.wall C b 1. I-COIL Unstable (without feedback) MARS prediction Stable (without feedback) MARS /VALEN prediction for zero rotation, with measured feedback system time response I-COIL ªZERO ROTATION C-COIL time no wall limit NO FEEDBACK 5 1 Rotation (km/s) 15
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 no-wall limit F.B on Feedback coil current amplitude No Feedback No Feedback With Feedback With Feedback 119666/119663 1 15 5 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.
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. 1. -1. -. -3. -4. -5. Present hardware Stable window.1. Gain (unnormalized) t w is.5 ms in MARS-F
MARS ANALYSIS PREDICTS THAT STABLE FEEDBACK GAIN RANGE IS NARROW l High-bandwidth 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 -3. -4. Stable window -5..1. Gain (unnormalized) t w is.5 ms in MARS-F
OVERALL SUMMARY l Active MHD Spectroscopy has been developed to investigate RWM stability (EX/3-1Rb) 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 I-coils has been demonstrated as an essential tool for achieving high b plasmas (EX/3-1Ra) Internal Coils are more effective and efficient than External Coils High b n close to the ideal-wall 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 High-bandwidth Audio-amplifiers to increase the range of stable operation Counter Neutral Beam Injection for greater control of plasma rotation assessing the rotational stabilization