Requirements for Active Resistive Wall Mode (RWM) Feedback Control

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1 Requirements for Active Resistive Wall Mode (RWM) Feedback Control Yongkyoon In 1 In collaboration with M.S. Chu 2, G.L. Jackson 2, J.S. Kim 1, R.J. La Haye 2, Y.Q. Liu 3, L. Marrelli 4, M. Okabayashi 5, H. Reimerdes 6, and E.J. Strait 2 1 FAR-TECH, Inc., San Diego, CA, USA 2 General Atomics, San Diego, CA, USA 3 UKAEA, Culham Laboratory, UK 4 Consorzio RFX, Padua, Italy 5 Princeton Plasma Physics Laboratory, Princeton, NJ, USA 6 Columbia University, New York, NY, USA 14 th Workshop on MHD Stability Control, November 9-11, 2009 Princeton Plasma Physics Laboratory, Princeton, New Jersey

2 Active feedback control safeguards high performance plasmas against the uncertainty of RWM stability boundary The RWM stabilization is essential to sustain high performance plasmas in ITER or reactorgrade devices The uncertainty of stability boundary of pressure-driven RWM challenges the evaluation of RWM stabilization process Even if RWM is passively stabilized, a coupling of marginally stable RWM with other MHD activities readily leads to the unstable RWM, requiring active feedback control 1 1 M. Okabayashi et al, Nucl. Fusion (2009) 1

3 Reproducible current-driven RWM helps us clarify both physics requirements and control specifications for feedback control Highly reproducible current-driven RWM enables us to explore the RWM feedback control (no or little external torque source) The RWM feedback control can be assessed using a reproducible RWM target at q 95 ~ 4. A systematic thorough investigation of various control parameters allows us to benchmark both RWM theory and control aspects BUT, the optimization of RWM feedback control is ultimately determined by the minimal level of plasma fluctuation beyond magnetics 2

4 Outline Introduction Schematic of active RWM feedback control Optimized feedback control (limited to PD controller for now) Gain scans Bandwidth requirements Phase-shifts Efficacy of active feedback control Physics requirements Internal vs external feedback coils Direct RWM feedback vs error field correction (EFC) Simplified Feedback control model Mode structure Possibility of 2nd least-stable RWM Discussion Conclusions and future works 3

5 The helical structure of the feedback is configured to match the structure of the n=1 RWM 4

6 Active feedback control system in DIII-D fully stabilizes current-driven RWM in parallel with EFC Tools Internal coils ( I-coils ): Direct Feedback + Dynamic error field correction (EFC) External coils ( C-coils ): Feed-forward EFC Ohmic discharge with high current ramp-up rate Feedback loop (τ p << τ w ) V FB n=1 Power Supply Controller (τ w,τ L/R, δi FB n=1 ) Plant (DIII-D/RWM) n 1 δ B = +? 1 Gsτ d d Ks () = Gp + 1+ sτ 1 sτ p + d G p,d : Gain τ p,d : time constant where p - proportional, and d - derivative? : Unknown n=1 error field 5

7 Current-driven RWM was obtained, diagnosed, and controlled with no external torque source present Plasma shape, p, q, and Ω 405 ms on Upper Single Null (close to Double Null shape) Monotonic pressure and q- profiles Plasma rotation profile is nearly flat according to CER measurement using carbon-vi line [nearly zero : (Ω 0 /ω A )< 0.1 %)] 6

8 Complete feedback stabilization of current-driven RWM at q 95 ~4 has been achieved in DIII-D q No feedback vs feedback 95 δb p n=1 (G) 0 φ n=1 (deg) IU 30 (A) ms Time (ms) RWM is observed to be i) non-rotating or moving slowly in co-i p direction at its birth, but ii) flips to the counter-i p direction as the mode grows up Balanced beam-pulse every 100 msec for 12 msec duration to measure q-profile and plasma rotations 7

9 Optimized feedback control Gain scans (G p only vs G p /G d ) Bandwidth requirements Phase-shifts Efficacy of active feedback control 8

10 An optimized gain has been found in the vicinity of unit flux gain (applied δψ r measured δψ θ ) 25 Maximum Mode Amplitudes (Gauss) vs G p Optimized 5 Unit flux gain Proportional Gain G p As the gain approaches the optimal level, the mode growth rate decreases as expected The higher coil currents at low gains are primarily attributable to an inadequate EFC to unknown error field 10 0 Optimized 9

11 The optimized RWM feedback control minimizes the plasma fluctuations beyond the plasma boundary No feedback (133021) Feedback (133018) n=1 Amp. [G] [kev] e Nov.08, :06: Core 1.7 R maj R [m] q~2 R [m] δt e 1.3 Edge Time [s] Time [s] RWM-induced edge fluctuations are also suppressed

12 The use of derivative gain broadened the effective gain range for RWM feedback stabilization Maximum Mode Amplitudes vs G p Unit flux gain Similarly finite amplitude of the coil currents at various G p values are associated with the EFC portion necessary for effective RWM stabilization. 11

13 The addition of G d minimizes the phase lag in time between RWM and the applied field Without G d (133017) With G d (133014) Core R [m] Edge e R maj R [m] 1.4 δt G p =40 e Time [s] Time [s] A value of G d =10G p is chosen to use voltage controller effectively as current controller, based on τ d and τ L/R of the feedback system [kev]

14 The voltage controller used for RWM feedback could work as current controller using derivative gain =>Still the bandwidth is limited by minimum (τ p -1, τ d -1 ) δi Plant,P(s) δb =>The high frequency role-off due to L/R time could be compensated by the choice of G d, which helps the system function as current controller. where K LR / Controller,K(s) K L/R δv () s = sτ K PCS L/ R and 1 Gd sτ K PCS ( s) = G p + 1+ sτ 1+ sτ p d d 13

15 Impact of DEFC on RWM feedback can be fully explored by the bandwidth scan Transition from DEFC to RWM-dominant regime - RWM: τ p < τ w - Dynamic EFC: τ p > τ w Feed-forward EFC: preprogrammed The low frequency EFC is necessary but not sufficient for RWM stabilization 14

16 The RWM feedback action should be taken faster than the mode growth time, as predicted 1 τ g : 3-4 ms When τ p < τ g : effective, while τ p > τ g :ineffective The used fixed gain provides δψ r ~ 5 x δψ θ on the midplane magnetic sensor 1 T. Strait et al, Nucl. Fusion (2003) 15

17 A phase-shifted n=1 field in the direction of co-i p rotation is more effective than in the opposite direction Maximum Mode Amplitudes [G] vs δφ FB Phase-shift dependency in MARS-F Stabilized A range of preferred toroidal phase shifts ahead of the RWM exists for effective feedback, consistent with theory 16

18 The efficacy of the feedback stabilization needs to be cautiously assessed based on magnetics alone 1.8 e G d = 10G p G p = 80 (133011) G p = 160 (133012) G p = 320 (133013).8 e Core 1.6 R maj.7.6 R [m] q~ Edge δt e Time [s] Time [s] Time [s] 0.05 Similar plasma responses based on magnetics may not reflect the detailed evolution of the RWM-associated internal structures. The choice of G d may not be optimal yet (likely due to mode coupling to coil currents, ) ( τ ) τ L / R eff L/ R 17

19 Physics Requirements Internal vs external feedback coils Direct RWM feedback vs error field correction (EFC) Simplified feedback control model Mode structure Possibility of 2nd least-stable RWM 18

20 The RWM feedback coils external to the vessel was found ineffective in stabilizing RWM The internal coils ( I-coils ) merit more effective coupling of the feedback field due to the proximity to the plasmas than the external coils ( C-coils ) This suggests that the error-field (EF) correction coils in ITER might not be a good choice for the purpose of RWM feedback control, though the investigation was not exhaustive. RWM growth time, τ g : 3 ms 19

21 Even after RWM stabilization, finite coil currents remain working as error field correction DEFC While the gain K increases, the δb gets smaller, but the time-averaged δi rarely changes Both DEFC and RWM feedback are working inside closed-loop but their roles are distinctive - DEFC: minimize the lack of axisymmetry of external field (low freq.) - RWM feedback: nullify the perturbed δb coming from unstable RWM (high freq.) 20

22 RWM feedback cannot be replaced by error-field correction (EFC) RWM growth is not influenced by EFC (i.e. no slope change) RWM growth time, τ g : 3-4 ms 21

23 Simplified feedback model is based on idealized current controller Measured perturbed field δb = δb RWM +δb EF +AδB FB where δb RWM : RWM, δb EF : Error field, A : Plasma response (amplification), and δb FB = -K δb = -αi coil K: Normalized gain (=G p /G p0 ) I coil : feedback current (=I EFC +δi RWM ), contributing to EFC and direct RWM FB 22

24 The key components in feedback control can be explicitly represented in modeling Assumptions Open loop K=0 shows finite δb = δb RWM + δb EF where δb RWM > 0 only for unstable RWM (δb RWM = 0 for stable RWM) δb EF > 0 can remain finite even when δb RWM = 0 Feedback is configured to oppose measured δb. 1 δb = δ BRWM + δ B 1 + KA I = K B + B α(1 + KA) δ δ { } EF { } coil RWM EF 23

25 Even after RWM stabilization, a finite I EFC is required to minimize the non-axisymmetric EF Closed loop: 1 When K>> 1, δb { δbef}, while δbrwm 0 KA I coil δ B α A ~ EF This suggests that when RWM is fully suppressed at high gain K, the DEFC could remain finite, regardless of the magnitude of K. Indeed, the feedback coil currents remained finite, even after the RWM was fully suppressed. This is attributable to EFC, not interacting with RWM directly. 24

26 Modeling shows the remained EF would not be sensitive to gain increase, consistent with experiments DEFC Even after RWM is fully suppressed, a finite amount of coil currents is required to provide EFC, whose role can be substituted by other slowly varying actuators 25

27 The internal mode structure observed in HFS is not necessarily the same as in LFS LFS 0: LFS ξ ( ) = m n r ξn ( r) cos( mθ), whereθ = m π : HFS Displacement calculation from MARS-F HFS The global structure of the current-driven RWM is unique in ideal MHD calculations, clearly different from tearing mode Rotational threshold for passive stabilization of currentdriven RWM is expected to be similar to RFP 26

28 The low frequency oscillatory behavior in high gain is indicative of the presence of 2 nd least-stable mode Based on the poles calculated in MARS-F for pressure-driven RWM Im(γτ w ) Re(γτ w ) The coupling of the 1 st and 2 nd least-stable modes has been predicted in theory for a long time. Need to distinguish the system pole and plasma pole (in progress) 27

29 MHD spectroscopy before and after current-driven RWM shows noticeable plasma responses at f= 400 Hz. Midplane probes I-coils Need to understand the plasma responses with respect to 1 st or 2 nd least-stable mode, as well as the RWM feedback algorithm 28

30 MHD spectroscopy prior to current-driven RWM shows noticeable plasma responses at f= 400 Hz Strong plasma response (30-40 % amplified) in the off-midplanes, but not at midplane: Why? Another peak near 700 Hz (not a second harmonic of driving frequency nor spurious): What is it? Responses from 1 st or 2 nd least-stable modes under marginally stabilized conditions? 29

31 Requirements of RWM feedback control Optimized feedback control Physics requirements Items Gain scans Bandwidth requirements Phase-shifts Efficacy of active feedback control Internal vs external feedback coils Direct RWM feedback vs error field correction (EFC) Mode structure Possibility of 2nd least-stable RWM Recommendations Advantage of G d use Bandwidth > τ -1 w Co-I p phase-shifts Minimal plasma perturbations Internal coils desirable Dual systems for low frequency EFC and high frequency FBK Need of further investigation 30

32 The requirements of RWM feedback control are established, taking into account theoretical and experimental aspects Direct RWM feedback cannot be replaced by error field correction (EFC) The bandwidth of the RWM feedback control should be wide enough to deliver the feedback action faster than the RWM growth time The benefits of G d and phase-shifted feedback need to be taken into account There was an indication of the presence of a second-least stable RWM which had been theoretically predicted but never identified in experiments. (cont d) 31

33 The understandings of RWM feedback control are being enhanced, having clarified several key issues The proximity of the feedback coils to the plasmas determines the degree of the effectiveness of RWM feedback Simplified feedback modeling shows that a finite amplitude of coil current is still required for EFC, even after the RWM is stabilized. Both modeling and experimental results are consistent, in that such finite amplitudes of DEFC would not be sensitive to gain values The indication of the 2 nd least stable RWM needs to be investigated to see if the optimized control parameters based on a single mode assumption are still valid 32

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