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 FARTECH, 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 911, 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 pressuredriven 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 currentdriven RWM helps us clarify both physics requirements and control specifications for feedback control Highly reproducible currentdriven 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 Phaseshifts 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 leaststable 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 DIIID fully stabilizes currentdriven RWM in parallel with EFC Tools Internal coils ( Icoils ): Direct Feedback + Dynamic error field correction (EFC) External coils ( Ccoils ): Feedforward EFC Ohmic discharge with high current rampup rate Feedback loop (τ p << τ w ) V FB n=1 Power Supply Controller (τ w,τ L/R, δi FB n=1 ) Plant (DIIID/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 Currentdriven 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 carbonvi line [nearly zero : (Ω 0 /ω A )< 0.1 %)] 6
8 Complete feedback stabilization of currentdriven RWM at q 95 ~4 has been achieved in DIIID 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) nonrotating or moving slowly in coi p direction at its birth, but ii) flips to the counteri p direction as the mode grows up Balanced beampulse every 100 msec for 12 msec duration to measure qprofile and plasma rotations 7
9 Optimized feedback control Gain scans (G p only vs G p /G d ) Bandwidth requirements Phaseshifts 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] RWMinduced 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 roleoff 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 RWMdominant regime  RWM: τ p < τ w  Dynamic EFC: τ p > τ w Feedforward 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 : 34 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 phaseshifted n=1 field in the direction of coi p rotation is more effective than in the opposite direction Maximum Mode Amplitudes [G] vs δφ FB Phaseshift dependency in MARSF 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 RWMassociated 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 leaststable RWM 18
20 The RWM feedback coils external to the vessel was found ineffective in stabilizing RWM The internal coils ( Icoils ) merit more effective coupling of the feedback field due to the proximity to the plasmas than the external coils ( Ccoils ) This suggests that the errorfield (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 timeaveraged δi rarely changes Both DEFC and RWM feedback are working inside closedloop 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 errorfield correction (EFC) RWM growth is not influenced by EFC (i.e. no slope change) RWM growth time, τ g : 34 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 nonaxisymmetric 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 MARSF HFS The global structure of the currentdriven 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 leaststable mode Based on the poles calculated in MARSF for pressuredriven RWM Im(γτ w ) Re(γτ w ) The coupling of the 1 st and 2 nd leaststable 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 currentdriven RWM shows noticeable plasma responses at f= 400 Hz. Midplane probes Icoils Need to understand the plasma responses with respect to 1 st or 2 nd leaststable mode, as well as the RWM feedback algorithm 28
30 MHD spectroscopy prior to currentdriven RWM shows noticeable plasma responses at f= 400 Hz Strong plasma response (3040 % amplified) in the offmidplanes, 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 leaststable modes under marginally stabilized conditions? 29
31 Requirements of RWM feedback control Optimized feedback control Physics requirements Items Gain scans Bandwidth requirements Phaseshifts Efficacy of active feedback control Internal vs external feedback coils Direct RWM feedback vs error field correction (EFC) Mode structure Possibility of 2nd leaststable RWM Recommendations Advantage of G d use Bandwidth > τ 1 w CoI p phaseshifts 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 phaseshifted feedback need to be taken into account There was an indication of the presence of a secondleast 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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