AUTOMATIC REAL-TIME TRACKING AND STABILIZATION OF MAGNETIC ISLANDS IN A TOKAMAK BY ECCD/ECRH

Transcription

1 AUTOMATIC REAL-TIME TRACKING AND STABILIZATION OF MAGNETIC ISLANDS IN A TOKAMAK BY ECCD/ECRH Enzo Lazzaro, J. O. Berrino, S. Cirant, G. D Antona, F.Gandini,G.Granucci and F.Iannone 1

2 Outline Summary of NTM physics and control issues Relation between measured ECE signals and state variables Real-time diagnostic and control principles and apparatus Recent results from of experiments on FTU tokamak Comments on control strategies 2

3 Summary of NTM physics and control issues Modified Rutherford equation for W(t) Early control of seed island: less power Frequency-phase tracking mandatory t R r s dw dt W seed Ê e 1/ 2 = r s D 0 + b p Á Á Ë s D boot r s W c W W c ( ) 2 - r s 1+ W W c D pol ˆ + r s D EC 2 Ê D pol ª g w ˆ Ê Á Á Ë w * Ë L s L n ˆ 2 2 riq W 3 D EC = 8qd EC pw 2 Squeezing a saturated island: maximum RF power required ( ) h W d EC Ê Á Ë J EC J boot ˆ cos df(t) RF power deposition on q=m/n surface required 3

4 Other aspects of NTM physics Plasma pressure profile is flattened within the island - J bs is turned off This drives a dj bs with the same helical pitch as the island The corresponding induced db has the same direction as the initial perturbation and enhances it. Non uniformity of pressure/temperature parallel to field lines,within island, drives a healing current dj // opposing dj bs and modifying the threshold size [1] t R r s dw dt = r s D 0 + b p r s W c È Í Í Î el Ê q Á W W c L p Á Ë 1+ W W c ( ) e W W c ( ) 6 1+ W W c ˆ - D neo-pol + r s D EC 1. Smolyakov A.I. and Lazzaro E. Phys. of Plasmas 11, 4353 (2004) 4

5 STATE AND CONTROL VARIABLES: For a single (m,n) mode the observable state variables {X i } are the Mirnov signal amplitude B q (t) or the ECE fluctuation dt e plus the rotation frequency w (t), the phase and the island radial location r island (q=m/n surface). Control variables {u i } : ECW power P EC and duty cycle (timing) Launching angles a,b determining the radius of P EC power deposition r dep CONTROL TASK: Reduce to zero (or minimum) the mode amplitude in minimal time The assesment of power requirements depends on ECCD efficiency h = J EC / P EC and on improved understanding of the physics of NTM ECCD efficiency h is highest for d EC /W < 1; J EC deposited on the O point in synchronism with island rotation should provide the maximum suppression ( stabilizing ) effect but as W is reduced d EC > W and h decreases; after a few cycles the lower efficiency prevails. fi frequency-phase tracking is required mainly for island detection (~1 ms time scale) CONCLUSION The most important task is tracking in real time r island and r dep (~1 s time scale) 5

6 DIIID Luce T., 3rd IAEA-TM on ECRH in ITER, Como,Italy, May

7 JT60U_early Ide S., 3rd IAEA-TM on ECRH in ITER, Como,Italy, May

8 Proof of principle experiments of NTM control by ECCD/ECH Suppression of (m,n) NTM requires efficient balancing of missing J boot with J EC on q=m/n surface, at r = r m,n Alignment of r dep with r m,n has been obtained by adjustment of [1-3] B tor : impossible in ITER R/z axis : short range, impractical It could be done by varying frequency beam steering by moving mirrors Stability of (m,n) TM variation of D at r ~ r m,n 1. H. Zohm et al Phys.of Plasmas 8,2009(2001) 2. R.J. La Haye et al Phys.of Plasmas 9,20051(2002) 3. K.Nagasaki et al Nucl.Fus. 43,(2003)L7-L10 4. S. Cirant Oct et 31st-Nov. al 18th 3rd, Fus En. Conf, Sorrento (2000) E. Lazzaro, EX3/3Active Control of MHD Stability 2005 DIII-D alignment system by change of R 8

9 Detection & Control action State variables: dt e or B q, frequency, phase, r island, r dep Polling for r dep with low duty cycle power pings Continuous polling for r island no reaction (W island ) until r dep r island e fb = B q search and suppress simple detection blind search sequential decision (multibeam) dedicated logic e fb = e dep = r dep -r island just align complex detection conscious search parallel decision (multibeam) multi-purpose logic (NTM & sawteeth) 9

10 Island recognition with T e diagnostics T e (kev) T T dte(kev) e,q=0 e,q=ϖ/m 0.6 ITER Scenario dte(kev) dte/t 0 (r-r m,n )/W c r (m) tor Multiple zeros possible with heating T e flattening fi loss of bootstrap current fl rotating NTM fl antisymmetric T e oscillations ECH (associated with ECCD) may 10 mask strict antisymmetry

11 Sensitive parameter for r island identification For each i th channel of local T e measurement o = ECE - i A i = o i P ij = 2 nosc i i T 2 ECE nosc i i T1 nosc = T 3 i oi A i sparo 14979Te channel o ECE <ECE> A channel T1 = 0.1msec T2 = 0.2msec T3 = 2.0msec Local P ij minimum fl O-point location DAS & DSP cycle: 0.02 ms 11

12 Correlation of the ECE fluctuations measured between nearby channels, both for natural and heated islands (e.g. r 1 =r s -x, r 2 =r s+ x) P 1,2 = dt e (r )dt 1. e(r )cosx(t)cos x(t) + df 2. ( 1-2 ) T µ Acos( df 1-2 ) The phase jump is effective on detecting the q=m/n radius, but not robust 0.06 dt e dt e,ece Pij 1 The concavity of the sequence of Pij is a robust observable that gives the radial position of q=m/n Sensitive transient T e measurements ECE preferable dte(kev) P ij -0.5 Cross-correlation with B q r tor 12

13 Principle of r island tracking algorithm P ij 1 if both i and j are on the same side with respect to the island O-point. P ij -1 if on opposite sides. A positive concavity in the P ij sequence locates the island. P i j 1 0 channels -1 13

14 P i,a P i,a P i,a Real-time multiple r dep detection (FTU data) by dt e and P gyrotron cross-correlation: ch o i = T e,i - T e,i T1 g a / b = DSP controls P gyrotron o i norm = o i A i Ï 1 if H.V. a / b ON Ì Ó -1 if H.V. a / b OFF P i,a / b = o norm i g a / b T 3 r dep s of many beams ON are detected at once in real time 14

15 TM D/C D IFP04 12 ANALOG FILTER Low pass 8th order 25KHz 12 FTU ECE CHANNELS FTU FSC enable FTU CLOCK 1MHz Prototype Tearing modes Real-time identification/control apparatus on test on FTU FTU GATES PRERUN -120 FSC -10 PROGRAMS DATA PARAMETERS COMM PORT GYROTRON I OUTPUT LEVEL ADAPTER TTL to 0-12 GYROTRON II DIGITAL I/O PROGRAM DATA PARAM. ON/OFF 32 ADC 12bit DSP A DSP B DSP D PC DSP C PROGRAM DATA PARAM. COMM PORT ETHERNET 50 khz sampling rate Identification of q-rational surfaces Identification of ECRH rdep INPUT LEVEL ADAPTER TTL to 0-12 CLOCK DIVIDER 50KHz VME BUS island tracking and automatic Oct 31st-Nov. by 3rd, 2005 E. Lazzaro, Active Control of MHD Stability 2005 stabilization ECRH 15

16 On-line Communication scheme among DSPs DSPA processes data from the other DSPs; DSP A takes decisions and issues the switch-on signal for the gyrotrons. DSP A can operate at lower frequency DSP B receives and stores data from the ADC, and it computes the power r dep by correlating the dte (nosc) fluctuation from DSP C with the On-Off trigger from DSP A. DSP C processes ADC data and produces nosc and the correlation Pij transferred to DSP A and DSP B and it selects the channels for frequency identification. From DSP C signals are sent to DSP D running the phase lock loop algorithm for mode 16 frequency and phase tracking.

17 D1 ( i) = Pi i 1 - Pi -1,, + i i = 2,...,11 DSP A 1 ˆ 2 Á Ê D i + = D 1( i + 1) - D 1( i ) i = 2,...,10 Ë 2 Ê 1 ˆ IF D 2Á i + > 0.3 Ë 2 Y Island Found Between ch i and ch i+1 i = i +1 N R Island = D1( i) i + D1( i + 1) ( i D1( i) + D1( i + 1) + 1) Y IF i < 10 N Next time step 17

18 Block-Diagrams of real time diagnostic control device Filter for ECE fluctuations (DSPD) 5 PLL loops with different w 0i cover the frequency range 50Hz-14KHz (DSPC) Real time evaluator of second difference of ECE signals correlator Pij (DSPA) Real time evaluator of ECE -Gyrotron Correlator Qij (DSPB) Decisional algorithm for steering actuator (DSPA) 18

19 r island detection in practice (FTU) 12-channels ECE polychromator m=2, n=1 axis presently the analysis is done in real time m=1,n=1 oscillation frequency 19 at minimum P ij

20 Coupled TMs are simultaneously detected axis (2,1) locks (2,1) (1,1) (3,2) sawteeth 20 (1,1) & (2,1) & (3,2) are coupled

21 FTU Detection and Gyrotron pulse control system 21

22 ECRH power deposition at different R by changes of the angle of the mirror FTU: B tor = 5.6 T EC beam ECE channels Gyrotron 3 Gyrotron 1 mirror plasma axis Resonance 140GHz 22

23 MHD control in FTU (2 beams) #27714 gy.3 gy.3 gy.1 gy.1 cross-correlation ECE vs. PEC T ECE profile B tor = 5.54 T in real-time by DSP modulation 15% duty cycle 23

24 MHD control in FTU (2 beams) ch.3 (gy.1 deposition) ch.2 Mode hit and suppressed! ch.1 (gy.3 deposition) gy.3 gy.1 gy 3 on Mode Trigger (sawtooth?) t feedback ON =0.4 s action: low fi high duty cycle 24

25 MHD control in FTU (2 beams) gyrotron on ch.1&2 symmetric to 8&9 phase inversion (island)on ch.10 25

26 MHD stabilisation on FTU Mode quenched ch10 opposition between ch09 and ch10 ch09 ch10 ch09 ursb switches from 10% to 90% ursa remains at 10% 26

27 Stabilisation without freq.- phase tracking Shot Identification of r dep and r island at t=0.7 has triggered Gyr 3 and led to mode suppression ( Channel 7 ) at t=0.82 also without phase tracking. Gyr 3 turns off at t=

28 Formal aspects of the control problem The physical objective is to reduce the ECE fluctuation to zero in minimal time using ECRH /ECCD on the position q=m/n identified by the phase jump method The TM control problem in the extended Rutherford form, belongs to a general class known in in the theory of multistage decision processes [*]. In a linearized form the governing equation for the state variable x(t) is dx dt = A(t)x(t) + B(t)u(t) with the initial condition x(0)=x0, and a control variable (steering function) u(t). The formal problem consists in reducing the state x(t) to zero in minimal time by a suitable choice of the steering function u(t) Several interesting properties of this problem have been studied [*] 28 [*] J.P. LaSalle, Proc. Nat. Acad. Of Sciences 45, (1959); R.Bellman,I. Glicksberg O.Gross, On the bang-bang control problem Q. Appl. Math (1956)

29 Formal aspects of the control problem Definition [*]: An admissible (piecewise measurable in a set Ω ) steering function u* is optimal if for some t*>0 x(t*,u*) =0 and if x(t,u) 0 for 0< t< t* for all u(t) Œ Ω Theorem 1 [*]: Anything that can be done by an admissible steering function can also be done by a bang-bang function Theorem 2 [*]: If for the control problem there exists a steering function u(t) Œ Ω such that x(t,u)=0, for t>0, then there is an optimal steering function u* in Ω. All optimal steering functions u* are of the bang-bang form Thus the only way of reaching the objective in minimum time is by using properly all the power available u(t) t Steering times can be chosen testing x(t < e 29

30 Comments on optimal control strategies Define critical width W crit (i.e. dte crit )on basis of required performance (e.g. DQ/Q<2%) Gyrotron (battery) is kept simmering at low duty cycle (10%) The PLL tracks ECE fluctuations induced by island Real-time estimate of P ij,locates r island Real-time estimate of P ia locates r dep (a) and steers mirrors by angle a Optimal Control problem: Minimization of r m,n (W) - r dep (a) 2 subject to W >W crit to trigger Gyr. to full power 30

31 CONCLUSIONS For the FTU tokamak we have developed and successfully tested a new strategy and fast correlation algorithms for real-time tracking of phase and radial location of magnetic islands as well as location of ECW power deposition. Our new strategy is based on polling ECW modulated power deposition and island position from the signals of a multichannel ECE diagnostic and a control action minimising r island -r dep 2 The diagnostic/control unit operates automatically in real-time actuating appropriately the ECW power launcher as soon as islands are detected Formal control theory supports the ideas of : Steering mirrors in real time, On-off switching of full RF power at discrete times Power requirements depend essentially on ratio J ECCD /J BOOT, and the radial location of ECW absorption profile Finally real time information of the radius of rational q surfaces is obtained and could be used for fast equilibrium reconstruction (in progress ) 31

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