Two classes of RWMs Internally non- resonant with -11 ≤ n < 0 Externally non- Resonant with

1. Intelligent shell experiments on EXTRAP T2REXTRAP T2R groupJ. R. Drake, Jenny-Ann Malmberg, Per Brunsell, Dmitriy YadikinChalmers theory groupD. Gregoratto, Y. Liu, A. BondesonRFX R. Paccagnella, S. Ortolani, P. Martin, G. Manduchi + many others

2. Intelligent shell experiments on EXTRAP T2ROutline of talk1. Intro to RFP RWMs and motivation.2. New RWM measurements on T2R3. Description of T2R sensor and active coil arrays4. Theory for feedback with partial shell coverage5. First results with intelligent shell feedback applied6. Plans for the future

3. Two classes of RWMs Internally non- resonant with -11 ≤ n < 0 Externally non- Resonant with 0 < n < 7

4. EXTRAP T2R front end Note: • The blue ”shell” surface • The spacing of the 64 TF coils

5. Suitability of EXTRAP T2R for resistive wall mode active control studies1. -relaxation < -shell < -pulse. 2. Internally resonant modes are rotating so their b-radial perturbation is suppressed. 3. Extensive magnetic diagnostics to measure mode spectra and growth rates. 4. RWM perturbations measured at b-r / B-equilib ≈ 10-3. 5. Both internally and externally non-resonant modes are observed. 6. Growth rates are dependent on current density and pressure profiles.

6. Suitability of EXTRAP T2R for resistive wall mode active control studies (continued).1. The surface where the saddle coils are installed is relatively accessable and well-defined. 2. Plasma current levels are low (<100 kA) so the power requirements for the amplifiers for the active saddle coils is modest. Cheap loudspeaker amplifiers can be used.

7. One PID controller to freeze flux at zero One active saddle coil coinciding with sensor coil One sensor coil Active mode control methods studied.Collaboration Alfven Lab, Consorzio RFX and Chalmers theory group.1. Intelligent shell - Alfven Lab taking the lead2. Mode analysis - RFXtaking the lead Voltage output to an array of active saddle coils Sensor coil array Real time mode analysis SIMO controller

8. Relevance of resistive wall mode active control studies done on the T2R reversed-field pinch1. The collaboration includes Anders Bondeson’s theory group at Chalmers and the RFX theory and experiment groups. Emphasis is on comparison of theory and experiment. 2. There are features of feedback systems common for both the tokamak and the RFP i.e. The systems are based on fields produced by arrays of active external coils interacting with plasma modes. 3. Role of field errors can be studied.

9. Observed Growth rates(w) for three RWMS. 80 60 40 20 0 red: n = -2 Theoretically stable. -exp /-theory= negative Small initial amplitude. green: n = -8 Theoretically unstable. -exp /-theory= 1.3 Large initial amplitude. blue : n = -10 Theoretically unstable. -exp /-theory= 1.5 Small initial amplitude. Ip -9 -10 -11 logebn 2 4 6 8 10 time (ms)

10. Observed Growth rates for n = -10 for two equilibria. 80 60 40 20 0 n = -10 (internally non res) green: ”High ” equilibrium Lower growth rate w= 1.4 blue : ”Low ” equilibrium Higher growth rate w= 4.1 Ip -9 -10 -11 logebn 2 4 6 8 10 time (ms)

11. Observed Growth rates for n = +5 for two equilibria. 80 60 40 20 0 n = +5 (externally non res) green: ”High ” equilibrium Higher growth rate w= 1.9 blue : ”Low ” Stable No growth Ip -9 -10 -11 logebn 2 4 6 8 10 time (ms)

12. Observed phase of RWMs in fixed lab frame Five shots overlaid in each panel n = -8 • Unstable (Th & Exp) • Large ”initial” amplitude • Mode phase is repro-ducible in the lab frame n = -10 • Unstable (Th & Exp) • Small ”initial” amplitude • Mode phase is random in the lab frame • Slow rotation +  2π 8

13. Observed phase of RWMs in fixed lab frame Five shots overlaid in each panel n = -2 • Theor stable - Exper unstable • Small ”initial” amplitude • Mode phase is repro-ducible in the lab frame n = +5 • Unstable (Th & Exp) • Small ”initial” amplitude • Mode phase varies in the lab frame • Sometimes slow rotation 2π 10

14. Raw data m = 1 B-radial perturbation (inboard - outboard) at 8 ms into discharge Five shots overlaid in each panel Low q • Some shot-to-shot variation. • Amplitudes higher than the high q case below. High q • No shot-to-shot variation (n = 8 domi-nated). • Amplitudes lower than the low q case above. 0 100˚ 200˚ 300˚ Toroidal angle

15. Summary of new experimental observations concerning RWM instabilities1. For many theoretically unstable modes, the experimentally observed growth rates are fairly well described by theory including a dependence on equilibrium profiles. 2. Some theoretically stable modes are observed to be unstable (i.e. n = -2). 3. Concerning the role of field errors: • Modes that have a high initial amplitude during the transient discharge start-up (i.e. n = -8), have a fixed phase in the lab frame. • The theoretically stable n = -2 mode has a fixed phase in the lab frame.

16. Feedback experiments underway on T2R1. Sensor coil array is in place in interspace between vacuum vessel and shell. • 4 (poloidal) x 64 (toroidal) • saddle coils ”outboard-top-inboard-bottom”. 2. Active coils in place outside shell at eight toroidal positions. • coils are ”1/32” wide (i.e. double the width of a sensor coil). • saddle coils ”outboard-top-inboard-bottom”. 3. ”m = 1” connected • Both sensor coils and saddle coils are series connected (i.e. ”top & bottom” and ”inboard & outboard”). 4. Present active coil array covers 25% of surface.

17. 110-degree toroidal sector of T2R toroidal direction 337.5˚ 0˚ 28˚ 90˚ outboard bottom Poloidal direction inboard top 61 62 63 64 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 B-r sensor coils 4(poloidal) x 64 (toroidal) positions diagnostic port sector outer shell weld shell gaps The frame of reference consists of 64 toroidal sectors numbered 1 to 64

18. 110-degree toroidal sector of T2R toroidal direction 337.5˚ 0˚ 28˚ 90˚ outboard bottom Poloidal direction inboard top 61 62 63 64 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 B-r sensor coils 4 (poloidal) x 64 (toroidal) positions The saddle coils for active feedback are twice the width of the sensor coils

19. 110-degree toroidal sector of T2R toroidal direction 337.5˚ 0˚ 28˚ 90˚ outboard bottom Poloidal direction inboard top 61 62 63 64 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 Cartoon of an n = 8 mode

20. Theory for both intelligent shell control and mode control has been done. Assumptions for partial coverage feedback in the T2R RFP1. Used T2R geometry and penetration times.But assume smooth resistive shell! 2. Assume B perturbation Fourier component information corresponding to 4 x 32 sensor coils. 3. Use 4 x 8 active coils corresponding to actual coil geometry and partial coverage (side band harmonics). 4. Consider only m = 1 nonresonant RW modes (i.e. zero for resonant modes and higher m modes. 5. Examine both intelligent shell case and mode analysis/control case.

21. Theory for partial coverage feedback in an RFPReferences:1. Feedback control of resistive wall modes in RFPs Paccagnella, Gregoratto and Bondeson Nuc Fusion 42 (2002) pg 1102 2. Output feedback with 4 x 32 sensors and 4 x 8 coils Gregoratto, Paccagnella, Liu and Bondeson Manuscript

22. Features of the feedback theory1. Assume Fourier component bn are known for the modes. 2. Eight active coil toroidal positions allows 8 control voltages Vn (n = -3,-2,-1,0,+1,+2,+3,+4) 3. Feedback law determines the 8 control voltages. 4. All the modes of interest are potentially ”controlled” (i.e. stabilised, destabilised, reduced growth rate, increased growth rate) 5. For intelligent shell case the gains in the feedback law are equal and positive (i.e. negative feedback). 6. For mode control case gains in the feedback law are different and are optimised (can be positive feedback).

23. RFX figure Block diagram for the control of a single RWM

24. Experiments with anaog controlled intelligent shell have started plasma current Controller Input is m = 1 connected sensor coil pair Amplifier Output to m = 1 connected saddle coil pair B-radial grows without feedback B-radial B-radial frozen at zero with feedback Active coil current Vacuum vessel Shell

25. Intelligent shell experiments Unfortunately not all the controllers were ready as of last week. The first experiments have been done with 12 analog controllers.This means that 6 of the 8 toroidal positions can be controlled.First test:Intelligent shell with 6 toroidal positions active which is equivalent to about 18% coverage).

26. Comparison of experiment with 6 toroidal positions and theory for 8 toroidal positions. Summary of feedback theory for targeted moden = -8Without feedback, the n = -8 mode is unstable and has a large initial amplitude.The n = -8 mode should be stable for the intelligent shell controller at 8 toroidal positions. The n = -8 should also be stable for the mode controller with active coils (1/32 wide) at 8 toroidal positions.

27. Partial intelligent shell. 6 toroidal positions - inboard/outboard+top/bottom(18% coverage)Green is without feedbackBlue is with feedback n = -8 The initial amplitude is lower. The growth rate is not changed. The phase is unchanged. Without FB With FB phase

28. n = -2 (impossible case)The harmonics ”controlled” are n = -10, -2, +6, +14.The n = -2 mode is theoretically stable but experimentally unstable.The n = -10 and +6 modes are unstable both in theory and experiment. The n = +14 is stable in theory and experiment.Feedback with partial coverage of 8 toroidal positions cannot stabilise all these modes.For the intelligent shell controller, the n = -10 growth rate can be decreased but the n = -2 and n = +6 have higher growth rates and the n = 14 is destabilised!The mode controller is better. However not all three unstable modes can be stabilised.

29. Partial intelligent shell. 6 toroidal positions - inboard/outboard+top/bottom(18% coverage)Green is without feedbackBlue is with feedback n = -10 The initial amplitude is not changed. The growth rate is not changed. The phase is changed. With FB Without FB phase

30. Partial intelligent shell. 6 toroidal positions - inboard/outboard+top/bottom(18% coverage)Green is without feedbackBlue is with feedback n = -2 The initial amplitude is slightly lower. The growth rate is slightly increased (in agreeement with theory). The phase is not changed. Without FB With FB phase

31. Partial intelligent shell. 6 toroidal positions - inboard/outboard+top/bottom(18% coverage)Green is without feedbackBlue is with feedback n = +6 The initial amplitude is not changed. The growth rate is slightly decreased (not in agreeement with theory). The phase is not changed. Without FB With FB phase

32. Test with 8 toroidal positions, but only inboard/outboard saddle coils activated. Unexpected result:The n = +6 mode is stabilised. The other modes are only slightly changed.

33. Partial intelligent shell. 8 toroidal positions - inboard/outboard( 12% coverage)Green is without feedbackBlue is with feedback Without FB b n = -10 b n = +6 With FB phase The n = +6 mode is stabilised. The n=-10 mode is slightly lower

34. Partial intelligent shell. 8 toroidal positions - inboard/outboard( 12% coverage)Green is without feedbackBlue is with feedback With FB b n = -8 b n = -10 Without FB phase The n = -8 mode is unchanged.. The n=+14 mode has a higher amplitude

35. Partial intelligent shell. 6 toroidal positions - inboard/outboard+top/bottom(18% coverage)Green is without feedbackBlue is with feedback b-radial pertur-bation late in pulse. Intelligent shell controllers at 6 toroidal positions indicated by vertical dashed line. With FB Without FB

36. Future experimentsWith the present 8 toroidal position set up we will continue the studies and compare experiment with theory.Both the intelligent shell controller and the RFX mode controller will be used (and compared with the analog IS). For these studies destabilisation is as interesting as stabilisation since the goal is to verify that the theory models the relevant physics.Study the field error effects. • initial amplitude. • destabilisation of a stable RWM. • phase. Add more active coils. Next step is 50% coverage.Use the flexibility of the RFX controller for mode rotation.