1. Perspectives of tearing modes control in RFX-mod Paolo Zanca Consorzio RFX, Associazione Euratom-ENEA sulla Fusione, Padova, Italy

2. RFX-mod contributions to TMs control (I) Demonstrated the possibility of the feedback control onto TMs Clean-Mode-Control (CMC) based on the de-aliasing of the measurements from the coils produced sidebands

3. RFX-mod contributions to TMs control (I) Demonstrated the possibility of the feedback control onto TMs Clean-Mode-Control (CMC) based on the de-aliasing of the measurements from the coils produced sidebands Not obvious results: phase-flip instability?

4. RFX-mod contributions to TMs control (I) Demonstrated the possibility of the feedback control onto TMs Clean-Mode-Control (CMC) based on the de-aliasing of the measurements from the coils produced sidebands Not obvious results: phase-flip instability? No-sign of phase-flip instability; equilibrium condition can be established where CMC induces quasi-uniform rotations of TMs

5. Wall-unlocking of TMs with CMC In general, the feedback cannot suppress the non-linear tearing modes requested by the dynamo. The feedback keeps at low amplitude the TMs edge radial field Improvement of the magnetic structure: sawtooth of the m=1 n=-7 which produces transient QSH configurations RFX-mod contributions to TMs control (II)

6. Increase the QSH duration → recipes under investigation Which are the possibilities to reduce further the TMs edge radial field? → Model required CMC optimizations

7. RFXlocking Semi-analitical approach in cylindrical geometry Newcomb’s equation for global TMs profiles Resonant surface amplitudes imposed from experiments estimates Viscous and electromagnetic torques for phase evolution Radial field diffusion across the shell(s) Feedback equations for the coils current It describes fairly well the RFX-mod phenomenology →L.Piron talk

8. General analysis of the TM control

9. plasma SensorsCoilsVessel Single-shell external coils

10. Normalized edge radial field The feedaback action keeps low the normalized edge radial field At best b ^ sens can be made close but not smaller than the ideal-shell limit

11. plasma SensorsCoilsVessel Feedback limit

12. plasma SensorsCoilsVessel Feedback limit

13. plasma Sensors b r =0 everywhere: impossible CoilsVessel Feedback limit

14. Role of the Vessel The stabilizing effect of the vessel is crucial for having low b ^ sens and moderate power request to the coils The shorter τ w the faster must be the control system (f c =1/Δt) to avoid feedback (high-gain) induced instabilities Optimum range: τ w >10ms better τ w  100ms

15. plasma Sensors Coils Vessel Single-shell Internal coils

16. plasma Sensors Coils Vessel Single-shell Internal coils

17. Continuous-time feedback → solution ω  ω 0 with b r (r sens )  0 for large gains Discrete-time feedback : including the latency Δt the high- gain instability may occur The good control region is not accessible for realistic TM amplitudes. For stable gains b ^ sens is determined by the ideal-shell limit, which is large due to the loose-fitting vessel required by the coils dimension

18. RFP design for good TM control (a personal view)

19. Premise The passive stabilization provided by a thick shell does not solve the wall-locking problem In the thick-shell regime wall-locking threshold ~σ 1/4 Feedback is mandatory to keep TMs rotating

20. Design in outline In-vessel coils not interesting Single structure (vessel=stabilizing shell) with the coils outside Close-fitting vessel to reduce the ideal-shell limit τ w  10ms-100ms with Δt  10μs-100μs

21. RFX-mod perspectives (a personal view)

22. RFX-mod layout 3ms vacuum-vessel, 100ms copper shell, ~25ms mechanical structures supporting the coils The control limit is mainly provided by the 100ms copper shell

23. RFX-mod status Gain optimization guided by RFXlocking simulations for the RFX-mod case m=1 TMs

24. Optimizations Get closer to the ideal-shell limit (minor optimization) Reduce the ideal-shell limit by hardware modifications (major optimization)

25. Minor optimizations Increase the coils amplifiers bandwidth: maximum current and rensponse time Acquisition of the derivative signal db r /dt in order to have a better implementation of the derivative control (to compensate the delay of the coils amplifiers) Compensation of the toroidal effects by static decoupler between coils and sensors only partially exploited Compensation of the shell non-homogeneities requires dynamic decoupler (work in progress)

26. Major optimization Approach the shell to the plasma edge possibly simplifying the boundary (removing the present vacuum vessel which is 3cm thick) Moving the τ w =100ms shell from b=0.5125m to b=0.475m (a=0.459) a factor 3 reduction of the edge radial field is predicted by RFXlocking

27. Conclusions CMC keeps TMs into rotation Edge radial field: ideal-shell limit found both with the in- vessel and out-vessel coils → b r (a)=0 cannot be realized The vessel=shell must be placed close the plasma → coils outside the vessel. Is a close-fitting vessel implementable in a reactor? The feedback helps the vessel to behave close to an ideal shell → τ w cannot be too short

28. spare

29. Edge radial field control by feedback

30. RFXlocking.vs. experiment

31. Normalized edge radial field: weak b rs dependence

32. b r (r m,n ) vs b r (a) experimental

33. Locking threshold The present analysis valid for  w <<r w cannot be extrapolated to very long  w

34. Edge radial field.vs. current time constant

35. a = 0.459m r w i = 0.475m c = 0.5815m Single mode simulations: external coils

36. Single-mode analysis: feedback performances dependence on  w

38. Multi-mode analysis: power dependence on  w

39. Edge radial field:  w dependence Data averaged on 0.1s simulation m=1

40. Normalized edge radial field: r wi dependence m=1

41. Normalized edge radial field: no r f dependence m=1

42. Out-vessel coils: signals 4x48 both for coils (c = 0.5815m) and sensors (r wi = 0.475m )

43. Single-shell: discrete feedback Δt = latency of the system

44. External coils: discrete feedback τ w =100ms

45. External coils: discrete feedback τ w =10ms

46. External coils: discrete feedback τ w =1ms

47. The in-vessel coils

48. Single mode simulations: frequency τ w = 1ms  100ms

49. Single mode simulations: I c, V c

50. Single mode simulations: edge b r

51. Multi-mode simulations: frequencies Averages over the second half of the simulation

52. Multi-mode simulations: plasma surface distortion

53. Multi-mode simulations: no phase-locking Ideal shell feedback

54. Multi-mode simulations: no phase-locking Incompatible with

55. Internal coils: discrete feedback stable solutions

57. The MHD model: Ψ wi, Ψ we Boundary conditions from Newcomb’s solution

58. The MHD model: Ψs From experiment No-slip condition

59. The MHD model: Ω θ, Ω Φ

60. The MHD model: δT EM

61. The MHD model: Ψ c Further variable: I c m,n

62. The MHD model: I c Further variable: I REF m,n RL equation for the plasma-coils coupled system

63. The MHD model: I REF Acquired by the feedback

64. Why a pure derivative control? When |   c m,n |>>1, from the RL equation one gets