Progress in understanding and. Progress in understanding and. Reversed Field Pinches. controlling QSH in. L. Marrelli

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1 Progress in understanding and Progress in understanding and controlling QSH in Reversed Field Pinches L. Marrelli Consorzio RFX Associazione EURATOM-ENEA sulla Fusione 10 th Active Control of MHD Stability Workshop, Madison, WI, 31/12-2/10/2005

2 Contributors F.Bonomo, A.Cravotta, P.Franz, P.Martin, P.Piovesan, I.Predebon, G.Spizzo, T. Bolzonella, S.Cappello, D.F.Escande, D.Gregoratto, G.Manduchi, R.Paccagnella, S.Ortolani, D. Terranova, P.Zanca, M. Zuin, P.Scarin, M. Agostini, G.Serianni, A. Luchetta, M. Cavinato, G. Marchiori, N. Vianello and the RFX team Consorzio RFX-Associazione EURATOM ENEA sulla Fusione B. E. Chapman, D. Craig, J. S. Sarff, S. C. Prager, MST Team Department of Physics, University of Wisconsin J.Drake, P.Brunsell, D.Yadikin, M.Cecconello, EXTRAP T2R team Division of Fusion Plasma Physics (Association EURATOM/VR), Alfvén Laboratory, Royal Institute of Technology, SE Y.Yagi, H.Koguchi, T.Shimada, Y.Hirano, TPE-RX team Fusion Plasma Group, Energy Electronics Institute, National Institute of Advanced Industrial Science and Technology (AIST), R.B. White Princeton Plasma Physics Laboratory, Princeton, NJ

3 Outline What is a Single Helicity (SH) Reversed Field Pinch? electrostatic nature of dynamo field transport properties QSH in passive shell experiments QSH in active control experiments QSH in Virtual Shell Experiments QSH control

4 QSH in RFX-mod n= -7 n= -8 n= -9 n= -10 # t [ms] t [ms] bφ [mt] Te [ev]

5 Single Helicity RFP B and J Perp. dynamo velocity v perp E =η J v B From Specyl 3d code (Cappello ( Cappello) The dynamo velocity field is an electrostatic drift, driven by the helical magnetic perturbation with m=1 (S.Cappello, APS2005 Invited talk)

6 E Charge separation in QSH: core helical capacitor =η J v B E = ρ c The plasma is globally neutral, but regions with positive or negative charge exist. Maxima and minima of charge separation describe a dipolar helix, which wraps around the helical magnetic axis φ min(φ) max(φ)

7 Electrostatic drift The E x B drift related with the modulated electrostatic field E ϕ provides the main contribution to the dynamo velocity field Electrostatic drift v v ϕ loop E ϕ B E 2 B loop 2 B B Total Plasma Flow

8 MH vs SH 3D viscoresistive MHD simulations show that the dynamo can be Laminar (Single Helicity) Turbulent (Multiple Helicity) (superposition of many SH) 0.15 b / B b / B n SH n Good magnetic flux surfaces Stochasticity by island overlap n

9 SH in experiments Transitions to narrow spectra are found in the RFP experiments ka, PPCD 19/10/ MST bθ m=1, n (mt) t [ms]...but the level of secondary modes remains relatively high => Quasi-SH

10 Experimental evidences of laminar dynamo Measurement of velocity fluctuations in MST [1] During Quasi-SH the spectrum of velocity fluctuations narrows an ordered (m=1,n=6) helical flow pattern emerges as the plasma approaches an helical state The dynamo electric field (m=1,n) is mainly due to the Quasi-SH mode QSH MH Eφ (Volts/m) n n [1] Piovesan P. et al, PRL 2004

11 What is a Single Helicity (SH) Reversed Field Pinch? electrostatic nature of dynamo field transport properties QSH in passive shell experiments QSH in active control experiments QSH in Virtual Shell Experiments QSH control

12 Enhanced temperature Helical structure Core T e in RFX-mod #17494 [1] Escande D.F. et al, PRL 85, 1662 (2000) [2] Franz P. et al, PRL 92, (2004) [3] Franz P. et al, Phys. Plas, in press

13 2D map of island temperature The 2D map of the electron temperature has been measured with multicolor SXR tomography for a QSH PPCD discharge and an hot island structure is found. MST PPCD QSH SXR imaging: P.Piovesan talk PPCD: R. O Connell talk

14 Modeling transport properties Test particle transport properties in 3 different field topologies with the same magnetic energy Montecarlo approach with the ORBIT code (hamiltonian guiding center) [1] [1]I.Predebon, et al. PRL 93, (2004) RFX geometry

15 Modeling transport properties electrons In Multiple Helicity, loss time has no poloidal dependence MH θ Poloidal angle ψp τl (ms)

16 Modeling transport properties electrons SH MH In Multiple Helicity, loss time has no poloidal dependence In Single Helicity, loss time is considerably higher θ Poloidal angle ψp τl (ms)

17 Modeling transport properties electrons SH QSH MH In Multiple Helicity, loss time has no poloidal dependence In Single Helicity, loss time is considerably higher In QSH the island provides better confinement Neoclassical effects are significant θ Poloidal angle ψp τl (ms)

18 Edge Transport in QSH Statistical properties of electrostatic edge turbulence differ in QSH 50 QSH MH l [mm] 30 λ X[mm] 1 10 Scale [µs] Electrostatic structures smaller in QSH regimes than in MH at all time scales Gas Puff Imaging diagnostic: P. Scarin et al. APS05

19 QSH: a selection process In RFX-mod the secondary modes amplitude spontaneously decreases when the spectrum tends to QSH... QSH B ~ b ϑ φ ( a )...similarly to other RFPs [%] dominant TPE-RX MST secondary N s b = n 2 1, n b 2 l 1, l 1 N s b = n 2 1, n b 2 l 1, l 1 Marrelli L. et al, PoP 9, p2868 (2002) Piovesan P, et al., PoP 11, p151(2004)

20 QSH states in RFX-mod n= -7 n= -8 n= -9 n= -10 # n= -7 n= -8 n= -9 n= -10 # t [ms] t [ms] bφ [mt] bφ [mt] passive shell virtual shell n= -7 n= -8 n= -9 n= -10 # n= -7 n= -8 n= -9 n= -10 # t [ms] natural evolution t [ms] bφ [mt] bφ [mt] feedback controlled

21 What is a Single Helicity (SH) Reversed Field Pinch? electrostatic nature of dynamo field transport properties QSH in passive shell experiments QSH in active control experiments QSH in Virtual Shell Experiments QSH control

22 Passive shell experiments At 600 ka stationary QSH are found setting-up of the discharge plays an important role # I [ka] Flux [Wb] 10 5 n= -7 n= -8 n= -9 n= bφ [mt] 6 4 brφ [mt] t[ms]

23 Intermittent SXR structures The appearance of islands is associated with a decrease of the secondary modes # ms # ms bφ (m=1,n) (mt) bφ (m=1,n) (mt) n = -8 n = -9 time (ms) ON OFF

24 Role of the equilibrium I p = 600kA N S < 3.2 n = -7 n = -8 n = -8 (ramping, I p = 600kA) The helicity of the dominant mode. is determined by the equilibrium parameters. F, reversal parameter D.F. Escande, et al., PRL, 2000 Θ, pinch parameter RFX n=5 stnd n=6 stnd F n=6 PPCD MST F QSH probability L. Marrelli, et al., PoP, 2002 Θ n=7 TPE-RX n=6 P. Piovesan, et al., PoP, 2004 I P (ka)

25 What is a Single Helicity (SH) Reversed Field Pinch? electrostatic nature of dynamo field transport properties QSH in passive shell experiments QSH in active control experiments QSH in Virtual Shell Experiments QSH control

26 Magnetic fluctuation spectra in V.S. During Virtual Shell (V.S.) operations the radial field component of the modes is significantly reduced the toroidal component is on average reduced and transitions to purer QSH spectra may occur dominant m=1 mode Average of secondary m=1 modes bφ m=1,n / Bθ(a) (%) N S N S passive shell virtual shell

27 Quasi-SH spectra are narrower in V.S. The preferred mode is the innermost resonant: n=-7 in present experiments RFX-MOD # m=1,n=-7 <m=1,n=8-15> bφ m=0, n (mt) bφ m=1, n<0 (mt)

28 Quasi-SH spectra are narrower in V.S. The preferred mode is the innermost resonant: n=-7 in present experiments RFX-MOD # m=1,n=-7 <m=1,n=8-15> bφ m=0, n (mt) bφ m=1, n<0 (mt)

29 Quasi-SH spectra are narrower in V.S. The preferred mode is the innermost resonant: n=-7 in present experiments RFX-MOD #17116 m=1,n=-7 <m=1,n=8-15> bφ m=0, n (mt) bφ m=1, n<0 (mt)

30 Quasi-SH spectra are narrower in V.S. The preferred mode is the innermost resonant: n=-7 in present experiments m=1,n=-7 RFX-MOD #17116 m=1,n=-7 RFX-mod <m=1,n=8-15> <m=1,n=7-15> m=1,n=-6 MST # bθ m=1, n (mt) bφ m=1, n<0 (mt) time (ms) This behavior is similar to MST standard discharges: MST has a close fitting thick shell m=1, n=-6 is the innermost resonant

31 T e in VS QSH Higher electron temperature is usually associated with QSH spectra n= -7 n= -8 n= -9 n= -10 # t [ms] bφ [mt] Te [ev] t [ms]

32 T e in VS QSH Higher electron temperature is usually associated with QSH spectra n= -7 n= -8 n= -9 n= -10 # t [ms] bφ [mt] Te [ev] t [ms]

33 Temperature vs secondary modes The enhancement of the temperature occurs when secondary modes decrease Loss time of test particles deposited outside the magnetic structure increases in QSH periods n= -7 n= -8 n= -9 n= -10 # t [ms] bφ [mt] Loss Time (ms) Te [ev] t [ms]

34 What is a Single Helicity (SH) Reversed Field Pinch? electrostatic nature of dynamo field transport properties QSH in passive shell experiments QSH in active control experiments QSH in Virtual Shell Experiments QSH control

35 Control Scenarios The system has been designed in order to allow operations with a variety of scenarios: 1. Natural evolution of a set of selected modes No control is done on a selected tearing helicity (or a subset) 2. Feedforward no matter what the amplitude of a selected mode is, the system generate a field of given amplitude (and phase) 3. Feedback the system control the amplitude and phase of the radial field of a selected helicity Only Natural and Feedback attempted so far

36 Control System Diagram In Selective Virtual Shell scenarios, each saddle coil power supply system is individually controlled by a PID. feedforward Sensor coils FFT spatial PID + filter Saddle Coils Power Supplies mag. field. references

37 Natural evolution: single mode Inhibiting the control of a innermost tearing modes, allows them to grow a QSH spectrum for the innermost resonant modes is reproducibly obtained, but n= -7 n= -8 n= -9 n= -10 # n= -7 n= -8 n= -9 n= -10 # n= -7 n= -8 n= -9 n= -10 # n= -7 n= -8 n= -9 n= -10 # n= -7 n= -8 n= -9 n= -10 n=-13 # t[ms] bφ [mt] br [mt] t[ms] t[ms] t[ms] t[ms]

38 Deformation of the plasma column... the radial component of the mode produces a helical deformation of the column. Interaction is better than in passive operations... but feedback control of the radial component allows to significantly reduce it! D.Terranova NB: Color coding is different for the two plots!

39 Feed-back: controlled evolution The radial field of tearing helicities can been kept at a reference value 8 6 # n= -7 n= -8 n= -9 n= # n= -7 n= -8 n= -9 n= # n= -7 n= -8 n= -9 n= reference bφ [mt] br [mt] t[ms] bφ [mt] br [mt] t[ms] bφ [mt] br [mt] t[ms]

40 stationary QSH n=-7 Transitions to narrower spectra may occur when the value of the radial component of m=1 n=-7 is kept constant by feedback control Determining the conditions for onset need more experiments 8 6 # n= -7 n= -8 n= -9 n= # n= -7 n= -8 n= -9 n= bφ [mt] br [mt] t[ms] bφ [mt] br [mt] t[ms]

41 QSH (slow) rotation The QSH mode (n=-8 and n=-7) can be reproducibly rotated in time (10 Hz) minimum amplitude? 8 # n= -7 n= -8 n= -9 n= radial component phase toroidal component phase bφ [mt] br [mt] Phase bφ [degree] time[ms]

42 QSH (slow) rotation The QSH mode (n=-8 and n=-7) can be reproducibly rotated in time (10 Hz) minimum amplitude? SXR structures appear # t= ms Z (m) # n= -7 n= -8 n= -9 n= R (m) W/m radial component phase toroidal component phase bφ [mt] br [mt] Phase bφ [degree] time[ms]

43 QSH (slow) rotation The QSH mode (n=-8 and n=-7) can be reproducibly rotated in time (10 Hz) minimum amplitude? SXR structures appear at different angles in time # t= ms Z (m) R (m) # t= ms R (m) W/m W/m Z (m) radial component phase toroidal component phase # n= -7 n= -8 n= -9 n= bφ [mt] br [mt] Phase bφ [degree] time[ms]

44 Extrap T2R: natural evolution Behavior is different in Extrap T2R (where tearing modes typically rotate) reference n=-13 off locking occurs Toroidal radial No significant growth of the toroidal component P. Brunsell D.Yadikin

45 Conclusions The RFP is not intrinsically chaotic: Single Helicity is a laminar equilibrium dynamo field has an electrostatic nature In RFX-mod QSH spectra are found Passive operations stationary QSH similar to RFX Virtual Shell operations QSH spectra are narrower but transient up to now Higher electron temperature is associated with QSH spectra Tearing mode control QSH spectra are obtained reproducibly natural evolution feedback controlled evolution slow rotation is possible

46 Future work QSH induction experiments determination of the optimal level of external helical perturbation tradeoff between spectrum width and plasma wall interactiom Virtual shell with ramping startup currently on going Better cancellation of radial field at the plasma boundary movement of the virtual shell from sensors to plasma edge Differential rotation of selected tearing helicities phase unlocking of tearing modes Interaction of QSH with RWM Selective V.S. shell experiments allowing simultaneous growth of tearing and RWM helicity