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Experimental study on the physical mechanism related to the hysteresis

Experimental study on the physical mechanism related to the hysteresis of the TM locking‐unlocking process to an external field in EXTRAP T2R. R. Fridström, L. Frassinetti, P. Brunsell. Department of Fusion Plasma Physics, School of Electrical Engineering,

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Experimental study on the physical mechanism related to the hysteresis

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  1. Experimental study on the physical mechanism related to the hysteresis of the TM locking‐unlocking process to an external field in EXTRAP T2R. R. Fridström, L. Frassinetti, P. Brunsell Department of Fusion Plasma Physics, School of Electrical Engineering, KTH Royal Institute of Technology (Association EURATOM-VR)

  2. Earlier results on TM locking-unlocking • The TM locking to an error fields has been studied in many devices. Examples are: JET, COMPASS, DIII-D, MAST, MST, LHD… • The unlocking process has been studied in not as many experiments and with less detail. Examples are: COMPASS, JET More recently in J-TEXT and EXTRAP T2R • The locking and unlocking process has been theoretical described by several authors: Fitzpatrick,Nave, Lazzaro… Fitzpatrick and Yu, PoP 2002

  3. OUTLINE • Introduction • - EXTRAP T2R • - Feedback system and RMPs • TM locking and unlocking to an external resonant field - The locking threshold - The unlocking threshold and the hysteresis • - Comparison of experimental data with models • Hysteresis: experimetal results on the physics mechanisms • that produces the hysteresis • - Viscous torque and electromagnetic (EM) torque - The torque balance • Conclusions 1

  4. EXTRAP T2R (m=1 n<-12) are resonant THE DEVICE (1,-12) (1,-13) (1,-14) (1,-15) EXTRAP T2R is a RFP with: • R=1.24m • a=0.18m • Ip ≈ 50-150kA • ne ≈ 1019m-3 • Te ≈ 300-600eV • tpulse≈ 90ms (1,-16) non-resonant harmonics TM 2

  5. active coils sensor coils THE FEEDBACK SYSTEM • Sensor coils 4 poloidal x 32 toroidal located inside the shell • Digital controller • Active coils 4 poloidal x 32 toroidal located outside the shell shell tshell≈13.8ms (nominal) (cm) Intelligent Shell, RMP n=-15 LCFS 1.0 0.8 0.6 0.4 0.2 0.0 br(mT) 0 10 20 30 40 50 60 70 Time (ms) • RMP applied using the RIS algorithm [Olofsson PPCF 2010] 3

  6. RMP and TM braking • The RMP produces the TM braking RMP TM velocity TM amplitude 4

  7. RMP and TM braking • The RMP produces the TM braking RMP RMP off RMP on Dv-25km/s TM velocity TM amplitude 4

  8. RMP and TM braking • The RMP produces the TM braking • During the braking phase, the velocity reduction is peaked at the RMP resonance RMP Velocity reduction profile Velocity reduction profile TM velocity TM amplitude Braking phase n=-15 resonance 4

  9. RMP and TM braking • The RMP produces the TM braking • During the braking phase, the velocity reduction is peaked at the RMP resonance • During the locking phase, a relaxation in the core region occurs RMP Velocity reduction profile Velocity reduction profile TM velocity TM amplitude Braking phase Locking phase 4

  10. The locking threshold locking • The locking threshold is calculated using several shots • In each shot, the RMP has a square waform but different amplitude. braking Slow rotating branch RMP (1,-15) (mT) 5

  11. TM locking and unlocking • To study the unlocking, a RMP with triangular waveform is used. RMP TM velocity TM amplitude 6

  12. TM locking and unlocking • To study the unlocking, a RMP with triangular waveform is used RMP TM velocity vϕ-profile relaxes Braking phase TM amplitude 6

  13. TM locking and unlocking • To study the unlocking, a RMP with triangular waveform is used RMP TM velocity vϕ-profile relaxes Braking phase TM amplitude Locking phase 6

  14. Unlocking threshold RMP • To estimate in a more accurate way the unlocking threshold: - the RMP is ramped up till locking occurs. - then it is ramped down and kept constant to a “plateau” value. • A stationary phase is obtained • The unlocking threshold is calculated during the stationary phase reference velocity with no RMP reference velocity with no RMP TM velocity 7

  15. Hysteresis in the locking-unlocking mechanism locking • The locking threshold is calculated using several shots • In each shot, the RMP has a square waform but different amplitude. • The unlocking threshold is calculated using a triangular wavefor followed by a plateau phase increasing RMP Slow rotating branch decreasing RMP RMP (1,-15) (mT) 8

  16. Hysteresis in the locking-unlocking mechanism unlocking locking • The locking threshold is calculated using several shots • In each shot, the RMP has a square waform but different amplitude. • The unlocking threshold is calculated using a triangular wavefor followed by a plateau phase • An hysteresis in the locking-unlocking process is present increasing RMP Slow rotating branch decreasing RMP RMP (1,-15) (mT) 8

  17. Hysteresis in the locking-unlocking mechanism unlocking locking • The locking threshold is calculated using several shots • In each shot, the RMP has a square waform but different amplitude. • The unlocking threshold is calculated using a triangular wavefor followed by a plateau phase • An hysteresis in the locking-unlocking process is present • A model describing the island evolution can qualitatively describe the dynamics increasing RMP Slow rotating branch decreasing RMP RMP (1,-15) (mT) 8

  18. Comparison experiment – model: time evolution • The model described in [Fitzpatrick et al., PoP (2001)] has been adapted to EXTRAP T2R • The viscosity is used as a free parameters in order to match the locking threshold • Reasonable qualitative agreement experiment model m=1m2/s RMP RMP TM velocity TM velocity TM amplitude TM island width 9

  19. Comparison experiment – model: v(r) profiles • The model described in [Fitzpatrick et al., PoP (2001)] has been adapted to EXTRAP T2R • The viscosity is used as a free parameters in order to match the locking threshold • Reasonable qualitative agreement experiment model vϕ-profile relaxes Braking phase m=1m2/s 10

  20. Comparison experiment – model: v(r) profiles • The model described in [Fitzpatrick et al., PoP (2001)] has been adapted to EXTRAP T2R • The viscosity is used as a free parameters in order to match the locking threshold • Reasonable qualitative agreement experiment model vϕ-profile relaxes vϕ-profile relaxes Braking phase m=1m2/s Locking phase 10

  21. Torques – as function of RMP amplitude • Experiments where the amplitude of the RMP is varied shot to shot • Viscous torque increase linearly until locking and then decrease to a constant value Volume integrated Torque locking threshold (a.u.) RMP (1,-15) (mT) 11

  22. Torques – as function of RMP amplitude • Experiments where the amplitude of the RMP is varied shot to shot • Viscous torque increase linearly until locking and then decrease to a constant value • EM torque increase linearly with RMP amplitude Volume integrated Torque locking threshold (a.u.) RMP (1,-15) (mT) 11

  23. Torques – as function of RMP amplitude • Experiments where the amplitude of the RMP is varied shot to shot • Viscous torque increase linearly until locking and then decrease to a constant value • EM torque increase linearly with RMP amplitude Volume integrated Torque locking threshold (a.u.) RMP (1,-15) (mT) 11

  24. Torques – as function of RMP amplitude • Experiments where the amplitude of the RMP is varied shot to shot • Viscous torque increase linearly until locking and then decrease to a constant value • EM torque increase linearly with RMP amplitude Volume integrated Torque locking threshold (a.u.) RMP (1,-15) (mT) 11

  25. Torques – as function of RMP amplitude • Experiments where the amplitude of the RMP is varied shot to shot • Viscous torque increase linearly until locking and then decrease to a constant value • EM torque increase linearly with RMP amplitude Volume integrated Torque locking threshold unlocking threshold (a.u.) RMP (1,-15) (mT) 11

  26. Torques – as function of RMP amplitude • Experiments where the amplitude of the RMP is varied shot to shot • Viscous torque increase linearly until locking and then decrease to a constant value • EM torque increase linearly with RMP amplitude (till locking occurs) Volume integrated Torque locking threshold unlocking threshold (a.u.) RMP (1,-15) (mT) 11

  27. Conclusions • Hysteresis in the TM locking – unlocking process to an external fied is observed. • Reasonable qualitative agreement between experimental results and model. • The Dv profile relaxation after the locking produces a reduction in the viscous torque • To unlock the TM: the RMP must be reduced well below the locking threshold in order to obtain a EM torque comparable to the viscous torque • The increased TM amplitude during the locking deepens the hysteresis. 12

  28. TM velocity

  29. TM velocity (m=1 n<-12) are resonant (1,-12) TM diagnostics (1,-13) (1,-14) … • Poloidal magnetic sensors: 4 poloidal x 64 toroidal positions • Resolution: -31≤n≤32 TM rotation and plasma rotation (1,-12) (1,-13) (1,-14) …

  30. active coils sensor coils No feedback 1.0 0.8 0.6 0.4 0.2 0.0 br(mT) 0 10 20 30 40 50 60 70 Time (ms) THE FEEDBACK SYSTEM • Sensor coils 4 poloidal x 32 toroidal located inside the shell • Digital controller • Active coils 4 poloidal x 32 toroidal located outside the shell shell tshell≈13.8ms (nominal) (cm) LCFS

  31. active coils sensor coils 1.0 0.8 0.6 0.4 0.2 0.0 br(mT) 0 10 20 30 40 50 60 70 Time (ms) THE FEEDBACK SYSTEM • Sensor coils 4 poloidal x 32 toroidal located inside the shell • Digital controller • Active coils 4 poloidal x 32 toroidal located outside the shell shell tshell≈13.8ms (nominal) (cm) Intelligent Shell LCFS

  32. Viscous torque: before the locking • Before the locking, the EM torque is balanced by the viscous torque Tvisc =TEM • The EM torque is proportional to the RMP amplitude. • The viscous torque is proportional to the second derivative of the angular velocity reduction profile ΔΩ(r) ≈ vϕ/R : Dv profile torque profile Braking phase Braking phase

  33. Viscous torque: during locking • After TM locking, ΔΩ(r) relaxes and viscous torque Tviscis reduced • The EM torque TEM is still proportional to the RMP amplitude • Unlocking occurs when the RMP amplitude is reduced so that TEM =Tvisc Dv profile torque profile Locking phase Locking phase

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