1. Resonant magnetic perturbation effect on the tearing mode dynamics in EXTRAP T2R: experimental results and modeling L. Frassinetti, K.E.J. Olofsson, P.R. Brunsell, J.R. Drake Alfvén Laboratory, Royal Institute of Technology KTH Stockholm

2. OUTLINE Resonant magnetic perturbation (RMP) Resonant magnetic perturbation (RMP) Why are RMPs important? Why are RMPs studied in EXTRAP T2R? Machine Diagnostics Feedback system TM dynamics with low RMP amplitude TM dynamics with high RMP amplitude TM locking to a RMP Fitzpatrick theory Interpretation of experimental results Modelling results Modelling results Experimental results Experimental results EXTRAP T2R EXTRAP T2R

3. WHY ARE RMPs IMPORTANT? [Abdullaev, PoP 16, 030701 (2009)] [Evans, NF 2008, 48 024002] 1. Neo-classical tearing mode stabilization RMP can interact with the NTM with stabilizing effects RMP can rotate a locked mode to move the O-point in the best position for ECCD stabilization [La Haye, PoP 9, 2051 (2002)] [Volpe, PoP 16, 102052 (2009)] RMPs can produce stochasticity in the plasma outer region the pressure gradient is reduced and the ELM effect mitigated. DIIID [Evans, NF 2008, 48 024002] JET [Liang, PRL 2007, 98 265004] 2. ELM suppression:

4. (2,1) TM amplitude (a.u.) Hender NF 1992 COMPASS-C Ivers,PoP 1996 HBT-EP time WHY TO STUDY RMP? 2. There are many theoretical papers that investigate the interaction between an RMP and a TM 3. But recently, not so many experimental results directly investigate the RMP effect on TMs 2. RMPs can be easily produced with EXTRAP T2R feedback system 1. The mechanisms for ELM mitigation are not yet totally understood 1. EXTRAP T2R plasma is characterized by rotating TMs WHY TO STUDY RMP in EXTRAP T2R?  EXTRAP T2R is a good device to test new feedback algorithms and study the MHD mode response to external perturbations

5. m=1 -30 -25 -20 -15 -10 -5 20 10 0 -10 0.3 0.2 0.1 0.0 b  1,n (mT)  1,n (krad/s) n EXTRAP T2R EXTRAP T2R is a RFP with: R=1.24m a=0.18m I p ≈ 80-150kA n e ≈ 10 19 m -3 T e ≈ 200-400eV t pulse ≈ 20ms (no FeedBack) t pulse ≈ 90ms (with IS) TM diagnostic b   4 poloidal x 64 toroidal local sensors (m=1 connected) located inside the shell. Sensitive to fast rotation. TM The device (1,-12) is often larger than the other TMs -12 -13 -14 0.0 0.2 0.4 0.6 0.8 1.0 r/a 0.10 0.08 0.06 0.04 0.02 0.00 -0.02 -0.04 q(r) Poincare map of magnetic field lines (poloidal section) (1,-12) island -1.0 -0.5 0.0 0.5 1.0 x/a 1.0 0.5 0.0 -0.5 z/a

6. by Olofsson E.  shell ≈13.8ms (nominal) shell EXTRAP T2R bcbc Sensor coils Sensor coils SENSOR COILS 4 poloidal x 32 toroidal sensor saddle coils (m=1 connected) located inside the shell Active coils Active coils ACTIVE COILS 4 poloidal x 32 toroidal active saddle coils (m=1 connected) located outside the shell Digital controller DIGITAL CONTROLLER The feedback plasma external helical magnetic perturbations shell b 1,n  b c Fourier harmonics in real time input to active coils V c (t)  V 1,n  min[ |b 1,n (t)-ref| ] [Olofsson, Fusion Engineering and Design 84, 1455 (2009)] m=1 n=-12 0 20 40 60 Time (ms) 0.6 0.4 0.2 0.0 b r 1,n (mT)

7. 0 20 40 60 Time (ms) 80 60 40 20 0 v 1,-12 (km/s) 80 60 40 20 0 v OV (km/s) 1.0 0.8 0.6 0.4 0.2 0.0 b r 1,n (mT) 120 100 80 60 40 20 0 Ip ()kA m=1 n=-12 0 20 40 60 Time (ms) 0.6 0.4 0.2 0.0 b r 1,n (mT) At present In EXTRAP T2R RMPs are applied to study: - effect on TM dynamics (present talk) - effect on the plasma flow (wednsday talk) Present RMP studies on EXTRAP T2R

8. TM DYNAMICS average of all other TMs (1,-12) Natural TM dynamics TM dynamics with low RMP amplitude RMP ≈ 0.3mT 1- amplitude: “modulated” RMP effect on the rotating TM: 2- velocity: “modulated” NO RMP 0 20 40 60 0.6 0.4 0.2 0.0 b r 1,n (mT) 100 80 60 40 20 0 Ip (kA) 0.6 0.4 0.2 0.0 b r 1,n (mT) 100 80 60 40 20 0 Ip (kA) 0 20 40 60 Time (ms) 19.60 19.65 19.70 phase Time (ms) 40 30 20 10 0  (krad/s) b  m,n (mT)      0.6 0.5 0.4 0.3 0.2 0.1 phase 40 30 20 10 0  (krad/s) b  m,n (mT)      0.4 0.3 0.2 0.1 14.68 14.70 14.72 14.74 14.76 14.78 Time (ms)

9. b  1,-12 (mT)  (krad/s) 40 30 20 10 0 0.20 0.15 0.10 0.05 0.00     AMPLIFICATION SUPPRESSION  =0  =  amplitudevelocitycorrelated TM amplitude and velocity are correlated phase shift with the phase shift between TM and RMP ampl. suppression TM DYNAMICS with low RMP amplitude decel. acceleration decel. Phenomenological explanation (wrong!) Toroidal angle b TM Toroidal angle b TM b RMP

10. b  1,-12 (mT) 0.5 0.4 0.3 0.2 0.1 0.0    (krad/s) 20 15 10 5 0   RMP ≈ 0.5mT TM DYNAMICS with high RMP amplitude suppression jump amplification deceleration acceleration jump 0.6 0.4 0.2 0.0 b r 1,n (mT) 0 20 40 60 Time (ms) 1- High oscillation with “complete” suppression 2- phase jumps b  m,n (mT) 0.6 0.5 0.4 0.3 0.2 0.1       (krad/s) 25 20 15 10 5 0 29.10 29.15 29.20 Time (ms) 

11. MODELLING Based on Fitzpatrick [Phys. Plasmas 8 4489 (2001)] 3 coupled partial differential equations: 1.TM evolution 2.Torque balance with 3.Helical velocity Viscous torqueEM torque braking torque due to eddy currents In the wall generated by the rotating TM braking torque due to interaction of the rotating TM with the static RMP Poloidal section Amplification and deceleration suppression and deceleration suppression and acceleration amplification and acceleration

12. b  1,-12 (mT)  (krad/s) 0.30 0.20 0.10 0.00      30 20 10 0 Time (ms) 0.00 0.02 0.04 0.06 0.08 0.10 n e (0)=0.9x10 19 m -3 FREE PARAMETERS  R =0.1ms =0.65 10 -7 kg/(m∙s) INITIAL CONDITIONS  0 =30krad/s b  TM (0)=0.12mT Reasonable agreement between model and experiment MODELLING the LOW RMP case TM amplitude is modulated TM velocity is modulated amplitude reduction in time (not evident on this time scale) velocity reduction in time (not evident on this time scale) b r RMP =0.3mT b  1,-12 (mT) 0.20 0.15 0.10 0.05 0.00    (krad/s) 40 30 20 10 0  

13. b  1,-12 (mT) 0.50 0.40 0.30 0.20 0.10 0.00       (krad/s) 15 10 5 0 Time (ms) 0.20 0.22 0.24 0.26 0.28 0.30 Reasonable agreement between model and experiment MODELLING the HIGH RMP case b r RMP =0.5mT TM amplitude is modulated TM velocity is modulated amplitude increases in time Phase jumps n e (0)=0.9x10 19 m -3 FREE PARAMETERS  R =0.1ms =0.65 10 -7 kg/(m∙s) INITIAL CONDITIONS  0 =50krad/s b  TM (0)=0.01mT b  1,-12 (mT) 0.50 0.40 0.30 0.20 0.10 0.00    (krad/s) 20 15 10 5 0  

14. b  1,-12 (mT) 0.50 0.40 0.30 0.20 0.10       Time (ms) 30.40 30.45 30.50 30.55 EXPERIMENT b r RMP =0.4mT TM LOCKING TO A RMP -Low RMPoscillation -Low RMP amplitude  “weak” oscillation in the TM amplitude and velocity -High RMPphase jumps -High RMP amplitude  “strong” modulation in the TM amplitude and phase jumps IS IT ALWAYS SO SIMPLE? locking oscillations jumps locking oscillations jumps MODEL b r RMP =0.4mT  R =0.1ms =0.65 10 -7 kg/(m∙s) n e (0)=0.9x10 19 m -3  0 =25krad/s b  TM (0)=0.2mT       b  1,-12 (mT) 0.50 0.40 0.30 0.20 0.10 Time (ms) 0.00 0.05 0.10 0.15 0.20 0.20

15. SCALING OF THE TM DYNAMIC PROPERTIES WITH THE RMP AMPLITUDE TM amplitude: 1- Suppression 1- Suppression for “low” RMP amplitudes 2- Amplification 2- Amplification for “high” RMP amplitudes TM dynamics: 1- Full rotation 1- Full rotation for “low” RMP amplitudes 2- Jumps 2- Jumps for “high” RMP amplitudes 3- Locking 3- Locking for “very high” RMP amplitudes time averaged amplitude Angle covered by the TM during one rotation b  1,-12 (mT) 0.50 0.40 0.30 0.20 0.10 0.00 0.0 0.2 0.4 0.6 0.8 1.0 b r 1,-12 (mT)       b r 1,-12 (mT) 0.0 0.2 0.4 0.6 0.8 1.0

16. SCALING OF THE TM DYNAMIC PROPERTIES WITH THE RMP AMPLITUDE TM amplitude: 1- Suppression 1- Suppression for “low” RMP amplitudes 2- Amplification 2- Amplification for “high” RMP amplitudes TM dynamics: 1- Full rotation 1- Full rotation for “low” RMP amplitudes 2- Jumps 2- Jumps for “high” RMP amplitudes 3- Locking 3- Locking for “very high” RMP amplitudes time averaged amplitude Angle covered by the TM during one rotation b  1,-12 (mT) 0.50 0.40 0.30 0.20 0.10 0.00 0.0 0.2 0.4 0.6 0.8 1.0 b r 1,-12 (mT)       b r 1,-12 (mT) 0.0 0.2 0.4 0.6 0.8 1.0

17. CONCLUSIONS An external RMP can affect the rotating TM and the corresponding magnetic island RMP produces The RMP produces: TM amplitude amplification or suppression TM velocity acceleration or deceleration oscillation “Low” RMP amplitude  “weak” oscillation in the TM amplitude and velocity phase jumps “High” RMP amplitude  “strong” modulation in the TM amplitude and phase jumps The locking to a RMP can be a complicated mechanism Fitzpatrick modelreasonable explanation The Fitzpatrick model gives a reasonable explanation of these phenomena useful tool for testing advanced feedback algorithm It is a useful tool for testing advanced feedback algorithm for TM control Work in progress and future work: 1- RMP with another helicity 2- RMP effect on plasma flow 3- … depending on the phase shift