1. Effects of external non-axisymmetric perturbations on plasma rotation L. Frassinetti, P.R. Brunsell, J.R. Drake, M.W.M. Khan, K.E.J. Olofsson Alfvén Laboratory, Royal Institute of Technology KTH Stockholm

2. OUTLINE Introduction Introduction Braking of plasma rotation due to non-axisymmetric perturbations - resonant perturbation  RMP - non-resonant pert.  non-RMP - Braking due to a RMP close to the axis (1) helicity resonant close to the axis far from the axis (2) helicity resonant far from the axis - Braking due to a non-RMP (3) internal non-resonant helicity Experimental results Experimental results - The machine and the feedback (quick overview) - Diagnostics EXTRAP T2R EXTRAP T2R n=-10 n=-12 n=-15

3. INTRODUCTION RMPs are an essential tool for ELM mitigation in tokamaks “positive” Do they have only “positive” effects on the plasma? NO For example RMPs can produce: -density pump out plasma braking -plasma braking Present understanding: the braking can be due to two phenomena (2) Neoclassical toroidal viscosity torque - Toroidal viscous force on plasma fluid as it flows through a non- axisymmetric perturbation - Collisions and particle drifts in non-axisymmetric field cause a non-ambipolar radial particle flux (radial current) which gives a toroidal force.RMP RMP RMP andNon-RMP From: Y. Sun (FZJ) (1) Localised electromagnetic torque - interaction between the static RMP and the corresponding TM

4. 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) The device by Olofsson E. shell Sensor coils Active coils  shell ≈13.8ms (nominal) SENSOR COILS 4 poloidal x 32 toroidal sensor saddle coils (m=1 connected) located inside the shell ACTIVE COILS 4 poloidal x 32 toroidal active saddle coils (m=1 connected) located outside the shell The feedback m=1 n=-12 Time (ms) 0 20 40 60 b r 1,n (mT) 0.6 0.4 0.2 0.0

5. r/a 0.0 0.2 0.4 0.6 0.8 1.0 v 1,n (km/s) 80 60 40 20 0 -20 OIII OII OV OIV Experimental v i r/a 0.0 0.2 0.4 0.6 0.8 1.0 v 1,n (km/s) 80 60 40 20 0 -20 Magnetic diagnostics b   4 poloidal x 64 toroidal local sensors (m=1 connected) located inside the shell. Plasma flow diagnostics 5-channel spectrometer for emissivity profile of impurities Modelled v i -30 -25 -20 -15 -10 n 80 60 40 20 0 -20 v 1,n (km/s) Poloidal velocity is not considered Plasma flow v(r): v(x,  ) is assumed Free parameters from minimization of modelled and experimental v i [Cecconello, PPCF 2006] Spectrometer for Doppler shift of ion lines OV velocity Time (ms) 0 10 20 30 40 50 60 80 60 40 20 0 V OV (km/s) I OV (au)  OV (au) brightness Reconstructed emissivity experimental modelled r/a OV emissivity 0.0 0.2 0.4 0.6 0.8 1.0 1.5 1.0 0.5 0.0 0.8 0.4 0.0

6. velocity profile (magnetics) 80 60 40 20 0 -20 v mag (km/s) 0.0 0.2 0.4 0.6 0.8 1.0 r/a BRAKING DUE TO A RMP (1,-12) (1,-12) most internal TM Braking occurs for all TMs Flow braking 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 q(r) 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 flow profile (spectroscopy) 80 60 40 20 0 -20 flow (km/s) r/a 0.0 0.2 0.4 0.6 0.8 1.0 before RMP during RMP before RMP during RMP Time (ms) 20.0 20.05 20.10 20.15 20.20 Phase (1,-19)    40.0 40.05 40.10 40.15 40.20 Time (ms) Phase (1,-19)   

7. BRAKING vs RMP amplitude RMP 0.4mT 10ms RMP 0.6mT 4ms 10msv~30km/s RMP 0.4 mT  braking in 10ms to v~30km/s 4msv~10km/s RMP 0.6 mT  braking in 4ms to v~10km/s (1,-12) is locked to the wall (RMP) but the other TMs still rotate! velocity profile (magnetics) 0.0 0.2 0.4 0.6 0.8 1.0 r/a 80 60 40 20 0 -20 v mag (km/s) 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) before RMP during RMP (1,-12) Average during RMP (each dot corresponds a different shot) 60 40 20 0 0.0 0.2 0.4 0.6 0.8 1.0 b r RMP (mT) V (km/s) The flow seems to brake with a lower rate

8. 0.0 0.2 0.4 0.6 0.8 r/a  v mag (km/s) 10 0 -10 -20 -30 0.0 0.2 0.4 0.6 0.8 r/a BRAKING DUE TO A RMP FAR FROM THE AXIS Any difference between -12 and -15? YES (1,-15) (1,-15) resonant at r/a~0.4 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 0 10 20 30 40 50 60 Time (ms) RMP (1,-12) velocity profile (magnetics) 0.0 0.2 0.4 0.6 0.8 r/a velocity profile (magnetics) before RMP during RMP RMP (1,-15) before RMP during RMP 0.0 0.2 0.4 0.6 0.8 r/a 80 60 40 20 0 -20 v mag (km/s) 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 q(r) region of max  v

9. BRAKING DUE TO A RMP FAR FROM THE AXIS Average during RMP (each dot corresponds a different shot) RMP (1,-15)RMP (1,-12) Comparison of braking due to RMP (1,-15) and RMP (1,-12) velocity profile (magnetics) before RMP during RMP (1,-12) 0.0 0.2 0.4 0.6 0.8 1.0 r/a 80 60 40 20 0 -20 v mag (km/s) before RMP during RMP (1,-15) 0.0 0.2 0.4 0.6 0.8 1.0 r/a 80 60 40 20 0 -20 v mag (km/s) 60 40 20 0 V mag (km/s) 0.0 0.2 0.4 0.6 0.8 1.0 1.2 b r RMP (mT)

10. 0.0 0.2 0.4 0.6 0.8 r/a  v mag (km/s) 10 0 -10 -20 -30 -40 -50 0.0 0.2 0.4 0.6 0.8 r/a 10 0 -10 -20 -30(1,-10) BRAKING DUE TO A non-RMP (1,-10) non-resonant Not a significant difference 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 0 10 20 30 40 50 60 Time (ms) 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 q(r) velocity profile (magnetics) 0.0 0.2 0.4 0.6 0.8 r/a 80 60 40 20 0 -20 RMP (1,-12) velocity profile (magnetics) 0.0 0.2 0.4 0.6 0.8 r/a 80 60 40 20 0 -20 v mag (km/s) non-RMP (1,-10)

11. RMP (1,-12) 0.0 0.2 0.4 0.6 0.8 b r RMP (mT) Average during RMP (each dot corresponds a different shot) non-RMP (1,-10) 0.0 0.2 0.4 0.6 0.8 60 40 20 0 V (km/s) b r RMP (mT) BRAKING vs non-RMP amplitude before RMP during RMP (1,-12) 0.0 0.2 0.4 0.6 0.8 1.0 r/a 0.0 0.2 0.4 0.6 0.8 1.0 r/a 80 60 40 20 0 -20 v mag (km/s) (1,-12) Not a significant differences so far 0 10 20 30 40 50 60 Time (ms) 60 40 20 0 V 1,-12 (km/s) v OV (km/s) 60 40 20 0 0.8 0.6 0.4 0.2 0.0 b r 1,n (mT) In this region the RMP is very perturbative

12. CONCLUSIONS MAIN CONCLUSION: clear evidence of plasma rotation braking due to external perturbations RMP (close to axis) RMP (far from axis) non-RMP(1,-10) Plasma flow (from spectroscopy) Braked Mode velocity (from magnetics) Braked Velocity profile Globally affected Velocity variation Peaked at the resonance (on axis) Peaked at the resonance (off axis) Peaked on the axis Role of the perturbation amplitude Braking increases with RMP amplitude Braking increases with RMP amplitude Braking increases with non-RMP amplitude