The influence of non-resonant perturbation fields: Modelling results and

1. The influence of non-resonant perturbation fields: Modelling results and Proposals for TEXTOR experiments S. Günter, V. Igochine, K. Lackner, Q. Yu IPP Garching • Resistive wall modes and error field amplification • Error field amplification and plasma rotation • Suppression of neoclassical tearing modes by external helical fields

2. Concept of advanced tokamaks Non-monotonic current profile Turbulence suppression high pressure gradients large bootstrap current fBS= N A q  0.8 … 0.9 N  4 … 5 MHD stability ?

3. Ultimate limit to maximum N is external kink mode For optimised current profiles (avoid double low order rational surfaces of same helicity) n·B|wall = 0 External kink mode can be stabilised by ideal walls n·B|wall = 0

4. External kink mode in AUG advanced scenarios Good agreement between theory and experiment Closeness to rational qa destabilising eigenfunction Günter et al., NF 2000

5. Stabilising influence of an ideal conducting wall • Closed wall in distance rw from plasma can be strongly stabilising, especially for: • broad current and pressure profiles • strong shaping of plasma cross section

6. 3d geometry of ideally conducting walls CAS3D: First code dealing with 3D wall and 3D plasma:

7. Destabilising effect of wall resistivity: RWMs Garofalo et al., PRL 1999

8. Simple model for RWMs and error field amplification Fitzpatrick´s (PoP 9(2002) 3459) analytical (inertial layer) model Instability drive of plasma mode increases Plasma rotation : stability parameter >0: ideal kink mode stabilised by infinitely conducting wall <0: in absence of rotation plasma is stable

9. increasing wall distance reduces coupling, perturbation can start slipping with respect to wall  rotation stabilizes mode Re(w) [wall frame] d/dc Effect of rotation for varying wall distance • can be modified by: - distance of wall (0 <  <1) at given instability drive ideal („plasma“) mode unstable detailed shape of marginal curve depends on plasma (dissipation) model torque balance between mirror current forces and viscous drag (or inertia) determines mode rotation frequency

10. more unstable plasma has larger ratio of field amplitude in plasma to wall => reduced wall coupling allows slip and rotational stabilization rotation destabilizes plasma in MHD stable region: electromagnetic coupling to wall opens relative velocity plasma-wall to Kelvin-Helmholtz drive (inertia needed) marginal curve corresponds to error field amplification condition (resistive wall mode can be interpreted to error field amplification of the induced wall-current field) Effect of rotation for varying instability drive • can be modified by: - variation of the MHD instability drive at given wall distance

11. Numerical treatment of RWMs anderror field amplification • In realistic geometry (coupling to internal resonances): • MARS (Bondeson) • VALEN (Bialek, Boozer) • CASTOR-A (Holties, Kerner) • - response to frequency dependent external perturbation field • modified to include differential plasma rotation, viscosity • resistive wall included (so far high resistivity only)

12. towards marginal stability Re P  jant B cos  ~  1/ 0 0.01 0.02 0.03 / A Increasing wall distance 1/ Numerical results: Error field amplification • Here for comparison with simple analytical theory: • frequency dependent external (3,1) perturbation field (qa < 3) • no internal resonances, no viscosity (torque onto plasma) Change in plasma stability by varying distance of ideally conducting wall

13. Numerical results: Error field amplification • Here for comparison with simple analytical theory: • frequency dependent external (3,1) perturbation field (qa < 3) • no internal resonances, no viscosity Maximum of absorbed power ~ -W~2pl Good agreement with analytical model for ideal plasma (scan in wall distance)

14. Numerical results: Error field amplification • Here for comparison with simple analytical theory: • frequency dependent external (3,1) perturbation field (qa < 3) • no internal resonances, no viscosity Maximum of absorbed power Good agreement with analytical model for ideal plasma (scan in N)

15. tor Re P  jant B cos  ~  1/ ~ Numerical results: torque on plasma Torque on the plasma due to external error fields: Maximum torque

16. reduction in resonant frequency, increasing torque increase in , mode growth  reduction in plasma frequency Influence of error fields on plasma rotation

17. Experiments on error field amplification on JET 59223 Saddle current[A] NB due to low field Bt=1T and high NBI w/walfven~ 4% 3.4li bN(%) PNBI[MW] Signal which sees no vacuum (or low bN) pick-up clearly rises as bNapproaches ideal limit br(0o) br(90o)

18. Influence of error fields on plasma rotation

19. Proposals for error field amplification experiments on TEXTOR – comparisons with theory • Frequency dependence in error field amplification: • discharges with qa<3 (and qa>3 for comparison), low li • scan in N/plasma rotationwithin one discharge, measure (3,1) amplitude increase compared to vacuum case • repeat for different frequency of antenna current • comparison with code calculations possible • Influence of error fields on plasma rotation: • compare torque onto plasma with theory (with and without q=3 surface) for different coil current frequencies and plasma pressures

20. Proposals for resistive wall mode experiments on TEXTOR • Develop scenarios with external (3,1) RWM mode • vacuum vessel: rw/a = 1.35, w = 14 ms • try to stabilize RWM by rotating external (3,1) perturbation fields • (compare required rotation velocity with theory)

21. jBS p Physics of neoclassical tearing modes (NTMs) Helical current parallel to plasma current drives magnetic islands unstable Magnetic islands driven by the loss of bootstrap current inside island

22. Interaction of NTMs with different helicity No simultaneous large NTMs of different helicities

23. Stabilising effect of additional helical field For finite perpendicular heat conductivity helical field perturbation reduces BS current perturbation caused by single magnetic island Contour plots of BS current perturbation Single magnetic island with external perturbation field

24. Stabilization of NTMs by external error fields DIII-D: suppression of (3,2) NTM onset successful, but strong reduction in plasma rotation observed n=3 perturbation field

25. Stabilization of NTMs by external error fields • On TEXTOR: rotating perturbation fields possible • (3,2) NTM stabilization by external (3,1) fields

26. Stabilization of NTMs by external error fields • On TEXTOR: rotating perturbation fields possible • NTM stabilization by external (3,1) fields for qa < 3 • if perturbation field too small use conditions with error field amplifications • Influence plasma rotation by external fields, study effect on NTM stability

27. Conclusions • “Rotating” external perturbation fields of a single helicity opens new possibilities for MHD experiments on TEXTOR: • error field amplification experiments, comparison with theory • - frequency dependence of error field amplification • - influence on plasma rotation • Resistive wall mode studies • Stabilization of NTMs by external perturbation fields

28. wall position  1 0 r plasma edge Newcomb criterion Cylindrical plasma: pointing vector into vacuum region ~ - ’|r=a For zero growth rate (ok for RWMs) it describes the energy released from plasma from infinitely slow perturbation (no energy converted to kinetic energy) r(=0) closer to plasma the larger ’|r=a (the more unstable the smaller r(=0) more unstable

29. Error field amplification influences plasma rotation Error field amplification  reduced plasma rotation  RWM growth Strait et al., IAEA 2002

30. Critical Rotation Scaling Strait et al., IAEA 2002