1. Cyclic MHD Instabilities Hartmut Zohm MPI für Plasmaphysik, EURATOM Association Seminar talk at the ‚Advanced Course‘ of EU PhD Network, Garching, September 30, 2008 Nonlinear cycles The sawtooth instability Edge Localised Modes (ELMs) The fishbone instability

2. Nonlinear Cycles

3. Nonlinear cycles in biology: predator-prey models

4. current driven instabilities pressure driven instabilities (kink mode) (interchange mode) Free energies to drive MHD modes

5. Ideal MHD:  = 0 flux conservation topology unchanged Resistive MHD:   0 reconnection of field lines topology changes Ideal and resistive MHD instabilities

6. The sawtooth instability

7. Ideal internal kink – displacement of plasma core

8. Resistive internal kink: island formation and reconnection

9. Nonlinearity in (1,1) mode before sawtooth crash

10. Stochastisation during sawtooth crash

11. Resistive internal kink: island formation and reconnection

12. Sawtooth cycles as seen in T e

13. Sawtooth crashes can trigger NTMs

14. Sawtooth tailoring by Electron Cyclotron Current Drive

15. Edge Localised Modes (ELMs)

16. H-mode characterised by edge transport barrier

17. Ballooning stability in the s-  diagram

18.  p before ELM consistent with ballooning limit

19. ELM onset NOT consistent with ballooning limit

20. Edge transport barrier causes large bootstrap current

21. Edge localised kink: the ‘peeling mode’

22. Pressure gradient Edge current density Stable region Unstable region Combined peeling-ballooning model

23. …still not the ultimate truth…

24. Different ELM ‘types’ exist

25. ELM cycles lead to quasi-stationarity

26. ELM impact on ITER wall is a concern

27. Plasma shaping can change the ELM type

29. Helical fields can suppress ELMs!

30. Pellet injection to control ELM frequency, mitigate impact

31. The Fishbone instability

32. Plasma heating  non-Maxwellian distribution functions

33. Landau damping: wave-particle interaction in phase space

34. Banana orbit of a trapped particle

35. The fishbone instability – characteristic time traces

36. The fishbone instability: predator-prey cycles

37. The fishbone instability – characteristic time traces

38. The fishbone instability reduces heating efficiency

39. ICRH on Fishbones Spectrogram of magnetic perturbations, JET discharge #66203 E A E Tornado Time (s) Frequency (kHz) A ‘zoo’ of fast particle driven instabilities exists

40. Alfven waves – continuum and gap modes B-field lines in a plasma can oscillate like a string of a guitar double periodic cylinder:  = k  v A gives continuum structure

41. Alfven waves – continuum and gap modes B-field lines in a plasma can oscillate like a string of a guitar double periodic cylinder:  = k  v A gives continuum structure this leads to strong damping of the modes (radial variation of  ) same colour – same n n = 2…6

42. Alfven waves – continuum and gap modes B-field lines in a plasma can oscillate like a string of a guitar double periodic cylinder:  = k  v A gives continuum structure in a torus, gaps open that allow Alfven resonances to extend over radius

43. Excitation of Alfven waves by Fast Particles Suprathermal ions with v  v A can excite Alfven waves which expel them in present day experiments, these ions come from heating systems in future reactors, this could expel  -particles that should heat the plasma! Magnetic perturbation Fast ion loss probe