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Cyclic MHD Instabilities

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

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Cyclic MHD Instabilities

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

  2. Nonlinear Cycles

  3. Nonlinear cycles in biology: predator-prey models

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

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

  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 Te

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

  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

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

  40. Alfven waves – continuum and gap modes • B-field lines in a plasma can oscillate like a string of a guitar • double periodic cylinder: w = kvAgives continuum structure

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

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

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

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