Internal kink mode stability in the presence of ICRH driven fast ions populations

1. Internal kink mode stability in the presence of ICRH driven fast ions populations F. Nabais, D. Borba, M. Mantsinen, M.F. Nave, S. Sharapov and JET-EFDA contributors

2. Outline Fast ions Effect of ICRH driven populations on Fast ions energy functional MHD energy functional Internal kink mode n=1, m=1 Perturbative method Quantitative results Sawteeth (F. Porcelli et al. Phys. Plasmas,1 (3), 470 (1994)) Variational method Qualitative results Sawteeth, (R. White et al. Phys. Fluids B 2, 745 (1990)) Fishbones Objective : Explain experimental observations in JET

3. Perturbative method eigenfunction perturbation Relevant equations, which include Finite Orbit Width effects, (F. Porcelli et al. Phys. Plasmas,1 (3), 470 (1994)) Adiabatic part - destabilizing

4. Perturbative method Non-adiabatic part - stabilizing Safety factor on axis Fast ions temperature CASTOR-K Location of the ICRH resonant layer Fast ions radial profile Sawteeth

5. Effect of the ICRH fast ions on sawteeth Non-adiabatic as function of q0 and THOT on-axis heating Blue regions: stabilizing Red regions: destabilizing Destabilizing Adiabatic part of increases with THOT (Preliminar results)

6. PICRH THOT ~ ne Application to experiments Experiments with low plasma densities Sawteeth destabilization occurred when:  ICRH power increases  Plasma density decreases Non-adiabatic as function of THOT

7. Application to experiments  Sawteeth destabilization coincides with an increase in THOT Numerical results show: The stabilizing effect of the non-adiabatic part of decreases as THOT increases, so this mechanism for sawtooth stabilization is weakened.  The destabilizing effect associated with the adiabatic part of is increased.  The non-adiabatic part of is dominant.

8. Variational method (R. White et al. Phys. Fluids B 2, 745 (1990)) Kink Branch Sawteeth Low frequency (B. Coppi and F. Porcelli P. R.L, 57, 2272 (1986)) Ion Branch Solutions of the internal kink dispersion relation: ω≈ ω*i Low frequency (diamagnetic) fishbones (L. Chen et. al P. R.L, 52, 1122 (1984)) (Ideal limit) High frequency Fishbone Branch High frequency (precessional) fishbones ω≈ <ωDhi>

9. Determination of the regions of stability Ideal (MHD) growth rate Stability governed mainly by Diamagnetic frequency Fast particles beta Marginal equation ω=real, ideal limit, ICRH population

10. Regions of stability I h

11. Magnetic spectrogram from JET Hybrid Fishbones Sawtooth Crash Precessional Fishbones Diamagnetic Fishbones

12. Variation of the relevant parameters Increases In between crashes the q=1 surface expands Increases In between crashes the ion bulk profile peaks : 3 kHz 20 kHz Decreases during a burst Increases between bursts

13. Variation of the regions of stability I h

14. Regions of stability I h

15. Solutions of the dispersion relation (R. White et al. Phys. Fluids B 2, 745 (1990)) Coalescent Ion-Fishbone branch βh decreases during the burst Precessional behaviour  ω*i2 Diamagnetic behaviour Fishbone branch ω*i1< ω*i2 h ω*i1 Ion branch

16. Magnetic perturbation for an hybrid fishbone Magnetic perturbation Time (s)

17. Modes and regimes Low frequency fishbones Ion mode Fishbone mode High frequency fishbones (Gorolenkov et al. “Fast ions effects on fishbones and n=1 kinks in JET simulated by a non-perturbative NOVA-KN code, this conference) Hybrid fishbones Coalescent ion-fishbone mode Both types of fishbones occuring simultaneously

18. Summary Perturbative Method - Accurate calculation ofHOT for a realistic geometry - Only for the “kink mode” Stabilizing term vanishes for high fast ions temperatures Variational Method - All branches of the dispersion relation - Predicts changes in instabilities behaviour knowing the relevant parameters - Simplified geometry and fast ions’ distribution function, suitable only for a qualitative approach Hybrid fishbones and both types of fishbones occuring simultaneously