Off-axis Fishbones in DIII-D

1. Off-axis Fishbones in DIII-D Bill Heidbrink Leaders of the Experiment G. Matsunaga, M. Okabayashi Energetic Particle Working Group R. Fisher, R. Moyer, C. Muscatello, D. Pace, W. Solomon, M. Van Zeeland, Y. Zhu

2. Fishbones can trigger Resistive Wall Modes • Fast ions & toroidal rotation help stabilize RWM • Fishbones cause reduction in both  triggers RWM • Low frequency, bursting instability with large effect on fast ions  utilize new EP diagnostics Okabayashi

3. High Beta plasma with q0 > 1 1.7 T 1.07 MA H-mode bN=2.6 4e19 m-3 All beam angles 1<qo<2 Classic (PDX) fishbone was an internal kink (q0<1)

4. Mode Frequency ~ 8 kHz  Fluctuations detected on all EP diagnostics Global mode w/ large amplitude near q=2 Okabayashi

5. Outline • Orbit Topology • Mirnov Analysis • Loss Measurements • Wave Distortion and Phase Slippage

6. Fast-ion Loss Detector (FILD) measures lost trapped ions at fishbone burst • Bright spot for ~80 keV, trapped fast ions • Loss orbit resembles banana orbits deposited by perpendicular beams Pace, Fisher

7. Perpendicular beams are born near the resonant frequency Van Zeeland • The p=0 curves represent the w = wpre resonance • Er approximately adds to precession frequency like Doppler shift • Counter-perp: ~9.5 kHz; Co-perp: ~6.7 kHz • Initial mode frequency: ~8 kHz • Modes w/o counter injection are different

8. Counter-perp beam ions are expelled onto the loss orbit measured by FILD Van Zeeland

9. Fishbones are driven at the precession frequency of the trapped fast ions Shinohara, Matsunaga

10. Outline • Modes are driven by precession-frequency resonance • Mirnov Analysis • Loss Measurements • Wave Distortion and Phase Slippage

11. Is the mode an energetic particle mode (EPM) or normal mode? Normal Mode nEP << ne Wave exists w/o EPs. Re(w) unaffected by EPs. EPs resonate with mode, altering Im(w) Energetic Particle Mode1 bEP ~ b EPs create a new wave branch Re(w) depends on EP distrib. function EPs resonate with mode, altering Im(w)

12. Initial frequency depends on toroidal rotation & precession frequency • Database of 388 bursts • Scales with rotation near q=2 but not central rotation • Best fit: nearly linear dependence (expected for both normal mode & EPM) • Precession frequency proportional to E/Ip • Data depends on E/Ip more weakly than fpre suggests normal mode?

13. Mode frequency chirps down (like classic fishbone) • Rotation frequency changes < 1 kHz but mode changes ~3 kHz • Large frequency sweep suggests EPM • Df increases with fast-ion losses  suggests EPM

14. Growth rate similar to classic fishbone • Growth rate scales with mode amplitude • Considerable variation in decay rate • Unlike PDX, average decay rate similar to growth rate

15. Strong distortion of waveform observed late in burst • Different from classic fishbone • Distortion varies with position (on internal fluctuation diagnostics)

16. Distortion greatest near maximum amplitude • Use variation in half-period to measure distortion • Other definitions give similar results

17. Distortion occurs in every burst

18. Distortion has (m,n)=(2,1) structure • Fundamental sine wave has (3,1) structure • VERTICAL POSITION TIME (ms) Okabayashi

19. Outline • Orbit Topology: Modes are driven by precession-frequency resonance • Mirnov Analysis: Waveform similar to classic fishbone except for distortion • Loss Measurements • Wave Distortion and Phase Slippage

20. Non-ambipolar losses cause sudden drop in electric field  toroidal rotation • Total fast-ion loss rate inferred from slope of neutrons • CER acquired in 0.5 ms bins • Conditionally average 8 similar bursts • Drop observed near q=2 • Losses act like a torque impulse—a negative beam blip (deGrassie PoP 2006) • Magnitude reasonable • <5% FIDA drops for R<208 cm

21. Losses increase with increasing mode amplitude • Linear dependence predicted for convective losses (classic fishbone) • Offset linear for convective with a threshold • Quadratic for diffusive • Fair fit to all 3 models

22. Losses have a definite phase relative to the mode • BILD saturated on most bursts • Relatively weak burst • Like “beacon” measured for classic fishbones • Phase consistent with Eqx Bfconvective transport

23. All Loss Diagnostics Observe the “Beacon” • Langmuir probe (ISAT) at 240o (-19 cm) • Ion cyclotron emission (ICE) at 255o (midplane) • Beam ion loss detector (BILD) at 60o (-12 cm) • Neutral particle analyzer (NPA) at 225o (q ~ -35o) • Fast ion loss detector (FILD) at 225o (R-1 port)

24. BES signal has large spikes at peak mode amplitude • BES channel near q=2 • Phase with mode preserved throughout burst • BES amplitude grows dramatically as mode distorts • Interpretation: BES signal is a combination of bipolar ne fluctuations and spikes of FIDA light as fast ions are expelled to high neutral density region at edge

25. Outline • Orbit Topology: Modes are driven by precession-frequency resonance • Mirnov Analysis: Waveform similar to classic fishbone except for distortion • Loss Measurements: Fast ions lost in a convective beacon • Wave Distortion and Phase Slippage

26. Phase of neutron oscillations slips relative to mode • Fluctuations caused by motion of confined fast ions relative to scintillator • Detrend neutron signal to observe oscillations clearly • Initially fast ions oscillate with mode • Phase slips over 360o • No slip in internal fluctuations

27. Phase slip occurs when distortion increases

28. Phase slip is linearly proportional to frequency chirp Okabayashi

29. A proportionality constant of 2 is consistently observed • Rate of neutron drop also correlates with frequency chirp rate Okabayashi

30. Does drag of the external kink on the wall cause phase slippage? • Classic fishbone is an internal kink • Classic fishbones had one angle of injection (greater anisotropy in velocity space) Okabayashi

31. Phase slippage occurs when mass changes frequency faster than driving frequency Wave & mass chirp together Mass chirps faster • Model wave & fast ions as a forced oscillator • Chirping does not produce phase slippage when wave & particle chirp at same rate • Suggests average precession frequency changes more than mode frequency  non-resonant population causes opposite phase slippage

32. Speculation about the distortion & phase slip • Higher n modes are destabilized because... • Modes cross the linear threshold as the f.i. profile evolves • Nonlinear coupling • Is distortion important? • No? The n=1 predator-prey cycle determines evolution • Yes? Losses peak when distortion is greatest, suggesting an important role in fast-ion transport • Is neutron phase slip important? • No? Non-resonant (co-perp) confined trapped ions produce neutron signal • Yes? Strong correlation with distortion & losses suggest a causal relationship

33. Comparison with Classic Fishbones Classic fpre resonance Df/f ~ 50% Predator-prey burst cycle Losses in “beacon” Losses ~ linear w/ Bmax Loss rate ~ chirp rate Weak distortion of wave Neutron oscillation stays in phase Not measured previously Off-axis fpre resonance Df/f ~ 50% Predator-prey burst cycle Losses in “beacon” Losses ~ linear w/ Bmax Loss rate ~ chirp rate Strong distortion of wave Neutron oscillation slips in phase Rapid Dvrot @ burst