FREQUENCY-SWEEPING ENERGETIC PARTICLE-DRIVEN AE
The history of FS instabilities driven by energetic ions started from an oscillatory “fishbone” instability, with the dominant mode numbers n = 1 and m = 1, first observed in experiments with perpendicular NBI on the Poloidal Divertor Experiment (PDX) tokamak [7.17]. The instability occurs in repetitive bursts, with the mode frequency decreasing by about a factor of 2 during each burst. Large fishbone bursts cause losses of NBI-produced energetic ions, thus reducing the efficiency of plasma heating. Experimentally, the fishbone mode structure was found to be of the “top hat” type similar to the internal kink mode [7.18] associated with the surface q= 1 in tokamak plasma. The frequency of the fishbone oscillations on PDX was found to be close to the magnetic precession frequency of the trapped beam ions, as well as to the diamagnetic frequency of thermal ions. Two different regimes have been identified for the linear phase of fishbone instability. The first regime of the so-called “precessional” fishbones [7.19] refers to the case when the mode frequency is much greater than the thermal ion diamagnetic frequency. In this case, trapped energetic ions via the resonance with their precessional motion destabilise the n = l, m=l mode emerging from the Alfven continuum. The mode frequency is essentially determined by the energetic particle population in this case, and the fishbone represents an energetic particle mode. In this case, the mode structure has singularities at the radii of local Alfven resonances (5.23) and significant continuum damping. Such fishbones are excited at relatively high values of the energetic ion pressure which overcomes the threshold value as determined by the continuum damping. In the non-linear phase, such fishbones could sweep in frequency due to the re-distribution of energetic ions and the MHD nonlinearity of the continuum damping [7.20]. The second regime [7.21,7.22] corresponds to the case of comparable precessional frequency of the beam ions and the diamagnetic frequency of thermal ions. The mode frequency could then reside in a low-frequency “gap” in the continuum associated with the diamagnetic frequency, thus avoiding continuum damping.
Fishbone oscillations were later observed in many other tokamaks with significant populations of energetic ions produced by ICRH, perpendicular and parallel NBI, see review [7.23] and references therein. Fishbones driven by supra-thermal electrons resulting from ECRH and LHCD were also observed and explained [7.24]. Significant further advances were achieved in theory and modelling of the fishbones, see [7.25,7.26] and references therein. We note, however, that in future large machines with significant populations of fusion-generated alpha particles, fishbones will be driven by alpha particles with characteristic energies of ~400 keV [7.27]. Because this energy range is well below the birth energy of 3.52 MeV, the possible re-distribution or losses of energetic resonant ions caused by the fishbone instability are not as dangerous as TAEs or other AEs with frequencies much higher than the fishbone frequency and evolving alpha particles with energy ~1 MeV and more.
Meanwhile, another type of energetic ion-driven instability with sweeping frequency, but of much higher frequency, was reported from DIII-D experiment with NBI [7.28]. This instability on DIII-D started from a frequency of ~90kHz, which is much higher than the fishbone frequency of ~20kHz, and very close to the TAE frequency of ~110kHz, and swept down in frequency by a factor of two in a very short time of ~2.5 ms. Due to the very fast sweep down in frequency, these beam-driven modes were called “chirping” modes. Toroidal mode numbers of the chirping modes were positive and in the range of n= 1,..., 8. The beam parallel velocity in this DIII-D experiment was sub-Alfvenic, Vbeam =0.3-0.5 VA, but beam pressure was large, >1%. Moreover, the
toroidal plasma rotation was also large. The chirping modes transported beam ions to the edge of the plasma. Bursts of chirping modes correlated with drops in neutron emission by 10%, which was much higher than that of the fishbones, <2%. Because these plasmas had significant beam-plasma neutrons, the reductions in neutron yield indicated the loss of beam from the plasma centre much higher than that during the fishbone.
The instability of chirping modes was then observed on JT-60U [7.6,7.29] and on small spherical tokamak START [7.30]. Despite the difference in the plasma size, both machines used NBI with velocities close to, or exceeding, the Alfven velocity. The experiment on JT-60U used negative NBI of very high energy of ~360 keV at magnetic field of ~1.2 T, while the experiment on START used very low magnetic field in the range of -0.2-0.4 T and H beam with energy of ~30 keV.
Two large spherical tokamaks, NSTX [7.31] and MAST [7.32], were built, and the chirping modes were found to become a dominant type of beam-driven instabilities in STs. Figure 7.12 illustrates the various Alfven instabilities that could exist in a typical MAST discharge. The discharge in Figure 7.12 was in L-mode phase, with the following parameters: I,,~730 kA, В, (0)=0.5 T,
FIGURE 7.12 Magnetic spectrograms for n=odd (top) and n=even (bottom) components of the outer midplane Mirnov coil signal for MAST discharge #12887. Different types of Alfvenic modes are seen. The dashed line represents time evolution of the TAE-gap centre with Doppler shift taken into account.
Figure 7.12 presents magnetic spectrograms for /r=odd and /г=even components of Mirnov coil signal for MAST discharge #12887 showing examples of various beam-driven modes. In this discharge, NBI was applied at 80 ms exciting TAE in an FL regime first. This mode was replaced by a set of n = odd bursts of up-down symmetric “clump-hole” modes (to be explained in next chapter) and и = even modes that first sweep up, and then sweep down in frequency. Later in the discharge, the chirping-down modes are seen with a long chirping-down phase in the n = even component.
Apart from the super-Alfvenic beam, the beam pressure was rather high on MAST, similar to [7.28]. Figure 7.13 shows values of Д*,ат and ДЬсгт = Д, + Д in a set of MAST discharges with NBI, which were calculated with TRANSP and EFIT. Each point represents one TRANSP/EFIT output and the lines represent transport trajectories for some individual discharges. The dashed line shows 2в
the margin of Деат/Д “ ^— = 1- Although beam fraction was as high as ~80% in some cases,
these high values were not typical for MAST.
Figure 7.14 provides a larger picture of long chirping-down modes. It is seen that the initial FS is nearly linear in time, and it gives the frequency deviation from the starting point by a factor of 2 (e.g., from ~120kHz down to ~60kHz) in ~1 ms. The mode amplitude increases significantly at the end of the linear chirping phase. Then, the sweeping rate decreases significantly, from~60kHz down to ~40kHz in ~2 ms, while the amplitude does not change much. Explanation of this long chirping-down modes is not an easy task, and the possible options will be described in Chapter 8.
Figure 7.14 Magnetic spectrogram showing long chirping modes with /г=even component in MAST discharge #12878.
FIGURE 7.13 Typical values of /}Ьеш and Д1кпи in MAST discharges with NBI (calculated with TRANSP and EFIT). Each point represents one TRANSP/EFIT output and the lines represent trajectories for individual discharges. The dashed line shows the Д*,ат/Д = 1 margin.
FIGURE 7.14 Magnetic spectrogram showing long chirping modes with n=even component in MAST discharge #12878.
In recent years, the phenomenon of rapid chirping of energetic beam-driven modes has been found on stellarators [7.33,7.34], in a dipole experiment [7.35], and in JET experiments with ICRH- accelerated ions [7.36]. Furthermore, in addition to the fishbones excited by fast electrons produced with ECRH and LHCD [7.24], rapid FS instabilities driven by runaway electrons were observed in DIII-D [7.37], as well as in mirror-confined plasma sustained by high-power microwaves [7.38]. The widespread of the FS phenomena suggests that all of them could be possible to explain within a framework of a generic theoretical model.
- 1. D.W. Ross et al„ Phys. Fluids 25 (1982) 652.
- 2. K. Appert et al., Plasma Phys. 24 (1982) 1147.
- 3. A. Fasoli et al., Nucl. Fusion 35 (1995) 1485.
- 4. S.E. Sharapov et al.. Nucl. Fusion 53 (2013) 104022.
- 5. W. Kerner et al., Nucl. Fusion 38 (1998) 1315.
- 6. K. Shinohara et al.. Nucl. Fusion 41 (2001) 603.
- 7. A. Fasoli et al.. Phys. Rev. Lett. 75 (1995) 645.
- 8. A. Fasoli et al.. Phys. Plasmas 7 (2000) 1816.
- 9. A. Fasoli et al.. Phys. Rev. Lett. 76 (1996) 1067.
- 10. P. Puglia et al.. Nucl. Fusion 56 (2016) 112020.
- 11. A. Fasoli et al.. Plasma Phys. Control. Fusion 52 (2010) 075015.
- 12. A. Fasoli et al.. Nucl. Fusion 36 (1996) 258.
- 13. J.P. Goedbloed et al.. Plasma Phys. Control. Fusion 35 (1994) B277.
- 14. S.E. Sharapov et al.. Phys. Lett. A289 (2001) 127.
- 15. A. Fasoli et al.. Plasma Phys. Control. Fusion 44 (2002) В159.
- 16. S.E. Sharapov et al.. Phys. Plasmas 9 (2002) 2027.
- 17. K. McGuire et al.. Phys. Rev. Lett. 50 (1983) 891.
- 18. M.N. Bussac et al.. Phys. Rev. Lett. 35 (1975) 1638.
- 19. L. Chen. R.B. White, and M.N. Rosenbluth, Phys. Rev. Lett. 52 (1984) 1122.
- 20. A. Odblom et al.. Phys. Plasmas 9 (2002) 155.
- 21. B. Coppi and F. Porcelli, Phys. Rev. Lett. 57 (1986) 2272.
- 22. B. Coppi. S. Migliuolo, and F. Porcelli. Phys. Fluids 31 (1988) 1630.
- 23. W.W. Heidbrink and G. Sadler, Nucl. Fusion 34 (1994) 535.
- 24. F. Zonca et al.. Nucl. Fusion 47 (2007) 1588.
- 25. L. Chen and F. Zonca. Nucl. Fusion 47 (2007) S727.
- 26. B.N. Breizman and S.E. Sharapov Plasma Phys. Control. Fusion 53 (2011) 054001
- 27. B. Coppi and F. Porcelli, Fusion Technology 13 (1988) 447.
- 28. W.W. Heidbrink. Plasma Phys. Conuol. Fusion 37 (1995) 937.
- 29. Y. Kusama et al., Nucl. Fusion 39 (1999) 1837.
- 30. M.P. Gryaznevich and S.E. Sharapov. Nucl. Fusion 40 (2000) 907.
- 31. E.D. Fredrickson et al.. Nucl. Fusion 46 (2006) S926.
- 32. M.P. Gryaznevich, S.E. Sharapov. Nucl. Fusion 46 (2006) S942.
- 33. K. Toi et al.. Plasma Phys. Control. Fusion 53 (2011) 024008.
- 34. A.V. Melnikov et al., Nucl. Fusion 58 (2018) 082019.
- 35. D. Maslovsky et al., Phys. Plasmas 10 (2003) 1549.
- 36. H.L. Berk et al.. Nucl. Fusion 46 (2006) S888.
- 37. A. Lvovskiy et al., Nucl. Fusion 59 (2019) 124004.
- 38. A.G. Shalashov et al.. Plasma Phys. Control. Fusion 61 (2019) 085020.