The internal kink stability of a tokamak in the presence of energetic particles is studied. It is found that there is a stable window when a finite population of energetic particles is present; also the relationship between the predictions of the fishbone theory of Chen-White-Rosenbluth and the fishbone theory of Coppi-Porcelli is explained. The theory indicates why in some experiments, such as those on PDX and TFTR, fishbone oscillations are likely to occur in conjunction with sawtooth modes, while in other experiments sawtooth suppression in the presence of hot particles is observed.
Integrated modelling of sawtooth cycles and fishbone oscillations in ASDEX Upgrade plasmas