Double-kink fishbone instability caused by circulating energetic ions

The destabilization of double kink modes by the circulating energetic ions in tokamaks with the plasma current having an off-axis maximum is studied. It is shown that the high-frequency fishbone instability [energetic particle mode (EPM)] and the low-frequency (diamagnetic) fishbones are possible for such an equilibrium, their poloidal and toroidal mode numbers being not necessarily equal to unity. A new kind of the EPM instability, “doublet fishbones,” is predicted. This instability is characterized by two frequencies; it can occur in a plasma with a nonmonotonic radial profile of the energetic ions when the particle orbit width is less than the width of the region where the mode is localized. It is found that the diamagnetic fishbone branch exists even when the orbit width exceeds the mode width; in this case, however, the instability growth rate is relatively small.