Role of MHD Nonlinearities in the Saturation of Fishbone Instabilities

The saturated kink theory of Rosenbluth et al.[1] is generalized to describe the effects of finite mode frequency and zonal flows. The generalized theory describes a family of saturated solutions exhibiting superposed current and vortex singularities and parametrized by the driving energy and the phase velocity of the mode in the plasma frame. Applications include fishbone oscillations as well as resonant magnetic perturbation for large plasma rotation frequency. A similarity property shows that the plasma displacement normalized to the driving energy is a function of the square of the phase velocity, also normalized to the driving energy. The implications for fishbone saturation will be discussed.

[1] M. N. Rosenbluth, R. Y. Dagazian, and P. H. Rutherford, Phys. Fluids 16, 1894 (1973).