Nonperturbative investigation of the kinetic and fluid nonlinear effects during the fishbone saturation with an hybrid reduced-MHD/kinetic model

This paper investigates nonlinear kinetic and fluid effects on precessional Fishbones, energetic particle-driven modes observed in tokamaks, through simulations performed close to and far from the instability threshold, with γ/ω≃10−1. A monoenergetic population of deeply trapped particles evolves in a reduced-phase space, considering only their toroidal precessional motion. The study focuses on a mode with poloidal mode number m=1 and toroidal mode number n=1, with particular emphasis on how frequency evolution influences the resonant energy exchange between the mode and energetic particles. The fishbone develops nonperturbatively at the location of the maximum gradient position of the energetic particles' distribution function, with a frequency corresponding to the toroidal precession frequency of the energetic particles. In the nonlinear regime, energetic particles are displaced in phase space, thereby modifying the mode frequency and causing a temporary loss of the resonance condition. Consequently, particles shift toward lower precessional frequencies, resulting in a down-chirping of the mode frequency. The primary nonlinear fluid effect is the generation of a zonal flow that prevents the down-chirping observed in the absence of fluid nonlinearities. This suppression preserves the resonance condition for a longer time. Therefore, when fluid nonlinear effects are included, the mode saturates at a higher level since a larger number of energetic particles are able to remain synchronized with the mode.