Critical energetic particle distribution in phase space for the Alfvén eigenmode burst with global resonance overlap

Comprehensive computer simulations of the Alfvén eigenmode burst, which is the synchronized sudden growth of multiple Alfvén eigenmodes (AEs) interacting with energetic particles, were conducted with continuous neutral beam injection, collisions, and particle losses. It is found that the energetic-particle distribution in phase space reaches a 'critical distribution' with a stairway structure where a resonance overlap triggers the Alfvén eigenmode burst. Before the burst, the gradual growth of the AEs associated with the beam injection broadens the resonant regions in phase space forming the distribution into a stairway shape. When the distribution reaches the 'critical distribution,' a resonance overlap triggers multiple resonance overlaps leading to the synchronized growth of AEs and the collapse of the distribution. For another run with the beam deposition power reduced to one-half, the energetic-particle distribution function just before the Alfvén eigenmode burst is close to that for the original beam power. This result indicates that the critical distribution for the Alfvén eigenmode burst is present.