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

Comprehensive computer simulations of the Alfven eigenmode burst, which is the synchronized sudden growth of multiple Alfven 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 Alfven 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 Alfven eigenmode burst is close to that for the original beam power. This result indicates that the critical distribution for the Alfven eigenmode burst is present.