Nonlinear excitation of subcritical fast ion-driven modes

In collisionless plasma, it is known that linearly stable modes can be destabilized (subcritically) by the presence of structures in phase-space. The growth of such structures is a nonlinear, kinetic mechanism, which provides a channel for free-energy extraction, different from conventional inverse Landau damping. However, such nonlinear growth requires the presence of a seed structure with a relatively large threshold in amplitude. We demonstrate that, in the presence of another, linearly unstable (supercritical) mode, wave-wave coupling can provide a seed, which can lead to subcritical instability by either one of two mechanisms. Both mechanisms hinge on a collaboration between fluid nonlinearity and kinetic nonlinearity. If collisional velocity diffusion is low enough, the seed provided by the supercritical mode overcomes the threshold for nonlinear growth of phase-space structure. Then, the supercritical mode triggers the conventional subcritical instability. If collisional velocity diffusion is too large, the seed is significantly below the threshold, but can still grow by a sustained collaboration between fluid and kinetic nonlinearities. Both of these subcritical instabilities can be triggered, even when the frequency of the supercritical mode is rapidly sweeping. These results were obtained by modeling the subcritical mode kinetically, and the impact of the supercritical mode by simple wave-wave coupling equations. This model is applied to bursty onset of geodesic acoustic modes in an LHD experiment. The model recovers several key features such as relative amplitude, timescales, and phase relations. It suggests that the strongest bursts are subcritical instabilities, with sustained collaboration between fluid and kinetic nonlinearities.