Stochastic effects on phase-space holes and clumps in kinetic systems near marginal stability

The creation and subsequent evolution of marginally-unstable modes have been observed in a wide range of fusion devices. This behaviour has been successfully explained, for a single frequency shifting mode, in terms of phase-space structures known as a `hole' and `clump'. Here, we introduce stochasticity into a 1D kinetic model, affecting the formation and evolution of resonant modes in the system. We find that noise in the fast particle distribution or electric field leads to a shift in the asymptotic behaviour of a chirping resonant mode; this noise heuristically maps onto microturbulence via canonical toroidal momentum scattering, affecting hole and clump formation. The profile of a single bursting event in mode amplitude is shown to be stochastic, with small changes in initial conditions affecting the lifetime of a hole and clump. As an extension to the work of Lang and Fu, we find that an intermediate regime exists where noise serves to decrease the effective collisionality, where microturbulence works against pitch-angle scattering.