On the structure of wave-particle interactions and nonlinear Alfvénic fluctuation dynamics

Nonlinear dynamics, such as saturation and frequency chirping of Alfvénic fluctuations driven by energetic particles are investigated by means of the nonlinear hybrid magnetohydrodynamics gyrokinetic code (XHMGC). Saturation mechanism due to resonance detuning and/or radial decoupling are discussed. It will be shown that saturation field level exhibits a quadratic scaling with the growth rate, in the former case; a linear scaling, in the latter case. The dominance of one or the other mechanism depends on the linear properties of the mode (in particular, the growth rate, the spatial structure and the radial dependence of the resonance frequency). For the frequency chirping of EPMs, phase locking has been proposed, within “fishbone” paradigm, to describe such chirping: the resonance condition with linearly resonant particles is maintained, while particles are radially displaced, through a continuous modification of the mode frequency. Meanwhile an additional scenario is possible: mode radial localization and frequency appear to be locked to the shear Alfvén continuum; once the linear resonance population has exhausted its driving capability (because of local flattening of the phase-space distribution function), the mode is shifted to non-exhausted regions of the phase space. The e↵ect is a succession of resonant excitations from di↵erent phase-space regions (each characterized by its own nonlinear evolution time), rather than mode adjustment to the evolution of the linearly-resonant particles. Both mechanisms demonstrate that the frequency chirping is due to the procedure of maximising the wave-particle power exchange.