On the Effect of Beating during Nonlinear Frequency Chirping

Abstract

Spectral analyses of energetic particle (EP) driven bursts of MHD fluctuations in magnetically confined plasmas often exhibit multiple simultaneous chirps. While the superposition of oscillations at multiple frequencies necessarily causes beating in the signal acquired by a localized external probe, self-consistent hybrid simulations of chirping EP modes in a JT-60U tokamak plasma have demonstrated the possibility of global beating, where the electromagnetic field vanishes globally between beats and reappears with opposite phase. This implies that there can be a single field mode that oscillates at multiple frequencies simultaneously when resonantly driven by multiple density waves in EP phase space. Conversely, this means that the EP density waves are mutually coupled and interfere with each other via the jointly driven field, a mechanism ignored in some theories. In this treatise, we study the role of field pulsations in general and beating in particular using the Hamiltonian guiding center orbit-following code ORBIT with a reduced wave-particle interaction model in realistic geometry. Through amplitude pulsations and phase jumps, beating is found to drive the evolution of EP phase space structures. Observations: (1) Beating causes density wave fronts to advance radially in pulses. The resulting chirps become staircase-like. (2) The beats facilitate convective transfer of material between neighboring layers of phase space density waves. On the one hand, this may delay detachment of solitary vortices. On the other hand, it facilitates the accumulation of hole and clump fragments into larger structures. (3) Long-range chirping occurs when massive holes or clumps detach and drift away from the turbulent belt around the seed resonance. The detached vortices can remain robust and, on average, maintain their concentric nested layers while being perturbed by the field's continued beating.