Model for spontaneous frequency sweeping of an Alfvén wave in a toroidal plasma

We study the frequency chirping signals arising from spontaneously excited toroidial Alfvén eigenmode (TAE) waves that are being driven by an inverted energetic particle distribution whose free energy is tapped from the generic particle/wave resonance interaction. Initially a wave is excited inside the Alfvén gap with a frequency determined from the linear tip model of Rosenbluth, Berk and Van dam (RBV) [1]. Hole/clumps structures are formed and are observed to chirp towards lower energy states. We find that the chirping signals from clump enter the Alfvén continuum which eventually produce more rapid chirping signals. The accuracy of the adiabatic approximation for the mode evolution is tested and verified by demonstrating that a WKB-like decomposition of the time response for the field phase and amplitude agree with the data. Plots of the phase space structure correlate well with the chirping dependent shape of the separatrix structure. A novel aspect of the simulation is that it performed close to the wave frame of the phase space structure, which enables the numerical time step to remain the same during the simulation, independent of the rest frame frequency.