Frequency chirping in the Alfvén continuum

A new kinetic code, CHIRP, shows how long range frequency chirping emerges from the energetic particle (EP) excitation of Alfvénic instability. Both a perturbative toroidal Alfvén eigenmode (TAE) and a non-perturbative energetic particle mode (EPM) can be driven unstable due to the EP pressure gradient. These instabilities produce phase space chirping structures in the form of holes or clumps. The code calculates the nonlinear resonant EP response of the poloidally coupled Alfvén wave equations, while the background plasma is assumed to respond linearly to the generated fields. At moderate EP pressure gradient, only TAEs are excited, that produce chirping structures that have only moderate frequency change which do not reach the continuum frequency. Larger pressure gradients excite an EPM mode that emerges in the lower continuum, which then chirps rapidly downward with its amplitude growing appreciably in time. An adiabatic theory was developed that accurately describes the late time evolution of the rapid frequency chirping. The strong correlation between the adiabatic theory and simulation is compatible with the view that the bulk of the EPM-trapped particles evolve in accordance with the conservation of their action.