Adiabatic theory of resonant particle dynamics with frequency chirping chorus waves in magnetospheric plasmas

Abstract

We present the adiabatic regime for the particles interacting with the frequency chirping waves in the inhomogeneous magnetic field. Despite the rapid change of the parameters during the interaction, we can construct an adiabatic invariant with new canonical coordinates, which is shown to be conserved as long as the particles stay trapped in the reference frame moving with the resonance. Assuming the trapped particle distribution as a function of the adiabatic invariant and the water-bag approximation, we derive an analytic form of the nonlinear current as a function of the inhomogeneous parameter that describes the frequency chirping and inhomogeneities in the background magnetic field. The nonlinear current expression is also examined in the Vlasov hybrid simulations, and the simulation results show that the nonlinear current can be well described by the adiabatic water-bag approximation, except for the chirping onset stage and the source region where the adiabatic approximation is invalid.