Application of nonlinear dynamical invariants in a single electromagnetic wave to the study of the Alfvén-ion-cyclotron instability

Dynamical invariants are derived for particles moving in a single, circularly polarized electromagnetic wave of arbitrary time dependence propagating parallel to a uniform background magnetic field. The invariant associated with helical symmetry is shown to restrict the particle motion to a very narrow region of velocity space. Features of the slow time-scale motion of fixed points associated with the existence of a fourth adiabatic invariant are described for the case of a slowly varying wave. Characteristics of the particle motion thus derived are applied to the analysis of 1d-3v simulations of the saturation of the Alfvén-ion-cyclotron (AIC) instability for a single wave. In particular, an explanation is offered for the appearance of a sharp edge in the velocity distribution function observed in the simulation.