Particle motion in the field of a modulated wave

Abstract

The motion of a charged particle in a modulated electrostatic wave is studied with special emphasis on a standing wave. It is shown numerically that the trajectories of particles which make transitions from being trapped to untrapped are always chaotic on a sufficiently long time scale, while the trajectories of particles which do not make transitions are regular. It is shown how to calculate the adiabatic invariant for this system using Lie perturbation techniques. Finally, the time scale on which large-scale chaos is visible is determined by calculating Lyapunov exponents.