The equations of motion for a particle in resonance with a small finite amplitude wave are solved approximately, using secularity free perturbation theory. The wave propagates at an arbitrary angle to a uniform background magnetic field in an infinite collisionless plasma. The wave fields include a longitudinal electrostatic component and elliptically polarized transverse electric and magnetic components. The trajectories of trapped and resonant untrapped particles are described, for each of the possible wave-particle resonances. These trajectories are used to construct an estimate of the nonlinear time dependent Landau damping rate of the wave.
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