Resonance, particle trapping, and Landau damping in finite-amplitude obliquely propagating waves

The equations of motion for a particle in resonance with a small finite amplitude wave (ω, k) are solved approximately, using secularity-free perturbation theory. The wave propagates at an arbitrary angle to a uniform background magnetic field B0, in an infinite collisionless plasma. The wavefields 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 waveparticle resonances defined by the condition kzVz−ω≈NqB0/m, where N is an integer. These trajectories are used to construct an estimate of the nonlinear time-dependent Landau damping rate of the wave.