Asymptotic Theory of Nonlinear Landau Damping and Particle Trapping in Waves of Finite Amplitude

A fully nonlinear, time-asymptotic theory of nonlinear Landau damping and resonant particle trapping in finite-amplitude waves is presented. The virial theorem and the conservation of the parallel adiabatic invariant are used to determine the time-asymptotic distribution function. The effect of trapped particles on the nonlinear wave dynamics is highly nontrivial and forces a significant departure from the conventional models of finite-amplitude waves.