Abstract
A normalized weighting function model for the average period of particles trapped in the potential wells of waves undergoing nonlinear Landau damping is considered. The model preserves the conservation properties of the trapped particles and relates them to the evolution of the wave envelope. It is valid when there are more shallowly trapped particles than deeply trapped particles, such as in long-time nonlinear Landau damping, as well as stabilities due to trapped particles at long times. The model is also useful for estimating the validity of the often invoked assumption that most trapped particles in nonlinear waves are deeply trapped.
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