Nonlinear motions and trapping of particles in a quasi-monochromatic wave

An asymptotic solution is given of hte particle motion in an arbitrary quasimonochromatic wave. Zero stationary magnetic field and untrapped particles are considered. The number of adiabatically trapped particles, the total momentum conservation and the space-averaged distribution function of non-resonant particles are derived for the case of an electrostatic wave with time-dependent amplitude.