Nonlinear adiabatic reflection of electrons by an electromagnetic wave in a plasma

A theoretical model is developed for the investigation of the adiabatic reflection of electrons from a spatially localized electromagnetic wave, taking into account the nonlinear trapping in the wave field. A complete analytical description of the adiabatic motion is given via the constancy of the Hamiltonian and the invariance of the adiabatic integral. The set of initial conditions for which reflection occurs is determined in detail as a function of the field amplitude and of the wave frequency for the case of electron-cyclotron waves in perpendicular propagation. The comparison with the results of the Lie transform approach is performed. It is found that trapping effects strongly modify the reflection process, giving rise to a substantial enhancement of the repulsive ponderomotive force. When trapping occurs, reflection is observed for a large set of initial conditions for which the perturbative approach predicts no reflection at any value of the perturbation.