Adiabatic nonlinear interaction of a localized electron cyclotron wave with a plasma

A theoretical model for the adiabatic nonlinear interaction of a localized electron cyclotron wave with a plasma is developed on the basis of the analysis of the electron motion in the wave field, through a relativistic Hamiltonian formalism, for a wave frequency close to a cyclotron harmonic in oblique propagation. The investigation of the electron energy transitions due to a single crossing of the radiation beam provides the computation of the absorbed power density. Its behavior is studied in detail in the case of first and second harmonics, where peculiar features are pointed out and are explained in terms of the basic characteristics of the nonlinear interaction process. For the weakly nonlinear case, completely analytical expressions for the absorbed power density are given.