Acceleration of a charged particle in the Redmond field

The motion of a relativistic charged particle in an external specified field of a planer single- and multifrequency circularly polarized electromagnetic wave of large amplitude in the presence of a constant uniform magnetic field (the Redmond field and the multifrequency Redmond field) when the relativistic consideration is required has been analyzed in detail. It is shown that the kinetic energy of a particle in the multi-frequency Redmond field depends not only on the intensity of the wave, and the frequencies of the carrier wave, but also on the direction of polarization of the wave (i.e., right- or left-handed), and the cyclotron frequency. The conditions required for autoresonant motion of a particle in an external field of a large-amplitude wave and the containment of a charged particle are considered.