On the motion of a charged particle in a plane monochromatic electromagnetic wave

The motion of a charged particle in the external specified field of a plane electromagnetic wave of large amplitude, when the relativistic consideration is required, is analysed in detail. The cases of different initial conditions for the motion of the charged particle and different polarisations of the wave are studied. It is shown that the expression for the kinetic energy of an electron oscillating in the transverse field of the wave, proposed in [1], is valid only in the nonrelativistic limit.