On the possibility of the autoresonant motion of an electron in a slow electromagnetic wave

The possibility of autoresonance in a slow electromagnetic wave propagating along the straight lines of the external magnetic field is discussed. It turns out that the autoresonant regime of the motion in such a wave is possible if some rather restrictive relations between the electric drift velocity and the phase velocity of the wave take place. It also depends on the polarization of the wave. The general case of the elliptical polarization is considered. The optical regime corresponds to the wave with linear polarization in the direction of the constant electric field. For this case our calculations show that energy of the particle can unlimitedly increase or decrease. The rate of acceleration can be even larger than in the case of 'vacuum wave'. Radiative forces will restrict this process.