We consider the acceleration of electrons in vacuum by means of the circularly-polirized electromagnetic wave, propagating along a magnetic field. We show that the electron energy growth, when using ultra-short and ultra-intense laser pulses (1 ps, 1018 W/cm2, CO2 laser) in the presence of a magnetic field, may reach up to the value 2,1 GeV. The growth of the electron energy is shown to increase proportionally with the increase of the laser intensity and the initial energy of the electron. We find that for some direction of polarization of the wave, the acceleration of electrons does not depend on the initial phase of the electromagnetic wave. We estimate the laser intensity, necessary for the electron acceleration. In addition, we find the formation length of photon absorption by electrons, due to which one may choose the required region of the interaction of the electrons with the electromagnetic wave and magnetic field. We also show that as a result of acceleration of electrons in the vacuum by laser radiation in a magnetic field one may obtain electron beam with small energy spread of the order δε/ε ≤ 10−2.

A scheme for electron acceleration by two crossing chirped lasers has been proposed. An important effect of a frequency chirp of the laser is investigated. Two high intensity chirped lasers, with the same amplitude and frequency, crossing at an arbitrary angle in a vacuum, interfere, causing modulation of laser intensity. An electron experiences a ponderomotive force due to the resultant field of lasers and gains considerable energy. For a certain crossing angle, the electron gains maximum energy due to the constructive interference. A frequency chirp of the laser plays an important role during the electron acceleration in a vacuum. The electron momentum increases due to the frequency chirp. Hence, the electron energy is enhanced during acceleration.