Analysis of electron acceleration in a vacuum beat wave

We present an exact analytic investigation of the electron dynamics in the field of two linearly polarized interfering copropagating laser beams of different frequencies, arbitrary intensities, and arbitrary relative polarizations. In one part of the paper, the laser fields are modelled by plane waves and in another part the fields are allowed to have one-dimensional sin(2) pulse shapes which model focusing in the propagation direction. The general situation in which the electron is injected at an angle with the common direction of wave propagation is considered throughout. A cycle-by-cycle analysis of the electron motion, and its momentum and energy exchange with the laser fields is conducted. It is found that an electron may be accelerated, even from rest, to GeV energies over short distances using present-day laser field intensities. This leads, in principle, to energy gradients in the TeV m(-1) range. The trajectory calculations also show clearly that the electron gets scattered away from its initial direction of motion during interaction with the laser fields. The transverse as well as longitudinal motions may be followed exactly using our equations, and predictions could thus be made concerning where the electron should, in principle, be ejected in order for it to emerge with a particular energy gain.