Electron acceleration by two crossed Bessel--Gaussian beams in vacuum

The direct acceleration of electrons by using two linearly polarized crossed Bessel--Gaussian (BG) beams with equal frequency and amplitude in vacuum is proposed and studied. It is shown that two linearly polarized BG beams of the same order (0 or 1) with a \pi-rad phase difference have a resultant non-zero longitudinal electric field on the z-axis and can be used, in principle, to accelerate electrons.