Electron acceleration by single and double laser beams

The longitudinal electric field of single and double Gaussian laser beams are used to accelerate electrons. The longitudinal field of the single beam is concentrated on the axis and is favourable for acceleration. A set of two beams is considered. Beams run parallel, collinearly, overlap partially and have a phase difference iπ in between. As a result, the transverse components of fields cancel each other while the longitudinal components are double-fold. In both schemes, the electrons are accelerated in lengths of the Rayleigh range, which is common to the plasma-based accelerators.