Effect of high-order field corrections in electron scattering by intense laser beams in vacuum

By considering the influence of high-order field corrections upon the elect ron-intense laser interactions in vacuum, we have demonstrated that great c are should be taken of the electromagnetic fields when dealing with the non linear relativistic Lorentz equation for the electron motion. Moreover, the precision of different field descriptions corresponding to first-order cor rections and paraxial approximation is investigated with examples of electr on trajectories. It has been found that the paraxial field equations are ac curate enough to describe the electron motion when the width of the laser b eam described by symmetric fields meets kw(0) greater than or similar to 60 . In the case of asymmetric fields, the paraxial approximation is not appro priate to be used. This research is of great interest for the choice of ele ctromagnetic fields in the study of laser acceleration of electrons.