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 electron-intense laser interactions in vacuum, we have demonstrated that great care should be taken of the electromagnetic fields when dealing with the nonlinear relativistic Lorentz equation for the electron motion. Moreover, the precision of different field descriptions corresponding to first-order corrections and paraxial approximation is investigated with examples of electron trajectories. It has been found that the paraxial field equations are accurate enough to describe the electron motion when the width of the laser beam described by symmetric fields meets kw₀ ≳ 60. In the case of asymmetric fields, the paraxial approximation is not appropriate to be used. This research is of great interest for the choice of electromagnetic fields in the study of laser acceleration of electrons.