Analysis of Relativistic Particle Orbit in a Transversely Focused High-Power Laser Field by Using the Noncanonical Lie Perturbation Method

A methodology describing the particle motion in a spatially localized high-power laser field in the relativistic regime is presented based on the noncanonical Lie perturbation method, which is comprehensive compared with those based on the conventional averaging method to the equation of motion. We successfully derived the relativistic ponderomotive force in a laser field with a radial intensity gradient and the corresponding particle dynamics up to the first order with respect to the expansion parameter e ∼ λ/L (= laser wavelength/scale length of the transverse laser amplitude). The longitudinal motion was found to be secular and characterized by a growing oscillation exhibiting a cubic dependence on the laser amplitude.