Relativistically Driven Charged Particle by a Circularly Polarized Shaped-Pulse: Analytical Solution of the Landau-Lifshitz Equation

Following the Landau–Lifshitz scheme, we describe a new analytical method for solving in closed form, the dynamics of an ultrarelativistic electron accelerated by the electric field of a highly intense circularly polarized shaped laser pulse. The procedure here shown can be generalized for the case of a laser pulse having arbitrary polarization. With the purpose of not only testing but assessing the accuracy of the analytical method developed, we integrated numerically the dynamic equations of a single charged particle for the case of a wave train, together with the concomitant comparison with an alternative analytical method previously published in the literature.