Explicit general solutions to relativistic electron dynamics in plane-wave electromagnetic fields and simulations of ponderomotive acceleration

Abstract

This study examines single-particle electron motions in both a plane electromagnetic wave and a Gaussian focus in vacuum. Exact, explicit analytic expressions for relativistic electron trajectories in a plane wave are obtained, using the proper time as a parameter, in the general case of arbitrary initial positions and velocities. It is shown that previous analyses can be completed using the proper-time parameter. The conditions under which localized oscillatory motions (‘figure-of-eight’ orbits) occur are derived from the new solutions. The general solutions are also connected with the figure-of-eight orbits by a Lorentz transformation. The analytic solutions for arbitrary initial conditions and an arbitrary initial field phase can be used to determine the ranges of electron ejection angle and emerging electron energy in a vacuum laser accelerator, in which electrons are ejected externally, and provide a basis for explaining the spectrum of nonlinear Thomson scattering radiation. Numerical solutions are used for electron motions in the focus of a Gaussian laser beam, and the mean motion allows one to test a new expression for the relativistic ponderomotive force. It is suggested that plane wave solutions can provide a basis for approximating the orbital motion of particles in Gaussian beams.