Nonlinear ponderomotive scattering of relativistic electrons by an intense laser field at focus

The relativistic dynamics of electrons subjected to the electromagnetic field of an intense, ultrashort laser pulse in vacuum is studied theoretically. The effects of both finite pulse duration and beam focusing are taken into account. It is found that when the quiver amplitude of the electrons driven by the laser field exceeds the focal spot radius of a Gaussian beam, the restoring force acting on the charge decays exponentially, and the electrons are scattered away from the focus. This physical process, known as ponderomotive scattering, effectively terminates the interaction within a laser wavelength, and the electrons can escape with very high energy, as the normalized laser field is of the order of or greater than unity. The relation between the scattering angle and the escape energy is derived analytically from the conservation of canonical momentum and energy in the photon field. For a linearly polarized laser field, the interaction produces two jets of high energy electrons. The theory is supplemented by detailed two-dimensional computer simulations.