Low-diffraction direct particle acceleration by a radially polarized laser beam

Two constants of the motion, which simplify the relativistic particle dynamics in a laser beam of radial polarization, are identified. Many-particle simulations based on the reduced set of equations of motion in a beam of relativistic intensity, demonstrate acceleration in vacuum to GeV energies of electrons, alpha particles and oxygen bare nuclei. The axially-injected particles are shown to be accelerated with negligible diffraction.