  We present a new analytical solution for the equation of motion of
relativistic electrons in the focus of a high-intensity laser pulse. We
approximate the electron's transverse dynamics in the averaged field of a long
laser pulse focused to a Gaussian transverse profile. The resultant
ponderomotive scattering is found to feature an upper boundary of the
electrons' scattering angles, depending on the laser parameters and the
electrons' initial state of motion. In particular, we demonstrate the angles
into which the electrons are scattered by the laser scale as a simple relation
of their initial energy to the laser's amplitude. We find two regimes to be
distinguished in which either the laser's focusing or peak power are the main
drivers of ponderomotive scattering. Based on this result, we demonstrate how
the intensity of a laser pulse can be determined from a ring-shaped pattern in
the spatial distribution of a high-energy electron beam scattered from the
laser. We confirm our analysis by means of detailed relativistic test particle
simulations of the electrons' averaged ponderomotive dynamics in the full
electromagnetic fields of the focused laser pulse.
