3-DIMENSIONAL RELATIVISTIC ELECTRON-SCATTERING IN AN ULTRAHIGH-INTENSITY LASER FOCUS

The relativistic dynamics of an electron submitted to the three-dimens ional field of a focused ultrahigh-intensity laser pulse are studied n umerically. The diffracting field in vacuum is modeled by the paraxial propagator and exactly satisfies the Lorentz gauge condition everywhe re.:In rectangular coordinates, the electromagnetic field is Fourier t ransformed into transverse and longitudinal wave packets, and diffract ion is described through the different phase shifts accumulated by the various Fourier components, as constrained by the dispersion relation . In cylindrical geometry, the radial dependence of the focusing wave is described as a continuous spectrum of Bessel functions and can be o btained by using Hankel's integral theorem. To define the boundary con ditions for this problem, the beam profile is matched to a Gaussian-He rmite distribution at focus, where the wave front is planar. Plane-wav e dynamics are verified for large f numbers, including canonical momen tum invariance, while high-energy scattering is predicted for smaller values of f at relativistic laser intensities. [S1063-651X(98)08210-5] .