Electron scattering and acceleration by a tightly focused laser beam

By numerically solving the relativistic equations of motion of a single electron in laser fields modeled by those of a Gaussian beam, we demonstrate electron capture by, reflection from, and transmission through the beam. In modeling the fields, terms of order up to ϵ⁵, where ϵ is the diffraction angle, are retained. All cases of capture are accompanied by energy gain that may reach a few GeV, from fields of present-day intensities. Reflection and transmission, on the other hand, result sometimes in no gain or even in a loss of energy. It is shown that a laboratory static magnetic field may be used to eject a captured electron, a process that sometimes results in even more energy gain. For example, a 2.5 T uniform magnetic field suffices to eject a 3.633 MeV electron injected at 6° to the axis of a linearly polarized beam of a 10 PW power output and aimed at a point near the focus. Such an electron gains 1128 MeV from the laser field alone. However, it emerges with a 1230 MeV net energy gain under the additional action of the small magnetic field.