Electron laser acceleration in vacuum: is the Gaussian beam description adequate?

Numerical solutions, to the fully relativistic equations of motion of a single electron injected sideways into the focal point of a tightly-focused laser beam, show that accurate electron energy gain calculations require that terms of order ε and higher, where ε is the diffraction angle, ought to be included in the description of the fields of a Gaussian beam focused down to a 5 μm waist radius. It is also demonstrated that, during acceleration, the phase velocity of the accelerating field stays subluminous and, hence, the electron surfs on the laser wave and gains energy from it.