Electron Acceleration by a Focused Gaussian Laser Pulse in Vacuum

<正> By numerically solving the relativistic equations of motion of a single electron in laserfields modeled by a Gaussian laser beam, we get the trajectory and energy of the electron. Whenthe drifting distance is comparable to or even longer than the corresponding Rayleigh length, theevolution of the beam waist cannot be neglected. The asymmetry of intensity in acceleration anddeceleration leads to the conclusion that the electron can be accelerated effectively and extracted bythe longitudinal ponderomotive force. For intensities above 10～(19) Wμm～2/cm～2, an electron's energygain about MeV can be realized, and the energetic electron is parallel with the propagation axis.