Relativistic self distortion of a Gaussian laser pulse in inhomogeneous plasma in one dimension is investigated. The relativistic mass effect causes different portions of the pulse to travel with different group velocities leading to the steepening of the pulse front and broadening of the rear. This asymmetry created in the pulse shape gives rise to stronger ponderomotive force on electrons at the front and weaker at the rear. The fast moving electrons under this force are shown to have very significant net energy gain. The energy gain increases with the density scale-length and then saturates.

Electron ponderomotive acceleration in a vacuum by a short-pulsed laser of TEM (1, 0) + TEM (0, 1) mode is studied in this paper using a 3-dimensional (3D) particle simulation. It was found that the laser can trap electrons in transverse and accelerate them with the longitudinal ponderomotive force at the same time. Through this electron trapping and acceleration scheme of TEM (1, 0) + TEM (0, 1) mode laser, the electron bunch is confined well in transverse and compressed remarkably in longitudinal. Therefore, a high energy, high density, and low emittances electron bunch is generated. For example, the result shows that for a laser with intensity of a0 = eE0 /mωc = 10, the laser spot size of w0 = 15λ, and the laser pulse length of Lz = 10λ, the maximum energy gain reaches 301 MeV and the average energy 57.7 MeV. The electron bunch transverse radius is about 350λ and the longitudinal size about 20λ. The property of this accelerated bunch is improved compared with that generated by the laser of TEM (0, 0) mode.