Electron acceleration by a propagating short ultra-intense laser pulse in a low-density plasma has been investigated. Electrons have the maximum energy when meeting the peak of the laser pulse. If a propagating laser pulse is abruptly stopped by a solid target, the highly energetic electrons will continue to move forward inertially and escape from the laser field. The envelope of the laser pulse is taken into account and there is an optimal position between the electron and the solid target. The electron maximum energy depends on the laser intensity and initial electron energy, and has nothing to do with the polarization of the pulse, but a linearly polarized laser pulse is more effective to accelerate electron than circularly polarized one under the same laser energy. The influence of the reflected light has been taken into account which makes our model more perfect and the results give good agreement with particle in cell simulations.

We present the study of the interaction of an intense circularly polarized pulse with a solid target with one-dimensional (1D) particle-in-cell (PIC) simulation. The evolvement of ion motion with time is explained by a purely kinetic description and by the theory of electrostatic shock in collisionless plasmas. Especially the formation of the stable profile with a "double-flat-top" in ion phase space is explained and validated visually. Assuming the initial state, we find that the ion distribution in the phase space agrees qualitatively with the PIC simulation results by using the particle-tracing approach.

Two-dimensional particle-in-cell simulations are taken to study the interaction of a relativistic, circularly polarized laser pulse with a preformed overdense plasma channel containing a slice of micron size. The laser pulse is confined in the channel, so it can keep higher intensity on a longer time scale inside the channel than the case without a channel. The electrons, both in the slice and from the channel, are pushed forward in the channel by the large light pressure of the laser pulse, followed by the ions accelerated by the electro static field generated by the charge separation. As a result, the acceleration of the slice is more efficient and has a better collimation than in the case without a preformed channel.