Particle-in-cell simulations of high energy electron production by   intense laser pulses in underdense plasmas
  The propagation of intense laser pulses and the generation of high energy electrons from the underdense plasmas are investigated using two dimensional particle-in-cell simulations. When the ratio of the laser power and a critical power of relativistic self-focusing is the optimal value, it propagates stably and electrons have maximum energies. 
Susumu Kato, Eisuke Miura, Mitsumori Tanimoto, Masahiro Adachi,   Kazuyoshi Koyama