Laser wakefield acceleration by petawatt ultra-short laser pulses
  An ultra-short (about 30 fs) petawatt laser pulse focused with a wide focal spot (about 100 microns) in a rarefied plasma (electron density of order 10^{17} per cm^3) excites a nonlinear plasma wakefield which can accelerate injected electrons up to the GeV energy without any pulse channelling. In these conditions, propagation of the laser pulse with an over-critical power for relativistic self-focusing is almost the same as in vacuum. The nonlinear quasi-plane wake plasma wave, whose amplitude and phase velocity vary along the laser path, effectively traps and accelerates injected electrons with a wide range of initial energies. Electrons accelerated along two Rayleigh lengths (about eight centimeters) can gain an energy up to 1 GeV. In particular, the electrons trapped from quite a long (of order 330 fs) non-resonant electron beamlet of 1 MeV particles eventually form a low emittance bunch with energies in the range 900 MeV and energy spread about 10%. All these conclusions follow from two-dimensional simulations performed in cylindrical geometry by means of the fully relativistic time-averaged particle code WAKE. 
L. M. Gorbunov, S. Yu. Kalmykov, and P. Mora