Ultrarelativistic regime in the propagation of an ultrastrong,   femtosecond laser pulse in plasmas
  The interaction of a multi-Petawatt, pancake-shaped laser pulse with an unmagnetized plasma is studied analytically and numerically in the regime of fully relativistic electron jitter velocities and in the context of the laser wakefield acceleration scheme. The study is applied to the specifications available at present time, or planned for the near future, of the Ti:Sa Frascati Laser for Acceleration and Multidisciplinary Experiments (FLAME) in Frascati. Novel nonlinear equation is derived by a three-timescale description, with an intermediate timescale associated with the nonlinear phase of the laser wave. They describe on an equal footing both the strong and moderate laser intensity regimes, pertinent to the core and the edges of the pulse. These have fundamentally different dispersive properties since, in the core, the electrons are almost completely expelled by a very strong ponderomotive force and the electromagnetic wave packet is imbedded in a vacuum channel and has (almost) linear properties, while at the pulse edges the laser amplitude is smaller and the wave is dispersive. The nonlinear phase provides a transition to a nondispersive electromagnetic wave at large intensities and the saturation of the previously known nonlocal cubic nonlinearity, without the violation of the imposed scaling laws. The temporal evolution of the laser pulse is studied by the numerical solution of the model equations in a two-dimensional geometry, with the spot diameter presently used in the self-injection test experiment (SITE) with FLAME. The most stable initial pulse length is found to be around 1 $\mu$m, which is several times shorter than presently available. A stretching of the laser pulse is observed, followed by the development of a vacuum channel and a very large electrostatic wake potential, as well as the bending of the laser wave front. 
Du\v{s}an Jovanovi\'c, Renato Fedele, Milivoj Beli\'c, and Sergio De   Nicola
physics.plasm-ph