Semi-analytical fluid study of the laser wake field excitation in the strong intensity regime

We present an analytical and numerical study of the interaction of a multi-petawatt, pancake-shaped laser pulse with an unmagnetized plasma. The study has been performed in the ultrarelativistic regime of electron jitter velocities, in which the plasma electrons are almost completely expelled from the pulse region. The calculations are applied to a laser wake field acceleration scheme with specifications that may be available in the next generation of Ti:Sa lasers and with the use of recently developed pulse compression techniques. A set of novel nonlinear equations is derived using a three-timescale description, with an intermediate timescale associated with the nonlinear phase of the electromagnetic wave and with the spatial bending of its wave front. They describe, on an equal footing, both the strong and the moderate laser intensity regimes, pertinent to the core and to the edges of the pulse.