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The wake field excitation in an unmagnetized plasma by a multi-petawatt,femtosecond, pancake-shaped laser pulse is described both analytically andnumerically in the regime with ultrarelativistic electron jitter velocities,when the plasma electrons are almost expelled from the pulse region. This isdone, for the first time, in fluid theory. A novel mathematical model isdevised that does not break down for very intense pump strengths, in contrastto the standard approach that uses the laser field envelope and theponderomotive guiding center averaging. This is accomplished by employing athree-timescale description, with the intermediate scale associated with thenonlinear phase of the electromagnetic wave and with the bending of its wavefront. The evolution of the pulse and of its electrostatic wake are studied bythe numerical solution in a two-dimensional geometry, with the spot diameter\geq 100 microns. It reveals that the optimum initial pulse length needs to besomewhat bigger than 1 micron (1-2 oscillations), as suggested by simpleanalytical local estimates, because the nonlocal plasma response tends tostretch very short pulses.

Dynamics of the wakefield of a multi-petawatt, femtosecond laser pulse in a configuration with ultrarelativistic electrons