Controlled wake field acceleration via laser pulse shaping

We consider the interaction of high-intensity laser pulses with underdense plasmas and address the problem of the excitation of strong and stable wake plasma waves with regular electric fields to provide effective acceleration of charged particles over appreciably long distances. It is known that a relativistically strong laser pulse longer than the wavelength of plasma waves, propagating in a plasma is subject to self-modulation. This may result in a nonstationary behavior of the produced plasma wake field/particle dephasing, and reduced net acceleration. In this paper we present the results of 1(2/2)-D and 2(1/2)-D particle in cell (PIC) simulations which demonstrate that regular wake electric fields may be obtained by a properly shaped laser pulse (sharp steepening of its leading front). These results are relevant to the design of the 100 MeV laser wake field electron acceleration experiment that uses a terawatt picosecond CO2 laser and is under construction at the Brookhaven Accelerator Test Facility.