On the phase velocity of plasma waves in a self-modulated laser wake-field accelerator

The properties of the wake field excited by a flattop laser pulse with a sharp leading edge and a power below the critical one for relativistic self-focusing are studied analytically and numerically with emphasis on the phase velocity of the plasma wave. The paraxial model describing modulation of the pulse spot size is shown to provide a good quantitative description, including preexponential factors, of the wake field during the linear stage of the resonant self-modulation instability. Though the phase velocity of the excited plasma wave is shown to be close to the group velocity of the laser pulse, the relativistic gamma-factor corresponding to the phase velocity, which is a crucial parameter for particle acceleration, can be substantially less than that of the group velocity. Fortunately, for the considered three-dimensional regime of self-modulation, the noticeable difference between these two gamma-factors takes place only in the initial stage of the instability and vanishes in the later stages. (C) 1996 American Institute of Physics.