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 relativis tic self-focusing are studied analytically and numerically with emphas is on the phase velocity of the plasma wave. The paraxial model descri bing modulation of the pulse spot size is shown to provide a good quan titative description, including preexponential factors, of the wake fi eld during the linear stage of the resonant self-modulation instabilit y. Though the phase velocity of the excited plasma wave is shown to be close to the group velocity of the laser pulse, the relativistic gamm a-factor corresponding to the phase velocity, which is a crucial param eter 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 tw o gamma-factors takes place only in the initial stage of the instabili ty and vanishes in the later stages. (C) 1996 American Institute of Ph ysics.