Self-Resonant Plasma Wake-Field Excitation by a Laser-Pulse with a Steep Leading-Edge for Particle-Acceleration

The self-modulational instability of a relatively long laser pulse with a power close to or less than the critical power for relativistic self-focusing in plasma is considered. Strong wake-field excitation occurs as the result of a correlated transverse and longitudinal evolution of the pulse. The dependence of the magnitude of the plasma wave on the duration of a flat-top pulse is investigated. The power necessary to reach 20% electron density modulation behind the laser pulse is shown to decrease as the pulse duration increases, while the phase velocity of the plasma wave remains close to the group velocity of the laser pulse. This provides an opportunity to operate a laser wake-field acceralator in the self-modulated regime at a subcritical laser power, at least twice less than the critical one, and to obtain a sufficiently large accelerating gradient (> 20 GV/m) in a region which is longer than that required for the acceleration of an ultrarelativistic particle.