Nonlinear optics above the power threshold for relativistic self-focusing

Recent advances in laser technology has heightened interest in the nonlinear interaction of high-density and ultrashort laser pulses with plasmas, where electrons are accelerated by plasma waves. The field gradient of a plasma wave is shown to exceed that of an RF linac four times and accelerates a picosecond bunch of electrons with over 1-nC of charge per bunch in a low-emittance beam. Electron acceleration over distances exceeding the Rayleigh range is also demonstrated. The self-focused laser pulse exerts enormous pressure on the plasma which forms a hollow density cavity in the wake of the laser pulse along the laser axis. This density channel acts as a waveguide that can guide a second collinear intense laser pulse well beyond the Rayleigh range.