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Nonlinear optics above the power threshold for relativistic self-focusing

Due to recent advances in laser technology, there is much current interest in the nonlinear optical interactions of high-intensity and ultrashort duration (fs) laser pulses with plasmas. Besides basic science, applications include advanced fusion energy, X-ray lasers, and ultrahigh-gradient electron accelerators. In these interactions, electrons are accelerated by plasma waves, which are driven by the displacement of plasma electrons by the longitudinal ponderomotive force of the laser light. Due to their greater mass, the ions remain stationary during an electron oscillation period, providing an electrostatic restoring force. The oscillating electrons thus create regions of net positive and negative charge. This forms an electrostatic wakefield that propagates with the laser pulse at at nearly the speed of light, which can trap and accelerate electrons. It is shown that the field gradient of a plasma wave exceeds that of an RF linac by four orders of magnitude and accelerates a picosecond bunch of electrons with over l-nC of charge per bunch in a low-emittance beam.