All-optical control of nonlinear focusing of laser beams in plasma beat wave accelerator

Nonlinear focusing of a bi-color laser in plasma can be controlled by varying the difference frequency Omega. The driven electron density perturbation forms a co-moving periodic focusing (de-focusing) channel if Omega is below (above) the electron Langmuir frequency omega(p). Hence, the beam focusing is enhanced for Omega < omega(p) and is suppressed otherwise. In particular, a catastrophic relativistic self-focusing of a high-power laser beam can be prevented all-optically by a second, much weaker, co-propagating beam shifted in frequency by Omega > omega(p). A bi-envelope equation describing the early stage of the mutual de-focusing is derived and analyzed. Later stages, characterized by a well-developed electromagnetic cascade, are investigated numerically. Stable propagation of the over-critical laser pulse over several Rayleigh lengths is predicted. The non-resonant plasma beat wave (Omega not equal omega(p)) can accelerate pre-injected electrons above 100 MeV with low energy spread.