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

The nonlinear focusing of a bi-color laser beam in tenuous plasmas can be all-optically enhanced or suppressed depending whether the beat wave frequency $\Omega$ is below or above the electron Langmuir frequency $\omega_p$. The driven electron density perturbation produces a co-moving index grating, which is focusing if $\Omega<\omega_p$ and de-focusing otherwise. Self-consistent guiding of a mildly over-critical long (many plasma periods) laser beam can be all-optically initiated by mixing with a second, much weaker, beam shifted in frequency by $\Omega>\omega_p$. The guiding effect initially owes to the de-focusing properties of the laser beat wave-driven 3D electron density perturbation. Electromagnetic cascading and resonant self-modulation contribute to the guiding process at propagation distances over one Rayleigh length. Acceleration in the non-resonant plasma beat wave yields quasi-monoenergetic bunched electron beams with the energy over a hundred MeV. In the case of $\Omega<\omega_p$, acceleration efficiency is generally higher because of nonlinear focusing enhanced by the plasma wave excitation. To achieve quasi-monoenergetic acceleration in this regime, electrons should be injected in the plasma wake at a distance from the plasma boundary.