Scalings for ultrarelativistic laser plasmas and quasimonoenergetic electrons

The similarity theory is derived for ultrarelativistic laser-plasma interactions. It is shown that the most fundamental S similarity is valid for both underdense and overdense plasmas. The particular case of tenious plasma is considered in great detail. It is shown that the electron dynamics in this case has two characteristic scales. The fast scale corresponds to relaxation to some attractor solution. The slow dynamics describes an adiabatic evolution of this attractor. This leads to a remarkable wave breaking exclusion rule in the three-dimensional geometry. A similarity theory for the slow dynamics allows obtaining simple "engineering" scalings for the maximum electron energies, the number of accelerated electrons, the electron beam density, and for the acceleration distance. These scalings are aimed at design of a compact high-energy laser-plasma accelerator generating electron beams suitable for practical applications.