Scalings for ultra-relativistic laser plasmas and monoenergetic   electrons
  The similarity theory is derived for ultra-relativistic laser-plasma interactions. First, it is shown that the most fundamental S-similarity is valid for both under- and overdense plasmas. Then, 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 3D 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 high-energy laser-plasma accelerator generating electron beams with superior properties. 
S.Gordienko, A.Pukhov