  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.
