Similarity for ultra-relativistic laser plasmas and the optimal acceleration regime

A similarity theory is developed for ultra-relativistic laser-plasmas. It is shown that the most fundamental S-similarity is valid for both under- and overdense plasmas. Optimal scalings for laser wake field electron acceleration are obtained heuristically. The strong message of the present work is that the bubble acceleration regime [see Pukhov, Meyer-ter-Vehn, Appl. Phys. B, vol. 74, 355 (2002)] satisfies these optimal scalings.