A similarity theory is developed for ultra-relativistic laser-plasmas. It is used to compare and optimize possible regimes of three-dimensional wake field acceleration. The optimal scalings for laser wake field electron acceleration are obtained analytically. The main message of the present work is that the bubble acceleration regime [see Pukhov A. & Meyer-ter-Vehn J. 2002. Appl. Phys. B74, 355] satisfies these optimal scalings.
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