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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.
Pukhov et al. (2006) studied this question.