Approximate Analytical Description of the Underdense Short Plasma Lens

Abstract

The perturbative approach for describing the underdense plasma--ultrarelativistic electron bunch system is developed, using the ratio n0nb as a small parameter (nb--bunch,n0--plasma electron densities). Focusing of the electron bunch emerged in the first approximation of the perturbative procedure as a result of the plasma electrons redistribution. Focusing gradient and strength for ultrarelativistic, flat, uniform and short bunch are obtained and compared with the previous results.

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