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 $\frac{n_0}{n_b}$ as a small parameter ($n_b$--bunch,$n_0$--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.