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
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.