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 0plasma 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. keywords:plasma focusing,underdense plasma lens,perturbative approach

Nonlinear two-dimensional potential plasma wake waves

“…Analysis of the one dimensional longitudinal,transverse and coupled transverse longitudinal plain nonlinear waves in cold relativistic plasma are given in the review [1] (see therein the references on original works).One dimensional nonlinear longitudinal waves,generated by the driving bunches with the infinite transverse dimensions,were considered in [2]- [8].…”

“…In the one dimensional nonlinear treatment [2]- [8] the magnetic field in the wake wave is also zero (by construction),due to the symmetry of the problem relative to transverse displasments.…”

“…From hydrodynamic equation of the plasma wake wave electrons motion,using (1), (2), (3) it is possible to obtain the relativistic equation of motion for the V z component of the generalized velocity:…”