The electric field of positron plasma wakefield accelerator driven by electron beam

Two electron bunches are focused on thin tantalum (⁷³Ta) foil placed at the entrance of the plasma, the first bunch is able to excite plasma wake after Ta foil for accelerating and focusing positron and the second bunch generated positron to be accelerated. Electric field for accelerating, E_Z, and focusing, E_X, depend on characteristics of electron bunches such as: amplitude, duration and frequency. In this paper, electron pulse is approximated as Dirac delta function and three first orders of b-splines; electric field E_Z and E_X are calculated by PIC (Particle-In-Cell) algorithm. The calculated results show that the maximum electric field E_max is obtained at the electron pulse as Dirac delta function; however, we would like to replace by the first order b-splines function for electron pulse. (author)