Two-Dimensional Nonlinear Regime in the Plasma Wakefield Accelerator

The effect of nonlinearity on plasma wake wave excited by a relativistic cylindrical charged bunch is investigated. It is shown that owing to the nonlinearity the amplitude of wake wave gets modulated in the longitudinal direction. The nonlinear wavelength in the excited field changes in the transverse direction with the result that the phase front is distored and a turbulence developed. The nonlinear phase front distortion may be compensated by radial change of unperturbed plasma density.