Evolution of relativistic electron current beam in a cold plasma with fixed background of ions

A numerical study of evolution of relativistic electron current beam in a cold homogeneous plasma with immobile ions has been carried out using one dimensional electrostatic relativistic particle-in-cell code. It is found that the beam current when longitudinally perturbed by imposing a relativistically intense wave, diminishes with time due to phase mixing effects, arising because of spatial variation of relativistic mass. Studies have been conducted for various flow velocities($v_{0}/c$) and relativistic intensities ($\frac{eE_{0}}{m\omega_{pe} c}$) of the perturbed wave. Rate of decay of current decreases with increasing flow velocity for a fixed ($\frac{eE_{0}}{m\omega_{pe} c}$); and for a given initial current the final magnitude of current decreases with increasing relativistic intensity of the perturbed wave.