Particle in cell simulation of relativistic Buneman instability in a current-carrying plasma

Non-linear evolution of the relativistic Buneman instability in a current-carrying plasma is investigated by a particle in cell simulation. These simulations show that as the time progresses, some electrons are trapped in phase space holes and thus counter-streaming and plateau can be formed. Moreover, the electron and ion density profiles indicate a periodic pattern of the density steepening. This density distribution is similar to the generation of the grating-like patterns which strongly depends on the initial electron velocity and saturation time. It is also shown that the electric field profile has the sawtooth form; charged particles can be accelerated by this field. Finally, it is found that increasing the electron velocity increases the saturation time and consequently the growth rate decreases which is in good agreement with the result obtained by the fluid model.