Wake waves generated by a proton bunch in an electron-positron-ion plasma

A nonlinear 1D model of longitudinal wake waves generated in a relativistic epi plasma by an ultrarelativistic modulated proton bunch is developed. The model is used for constructing the score of concentration profiles of the concentrations of the plasma component in the wake wave. It is shown that the wave period increases with the concentration of the ion component of the plasma and with the proton bunch density.