The dynamics of an electron–ion plasma is studied when a mono-energetic relativistic electron beam penetrates the expanding plasma. Combined effects of thermal pressure and ambipolar electrostatic potential are considered for fully relativistic multi-fluids model where the quasi-neutrality assumption is used for a beam–plasma system. Relativistic effects are considered for both density and velocity of the beam fluid. Ion acceleration is depicted through a spike-like structure resulting from non-local charge separation and associated with the beak-down of quasi-neutrality. The beam initial speed is found to enhance the spike amplitude and change its position. Moreover, relativistic effects are particularly found significant for a non-thermal plasma.
