• filamentation instability
• pair plasmas
• radiation reaction

This work analyze the linear and non-linear phase of filamentation instability which grows when two electron-positron neutral beams counter-stream, both from an analytical and a numerical point of view. We use a particle-in-cell (PIC) code performing simulations in both one and two spatial dimensions. We study, also, the effects due to the radiation reaction (RR) force, that accounts for the energy and momentum loss by a charged particle due to the emission of incoherent e.m. radiation.