Aims. The change in the distribution function of electron-positron pair beams determines whether GeV photons can be produced as
secondary radiation from TeV photons. We will discuss the instabilities driven by pair beams.
Methods. The system of a thermal proton-electron plasma and the electron-positron beam is collision free. We have, therefore, used
the particle-in-cell simulation approach. It was necessary to alter the physical parameters, but the ordering of growth rates has been
Results. We were able to show that plasma instabilities can be recovered in particle-in-cell simulations, but their e ect on the pair
distribution function is negligible for the beam-background energy density ratios typically found in blazars