  Compton scattering of gamma rays propagating in a pair plasma can drive the
formation of a relativistic electron positron beam. This process is scrutinised
theoretically and numerically via particle-in-cell simulations. In addition, we
determine in which conditions the beam can prompt a beam-plasma instability and
convert its kinetic energy into magnetic energy. We argue that such conditions
can be met at the photosphere radius of bright Gamma Ray Bursts.
