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

Compton driven beam formation and magnetisation via plasma microinstabilities