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The origin of the gamma-ray halo around pulsars is associated with the reduced diffusivity of energetic particles responsible for gamma-ray emission with respect to the mean-free path they adopt in the interstellar medium. A possible explanation for this behaviour is that the energetic particles released from the pulsarwind termination shock themselves trigger the turbulence necessary to explain this reduced diffusivity. In order to test the ability of the electron-positron beam to trigger an efficient streaming instability we are in the process of conducting a series of b simulations using both the PIC-MHD technique to follow the evolution of both the electron-positron beam and the thermal background plasma and determine whether the beam can trigger the necessary instabilities. We find that the passage of the electron-positron beam through the thermal plasma triggers streaming instabilities that lead to local amplification of the magnetic field.

Using PIC-MHD to model the interaction between an electron-positron beam and a thermal plasma