Conditions for the onset of the current filamentation instability in the laboratory

Current Filamentation Instability (CFI) is capable of generating strong magnetic fields relevant to explain radiation processes in astrophysical objects and lead to the onset of particle acceleration in collisionless shocks. Probing such extreme scenarios in the laboratory is still an open challenge. In this work, we investigate the possibility of using neutral $e^{-}$ $e^{+}$ beams to explore the CFI with realistic parameters, by performing 2D particle-in-cell simulations. We show that CFI can occur unless the rate at which the beam expands due to finite beam emittance is larger than the CFI growth rate and as long as the role of competing electrostatic two-stream instability (TSI) is negligible. We also show that the longitudinal energy spread, typical of plasma based accelerated electron-positron fireball beams, plays a minor role in the growth of CFI in these scenarios.