Wakefield-driven filamentation of warm beams in plasma

Charged and quasi-neutral beams propagating through an unmagnetised plasma are subject to numerous collisionless instabilities on the small scale of the plasma skin depth. The electrostatic two-stream instability, driven by longitudinal and transverse wakefields, dominates for dilute beams. This leads to modulation of the beam along the propagation direction and, for wide beams, transverse filamentation. A three-dimensional spatiotemporal two-stream theory for warm beams with a finite extent is developed. Unlike the cold beam limit, diffusion due to a finite emittance gives rise to a dominant wavenumber, and a cut-off wavenumber above which filamentation is suppressed. Particle-in-cell simulations with quasineutral electron-positron beams in the relativistic regime give excellent agreement with the theoretical model. This work provides deeper insights into the effect of diffusion on filamentation of finite beams, crucial for comprehending plasma-based accelerators in laboratory and cosmic settings.