Streaming instabilities in converging geometry

We present an investigation into counter-streaming electron beams converging towards, and diverging from, a single point in two dimensions, leading to two-stream and current filamentation instabilities, which have radial and azimuthal density modulations, respectively. Using a semi-analytical approach and numerical simulations, we find no evidence for the two-stream instability in this geometry, but show that the system is unstable to the development of current filamentation