Filamentary Instability of a Relativistic Electron Beam

The transverse electromagnetic or filamentary instability is reconsidered in light of recent experiments which were unable to suppress the instability by increasing the beam transverse temperature. I find that only the applied magnetic field can stabilize the mode. While the beam temperature can cause stabilization in a collisionless, ν=0, plasma, for finite ν the beam is unstable to filamentation if ωpb²β²γ>Ωce², regardless of its temperature.