  The linear instability that induces a relativistic electron beam passing
through a return plasma current to filament transversely is often related to
some filamentation mode with wave vector normal to the beam or confused with
Weibel modes. We show that these modes may not be relevant in this matter and
identify the most unstable mode on the two-stream/filamentation branch as the
main trigger for filamentation. This sets both the characteristic transverse
and longitudinal filamentation scales in the non-resistive initial stage.
