  Collisionless shocks are ubiquitous in astrophysics and in the lab. Recent
numerical simulations and experiments have shown how they can arise from the
encounter of two collisionless plasma shells. When the shells interpenetrate,
the overlapping region turns unstable, triggering the shock formation. As a
first step towards a microscopic understanding of the process, we analyze here
in detail the initial instability phase. On the one hand, 2D relativistic PIC
simulations are performed where two symmetric initially cold pair plasmas
collide. On the other hand, the instabilities at work are analyzed, as well as
the field at saturation and the seed field which gets amplified. For mildly
relativistic motions and onward, Weibel modes govern the linear phase. We
derive an expression for the duration of the linear phase in good agreement
with the simulations. This saturation time constitutes indeed a lower-bound for
the shock formation time.

High Energy Astrophysical Phenomena;Plasma Physics