  Energetic electromagnetic emissions by astrophysical jets like those that are
launched during the collapse of a massive star and trigger gamma-ray bursts
(GRBs) are partially attributed to relativistic internal shocks. The shocks are
mediated in the collisionless plasma of such jets by the filamentation
instability of counterstreaming particle beams. The filamentation instability
grows fastest only if the beams move at a relativistic relative speed. We model
here with a particle-in-cell (PIC) simulation the collision of two cold pair
clouds at the speed c/2 (c: speed of light). We demonstrate that the two-stream
instability outgrows the filamentation instability for this speed and is thus
responsible for the shock formation. The incomplete thermalization of the
upstream plasma by its quasi-electrostatic waves allows other instabilities to
grow. A shock transition layer forms, in which a filamentation instability
modulates the plasma far upstream of the shock. The inflowing upstream plasma
is progressively heated by a two-stream instability closer to the shock and
compressed to the expected downstream density by the Weibel instability. The
strong magnetic field due to the latter is confined to a layer 10 electron skin
depths wide.
