  It is generally accepted that magnetic fields generated in the nonlinear
development of the transverse Weibel instability provide effective
collisionality in unmagnetized collisionless shocks. Recently, extensive two
and three dimensional simulations improved our understanding of the growth and
saturation of the instability in colliding plasma shells. However, the
steady-state structure of the shock wave transition layers remains poorly
understood. We use basic physical considerations and order-of-magnitude
arguments to study the steady state structure in relativistic unmagnetized
collisionless shocks in pair plasmas. The shock contains an electrostatic layer
resulting from the formation of stationary, magnetically-focused current
filaments. The filaments form where the cold upstream plasma and the
counterstreaming thermal plasma interpenetrate. The filaments are not entirely
neutral and strong electrostatic fields are present. Most of the downstream
particles cannot cross this layer into the upstream because they are trapped by
the electrostatic field. We identify the critical location in the shock
transition layer where the electromagnetic field ceases to be static. At this
location, the degree of charge separation in the filaments reaches a maximum
value, the current inside the filaments comes close to the Alfv\'en limit, and
the phase space distribution function starts to isotropize. We argue that the
radius of the current filaments upstream of the critical location is about
twice the upstream plasma skin depth. Finally, we show that some downstream
particles cross the electrostatic layer and run ahead of the shock into the
preshock medium without causing instability. These particles may play an
important role in particle acceleration.
