  We investigate the long-time evolution of magnetic fields generated by the
two-stream instability at ultra- and sub-relativistic astrophysical
collisionless shocks. Based on 3D PIC simulation results, we introduce a 2D toy
model of interacting current filaments. Within the framework of this model, we
demonstrate that the field correlation scale in the region far downstream the
shock grows nearly as the light crossing time, lambda(t) ~ ct, thus making the
diffusive field dissipation inefficient. The obtained theoretical scaling is
tested using numerical PIC simulations. This result extends our understanding
of the structure of collisionless shocks in gamma-ray bursts and other
astrophysical objects.
