  Models for the synchrotron emission of gamma-ray burst afterglows suggest
that the magnetic field is generated in the shock wave that forms as
relativistic ejecta plow through the circum-burst medium. Transverse Weibel
instability efficiently generates magnetic fields near equipartition with the
post-shock energy density. The detailed saturated state of the instability, as
seen in particle-in-cell simulations, consists of magnetically self-pinched
current filaments. The filaments are parallel to the direction of propagation
of the shock and are about a plasma skin depth in radius, forming a
quasi--two-dimensional structure. We use a rudimentary analytical model to
argue that the Weibel filaments are unstable to a kink-like mode, which
destroys their quasi--two-dimensional structure. For wavelengths longer than
than the skin depth, the instability grows at the rate equal to the speed of
light divided by the wavelength. We calculate the transport of collisionless
test particles in the filaments experiencing the instability and show that the
particles diffuse in energy. This diffusion marks the beginning of
thermalization in the shock transition layer, and causes initial magnetic field
decay as particles escape from the filaments. We discuss the implications of
these results for the structure of the shock and the polarization of the
afterglow.
