  We report the observation of longitudinal filamentation of an
electron-positron pair plasma in a beam-driven QED cascade. The filaments are
created in the "pair-reflection" regime, where the generated pairs are
partially stopped and reflected in the strong laser field. The density
filaments form near the center of the laser pulse and have diameters similar to
the laser wavelength. They develop and saturate within a few laser cycles and
do not induce sizable magnetostatic fields. We rule out the onset of two-stream
instability or Weibel instability and attribute the origin of pair
filamentation to laser ponderomotive forces. The small plasma filaments induce
strong scattering of laser energy to large angles, serving as a signature of
collective QED plasma dynamics.
