2D structures of electron bunches in relativistic plasma cavities

The spatial structure of an ultra-low emittance electron bunch in a plasma wakefield blowout regime is studied. The full Li\'{e}nard-Wiechert potentials are considered for mutual inter-particle interactions in the framework of the equilibrium slice model (ESM). This model uses the quasi-static theory which allows to solve the Li\'{e}nard-Wiechert potentials without knowledge of the electrons' history. The equilibrium structure we find is similar to already observed hexagonal lattices but shows topological defects. Scaling laws for interparticle distances are obtained from numerical simulations and analytical estimations.