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Using symmetry conditions and conformal mapping techniques, the two-dimensional problem of potentials due to a periodic assembly of thin line charges is first solved. The three-dimensional problem obtained by placing one and two cross-wire meshes parallel to a ground plane are then analyzed for evaluating the effectiveness of such structures in trapping Compton electrons in the system-generated EMP simulators. The parametric analysis conducted here indicates that such structures can successfully trap electrons with velocities considerably in excess of the escape velocity. By considering only very thin wire structures, the relatively unimportant parameter of direct collision of the electrons with the mesh is removed. Parametric analysis yields data suitable for maximizing trapping efficiency as a function of the kinetic energy of the Compton electrons.