The characteristics of ion beams and conics as seen in two-dimensional numerical simulations in which the plasmas are driven by current sheets of a finite thickness are described. It is shown that the most energetic ions in the simulations have pitch angles near 90 deg, implying a large perpendicular acceleration of the ions. Large perpendicular electric fields, similar to those measured in electrostatic shocks, are mainly confined near the edges of the current sheets, where E-perpendicular is much larger than E-parallel. Double layers with E-perpendicular about equal to, and spatially separated from, E-parallel form in the interior of wide current sheets. Such double layers have upward electric fields in the region of the upward current. Downward electric fields develop outside the current sheet.