A numerical simulation is performed to identify the physical mechanisms for the generation of the nighttime region 0 and region 1 field-aligned currents (FACs) in conditions of a steady solar wind with a southward or weak interplanetary magnetic field. The generation of region 0/region 1 FACs observed near the poleward edge of the auroral oval is closely associated with the dynamics of ion beams produced by nonadiabatic acceleration in the tail current sheet. After ejection from the current sheet, ion beams advance toward the Earth along the nearly straight field lines. During such a time interval, the ions have insignificant magnetic drift velocities. Subsequently, they are reflected at low-altitude mirror points, and under the influence of inward convection they pass the equator on magnetic shells that are further in. At that moment they attain large magnetic (curvature) drift velocities. Accordingly, in a steady state, the magnetic drift speed averaged over all the ions in a flux tube increases with decreasing invariant latitude; it starts to increase significantly at a certain magnetic shell. In the present paper this magnetic shell is identified with the interface demarcating the nonadiabatic and adiabatic regions in the tail current sheet. An essential point for the region 1 FAC generation is distortion of this interface, namely inclination of the interface to the direction of the average magnetic drift velocity. The generation of region 0 FACs is due to anomalous cross-field diffusion of energized ions near the poleward edge of the auroral oval. Latitudinal profiles of magnetic field perturbations arising from region 0/region 1 FACs in the simulation are remarkably similar to observed magnetic field signatures of the region 0/region 1 thin-current-sheet systems.