A simple representation of the global circuit of Birkeland currents is developed, based on a representation of the current density j in terms of Euler potentials (&agr;, &khgr;). The underlying magnetic field, which shares with j the potential &agr;, is assumed to be dipolar, making the model applicable mainly to region 2 Birkeland currents, although a similar approach could also be used for region 1. A form of j is chosen that gives a current sheet with peak outflow at dawn and peak inflow at dusk (or vice versa), connected across a flat polar cap sheet. The current is further assumed to flow in a thin layer enclosing the dipole fieldline surface L=10, and to close symmetrically across noon and midnight. To produce the asymmetry expected of the partial ring current, a (full) ring current jRC is added to the configuration, and a suitable function G(&ggr;) defining the currents was selected. The field of the current sheet is then numerically derived by Biot-Savart integration and the magnetic scalar potential &PSgr;, which consists of a cosϕ component and an axisymmetrical one, is approximated in three regions of space. It is found that the superposition of harmonics of the same type, centered at different ''foci,'' provided a flexible and powerful representation of harmonic functions, accurate here within less than 1%. Appendix A discusses the Euler potentials of the magnetic field B and Appendix B developes an interpolation formula by which current sheets of finite width could be consistently represented. Future plans are described for deforming configurations of this type to represent region 1 currents and for bypassing the tedius Biot-Savart integration.