A simple model of Birkeland currents

The paper develops a simple representation of the global circuit of Birkeland currents on the basis of a representation of the current density (j) in terms of Euler potentials (alpha, chi). The underlying magnetic field, which shares the potential alpha with j, is assumed to be dipolar, making the model applicable chiefly to region 2 Birkeland currents. 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 superposition of harmonics of the same type, centered at different 'foci', are found to provide a flexible and powerful representation of harmonic functions, accurate within less than 1 percent. An interpolation formula by which current sheets of finite width could be consistently represented is developed.