A note on the vector potential of Connerney et al.ʹs model of the equatorial current sheet in Jupiterʹs magnetosphere

We derive approximate analytic forms for the vector potential of the model jovian equatorial current sheet proposed by Connerney et al. (J. Geophys. Res. 86 (1981) 8370.) and compare them with numerical values derived from exact integral expressions. The vector potential is of great utility in mapping magnetic field lines in the axisymmetric approximation, in deriving model magnetic field components which are guaranteed to be divergence-free at each order of approximation, and in generalising the model to non-planar current sheet configurations. Two approximations are derived, valid for radial distances which are small and large compared with the distance of the inner edge of the model current sheet, respectively. These analytic forms are shown to provide excellent approximations within their respective regimes of validity, and are employed to generate field line maps via contours of the flux function. Corresponding divergence-free magnetic field components are also derived and compared with numerical values, and with the approximate forms suggested by Connerney et al. (1981).