Fig. 5a-d. Evidence that the (axisymmetric ) vector potential series Eq. (53) converges, up to a vanishingly thin boundary layer, to the benchmark vector potential Eq. (23) using (but see the discussion in Clegg et al. 2000b). In a and b the components and are plotted against radius (open inner boundary at to the closed outer boundary at ) for the exact and for the series solution including 50 radial modes. In a the two lines effectively coincide. In c and d a zoom view of is shown , with better convergence using 100 and 500 modes, plotted against the exact solution.