Shifted-circle model and different current closure options that are considered. The axis of the flux rope is approximated by the solid blue circle, which has foot points fixed at x = ± x_f and apex height z_ap. Given x_f and z_ap, the radius of curvature, R_sc; center of curvature, z_sc; and angle, ϕ_f, can be determined, making this a 1D model with a single parameter, z_ap. The dashed curves represent different potential paths that the return current can take below the solar surface at z = 0. The return currents (dashed lines) shown are either fixed paths or a dynamic image current (purple). The fixed paths are horizontal closure between the foot points (red), vertical paths off to z → −∞ (yellow), a fixed semicircular path (green), and a full circle (cyan).