(a) Numerically calculated hoop force and (b) critical decay index as a function of z_ap/x_f for ε = 0.5, ℓ_i = 0.5, and n_I = 0. Here F_h and ﹩{n}_{\mathrm{cr}}^{}﹩ have been plotted for all of the current closures shown in Figure 2, as well as for no closure, the unphysical situation where there are no return currents. The plots all begin at z_ap = a because below this height, part of the rope would be below z = 0 and the model breaks down. The hoop force calculations have been done numerically via the Biot–Savart law. For plots varying the other two input parameters, ε and ℓ_i, see Figure 9.