Denominator of the expression on the rhs of Eqs. (37) (left panel, vertical field) and (44) (right panel, toroidal field). These expressions are strongly dependent on the orbital radius, which is set to r₀ = 8M here. The various colors encode various values of ι in [0, 30 ° ] (left panel) or [0, 90 ° ] (right panel). In the vertical case, the denominator has a root only for ι < ι₀(r₀), and this critical angle verifies ι₀ ≈ 20° for r₀ = 8M. The condition ι < ι₀(r₀) leads to two QU loops, while higher inclinations lead to a single QU loop. In the toroidal case, all values of ι lead to the existence of two roots, so there will always be two loops, whatever the inclination.