Trajectories of magnetic field lines starting on the wall in nonresonant stellarator divertor

The HSX magnetic field or a simple magnetic field line Hamiltonian, Phys. Plasmas 25, 092505 (2018), describes field line behavior in a stellarator with a non-resonant divertor. When field lines integrations are followed inward from a uniform grid on a wall that is well outside the outermost confining surface, almost all the lines reenter the wall before their toroidal position has advanced by even a period of the stellarator. Nevertheless, approximately 2% of the lines make tens of toroidal transits before reentering the wall. All but a fraction of a toroidal transit of the lines that make many toroidal transits are spent near the outermost confining surface. These lines are interacting with cantori that lie just outside that surface. Cantori are smooth toroidal surfaces that resemble an irrational magnetic surface but with pairs of small holes called turnstiles through which equal amounts of magnetic flux can cross going inward or outward. Although the field lines that cross the wall and reenter it are in principle chaotic, the field lines make too few toroidal transits to distort the shape of magnetic flux tubes except when interacting with cantori. The smallness of the turnstiles of the cantori give collimated flux tubes that strike the walls before they can distort significantly. This explains the tight collimation of diverted field lines seen in studies of non-resonant divertors.