Calculation of footprints of magnetic field lines in the two-mode nonresonant stellarator divertor

There are three parameters in the Hamiltonian function for the trajectories of magnetic field lines in nonresonant stellarator divertor. They are called the shape parameters. They control the elongation, triangularity, and the sharpness of edges on the outermost confining magnetic surface in nonresonant divertor. When we set the parameter that controls the sharpness of edges on the outermost surface equals to zero, we get a two-mode nonresonant divertor. The outmost surface in two-mode divertor is at r = 0.8947b where b is minor radius in the poloidal angle = 0 in the poloidal plane defined by toroidal angle of the period = 0. We start the field lines just outside the outermost surface in this poloidal plane. We use the method for calculation of full 3D magnetic turnstiles developed in [[A. Punjabi and A. H. Boozer, Phys. Plasmas 29, 012502 (2022)]. The intersection of the magnetic turnstiles with the wall gives the magnetic footprint on the wall. It appears that (1) The loss-times of field lines in two-mode divertor are quite large, (2) The footprints have fixed locations on the wall and the sizes of footprints are considerably small compared to the footprints in nonresonant divertor [[A. H. Boozer and A. Punjabi, Phys Plasmas 25, 092505 (2018); A. Punjabi and A. H. Boozer, Phys. Plasmas 27, 012503 (2020) (Editors Pick)]. This work is supported by DOE OFES grants DE-SC0020107 and DE-FG02-07ER54937 to Hampton University, and DE-FG02-03ER54696 to Columbia University. Research used resources of the NERSC, supported by the Office of Science, US DOE, under Contract No. DE-AC02-05CH11231.