<< ️This (AA) work shows that the interiors of perturbed zero-helicity vortices display simply connected topology with a crescent-shaped boundary. Flux surfaces in fluid and magnetic vortices were explored analytically, while particle trajectories in the context of plasma confinement were examined numerically, demonstrating the existence of both toroidal and simply connected topologies. >>
<< ️Numerical simulations of particle trajectories were conducted in the context of fusion confinement to calculate particle trajectories in a perturbed Soloviev equilibrium where simply connected flux surfaces were observed. The orbits often displayed crescent shapes, yet showed several marked differences from the flux surfaces, e.g., gyro-radii of size comparable to the crescent diameter, asymmetric crescents, connections between well-separated crescent tips, and possibly toroidal shapes, with an inversion of the roles played by the major and minor axes. >>
<< ️This new topology appears for perturbations in a broad class, with amplitudes and spatial variance allowed to be arbitrarily small. A corollary of this work proves the closedness of field lines under odd-parity perturbations of zero-helicity vortices. >>
Taosif Ahsan, Samuel A. Cohen, Alan H. Glasser. Perturbed Toroidal Vortices Display Internal Simply Connected Topology. arXiv: 2507.04596v1 [math-ph]. Jul 7, 2025.
Also: vortex, particle, transition, in https://www.inkgmr.net/kwrds.html
Keywords: gst, vortex, particle, transition, foliated torus, toroidal vortices, banana orbits.