Axisymmetric magnetic vortices with swirl

New solutions for compact vortex rings and vortices in the presence of swirl and toroidal magnetic field are presented. Steady solutions are found for thin-core vortex rings, generalizing the classical results of Kelvin and Hicks. An exact family of steady spherical solutions is found in the case when the underlying governing equation, originally due to Hicks, is linear. Proper matching of the pressure is critical in obtaining these solutions, for which another 19th century equation proves key. Contour dynamics simulations show the existence of counter-propagating dipolar structures when both swirl and magnetic fields are present.