Stability of magnetic rings. (15th August 2021) - Hoang, Tuan Minh; Cortes, David Vazquez
Abstract: Linear stability of magnetic rings consisting of permanently magnetized particles p of the same magnetization is studied. Employing Lagrange's approach and multipole moments, we determine the stability criterion in closed form. We then apply this criterion to characterize the stability for two scenarios in which the ring is i) compressed by dipolar loading due to a central point dipole and ii) compressed by mechanical loading. In contrast to previous works which show break up of magnetic rings under homogenous external magnetic field when instability occurs, we find that the ring does not break up when instability arises in both situations considered. However, the loading scenario decides instability modes via which the magnetic ring first loses its stability. For the first scenario, the ring deforms into planar but noncircular shapes via in-plane instability modes, regardless of ring sizes. For the other scenario, the ring deforms into planar but noncircular or nonplanar shapes via in-plane or out-of-plane instability modes for, respectively, small ring sizes or sufficiently large ring sizes. Finally, a simple experiment for the case of dipolar loading is proceeded and experimental results show good agreement with theoretical predictions.