Radial oscillations of cylindrical magnetic domains — bubbles

The equations of motion for radial oscillations of cylindrical domains (bubbles) are formulated for both a close packed hexagonal arrangement of bubbles and an isolated bubble. The non-linear differential equation is then linearized and solved in the small oscillation approximation. For the case of the isolated bubble the solution is presented together with graphs and an extensive discussion. Equations and graphs determining the resonance frequency and the wall damping as a function of bubble diameter and material parameters are presented.