Magnetic-island formation and destruction in a levitron

The effect of non-axisymmetric perturbations on the magnetic surfaces of a levitron is investigated. A Hamiltonian theory is developed for predicting the formation of both primary and secondary magnetic islands for the main resonances. Numerical calculations are made for a range of levitron parameters and compared with results of the Hamiltonian theory. Good agreement is obtained both for island width and for local rotational transform of the islands. A simple criterion for island destruction and the consequent stochasticity of the field lines agrees well with numerical results. A ring tilt of 0.5 degree is found to destroy the magnetic surfaces in the neighbourhood of the main resonances (i = π, 2π).