Stability of levitation of solid and liquid conducting spheres in high frequency electromagnetic fields. I. computational results

The conditions for stability with respect to rotational and vibrational perturbations in the hovering of an electrically conducting sphere levitated in the electromagnetic field of a high frequency inductor are examined theoretically. The inductor consists of a circular winding with an alternating current. The basic criterion controlling the levitation stability of the sphere is the relative frequency ω* = μ0σωR₀²(where σ and R are the electrical conductivity and radius of the sphere and CO is the angular frequency of the inductor current). For ω* < ω*_c, the levitation is stable and for ω* > ω*_c, it is unstable, with a critical relative frequency (ω*_c = 10 ± 2 for both types of perturbations. The calculations are in good agreement with experimental data. The experiment is described briefly here, since a separate paper will be devoted to it.