Publications Repository - Helmholtz-Zentrum Dresden-Rossendorf

This paper presents a theoretical study of oscillatory and rotational instabilities of a solid spherical body levitated electromagnetically in axisymmetric coils made of coaxial circular loops. We apply our previous theory to analyze the static and dynamic stability of the sample depending on the AC frequency and the position of the sample in the coils for several simple configurations. An original analytical approach is introduced employing a gauge transformation for the vector potential. First we calculate the spring constants which define the frequency of small-amplitude oscillations. For static stability the spring constants must be positive. Dynamic instabilities are characterized by critical AC frequencies which, when exceeded, may result either in a spin-up or oscillations with increasing amplitude. It is found that the critical frequencies increase with the non-uniformity of the field. We show that for a spherically harmonic field the critical frequency for the spin-up instability in a field of degree l coincides with the critical frequency for the oscillatory instability in a field of degree l+1.