Oscillatory instability of electromagnetically levitated solid bodies

This paper presents a linear-stability analysis of small-amplitude oscillations of a solid body suspended in an alternating magnetic field. An original theory is developed for an arbitrary configuration of the magnetic field. Stability of a solid sphere in an axisymmetric linear magnetic field is calculated analytically. Oscillations of the sphere are found to develop as the frequency of the held exceeds a certain critical threshold relative to the characteristic diffusion time of the magnetic field in the sphere. The critical frequency for the onset of oscillations in a linear magnetic field coincides with the critical frequency for the spin-up instability in a uniform magnetic field. The growth rate of oscillations attains a maximum at some frequency above the threshold and approaches zero at high frequencies.