Static and dynamic forces on a permanent magnet levitating between superconducting surfaces

A charged magnetic microsphere (radius 100 µm) is levitating inside a superconducting niobium capacitor. Because of its charge of about 1 pC, oscillations about the equilibrium position can be excited and detected electrically. The properties of this oscillator are investigated in order to study the static and dynamic forces of magnetic levitation. We find resonance frequencies between 200 Hz and 600 Hz. The resonance frequency and the damping are amplitude dependent due to nonlinear return forces and nonlinear friction, respectively. At small amplitudes the Q value is about 106 in vacuum. A dc field can be applied to change the equilibrium position and consequently the resonance frequency. From the data the spatial dependence of the static force and of the dynamic stiffness can be determined and an empirical relation between both is established. Quite often, we find a hysteretic behavior of the static force whereas the stiffness is a reversible function of the position. Amplitude dependent damping is observed both in the decay of the free oscillations and in the dependence of the amplitude of the forced oscillations on the driving force