The Levitron(TM): An adiabatic trap for spins

A magnet in the form of a spinning-top can float stably above a repelling magnetic base. The principal mechanism of stability is static equilibrium in a potential energy held E, arising dynamically from the adiabatic coupling of the spin with the magnetic field B of the base and involving the magnitude B of this field. E is close to a harmonic potential, that is, one whose Laplacian is zero, for which Earnshaw's theorem would forbid stable equilibrium. Therefore its minimum is very shallow, and requires the mass of the top to be adjusted delicately so that it hangs within a small interval of height. The stability interval is increased by a post-adiabatic dynamic coupling of the velocity of the top to B, through an effective 'geometric magnetic field' constructed from the spatial derivatives of B; this effect gets stronger as the top is spun faster. The device is analogous to several traps for microscopic particles.