Magnetic field inhomogeneity and torque in high temperature superconducting magnetic bearings

We give experimental evidence for the connection between magnetic field inhomogeneity of a permanent magnet and torque on the rotor in a high temperature superconducting bearing. Spin-down measurements below 14 Hz are used to demonstrate a high degree of correlation between variations in the angular speed of the rotor within a single period of rotation with the measured spatial structure of the magnetic field of the rotor. At frequencies below ∼1 Hz the fractional speed variation within a single period of rotation is inversely proportional to the square of the mean frequency of rotation. We propose that a dipole-dipole interaction gives rise to the torques that lead to speed variations and we show that this interaction explains the observed functional dependence on frequency. At frequencies above ∼1 Hz the measured magnitude is about 1% of the mean frequency of rotation, consistent with the noise level in the experiment. The results imply that arcminute accuracy angular encoding of the rotor can be achieved with a single measurement of angle in each period.