Eddy current effects in plain and hollow cylinders spinning inside homogeneous magnetic fields: application to magnetic resonance.

We present a thorough analysis of eddy currents that develop in a rectangular cross section toroid rotating in a uniform magnetic field. The slow rotation regime is assumed. Compact expressions for the current density, the total dissipated power, and the braking torque are given. Examination of the topology of current lines reveals that depending upon the relative dimensions of the side and length of the toroid two different regimes exist. The conditions of existence of the two regimes are analytically established. In view of nuclear magnetic resonance (NMR) applications, we derive the angular variation of the magnetic field created by eddy currents and lay down the formalism necessary for calculating the effect of this field on the NMR spectra of the conductor itself or of a sample co-rotating with the conductor, a situation encountered when dealing with rotating detectors. Examples of calculations for cases of practical interest are presented. The theory is confronted with available data, and we give guidelines for the design of optimized rotating micro-coils.