Abstract: Pole piece structures for permanent magnets and electromagnets, more particularly for superconducting electromagnets, and pole piece extensions and shields adapted, separately and in combination, to achieve a high concentration of the magnetic flux along the principal magnetic axis of the pole pieces, and preventing magnetic flux leakage and dispersion. The pole pieces are preferably conical or frusto-conical, or in the form of hollow cylinders or conical cylinders or, alternatively, provided with a tapered step ending in a pointed cylinder, a flat cylinder, or a hollow cylinder. The pole piece configurations provide a high concentration of magnetic flux intensity in the magnetic gap between the pole pieces either along the centerline of the pole pieces or in a cylindrical space disposed axially along the centerline of the pole pieces.