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This paper presents a method to model the permanent block as the current pairs for calculating the magnetic fields. In 2D complex plane, by using current pairs to represent the permanent block, the field in the space can be given a complex shape. When one transfers it into Taylor series, easy axis condition and the field strength inside the magnet aperture or in outside space can be derived when one wants to get pure 2N-poles field in the concerned space. The image effect, which changes an outward permanent magnet into an inward one when an iron shield surrounds, is also discussed in this paper. Magnetic efficiencies between several types of permanent magnets are also presented in this paper. (c) 2006 Elsevier B.V. All rights reserved.

Axial magnetic fields produced by axially and radially magnetized permanent magnet rings were studied. First, the axial magnetic field produced by a current loop is introduced, from which the axial field generated by an infinitely thin solenoid and by an infinitely thin current disk can be derived. Then the axial fields produced by axially and by radially magnetized permanent magnet rings can be obtained. An analytic formula for the axial fields produced by two axially magnetized rings is given. A permanent magnet with a high axial gradient field is fabricated, the measured results agree with the theoretical calculation very well. As an example, the axial periodic field produced by an arrangement of alternating axially and radially magnetized rings has been discussed.