Magnet design for large air-gaps

A simple basis for the design of magnets with large air-gaps is developed, in the first place for magnets of constant cross-section. This is applied to permanent magnets having gap lengths comparable with the pole diameter, and is shown to give results in satisfactory agreement with experiment. The treatment is then extended to magnets of tapered section and, with the aid of experimental results for such magnets, simple design relationships are obtained for these also. The special case of a pair of bar magnets is briefly considered. The relationship between gap dimensions and the degree of non-uniformity of the gap field is then discussed, with particular reference to requirements for magnetron magnets. A comparison is made between some alternative forms of permanent magnet construction with the conclusion that they differ negligibly in magnetic efficiency; the other factors which may determine the best form for a particular application are briefly reviewed. The approximate relationship between performance and minimum attainable weight of magnetron magnets in typical modern alloys is presented in simple form. The treatment given in the paper is not valid for designs in which the required gap field strength approaches the optimum flux density for the magnet material used, though it may provide a convenient basis for empirical extension to cover such cases.