Wavelength response of ring-type head with arbitrary gap depth

In 1953 Westmijze found analytic solutions for the fields and wavelength responses of ring-type-head models with zero and infinite gap depths and demonstrated that the wavelength responses for these two extreme cases are substantially different. A model two-dimensional electromagnet that is equivalent to a more general ring-type-head model that takes into consideration a final gap-depth value is considered. It is shown that the Westmijze head models are actually two specific cases of this more general model. Using the theory of complex analytic functions, the gap between the two Westmijze models is bridged and an analytic solution for the wavelength response of a ring-type head with an arbitrary gap depth is derived. Graphs of the responses calculated for several gap depths are presented. These graphs illustrate that the gap depth has no practical effect on wavelength response as long as the ratio of pole thickness to gap size exceeds 0.5. However, further decrease of this ratio causes considerable changes in wavelength responses