Improved field equations for ring heads

The magnetic field components produced by a ring head are expressed in terms of the values of Hxacross the gap using Poisson integrals [1]. A finite difference solution of Laplace´s equation for the scalar potential is used to get values for Hxacross the gap. A rational approximation to these values is used in the Poisson integrals, yielding field equations which are more accurate than Karlqvist´s equations [2] and considerably easier to use than Fan´s equations [3]. A large-scale ring head was constructed and used to obtain measured field components which are compared with the numerical solution, the derived field equations, and Karlqvist´s equations in this paper. These comparisons show that unlike Karlqvist´s equations, the new equations remain accurate very close to the ring head surface.