Improved field equations for ring heads

The magnetic field components produced by a ring head are expressed in terms of the values of H
x
across the gap using Poisson integrals [1]. A finite difference solution of Laplace's equation for the scalar potential is used to get values for H
x
across 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.