The theoretical basis is discussed, and a stable, accurate, and efficient numerical procedure given for calculating the winding distribution that is needed on a designated target yoke so that the magnetic field it produces in a specified region of space is identical with that generated by a given primary yoke. This capability is useful for characterizing the mapping properties of equivalent electromagnetic coils, a central issue in the synthesis and design of yokes for color television and monitor tubes. The formulation incorporates and generalizes the conventional integral equation method of magnetostatics. In common with the latter method, it is based on the linear integral relation between the magnetic potential and its two sources: the rsquo;rsquo;effective charge densityrsquo;rsquo; on core surfaces and the current distribution on winding surfaces. However, whereas the conventional method seeks to determine the former source (given details of the latter source) from a single Fredholm equation of the first kind, the present method is designed, in addition, to determine (if desired) both sources simultaneously as the solution of a pair of such integral equations. Although the formal statement of solution is valid for arbitrary coil geometry, the numerical procedure for applying it is given here only for coil geometries of axial symmetry, where the ability to expand the field quantities in angular harmonics allows one to resolve the problem into a sequence of twohyphen;dimensional problems, one for each harmonic. It is demonstrated that the known proneness of Fredholm equations of the first kind to be ill conditioned is heightened in the present method, more so than in the conventional problem. The core of the numerical procedure is thus a smoothing algorithm for suppressing highhyphen;frequency, largehyphen;amplitude oscillations that are an unwanted feature of any direct solution of such an illhyphen;conditioned system.
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