Axially Symmetric Systems for Generating and Measuring Magnetic Fields. Part I

This is Part I of a systematic discussion of axially symmetric magnetic fields, both central and remote from the origin, search coils reporting the field or gradient at a single point, and mutual inductances. Here the central uniformity of symmetrical fields and gradients is analyzed by zonal harmonic expansion. Laplace's equation and symmetry restrict these fields to a few types, regardless of the detailed geometry of the generating system. Universal error‐contour maps are derived for the central field or gradient in systems having errors of second, fourth, or sixth order, and for hybrid types combining second and fourth. One hybrid has an oblate error field suitable for cloud‐chamber and orbital applications.Source systems include circular filaments, cylindrical or plane circular current sheets, and thick solenoids of rectangular or notched section. Each type of source may be designed to produce any of the field patterns. To this end, source constants derived for the particular source type are combined ...