A method for producing highly uniform field characteristic with line currents

Symmetries in basic equations for dipole fields of line currents allow the use of a relatively small number of conductors to produce highly uniform transverse (dipole) magnetic fields over a large fraction of the interior of the cylinder on which the wires are located. For example, a simple 12‐wire array has better than 1 ppm field uniformity for radii up to 1/3 of the cylinder radius, and better than 0.1% uniformity over more than 1/3 of the cylinder area, and a 50‐wire array would have approximately 0.001 ppm uniformity over half the cylinder area if sufficient construction accuracy could be maintained. The configurations are simply transformed to quadrupoles, sextupoles, and higher multipoles that have highly uniform appropriate radial field derivatives. Shielded systems are also described.