The Theoretical Basis of Rectangular Magnet and Coil Design
National Research Council Canada
A solution is given in Cartesian coordinates to the expansion of the field produced by a current element in a basis set comprising solutions of Laplaces equation. With this apparently new solution to a vexing problem, it is shown that there is a weighted Fourier relationship between a target magnetic field and a current distribution in parallel xy planes; and a Laplace transform relationship between current and field z variation. An example is given of the current distribution needed to produce a field homogeneous over a cuboid, and the relationship between target field roll-off and field z variation highlighted.