An optimization method based on the zonal harmonic description of the magnetic field, suitable for the design of axially symmetric magnetic sources, is presented. Expressions of both axial Bz and radial Bρ components of the magnetic field are obtained as the infinite sum of the zonal harmonics. For arrangements having as the basic building block an axially magnetized cylinder, analytical formulas for all zonal momenta Ml have also been derived up to the 11th order ( l=11 ). Through the relationships established by these formulas, a procedure of optimization is initiated to find arrangements of permanent magnet rings that fulfill wished goals of design. Two examples of application have been presented: a pair of rings arrangement (PRA) for a maximally homogeneous gradient field and the four-ring arrangement (FRA) for a maximally homogeneous magnetic field. Several optimized configurations have been found, both for the PRA and FRA cases. For the PRA of thin thickness, geometrical conditions found reproduce those of the known Maxwell pair of current loops for the generation of gradients. The uniformity in gradients so achieved reaches 0.5% within a region with radius 28% of the gap between the lower and upper rings.

For more about this article see link below. 

https://ieeexplore.ieee.org/document/10795436

For the open access PDF link of this article please click here.