Design of arbitrarily homogeneous permanent magnet systems for NMR and MRI: Theory and experimental developments of a simple portable magnet

Starting from general results of magnetostatics, we give fundamental considerations on the design and characterization of permanent magnets for NMR based on harmonic analysis and symmetry. We then propose a simple geometry that takes advantage of some of these considerations and discuss the practical aspects of the assembly of a real magnet based on this geometry, involving the characterization of its elements, the optimization of the layout and the correction of residual inhomogeneities due to material and geometry imperfections. We report with this low-cost, light-weight magnet (100 euros and 1.8 kg including the aluminum frame) a field of 120 mT (5.1 MHz proton) with a 10 ppm natural homogeneity over a sphere of 1.5 mm in diameter.