Influence of the distribution of the properties of permanent magnets on the field homogeneity of magnet assemblies for mobile NMR

We optimised the magnetic field homogeneity of two canonical designs for mobile microfluidic NMR applications: two parallel magnets with an air gap and a modified Halbach array. Along with the influence of the sample length, general design guidelines will be presented. For a fair comparison the sensitive length of the sample has been chosen to be the same as the gap size between the magnets to ensure enough space for the transmitting and receiving unit, as well as basic electric shimming components. Keeping the compactness of the final device in mind, a box with an edge length 5 times the gap size has been defined, in which the complete magnet configuration should fit. With the chosen boundary conditions, the simple parallel cuboid configuration reaches the best homogeneity without active shimming (0.5$\mathrm{B_{s}}$, 41 ppm), while the Pseudo-Halbach configuration has the highest field strength (0.9$\mathrm{B_{s}}$, 994 ppm), assuming perfect magnets. However, permanent magnet configurations suffer from imperfections, such as magnetisation, fabrication and positioning errors, which results in worse magnetic field homogeneities than expected from simulations using a fixed optimised parameter set. We present a sensitivity analysis for a magnetic cube and the results of studies of the variations in the magnetisation and angle of magnetisation of magnets purchased from different suppliers, composed of different materials and coatings, and of different sizes. We performed a detailed Monte Carlo simulation on the effect of the measured distribution of magnetic properties on the mentioned configurations. The cuboid design shows a mean homogeneity of 430 ppm (std dev. 350 ppm), the Pseudo-Halbach has a mean homogeneity of 1086 ppm (std dev. 8 ppm).