This post will go over the various FEMM 4.2 simulations we did to estimate magnetic field strengths and magnet placements for our NMR Mandhalas.
In order to do the simulations for the NMR Mandhala, it was very useful to first go over the following tutorials, since we were essentially simulating the effects of multiple N52 permanent magnets. One can then simple extend these tutorials to simulate multiple permanent magnets in the particular placement and orientation necessary for the NMR mandhala (see DOI 10.1002/cmr.b.20018).
It is important to note that this is a 2D simulator which assumes the magnetic configuration conntinues infinitely in the third dimension. This has a tendency to calculate stronger fields than are actually generated by our finite sized magnets, but still gives a good sense of the scaling of magnetic field strength for different configurations of magnets.
We first arranged eight N-52 ½” cubes from K&J Magnetics (Brmax = 14,800 Gauss and BHmax 52 MGOe) in an NMR Mandhala with 4 cm inner diameter and 8 cm outer diameter. Later we instead used eight N-52 1⁄2 x 1⁄2 x 2” magnets to more closely approximate the theory. The simulated magnetic field resulting from this arrangement is shown below.
To boost the magnetic field further, we added a center mandhala using eight 1/4” x 1/4” x 1” N-52 magnets (B44X0 N-52 from K&J Magnetics). The simulated field of the two mandhalas together is given below (though experimentally the field was closer to 0.4 Tesla).