Rotation patterns of a mangle-type magnetic field source optimized via covariance matrix adaptation evolution strategy with 3D finite element method

Abstract

Mangle-type magnetic field sources offer high accessibility to the interior and ease of fabrication and operation. The rotation pattern of such magnetic field sources with four magnets has been investigated using a covariance matrix adaptation evolution strategy; however, the use of 2D finite element method (FEM), which assumes an infinite magnet length, results in significant differences between the FEM calculations and experimental results. Thus, this study has adopted the 3D FEM; the optimization results were compared with those of 2D FEM. This optimization aimed to generate a homogeneous magnetic field with the required magnitude and direction. The magnet angles for the highest field were uniquely determined, which were the same as those of 2D FEM. The magnet angles for zero field were different between 2D and 3D FEMs; although infinite variation was obtained via 2D FEM, only two sets of angles were obtained via 3D FEM. The angles discovered with 3D FEM were spiral, wherein the magnetic flux from the north pole of the magnet enters the south pole of the next magnet without straying into the central region. By measuring the surface magnetic flux densities of the magnets and using them in 3D FEM calculations, the results were found to be in good agreement with those of the experiments.