Optimization of rotation patterns of a mangle-type magnetic field source using covariance matrix adaptation evolution strategy

A mangle-type magnetic field source with four permanent magnets is capable of generating a magnetic field with an arbitrary magnitude and direction. In this study, the rotation pattern of magnets was optimized to maximize the field uniformity by using a covariance matrix adaptation evolution strategy. Starting with random angles of magnets, angles generating the highest magnitude of the magnetic field were calculated with values similar to those of a Halbach cylinder. Although reproducible results were not obtained for a zero magnetic field, a symmetric pattern about the origin after multiple trials of optimization is likely. As the rotation pattern for continuously varying magnitude and direction of the magnetic field could not be found using the covariance matrix adaptation evolution strategy alone, artificial initial guesses were introduced, and the optimization was successful. It was demonstrated that the application of an optimized pattern requires caution with regard to the degradation of the maximum magnetic field and linearity of change in the magnitude and direction of the magnetic field.