A Passive Shimming Method for Halbach Magnet Based on Numerical Optimization Algorithm

In recent years, Halbach magnet has been extensively used in miniaturized NMR spectrometers. However, the inhomogeneity of the magnetic field of permanent magnets poses a challenge to passive shimming method. In this paper, we conducted a passive shimming study of Halbach permanent magnet array structure which is mechanically adjustable. We modeled the relationship between the radial position of the magnetic blocks and magnetic field homogeneity. Then, an optimization algorithm combining the Levenberg-Marquardt method and quasi-Newton method was utilized to optimize the magnetic field homogeneity by adjusting the radial positions of the magnetic blocks. With this approach, the homogeneity of a 1.03 T Halbach magnet was improved from 7 391×10-6 to 154.23×10-6 in a sphere with a radius of 2.5 mm. This work provides a flexible and convenient passive shimming method for compact Halbach magnet, which has the potential to be applied in NMR spectrometers and other instruments that require high magnetic field homogen