Active shim coils design for Halbach magnet based on inverse boundary element method

With advantages of small volume, high field strength, and compact stray field, the Halbach array magnet is of great potential in desktop NMR applications. However, field inhomogeneity poses a main obstacle to its applications. Active shimming is necessary for improving the field homogeneity. An active shim coil design method for cylindrical Halbach magnet based on inverse boundary element method (iBEM) is introduced in this work. Shim coils targeting 1st similar to 3rd and Z4/Z5/Z6 spherical harmonic (SH) terms were designed with constraints of field accuracy, resistance, inductance, and current density. Wire loops and symmetric property influence were discussed to further improve the performance of high-order shim coils. Finally, with the prototype of the shim coils constructed, field pattern and SH transformation proved that the coils designed could fit the target SH distribution, though contamination from low-order components existed in highorder terms. A practical shimming experiment on the Halbach magnet has improved the homogeneity from 40.3 ppm to 3.8 ppm in radius 2.5 mm, height 5 mm cylindrical sample space, verifying the coils' compensation ability. This work provides a flexible inverse coil design method for cylindrical Halbach magnet and discusses the high-order shim coil design and implementation, which is potential in nuclear magnetic resonance applications based on Halbach magnet arrays. (c) 2022 The Authors. Publishing services by Elsevier B.V. on behalf of KeAi Communications Co. Ltd. This is an open access article under the CC BY-NC-ND license (http:// creativecommons.org/licenses/by-nc-nd/4.0/).