The Design of Decoupled Even-Order Zonal Superconducting Shim Coils for a 9.4 T Whole-Body MRI

A novel active shimming method is proposed for the correction of magnetic field nonuniformity of superconducting (SC) magnet for magnetic resonance imaging. Active shimming utilizes several coils to correct specific field harmonic components appear in the inhomogeneous field, and each coil is usually designed independently to the others, and also takes no account of the presence of the main magnet coil blocks. However, the magnetic coupling among these SC shim coils exists, and also the interaction between those zonal even-order shim coils and the main magnet are particularly significant. This coupling/interaction can lead to the drift of main field and even a possible destruction of shim coils by quench due to tremendous energy transferred from the main magnet. In this paper, we attempt to develop magnetic decoupling technologies for the reduction of magnetic interactions between the shim coil and main magnet. Specifically, a hybrid optimization algorithm, including linear and nonlinear programming, is proposed to design a set of decoupled even-order zonal shim coils. The linear programming determines the globally optimal topology and preliminary position of the shim coils. Then, the nonlinear programming is applied to further optimize the position and the turn number of the shim coils, ensuring the designed coils are capable of correcting the unwanted field deviation. Taking the example of Z2 shim coil, compared with the conventional Z2 shim coil, the proposed method significantly reduces the mutual inductance between the Z2 shim coil and the main magnet. For the same field deviation in the tested case, the mutual inductance has been decreased from 83 to 2.3 H. We also further analyze the influence of system parameters and main magnet structure on the optimal topology of decoupled Z2 shim coil. Z4 and Z6 shim coils are also designed with excellent decoupling effect. In our future work, a whole set of active shim coils decoupled from each other and also the main magnet and will be designed and tested in the 9.4 T whole-body MRI system.