Design and Optimization of Gradient Coils for Low-field Halbach Array Scanners Using the Discrete Wire Method

Halbach array magnets are usually preferred for low-field, portable, point-of-care scanners due to their ability to generate a more homogeneous magnetic field. An efficient gradient coil design for Halbach array scanners is desired to get high-quality magnetic resonance (MR) images. However, there is still a challenge in obtaining desirable linearity and efficiency at the target diameter of spherical volume (DSV) for axial gradient coils using target field methods. This work aims to investigate the discrete wire approach to design efficient gradient coils for Halbach array scanners. The coil turns of each quadrant of both transverse and axial gradient coils were parameterized using quasi-elliptic functions. The gradient coils are then optimized to maximize the coil's efficiency while keeping the linearity error and the maximum field deviation less than 10% and lower than 5%, respectively. The coil geometric parameters, current, turn locations, center of a quadrant, and quasi-elliptic parameters are used as the design variables. Results showed that the designed Y, X, and Z (axial), gradient coils could achieve 2.84 mT/m/A, 2.40 mT/m/A, and 1.21 mT/m/A, respectively over a cylindrical volume with a length of 6 cm and a diameter of 6 cm. This method will be further investigated to design gradient coils for diffusion-weighted imaging (DWI) applications at low field.