Equivalent magnetic dipole method for designing gradient coils of the Halbach magnetic resonance device

Abstract

Based on the equivalent magnetic dipole theory, a method for designing gradient coils of the Halbach magnet is proposed. Minimizing the energy consumption of the gradient coil is set as the optimal object, and the variance between the calculated and expected magnetic fields is taken as the penalty function. In this way, a quadratic optimization problem that cannot easily satisfy the magnetic field constraint condition can be easily transformed into an unconstrained optimization problem. By using the lsqnonlin optimization toolbox of Matlab, the distribution of the stream function on the cylindrical surface is calculated, and the three gradient coils of the Halbach magnet are obtained according to the contour of the stream function. To validate the designed coils, the Biot-Savart law is applied to calculate the distribution of the magnetic field. The results show that the magnetic field distribution agrees well with the design object. The gradient coils are fabricated and the magnetic field distributions in the region of interest are measured. The measured data are almost similar with the calculated data, and the measured gradient uniformity of $x(y)$ and $z$ coils are 4.47% and 2.34%, respectively, which are less than 5% of the commercial gradient coil requirements.