Precise Upper Surface Shimming Algorithm for Isochronous Cyclotrons With the Gauss–Newton Iteration Method

Magnetic field shimming is crucial for achieving isochronous acceleration in a cyclotron. Matrix methods based on least square fitting are commonly used to calculate the cutting curve of a shimming bar. However, this matrix method becomes inapplicable when dealing with cases of nonlinear shimming effects. An algorithm based on the Gauss-Newton iteration method to address shimming problems with nonlinear effects has been proposed. Numerical and experimental results demonstrate the effectiveness and accuracy of this algorithm. It has been applied to a compact positron emission tomography (PET) cyclotron developed at China Institute of Atomic Energy (CIAE).