An improved matrix method for magnet shimming in compact cyclotrons

The magnet shimming of compact cyclotrons generally consists of iterative procedures. The isochronous field error can be obtained with accurate ion gyration frequency along the radius calculated by numerical integration. The method related on the transformation from the isochronous field error to the geometry change of the magnet pole is a critical procedure during magnet design and field shimming. Compared with previous shimming schemes, an improved matrix method combining multiple linear regression with systematic artificial adjustment is proposed. The study demonstrated that the proposed method has a fast convergence for field isochronism, while maintaining stable and safety characteristics during shimming process.