Research on First Harmonic Shimming Method of Cyclotron Based on Least Norm Square Solution

The magnetic field measurement of cyclotron and the shimming of isochronous magnetic field are one of the important links in cyclotron. Due to the influence of factors such as processing errors, installation errors, and inhomogeneity of the magnetic properties of mag-net materials, the main magnetic field of the cyclotron will usually deviate from the required isochronous magnetic field and contain a certain amplitude of the first harmonic magnetic field. The existence of the first harmonic magnetic field will rapidly increase the transverse oscillation amplitude and cyclic emittance of the particles, eventually causing beam loss. In order to improve the beam quality of the cyclotron, the shimming technology of the first harmonic magnetic field is essential. In this paper, through the finite element simulation calculation of the main magnet of the cyclotron, a quantitative algorithm for the first harmonic shimming based on the least norm square solution is proposed. At present, this method is being pre-pared for apply to the magnetic field shimming of the 10MeV high-current proton cyclotron of the CIAE.