Evaluation of the Magnetic Field Error Due to Manufacturing Tolerance of Superconducting Magnet for the J-PARC Muon G-2/Edm Experiment

The J-PARC Muon $g-2$ /EDM Experiment uses a superconducting solenoid magnet to store positive muons, which generates a magnetic field of $3 \,\rm {T}$ . A highly uniform magnetic field is required, which is less than $0.2 \,\mathrm{ppm_{p-p}}$ (peak-to-peak) in a muon storage region of $(333\pm 15)\,\mathrm{mm}$ in radius and $\pm 50 \,\mathrm{mm}$ in height around the magnet center. The magnetic field error due to manufacturing tolerance was evaluated with a Monte Carlo simulation. This paper introduces the evaluation of magnetic field error due to manufacturing tolerance with a Monte Carlo simulation implemented in C++17. Assuming tolerance to be within $0.1\,\mathrm{mm}$ or $0.1$ mrad, the uniformity was calculated to be $179 \,\mathrm{ppm_{p-p}}$ at the worst case. We performed shimming simulation by using truncated singular value decomposition regularization. As a result, it was confirmed that the worst field error could be compensated to the uniformity of $0.17 \,\mathrm{ppm_{p-p}}$ with a present shimming system. Furthermore, we performed the shimming simulation for wider range of the manufacturing tolerances to investigate the shimming system limit. We concluded that the magnet had to be manufactured with an accuracy less than at least $0.5\,\mathrm{mm}$ or $0.5$ mrad.