Study of Vibration Effect on Magnetic Field Homogeneity in the Magnet System for the $g-2$/EDM Experiment at the J-PARC

In a superconducting solenoid used as the muon storage magnet in the J-PARC $g-2$ /EDM experiment, high homogeneous magnetic field of less than $\mathbf {\pm }$ 0.1 ppm at 3 T is required. A study on source of magnetic field disturbance is much important to achieve such high homogeneous magnetic field, and a vibration is one of the serious concerns in terms of dynamic error source of magnetic field. Two vibration sources were considered, a seismic vibration and GM cryocoolers. A frequency response analysis was carried out in the magnet system to evaluate the magnitude of the vibration of magnet using ANSYS. The analysis results shows that the displacement of main coil due to a seismic vibration at J-PARC would be about 0.69 and 0.43 $\boldsymbol{\mu }$ m in the horizontal and vertical direction at maximum, respectively. The coil vibration caused by GM cryocoolers was calculated to be negligible, less than 1 $\mathbf {\times }$ $\mathbf {10^{-3}}$ $\boldsymbol{\mu }$ m, thanks to the vibration isolation design of a cold box and a liquid helium transfer tube. The evaluated magnetic field error due to the cryocooler vibration was less than $\pm$ 1 $\mathbf {\times }$ $\mathbf {10^{-4}}$ ppm, which was much smaller than the requirement of $\pm$ 0.1 ppm. On the other hand, the magnetic field error due to the coil displacement was evaluated to be $\pm$ 0.043 and $\pm$ 0.008 ppm in the horizontal and vertical directions, these were not negligibly small compared with the requirement, especially in the horizontal direction. In order to reduce the vibration conducted through the ground, the vibration dumping system is planned to be implemented in the practical magnet system.