Calculation of Magnetic Noise of Cylindrical Ferrite Shield

Ferrite shields can provide lower magnetic noise environments, which are indispensable for certain ultrasensitive measurements. Previous studies have presented analytical formulas for the magnetic noise in the axial direction of thin-wall cylindrical ferrite shields. However, the magnetic noise along both axes and for any thickness can only be calculated with the finite element method (FEM), which has very low computational efficiency. In this study, based on the analysis of magnetic noise using the FEM and by comparing the analysis results to those of analytical calculations, we extend the application range of the previous analytic formulas, and meanwhile obtain an explicit optimal thickness of the ferrite shield. In addition, we provide an empirical formula for calculating a factor linked to the aspect ratio to replace the previous complex formula. Using our formulations, researchers can conveniently evaluate magnetic noise in both the axial and radial directions for any thickness, and optimize the structural parameters of cylindrical ferrite shields.