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High-permeability magnetic shields generate magnetic field noise that canlimit the sensitivity of modern precision measurements. We show thatcalculations based on the fluctuation-dissipation theorem allow quantitativeevaluation of magnetic field noise, either from current or magnetizationfluctuations, inside enclosures made of high-permeability materials. Explicitanalytical formulas for the noise are derived for a few axially symmetricgeometries, which are compared with results of numerical finite elementanalysis. Comparison is made between noises caused by current and magnetizationfluctuations inside a high-permeability shield and also betweencurrent-fluctuation-induced noises inside magnetic and non-magnetic conductingshells. A simple model is suggested to predict power-law decay of noise spectrabeyond quasi-static regime. Our results can be used to assess noise fromexisting shields and to guide design of new shields for precision measurements.

Calculation of Magnetic Field Noise from High-Permeability Magnetic Shields and Conducting Objects with Simple Geometry