This paper gives a general theory of shielding efficiencies for magnetic shields including single-layer and multishell cylindrical ones. The differences of shielding efficiencies between multishell cylindrical shields with and without end-caps are also discussed. The optimum parameters (the innermost radius and length and radial and axial air gap) for five-shell cylindrical magnetic shields are expressed here after a detail theoretical analysis. While three of the four parameters are fixed, the optimum value of the last one is found. The residual magnetic field inside a set of three nested magnetic shields is measured experimentally, which is found to agree well with the theory.
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