Attenuation of low-frequency electromagnetic fields in permeable and conducting chimneys

For practical reasons shielded rooms cannot be manufactured perfectly closed; openings are necessary to enable an exchange of data and transport of energy and air through the shielding walls. To avoid a severe degradation of the overall shielding efficiency, the openings are often equipped with tubes, sometimes also called chimneys. It is beyond the scope of this paper to perform an exact calculation of the total field excited by a special source distribution. However, analytical expressions for the decay constants of the electromagnetic field inside a permeable and conducting semi-infinite tube with rectangular cross section are derived. The decay constants of the different modes that are excited corresponding to the symmetry properties of the exciting field are compared to identify the dominant mode with the lowest decay constant. It characterizes the shielding efficiency.