Analytical evaluations of coupling impedances of resistive and magnetic bellows

A theory is developed to calculate both the longitudinal and transverse impedances of magnetic as well as resistive bellows with cylindrical symmetry that is sandwiched between chambers with perfectly conductive metal fittings. Analytical estimations of the impedances are necessary because the skin depth is too small to make sufficiently tiny mesh sizes in current numerical codes. The impedances of bellows made of materials having both large conductivity and permeability are drastically increased owing to magnetic effects, compared with those of bellows made of perfectly conductive materials.