Impedance of Layered Vacuum Chambers for Large Colliders

We calculate the transverse resistive wall impedance of the LHC beam screen, consisting of a tube of stainless steel with a thin inside layer of copper. For this we use an algorithm for the calculation of the electromagnetic fields of an oscillating circular cylindrical beam surrounded by any number of concentric layers of arbitrary material properties. The results for the impedance of the LHC beam screen and the growth rates of the resistive-wall instability are compared with earlier calculations using approximate formulae with wall penetration factors. The same algorithm is also used to estimate the impedance of a beam screen in a much larger machine, a Future Large Hadron Collider FLHC, where the penetration factor method would give incorrect results.