Image Currents in Azimuthally Inhomogeneous Metallic Beam Pipes

We consider an ultra-relativistic particle travelling on-axis in an infinitely long cylindrical metallic beam pipe with azimuthally varying conductivity. A semi-analytical solution, obtained by applying approximate boundary conditions, predicts an image current distribution on the pipe walls practically independent of the azimuth, at least in the frequency range relevant for future machines such as the LHC. We discuss numerical simulations and bench measurements which confirm the theoretical predictions. Implications for the beam-induced ohmic losses in the copper coated, welded LHC beam screen are also addressed.