Modelling Wake Impedance of a Rough Surface in Application to the FCC-hh Beamscreen

The inner surface of the future circular collider (FCC-hh) beamscreen is proposed to be laser-treated in order to mitigate the electron cloud build-up. However, the rough structure of the treated surface can result in unwanted impedance increase, potentially leading to the transverse mode coupling instability (TMCI). Three models have been adopted to estimate the wake impedance of a beamscreen with a rough surface. The models use the resistive wall formalism generalized for the case of an arbitrary surface impedance. The results apply to a beamscreen of a circular cross-section with the homogeneously rough inner surface for the case of ultrarelativistic particles. The free parameters of the models were fit into preliminary measurements of the surface resistivity, giving, as a result, a range of the real and the imaginary parts of the wake impedance.