Nonperturbative algorithm for the resistive wall impedance of general cross-section beam pipes

We present an algorithm for calculating the impedance of infinitely long beam pipes with arbitrary cross section. The method is not restricted to ultrarelativistic beams or perturbative approximations with respect to the wall surface impedance or skin penetration depth. We exemplify our algorithm with a calculation of the impedance for rectangular metallic beam pipes. Unlike the situation in the perturbative regime, where the beam pipe geometry modifies the metallic resistive-wall impedances by only a multiplicative factor, the beam pipe geometry has a more complex influence on the impedance when nonultrarelativistic effects are significant and in the ultrarelativistic regime at both small and large frequencies. Since our algorithm requires the boundary conditions at the beam pipe wall to be provided as linear relations between the transverse components of the electromagnetic field, we discuss a general algorithm to calculate these boundary conditions for multilayer beam pipes with arbitrary cross section.