Modeling of Beam-Wall Interaction in a Finite-Length Metallic Pipe With Multiple Surface Perturbations

Transient electromagnetic fields excited by an ultrashort high-current relativistic electron bunch passing through an undulator beam pipe can induce an energy variation along the beam itself, which will limit the performance of a free electron laser. Three major sources of the field excitation exist: resistive wall, roughness, and an oxide layer. The objective of this paper is to develop a multiscale model for estimating effects of all these surface perturbations on the bunch in a cylindrical metallic beam pipe with a finite length. To do this, the recently developed dispersion-free finite-difference time-domain scheme based on the Newmark-Beta method was conceptually extended to a unified surface impedance boundary condition of the three perturbations including the anomalous skin effect. The developed numerical model is verified in comparison with analytical steady-state solutions. Numerical results show that the energy spread of a finite aluminum pipe is less than that of a finite copper pipe with the same length.