Simulation of electromagnetic scattering through the E-XFEL third harmonic cavity module

The European XFEL (E-XFEL) is being fabricated in Hamburg to serve as an X-ray Free Electron Laser light source. The electron beam will be accelerated through linacs consisting of 1.3GHz superconducting cavities along a length of 2.1km. In addition, third harmonic cavities will improve the quality of the beam by line arising the field profile and hence reducing the energy spread. There are eight 3.9GHz cavities within a single module AH1 of E-XFEL. The beam-excited electromagnetic(EM) field in these cavities can be decomposed into a series of eigenmodes. These modes are, in general, not cut-off between one cavity and the next, as they are able to couple to each other through out the module. Here for the first time, we evaluate components of the scattering matrix for module AH1. This is a computation ally expensive system, and hence we employ a Generalized Scattering Matrix(GSM)technique to allow rapid computation with reduced memory requirements. Verification is provided on reduced structures, which are compared to finite element mesh-based codes. The mode spectrum for the dipole bands of interest in an eight-cavity chain have been calculated and external Q factors for the modes are derived.