FEM simulations of metamaterial impact on the longitudinal beam-coupling impedance of a rectangular beam pipe

When a particle beam travels through an accelerator structure like the LHC, energy is lost to the structure itself. This phenomenon is described through the beam-coupling impedance and is ideally reduced to improve beam quality and energy efficiency. In this paper, the use of metamaterials with negative permeability is investigated as a method of reducing impedance. A fast and cost-effective way of obtaining non-isotropic negative permeability is given by the construction of an array of metallic implants known as `split-ring resonators´ (SRRs). In this study, rectangular waveguides loaded with SRRs are studied and the longitudinal beam-coupling impedance is observed. This set-up is studied using wake-field simulations and the results are presented and discussed. This research calls for more study considering metamaterial insertions in circular waveguides and deeper feasibility studies.